Optical Fiber Telecommunications IV-B Systems and Impairments [4 ed.] 9780123951731, 0123951739

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OPTICAL FIBER TE LEC 0 M MU N ICAT I SYSTEMS AND IMPAIRMENTS

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OPTICAL FIBER TELECOMMUNICATIONS IV B SYSTEMS AND IMPAIRMENTS

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OPTICAL FIBER TELECOMMUNICATIONS IV B SYSTEMS AND IMPAIRMENTS

Edited by

IVAN P.KAMINOW Bell Laboratories (retired) Kaminow Lightwave Technology Holmdel, New Jersey

TINGYE LI AT&T Labs (retired) Boulder, Colorado

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ACADEMIC PRESS An Elsevier Science Imprint

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This book is printed on acid-free paper. @

Copyright @ 2002, Elsevier Science (USA). All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system,without permission in writing from the publisher. The appearance of the code at the bottom of the h s t page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of speci6c clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for pre-2001 chapters are as shown on the title pages. If no fee code appears on the title page, the copy fee is the same as for current chapters. $35.00.

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Academic Press

An Elsevier Science Imprint 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http://www.academicpress.com

Academic Press Harcourt Place, 32 Jamestown Road,London NW17BY, UK http://www.academicpress.com

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Library of Congress Control Number: 2001098830

International Standard Book Number: 0-12-395173-9 PRINTED IN CHINA 02 03 04 05 06

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For Florence and Edith, with love

Contents

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Contributors

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Chapter 1 Overview

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Ivan 19 Kaminow

Chapter 2 Growth of the Internet

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Kerry G. Coflman and Andrew M. Odbzko

Chapter 3 Optical Network Architecture Evolution

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John Strand

Chapter 4 Undersea Communication Systems

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Neal S. Bergano

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Chapter 5 High-Capacity, Ultra-Long-Haul Networks

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John Zyskind, Rick Bany, Graeme Pendock, Michael Cahill, and Jinendra Ranka

Chapter 6 Pseudo-Linear Transmission of High-speed TDM Signals: 40 and 160 Gb/s Red-Jean Essiambre, Gregory Raybon, and Benny Mikkelsen

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Contents

Chapter 7 Dispersion-Managed Solitons and Chirped Return to Zero: What Is the Difference?

305

Curtis R. Menyuk, Gary M. Carter; WilliamL. Kath, and Ruo-Mei Mu

Chapter 8 Metropolitan Optical Networks

329

Nasir Ghani, Jin-B Pan, and Xin Cheng

Chapter 9 The Evolution of Cable TV Networks

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Xiaolin Lu and OIeh Sneizka

Chapter 10 Optical Access Networks

438

Edward Harstead and Pieter H. van Heyningen

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Chapter 11 Beyond Gigabit: Application and Development of High-speed Ethernet Technology

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Cedric E Lam

Chapter 12 Photonic Simulation Tools

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Arthur J. Lowery

Chapter 13 Nonlinear Optical Effects in WDM Transmission

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Polina Bayvel and Robert Killey

Chapter 14 Fixed and Tunable Management of Fiber Chromatic Dispersion Alan E. Willner and Bogdan Hoanca

Chapter 15

Polarization-ModeDispersion

Herwig Kogelnik, Robert M. Jopson, and Lynn E. Nelson

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Chapter 16

Bandwidth-Efficient Modulation Formats for Digital Fiber Transmission Systems

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Jan Conradi

Chapter 17

Error-Control Coding Techniques and Applications

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E! Vjay Kumar, Moe Z. Win, Hsiao-Feng Lu, and Costas N. Georghiades

Chapter 18

Equalization Techniques for Mitigating Transmission Impairments

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Moe Z. Win, Jack H. Winters, and Giorgio M. Etetta

Index to Volumes IVA and IVB

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Contributors

D. A. Ackerman (A:587), Agere Systems, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Daniel Y. Al-Salameh (A295), JDS Uniphase Corporation, 100 Willowbrook Road, Bldg. 1,Freehold, New Jersey 07728-2879 Rick Barry (B: 198), Sycamore Networks, 10 Elizabeth Drive, Chelmsford, Massachusetts 01824-4111 Polina Bayvel (B:61 l), Optical Networks Group, Department of Electronic and Electrical Engineering, University College London (UCL), Torrington Place, London WCl E 7JE, United Kingdom Neal S. Bergano (B: 154), Tyco Telecommunications,250 Industrial Way West, Eatontown, New Jersey 07724-2206 Lee L. Blyler (A:17), OFS Fitel, LLC, 600 Mountain Avenue, Murray Hill, New Jersey 07974 Raymond K. Boncek (A: 17), OFS Fitel, LLC, 600 Mountain Avenue, Murray Hill, New Jersey 07974 Michael Cahil (B: 198), SycamoreNetworks, 10 Elizabeth Drive, Chelmsford, Massachusetts 01824-4111 Gary M. Carter (B:305), Computer Science and Electrical Engineering Department, TRC-201A, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250 and Laboratory for Physical Sciences, College Park, Maryland Connie J. Chang-Hasnain (A:666), Department of Electrical Engineering and Computer Science, University of California, Berkeley, California 94720 and Bandwidth 9 Inc., 46410 Fremont Boulevard, Fremont, California 94538 Young-Kai Chen (A:784), Lucent Technologies, High Speed Electronics Research, 600 Mountain Avenue, Murray Hill, New Jersey 07974 Xin Cheng (B:329), Sorrento Networks Inc., 9990 Mesa Rim Drive, San Diego, California 9212 1-2930

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Contributors

Dominique Chiaroni(A:732), Alcatel Research & Innovation, Route de Nozay, F-9 1461 Marcoussis cedex, France

Kerry G. Coffman (B:17), AT&T Labs-Research, A5-1D03, 200 Laurel Avenue South, Middletown, New Jersey 07748

Jan Conradi (B:862), Director of Strategy,Corning Optical Communications, Corning Incorporated,MP-HQ-Wl-43, One River Front Plaza, Corning, New York 14831 Santanu J L Das (A:17), OFS Fitel, LLC, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Emmanuel Desurvire (A:732), Alcatel Technical Academy, Villarceaux, F-9 1625 Nozay cedex, France

David J. DiGiovanni (A:17), OFS Fitel, LLC, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Christopher R Doerr (A:405), Bell Laboratories, Lucent Technologies, 791 Holmdel-Keyport Road, Holmdel, New Jersey 07733 Adam Ellison (A:80), Corning, Inc., SP-FR-05, Corning, New York 14831

L. E. Eng (A:587), Agere Systems, Room 2F-204, 9999 Hamilton Blvd., Breinigsville, Pennsylvania 18031-9304 Turan Erdogan (A:477), Semrock, Inc., 3625 Buffalo Road, Rochester, New York 14624 RenkJean Essiambre (B:232), Bell Laboratories, Lucent Technologies, 79 1 Holmdel-KeyportRoad, Holmdel, New Jersey 07733 Costas N. Georghiades (B:902), Texas A&M University, Electrical Engineering Department, 237 Wisenbaker, College Station, Texas 77843-3128 Nasir Ghani (B:329), Sorrento Networks Inc., 9990 Mesa Rim Drive, San Diego, California 92121-2930 Steven E. Golowich (A:17), Bell Laboratories, Lucent Technologies, Room 2C-357,600 Mountain Avenue, Murray Hill, New Jersey 07974 Christoph S. Harder (A:563), Nortel Networks Optical Components, Binzstrasse 17, CH-8045 Zurich, Switzerland Edward Harstead (B:438), Bell Laboratories, Lucent Technologies, 101 Crawford Corners Road, Holmdel, New Jersey 07733 Bogdan Hoanca (B:642), Phaethon Communications, Inc., Fremont, California 96538

zyxwvut zyxwv Contributors

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J. E. Johnson (A587), Agere Systems, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Robert M. Jopson (B:725), Crawford Hill Laboratory, Bell Laboratories, Lucent Technologies, 79 1 Holmdel-Keyport Road, Holmdel, New Jersey 07733

Ivan P. Kaminow (A: 1,B: l), Bell Laboratories (retired), Kaminow Lightwave Technology, 12 Stonehenge Drive, Holmdel, New Jersey 07733 Bryon L. Kasper (A:784), Agere Systems, Advanced Development Group, 4920 Rivergrade Road, Irwindale, California 91706-1404 William L. Kath (B:305), Computer Science and Electrical Engineering Department, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250 and Applied Mathematics Department, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3125 L. J. P. Ketelsen (A:587), Agere Systems, 600 Mountain Avenue, Murray Hill, New Jersey 07974

P. A. Kiely (A:587), Agere Systems, 9999 Hamilton Blvd., Breinigsville, Pennsylvania 18031-9304 Robert Killey (B:61 l), Optical Networks Group, Department of Electronic and Electrical Engineering, University College London (UCL), Torrington Place, London WClE 7JE, United Kingdom Herwig Kogelnik (B:725), Crawford Hill Laboratory, Bell Laboratories, Lucent Technologies, 79 1 Holmdel-Keyport Road, Holmdel, New Jersey 07733 StevenK Korotky (A295), Bell Laboratories, Lucent Technologies,Room HO 3C-351,101 Crawfords Corner Road, Holmdel, New Jersey 07733-1900

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P. Mjay Kumar (B:902), Communication Science Institute, Department of Electrical Engineering- Systems,University of Southern California, 3740 McClintock Avenue, EEBSOO, Los Angeles, California 90089-2565 and Scintera Networks, Inc., San Diego, California

Cedric E Lam (B:514), AT&T Labs-Research, 200 Laurel Avenue South, Middletown, New Jersey 07748

Bruno Lavigne (A:732), Alcatel CIT/ Research & Innovation, Route de Nozay, F-91461 Marcoussis cedex, France Olivier Leclerc (A732), Alcatel Research & Innovation, Route de Nozay, F-91460 Marcoussis cedex, France

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Contributors

David S. Levy (A295), Bell Laboratories, Lucent Technologies, Room HO 3B-506, 101 Crawfords Corner Road, Holmdel, New Jersey 07733-3030

Arthur J. Lowery (B:564), VPIsystems Inc., Design Center Group, 17-27 Cotham Road, Kew, Melbourne 3101, Australia Xiaolin Lu (B:404), Morning Forest, LLC, 8804 S. Blue Mountain Place, Highlands Ranch, Colorado 80126

Hsiao-Feng Lu (B:902), Communication Science Institute, Department of ElectricalEngineering- Systems, University of Southern California, 3740 McClintock Avenue, EEBSOO, Los Angeles, California 90089-2565 Amaresh Mahapatra (A:258), Linden Corp., 10 Northbriar Road, Acton, Massachusetts 01720

T. G. B. Mason (A:587), Agere Systems, 9999 Hamilton Blvd., Breinigsville, Pennsylvania 18031-9304

Curtis R. Menyuk (B:305), Computer Science and Electrical Engineering Department, TRC-201A, University of Maryland Baltimore County 1000 Hilltop Circle, Baltimore, Maryland 21250 and PhotonEx Corporation, 200 MetroWest Technology Park, Maynard, Massachusetts 0 1754 Benny Mikkelsen (B:232), Mintera Corporation, 847 Rogers Street, One Lowell Research Center, Lowell, Massachusetts 01852 John Minelly (A:80), Corning, Inc., SP-AR-02-01, Corning, New York 14831 Osamu Muuhara (A:784), Agere Systems, Optical Systems Research, 9999 Hamilton Blvd., Breinigsville, Pennsylvania 18031 Stefan Mohrdiek (A:563), Nortel Networks Optical Components, Binzstrasse 17, CH-8045 Ziirich, Switzerland Ruo-Mei Mu (B:305), Tyco Telecommunications, 250 Industrial Way West, Eatontown, New Jersey 07724-2206 Edmond J. Murphy (A:258), JDS Uniphase, 1985 Blue Hills Avenue Ext., Windsor, Connecticut 06095 Timothy 0. Murphy (A:295), Bell Laboratories, Lucent Technologies, Room HO 3D-516, 101 Crawfords Corner Road, Holmdel, New Jersey 077333030 Lynn E. Nelson (B:725), OFS Fitel, Holmdel, New Jersey 07733 Andrew M. Odlyzko (B:17), University of Minnesota Digital Technology Center, 1200 Washington Avenue S., Minneapolis, Minnesota 55415

zyxwvut zyxwvu Contributors

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Jin-Yi Pan (B:329), SorrentoNetworks Inc., 9990 Mesa Rim Drive, San Diego, California 92121-2930

Sunita 18. Pate1 (A:295), Bell Laboratories, Lucent Technologies, Room HO 3D-502,101 Crawfords Comer Road, Holmdel, New Jersey 07733-3030

Graeme Pendock (B: 198), Sycamore Networks, 10 Elizabeth Drive, Chelmsford, Massachusetts 01824-4111 Jinendra Ranka (B: 198), Sycamore Networks, 10 Elizabeth Drive, Chelmsford, Massachusetts 01824-4111 Gregory Raybon (B:232), Bell Laboratories, Lucent Technologies, 79 1 Holmdel-Keyport Road, Holmdel, New Jersey 07733 Gaylord W. Richards (A:295), Bell Laboratories, Lucent Technologies,Room 6L-219,2000 Naperville Road, Naperville, Illinois 60566-7033 Karsten Rottwitt (A:213), Orsted Laboratory, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, Copenhagen dk 2 100, Denmark Bertold E. Schmidt (A:563), Nortel Networks Optical Components, Binzstrasse 17, Ch-8045 Zurich, Switzerland Oleh Sniezko (B:404), Oleh-Lightcom, Highlands Ranch, Colorado 80126 Leo H. Spiekman (A:699), Genoa Corporation, Lodewijkstraat 1A, 5652 AC Eindhoven, The Netherlands Atul K. Srivastava (A:174), Onetta Inc., 1195 Borregas Avenue, Sunnyvale, California 94089 Andrew J. Stentz (A:213), Photuris, Inc., 20 Corporate Place South, Piscataway, New Jersey 08809 John Strand (B:57), AT&T Laboratories, Lightwave Networks Research Department,RoomA5-106,200LaurelAvenue, Middletown, New Jersey 07748 Thomas A. Strassser (A:477), Photuris Inc., 20 Corporate Place South, Piscataway, New Jersey 08854 Yan Sun (A:174), Onetta Inc., 1195 Borregas Avenue, Sunnyvale, California 94089 Eric S. Tentarelli (A:295), Bell Laboratories, Lucent Technologies, Room HO 3B-530,101 Crawfords Corner Road, Holmdel, New Jersey 07733-3030 Pieter H. van Heyningen (B:438), Lucent Technologies NL, PO. Box 18, Huizen 1270AA,The Netherlands

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Contributors

Giorgio M. Vitetta (B:965), University of Modena and Reggio Emilia, Department of Information Engineering, Via Vignolese 905, Modena 41100, Italy W. White (A:17), OFS Fitel, LLC, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Alan E. Willner (B:642), University of Southern California, Los Angeles, California 90089-2565 Moe Z. Win (B:902, B:965), AT&T Labs-Research, Room A5-1D01, 200 Laurel Avenue South, Middletown, New Jersey 07748-1914 Jack H. Winters (B:965), AT&T Labs-Research, Room 4-147, 100 Schulz Drive, Middletown, New Jersey 07748-1914 Martin Zirngibl (A:374), Bell Laboratories, Lucent Technologies, 79 1 Holmdel-KeyportRoad, Holmdel, New Jersey 07733-0400 John Zyskind (B: 198), Sycamore Networks, 10 Elizabeth Drive, Chelmsford, Massachusetts 0 1824-4111

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Ivan P.Kaminow

Bell Laboratories (retired),Kaminow Lightwave Technology, Holmdel, New Jerscy

Introduction Modern lightwave communications had its origin in the first demonstrations of the laser in 1960. Most of the early lightwave R&D was pursued by established telecommunications company labs (AT&T, NTT, and the British Post Office among them). By 1979, enough progress had been made in lightwave technology to warrant a book, Optical Fiber Telecommunications(OFlJ, edited by S. E. Miller and A. G. Chynoweth, summarizing the state of the art. Two sequels have appeared: in 1988, OFT 11, edited by S. E. Miller and I. P. Kaminow, and in 1997, OFT 111 (A & B), edited by I. P. Kaminow and T. L. Koch. The rapid changes in the field now call for a fourth set of books, OFTW (A & B). This chapter briefly summarizes the previous books and chronicles the remarkably changing climates associated with each period of their publication. The main purpose, however, is to summarize the chapters in OFT IV in order to give the reader an overview.

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History While many excellent books on lightwave communications have been published, this series has developed a special character, with a reputation for comprehensiveness and authority, because of its unique history. Optical Fiber Telecommunications was published in 1979, at the dawn of the revolution in lightwave telecommunications. It was a stand-alone work that aimed to collect all available information on lightwave research. Miller was Director of the Lightwave Systems Research Laboratory and, together with Rudi Kompfner, the Associate Executive Director, guided the system research at the Crawford Hill Laboratory of AT&T Bell Laboratories; Chynoweth was an Executive Director in the Murray Hill Laboratory, leading the optical fiber research. Many groups were active at other laboratories in the United States, Europe, and Japan. OFT, however, was written exclusively by Bell Laboratories authors, who nevertheless aimed to incorporate global results. 1 OPTICAL FIBER TELECOMMUNICATIONS, VOLUME IVB

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Copyright 0 2002, Elsevier Science (USA). All rights of reproduction in any form reserved. ISBN 0-12-395173-9

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zyxwvutsrq zyxwvu zyxwvu Ivan P. Kaminow

Miller and Chynoweth had little trouble finding suitable chapter authors at Bell Labs to cover practically all the relevant aspects of the field at that time. Looking back at that volume, it is interesting that the topics selected are still quite basic. Most of the chapters cover the theory, materials, measurement techniques, and properties of fibers and cables (for the most part, multimode fibers). Only one chapter covers optical sources, mainly multimode AlGaAs lasers operating in the 800- to 900-nm band. The remaining chapterscover direct and externalmodulation techniques,photodetectors and receiver design, and system design and applications Still, the basic elements of the present day systems are discussed: low-loss vapor-phase silica fiber and double-heterostructurelasers. Although system trials were initiated around 1979, it required several more years before a commercially attractive lightwave telecommunications system was installed in the United States. The AT&T Northeast Corridor System, operating between New York and Washington, DC, began service in January 1983, operating at a wavelength of 820 nm and a bit rate of 45 Mb/s in multimode fiber. Lightwave systems were upgraded in 1984 to 1310nm and 417 or 560 Mb/s in single-mode fiber in the United States as well as in Europe and Japan. The year 1984 also saw the Bell System broken up by the court-imposed “Modified Final Judgment” that separated the Bell operating companies into seven regional companies and left AT&T as the long distance camer as well as a telephone equipment vendor. Bell Laboratories remained with AT&T, and Bellcore was formed to serve as the R&D lab for all seven regional Bell operating companies (RBOCs). The breakup spurred a rise in diversity and competition in the communications business. The combination of technical advances in computers and communications, growing government deregulation, and apparent new business opportunities all served to raise expectations. Tremendoustechnical progresswas made during the next few years, and the choice of lightwave over copper coaxial cable or microwave relay for most longhaul transmission systems was assured. The goal of research was to improve performance, such as bitrate and repeater spacing, and to find other applications beyond point-to-point long haul telephone transmission. A completely new book, Optical Fiber Telecommunications11,was published in 1988 to summarize the lightwave R&D advancesat the time. To broaden the coverage, nonBell Laboratories authors from Bellcore (now Telcordia), Corning, Nippon Electric Corporation, and several universities were represented among the contributors. Although research results are described in OFT 11, the emphasis is much stronger on commercial applications than in the previous volume. The initial chapters of OFT 11 cover fibers, cables, and connectors, dealing with both single- and multimode fiber. Topics include vapor-phase methods for fabricating low-loss fiber operating at 13 10 and 1550 nm, understanding chromatic dispersion and nonlinear effects, and designing polarization-maintaining fiber. Another large group of chapters deals with

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1.Overview

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a range of systems for loop, intercity, interoffice, and undersea applications. A research-oriented chapter deals with coherent systems and another with possible local area network designs, including a comparison of time-division multiplexing (TDM) and wavelength division multiplexing (WDM) to efficiently utilize the fiber bandwidth. Several chapters cover practical subsystem components, such as receivers and transmitters and their reliability. Other chapters cover photonic devices, such as lasers, photodiodes, modulators, and integrated electronic and integrated optic circuits that make up the subsystems. In particular, epitaxial growth methods for InGaAsP materials suitable for 1310 and 1550nm applications and the design of high-speed single-mode lasers are discussed in these chapters. By 1995, it was clear that the time had arrived to plan for a new volume to address recent research advances and the maturing of lightwave systems. The contrast with the research and business climates of 1979 was dramatic. Sophisticatedsystem experiments were being performed utilizing the commercial and research components developed for a proven multibillion-dollar global lightwave industry. For example, 10,000-kmlengths of high-performance fiber were assembled in several laboratories around the world for nonreturn-to-zero (NRZ), soliton, and WDM transmission demonstrations. Worldwide regulatory relief stimulated the competition in both the service and hardware ends of the telecommunications business. The success in the long-haul market and the availability of relatively inexpensive components led to a wider quest for other lightwave applications in cable television and local access network markets. The development of the diode-pumped, erbium-doped fiber amplifier (EDFA) played a crucial role in enhancing the feasibility and performance of long-distance and WDM applications. By the time of publication of OFT 111 in 1997, incumbent telephone companies no longer dominated the industry. New companies were offering components and systems and other startups were providing regional, exchange, and Internet services. In 1996, AT&Tvoluntarilyseparated its long distance serviceand telephone equipment businesses to better meet the competition. The former kept the AT&T name, and the latter took on the name Lucent Technologies. Bell Labs remained with Lucent, and AT&T Labs was formed. Bellcore was put up for sale, as the consolidating and competing RBOCs found they did not need a joint lab. Because of a wealth of new information, OFTIII was divided into two books, A and B, covering systems and components, respectively. Many topics of the previous volumes, such as fibers, cables, and laser sources, are updated. But a much larger list of topics covers fields not previously included. In A , for example, transceiver design, EDFAs, laser sources, optical fiber components,planar (silica on silicon) integrated circuits, lithium niobate devices, and photonic switching are reviewed. And in By SONET (synchronous optical network) standards, fiber and cable design, fiber nonlinearities, polarization effects, solitons, terrestrial and undersea systems, high bitrate transmission, analog

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cable systems,passive optical networks (PONS),and multiaccess networks are covered. Throughout the two books, erbium amplifiers and WDM are common themes. It is difficult to overstate the impact these two technologies have had in both generating and supporting the telecommunications revolution that coincided with their commercialintroduction. The EDFA was first reported in about 1987 by researchers at Southampton Universityin the UK and at AT&T Bell Labs. In 1990, driven by the prospect of vast savings offered by WDM transmission using EDFAs, Bell Labs began to develop long-haul WDM systems. By 1996, AT&T and Alcatel had installed the first transatlantic cable with an EDFA chain and a single 5 Gb/s optical channel. AT&T installed the first commercialterrestrial WDM system employing EDFAs in 1995. Massive deployment of WDM worldwide soon followed. WDM has made the exponential tratlic growth spurred by the coincident introduction of the Internet browser economically feasible. If increased TDM bitrates and multiple fibers were the only alternative, the enthusiastic users and investors in the Internet would have been priced out of the market.

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Optical Fiber TelecommunicationsIV BA CKGROWD There was considerableexcitementin the lightwaveresearchcommunityduring the 1970s and early 1980s as wonderful new ideas emerged at a rapid pace. The monopoly telephone system providers, however, were less enthusiastic. They were accustomed to moving at their own deliberate pace, designingequipment to install in their own systems, which were expected to have a long economic life. The long-range planners projected annual telephone voice traffic growth in the United States at about 5-lo%, based on population and business growth. Recent years, on the other hand, have seen mind-numbing changes in the communication business-especially for people brought up in the telephone environment. The Internet browser spawned a tremendous growth in data traillc, which in turn encouraged visions of tremendous revenue growth. Meanwhile, advances in WDM technology and its wide deploymentsynergistically supported the Internet traffic and enthusiasm. As a result, entrepreneurs invested billions of dollars in many companies vying for the same slice of pie. The frenzy reached a peak in the spring of 2000 and then rapidly melted down as investors realized that the increased network capacity had already outstripped demand. As of October 2001, the lightwave community is waiting for a recovery from the current industry collapse. Nevertheless, the technical advances achieved during these last five years will continue to impact telecommunications for years to come. Thus, we are proud to present a comprehensive and forward-lookingaccount of these accomplishments.

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Survey of O F T W A and B

Advances in optical network architectures have followed component innovations. For example, the low loss fiber and double heterostructure laser enabled the first lightwave system generation; and the EDFA has enabled the WDM generation. Novel components (such as tunable lasers, MEMS switches, and planar waveguide devices) are making possible more sophisticatedoptical networks. At the same time, practical network implementationsuncover the need for added device functionality and very low cost points. For example, 40 Gb/s systems need dynamic dispersion and PMD compensationto overcome system impairments. We have divided OFTIV into two books: book A comprises the component chapters and book B the system and system impairment chapters.

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BOOKA: COMPONENTS

Design of Optical Fibers for Communications Systems (Chapter 2) Optical fiber has been a key element in each of the previous volumes of OFT. The present chapter by DiGiovanni, Boncek, Golowich, Das, Blyler, and White reflects a maturation of the field: fiber performance must now go beyond simple low attenuation and must exhibit critical characteristicsto support the high speeds and long routes on terrestrial and undersea systems. At the same time, fiber for the metropolitan and access markets must meet demandingprice points. The chapter reviews the design criteria for a variety of fibers of current commercial interest. For the traditional long-haul market, impairments such as dispersion slope and polarization mode dispersion (PMD) that were negligible in earlier systems are now limiting factors. If improved fiber design is unable to overcome these limits, new components will be required to solve the problem. These issues are addressed again from different points of view in later systems and components chapters in O F T N A and B. The present chapter also reviews a variety of new low-cost fiber designs for emerging metropolitan and access markets. Further down the network chain, the design of multimode glass and plastic fiber for the highly cost-sensitivelocal area network market are also explored. Finally, current research on hollow core and photonic bandgap fiber structures is summarized.

New Materials for Optical Amplifiers (Chapter 3)

In addition to transport, fiber plays an important role as an amplifying medium. Aluminum-doped silica has been the only important commercial host and erbium the major amplifying dopant. Happily, erbium is soluble in AI-silica and provides gain at the attenuation minimum for silica transmission fiber. Still, researchers are exploring other means for satisfying demands

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Ivan P. Kaminow

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for wider bandwidth in the 1550nm region as well as in bands that might be supported by other rare-earth ions, which have low efficiency in silica hosts. Ellison and Minelly review research on new fiber materials, including fluorides, alumina-doped silica, antimony silicates, and tellurite. They also report on extended band erbium-doped fiber amplifiers (EDFAs), thulium-doped fiber amplifiers, and 980 nm ytterbium fiber lasers for pumping EDFAs.

Advances in Erbium-Doped Fiber Amplifiers (Chapter 4) The development of practical EDFAs has ushered in a generation of dense WDM (DWDM) optical networks. These systems go beyond single frequency or even multifrequency point-to-point links to dynamic networks that can be reconfigured by adddrop multiplexers or optical cross-connects to meet varying system demands. Such networks place new requirements on the EDFAs: they must maintain flatness over many links, and they must recover from sudden drops or adds of channels. And economics drives designs that provide more channels and denser spacing of channels. Srivastava and Sun summarize recent advances in EDFA design and means for coping with the challenges mentioned above. In particular, they treat long wave L-band amplifiers, which have more than doubled the conventional C-band to 84nm. They also treat combinations of EDFA and Raman amplification, and dynamic control of gain flatness.

Raman Amplification in Lightwave Communication Systems (Chapter 5) Raman amplification in fibers has been an intellectual curiosity for nearly 30 years; the large pump powers and long lengths required made Raman amplifiers seem impractical. The advent of the EDFA appeared to drive a stake into the heart of Raman amplXers.Now, however, Raman amplifiers are rising along with the needs of submarine and ultralong-haul systems. More powerful practical diode pumps have become available; and the ability to provide gain at any wavelength and with low effective noise figure is now recognized as essential for these systems. Rottwitt and Stentz review the advances in distributed and lumped Raman amplifierswith emphasis on noise performance and recent system experiments.

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Electrooptic Modulators (Chapter 6) Modulators put the payload on the optical carrier and have been a focus of attention from the beginning. Direct modulation of the laser current is often the cheapest solution where laser linewidth and chirp are not important. However, for high performance systems, external modulators are needed. Modulators based on the electrooptic effect have proven most versatile in meeting performance requirements, although cost may be a constraint.

1.Overview

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Titanium-diffusedlithium niobate has been the natural choice of material, in that no commercial substitutes have emerged in nearly 30 years. However, integrated semiconductor electroabsorption modulators are now offering strong competition on the cost and performance fronts. Mahapatra and Murphy briefly compare electroabsorption-modulated lasers (EMLs) and electrooptic modulators. They then focus on titaniumdiffused lithium niobate modulators for lightwave systems. They cover fabrication methods, component design, system requirements, and modulator performance. Mach-Zehnder modulators are capable of speeds in excess of 40Gb/s and have the ability to control chirp from positive through zero to negative values for various system requirements. Finally, the authors survey research on polymer electroopticmodulators, which offer the prospect of lower cost and novel uses.

Optical Switching in Transport Networks: Applications, Requirements, Architectures, Technologies, and Solutions (Chapter 7) Early DWDM optical line systems provided simple point-to-point links between electronic end terminals without allowing access to the intermediate wavelength channels. Today’s systems carry over 100 channels per fiber and new technologies allow intermediate routing of wavelengths at add/drop multiplexers and optical cross-connects. These new capabilities allow “optical layer networking,” an architecture with great flexibility and intelligence. AI-Salameh, Korotky, Levy, Murphy, Patel, Richards, and Tentarelli explore the use of optical switchingin modern networking architectures. After reviewing principles of networking, they consider in detail various aspects of the topic. The performance and requirements for an optical cross connect (OXC) for opaque (with an electronic interface and/or electronic switch fabric) and transparent (all-optical) technologies are compared. Also, the applications of the OXC in areas such as provisioning, protection, and restoration are reviewed. Note that an OXC has all-optical ports but may have internal electronics at the interfaces and switch fabric. Finally, several demonstration OXCs are studied, including small optical switch fabrics, wavelength-selective OXCs, and large strictly nonblocking cross connects employing microelectromechanical system (MEMS) technology. These switches are expected to be needed soon at core network nodes with 1000 x 1000 ports.

Applications for Optical Switch Fabrics (Chapter 8) Whereas the previous chapter looked at OXCs from the point of view of the network designer, Zirngibl focuses on the physical design of OXCs with capacities greater than 1Tb/s. He considers various design options including MEMS switch fabrics, transparent and opaque variants, and nonwavelength-blocking

8

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Ivan P.Kaminow

configurations He finds that transport in the backplane for very large capacity (bitrate x port number) requires optics in the interconnectsand switch fabric. He goes beyond the cross-connect application, which is a slowly reconfigurable circuit switch, to consider the possibility of a high-capacity packet switch, which, although schematically similar to an OXC, must switch in times short relative to a packet length. Again the backplaneproblem dictatesan optical fabric and interconnects. He proposes tunable lasers in conjunction with a waveguide grating router as the fast optical switch fabric.

Planar Lightwave Devices for WDM (Chapter 9) The notion of integrated optical circuits, in analogy with integrated electronic circuits, has been in the air for over 30 years, but the vision of large-scale integration has never materialized. Nevertheless, the concept of small-scale planar waveguide circuits has paid off handsomely. Optical waveguiding provides efficientinteractions in lasers and modulators, and novel functionalityin waveguide grating routers and Bragg gratings. These elements are often linked together with waveguides. Doerr updates recent progress in the design of planar waveguides, starting with waveguide propagation analysis and the design of the star coupler and waveguide grating router (or arrayed waveguide grating). He goes on to describe a large number of innovativeplanar devices such as the dynamic gain equalizer, wavelength selective cross connect, wavelength adddrop, dynamic dispersion compensator, and the multifrequency laser. Finally, he compares various waveguide materials: silica, lithium niobate, semiconductor, and polymer.

Fiber Grating Devices in High-Performance Optical Communication Systems (Chapter 10) The fiber Bragg grating is ideally suited to lightwave systems because of the ease of integrating it into the fiber structure. The technology for economically fabricating gratings has developed over a relatively short period, and these devices have found a number of applicationsto which they are uniquely suited. For example, they are used to stabilize lasers, to provide gain flattening in EDFAs, and to separate closely spaced WDM channels in adddrops. Strasser and Erdogan review the materials aspects of the major approaches to fiber grating fabrication. Then they treat the properties of fiber gratings analytically. Finally, they review the device properties and applications of fiber gratings.

Pump Laser Diodes (Chapter 11) Although EDFAs were known as early as 1986, it was not until a high-power 1480nm semiconductorpump laser was demonstratedthat people took notice.

1.Overview

9

Earlier, expensive and bulky argon ion lasers provided the pump power. Later, 980nm pump lasers were shown to be effective. Recent interest in Raman amplifiers has also generated a new interest in 1400nm pumps. Ironically, the first 1480nm pump diode that gave life to EDFAs was developed for a Raman amplifier application. Schmidt, Mohrdiek, and Harder review the design and performance of 980 and 1480nm pump lasers. They go on to compare devices at the two wavelengths, and discuss pump reliability and diode packaging.

TelecommunicationLasers (Chapter 12)

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zyxw

Semiconductor diode lasers have undergone years of refinement to satisfy the demands of a wide range of telecommunication systems. Long-haul terrestrial and undersea systems demand reliability, speed, and low chirp; short-reach systems demand low cost; and analog cable TV systems demand high power and linearity. Ackerman, Eng, Johnson, Ketelsen, Kiely, and Mason survey the design and performance of these and other lasers. They also discuss electroabsorption modulated lasers (EMLs) at speeds up to 40 Gb/s and a wide variety of tunable lasers.

VCSELs for Metro Communications (Chapter 13) Vertical cavity surface emitting lasers (VCSELs) are employed as low-cost sources in local area networks at 850nm. Their cost advantage stems from the ease of coupling to fiber and the ability to do wafer-scale testing to eliminate bad devices. Recent advances have permitted the design of efficient long wavelength diodes in the 1300-1600 nm range. Chang-Hasnain describes the design of VCSELs in the 1310 and 1550nm bands for application in the metropolitan market, where cost is key. She also describes tunable designs that promise to reduce the cost of sparing lasers.

Semiconductor Optical Amplifers (Chapter 14) The semiconductor gain element has been known from the beginning, but it was fraught with difficulties as a practical transmission line amplifier: it was difficult to reduce reflections, and its short time constant led to unacceptable nonlinear effects. The advent of the EDFA practically wiped out interest in the semiconductor optical amplifier (SOA) as a gain element. However, new applications based on its fast response time have revived interest in SOAs. Spiekman reviews recent work to overcome the limitations on SOAs for amplification in single-frequency and WDM systems. The applications of main interest, however, are in optical signal processing, where SOAs are used in wavelength conversion, optical time division multiplexing, optical phase

10

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Ivan P. Kaminow

conjugation, and all-optical regeneration. The latter topic is covered in detail in the following chapter.

All-Optical Regeneration: Principles and WDM Implementation (Chapter 15) A basic component in long-haul lightwave systems is the electronic regenerator. It has three functions: reamplifying, reshaping, and retiming the optical pulses. The EDFA is a 1R regenerator; regenerators without retiming are 2R; but a full-scale repeater is a 3R regenerator. A separate 3R electronic regenerator is required for each WDM channel after a fixed system span. As the bitrate increases, these regenerators become more expensive and physically more difficult to realize. The goal of ultralong-haul systems is to eliminate or minimize the need for electronic regenerators (see Chapter 5 in Volume B). Leclerc, Lavigne, Chiaroni, and Desurvire describe another approach, the all-optical3R regenerator. They describe avariety of techniques that have been demonstratedfor both single channel and WDM regenerators. They argue that at some bitrates, say 40 Gb/s, the optical and electronic alternatives may be equally difficult and expensive to realize, but at higher rates the all-optical version may dominate.

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High Bitrate Tkansmitters, Receivers, and Electronics (Chapter 16) In high-speed lightwave systems, the optical components usually steal the spotlight. However, the high bitrate electronics in the terminals are often the limiting components. Kasper, Mizuhara, and Chen review the design of practical high bitrate (10 and 40 Gb/s) receivers, transmitters, and electronic circuits in three separate sections. The first section reviews the performance of various detectors, analyzes receiver sensitivity, and considers system impairments. The second section covers directly and externally modulated transmitters and modulation formats like return-to-zero (RZ) and chirped RZ (CRZ). The final section covers the electronic circuit elements found in the transmitters and receivers, including broadband amplifiers, clock and data recovery circuits, and multiplexers.

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BOOK B: SYSTEMS AND IMPAIRMENTS Growth of the Internet (Chapter 2)

The explosion in the telecommunicationsmarketplace is usually attributed to the exponentialgrowth of the Internet, which began its rise with the introduction of the Netscape browser in 1996. Voice traffic continues to grow steadily, but data traffic is said to have already matched or overtaken it. A lot of selfserving myth and hyperbole surround these fuzzy statistics. Certainly claims of doubling data t r a c every three months helped to sustain the market frenzy.

1.Overview

11

On the other hand, the fact that revenues from voice traffic still far exceed revenues from data was not widely circulated. Coffman and Odlyzko have been studying the actual growth of Internet traffic for several years by gathering quantitative data from service providers and other reliable sources. The availability of data has been shrinking as the Internet has become more commercial and fragmented. Still, they find that, while there may have been early bursts of three-month doubling, the overall sustained rate is an annual doubling. An annual doubling is a very powerful growth rate; and, if it continues, it will not be long before the demand catches up with the network capacity. Yet, with prices dropping at a comparable rate, faster traffic growth may be required for strong revenue growth.

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Optical Network Architecture Evolution (Chapter 3) The telephone network architecture has evolved over more than a century to provide highly reliable voice connections to a global network of hundreds of millions of telephones served by different providers. Data networks, on the other hand, have developed in a more ad hoc fashion with the goal of connecting a few terminals with a range of needs at the lowest price in the shortest time. Reliability, while important, is not the prime concern. Strand gives a tutorial review of the Optical Transport Network employed by telephone service providers for intercity applications. He discussesthe techniques used to satisfy the traditional requirements for reliability, restoration, and interoperability.He includes a refresher on SONET (SDH). He discusses architectural changes brought on by optical fiber in the physical layer and the use of optical layer cross connects. Topics include all-optical domains, protection switching, rings, the transport control plane, and business trends.

Undersea Communication Systems (Chapter 4) The oceans provide a unique environment for long-haul communication systems. Unlike terrestrial systems, each design starts with a clean slate; there are no legacy cables, repeater huts, or rights-of-way in place and few international standards to limit the design. Moreover, there are extreme economic constraints and technological challenges For these reasons, submarine systems designers have been the first to risk adopting new and untried technologies, leading the way for the terrestrial ultralong-haul systemdesigners (see Chapter 5). Following a brief historical introduction, Bergano gives a tutorial review of some of the technologies that promise to enable capacities of 2Tbh on a single fiber over transoceanic spans. The technologies include the chirped RZ (CRZ) modulation format, which is compared briefly with NRZ, RZ, and dispersion-managed solitons (see Chapters 5,6, and 7 for more on this topic). He also discusses measures of system performance (the Q-factor), forward

zyxw

12

zyxwvutsr zyxwvu zyxwvu zyxw zyxw Ivan P.Kaminow

error correcting(FEC) codes (see Chapters 5 and 17), long-haulsystem design, and future trends.

High Capacity, Ultralong-Haul Transmission (Chapter 5) The major hardware expense for long-haul terrestrial systems is in electronic terminals, repeaters, and line cards. Since WDM systems permit traffic with various destinationsto be bundled on individualwavelengths, great savingscan be realized if the unrepeatered reach can be extended to 2000-5000 km, allowing traffic to pass through nodes without optical-to-electrical (O/E) conversion. As noted in connection with Chapter 4, some of the technologypioneered in undersea systems can be adapted in terrestrial systems but with the added complexities of legacy systems and standards. On the other hand, the terrestrial systems can add the flexibilityof optical networkingby employingoptical routing in add/drops and OXCs (see Chapters 7 and 8) at intermediatepoints. Zyskind, Barry, Pendock, and Cahill review the technologies needed to design ultralong-haul (ULH) systems. The technologies include EDFAs and distributed Raman amplification, novel modulation formats, FEC, and gain flattening. They also treat transmission impairments (see later chapters in this book) such as the characteristics of fibers and compensators needed to deal with chromatic dispersion and PMD. Finally, they discuss the advantages of optical networking in the efficient distribution of data using IP (Internet Protocol) directly on wavelengths with meshes rather than SONET rings.

Pseudo-Linear Transmission of High-speed TDM Signals: 40 and 160 Gb/s (Chapter 6) A reduction in the cost and complexity of electronic and optoelectroniccomponents can be realized by an increase in channel bitrate, as well as by the ULH techniquesmentioned in Chapter 5. The higher bitrates, 40 and 160Gb/s, present their own challenges, among them the fact that the required energy per bit leads to power levels that produce nonlinear pulse distortions. Newly discovered techniques of pseudo-linear transmission offer a means for dealing with the problem. They involve a complex optimization of modulation format, dispersion mapping, and nonlinearity. Pseudo-linear transmission occupies a space somewhere between dispersion-mapped linear transmission and nonlinear soliton transmission (see Chapter 7). Essiambre, Raybon, and Mikkelsen first present an extensive analysis of pseudo-linear transmission and then review TDM transmission experiments at 40 and 160Gb/s.

Dispersion Managed Solitons and Chirped RZ: What Is the Difference? (Chapter 7) Menyuk, Carter, Kath, and Mu trace the evolution of soliton transmission to its present incarnation as Dispersion Managed Soliton (DMS) transmission

zy

zyxwvut zyxwv 1.Overview

13

and the evolution of NRZ transmission to its present incarnation as CRZ transmission. Both approaches depend on an optimization of modulation format, dispersion mapping, and nonlinearity, defined as pseudo-linear transmission in Chapter 6 and here as “quasi-linear” transmission. The authors show how both DMS and CRZ exhibit aspects of linear transmission despite their dependence on the nonlinear Icerr effect. Remarkably, they argue that, despite widely disparate starting points and independent reasoning, the two approaches unwittingly converge in the same place. Still, on their way to convergence, DMS and CRZ pulses exhibit different characteristicsthat suit them to different applications: For example, CRZ produces pulses that merge in transit along a wide undersea span and reform only at the receiver ashore, while DMS produces pulses that reform periodically, thereby permitting access at intermediate adddrops.

Metropolitan Optical Networks (Chapter 8) For many years the long-haul domain has been the happy hunting ground for lightwave systems, since the cost of expensive hardware can be shared among many users. Now that component costs are moderating, the focus is on the metropolitan domain where costs cannot be spread as widely. Metropolitan regions generally span ranges of 10 to 100km and provide the interface with access networks (see Chapters 9, 10, and 11). SONETBDH rings, installed to serve voice traffic, dominate metropolitan networks today. Ghani, Pan, and Chen trace the developing access users, such as Internet service providers, local area networks, and storage area networks. They discuss a number of WDM metropolitan applications to better serve them, based on optical networking via optical rings, optical adddrops, and OXCs. They also consider 1P over wavelengths to replace SONET. Finally, they discuss possible economical migration paths from the present architecture to the optical metropolitan networks.

The Evolution of Cable TV Networks (Chapter 9) Coaxial analog cable TV networks were substantially upgraded in the 1990s by the introduction of linear lasers and single-modefiber. Hybrid Fiber Coax (HFC) systems were able to deliver in excess of 80 channels of analog video plus a wide band suitable for digital broadcast and interactive services over a distance of 60 km. Currently high-speed Internet access and voice-over-IP telephony have become available,making HFC part of the telecommunications access network. Lu and Sniezko outline past, present, and future HFC architectures. In particular, the mini fiber node (mFN) architecture provides added capacity for two-way digital as well as analog broadcast services. They consider a number of mFNvariants based on advancesin RF, lightwave,and DSP (digital signal processor) technologies that promise to provide better performance at lower cost.

14

zyxwvutsrq zyxwvu zyxw Ivan P.Kaminow

Optical Access Networks (Chapter 10)

The access portion of the telephone network, connecting the central office to the residence, is called the “loop.” By 1990 half the new loops in the United Stateswere served by digital loop carrier (DLC), a fiber severalmiles long from the central office to aremote terminal in aneighborhoodthat connects to about 100 homes with analog signals over twisted pairs. Despite much anticipation, fiber hasn’t gotten much closer to residences since. The reason is that none of the approachesproposed so far is competitivewith existing technology for the applicationspeople will buy. Harstead and van Heyningen survey numerous proposals for Fiber-in-theLoop (FITL) and Fiber-to-the-X (FTTX), where X = Curb, Home, Desktop, etc. They consider the applications and costs of these systems. Considerable creativity and thought have been devoted to fiber in the access network, but the economics still do not work because the costs cannot be divided among a suflicient number of users. An access technology that is successful is Digital Subscriber Line (DSL) for providing high-speed Internet over twisted pairs in the loop. DSL is reviewed in an Appendix.

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Beyond Gigabit: Development and Application of High-speed Ethernet Technology (Chapter 11) Ethernet is a simple protocol for sharing a local area network (LAN). Most of the data on the Internet start as Ethernet packets generated by desktop computers and system servers. Because of their ubiquity, Ethernet line cards are cheap and easy to install. Many people now see Ethernet as the universal protocol for optical packet networks. Its speed has already increased to 1000Mb/s, and 10 Gb/s is on the way. Lam describes the Ethernet system in detail from protocols to hardware, including 10 Gb/s Ethernet. He shows applications in LANs, campus, metropolitan, and long distance networks.

Photonic Simulation Tools (Chapter 12) In the old days, new devices or systems were sketched on a pad, a prototype was put together in the lab, and its performance tested. In the present climate, physical complexity and the expense and time required rule out this bruteforce approach, at least in the early design phase. Instead, individual groups have developed their own computer simulators to test numerous variations in a short time with little laboratory expense. Now, several commercial vendors offer general-purposesimulators for optical device and system development. Lowery relates the history of lightwave simulators and explains how they work and what they can do. The user operates from a graphic user interface (GUI) to select elements from a library and combine them. The simulated device or system can then be run and measured as in the lab to determine

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1.Overview

15

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zyxwvu

attributes like the eye-diagram or bit-error-rate. In the end, a physical prototype is required because of limits on computation speed among other reasons.

THE PRECEDING CRAPTERS RAVE DEALT WITH SYSTEM DESIGN; THE REMAIMNG CHAPTERS DEAL WlTH SYSTEM IMPAIRMENTS AND METHODS FOR MITIGATING THEM Nonlinear Optical Effects in WDM Systems (Chapter 13)

Nonlinear effects have been mentioned in different contexts in several of the earlier system chapters. The Kerr effect is an intrinsic property of glass that causes a change in refractive index proportional to the optical power. Bayvel and Killey give a comprehensive review of intensity-dependent behavior based on the Ken effect. They cover such topics as self-phase modulation, cross-phase modulation, four-wave mixing, and distortions in NRZ and RZ systems.

F%ied and "unable Management of Fiber Chromatic Dispersion (Chapter 14) Chromatic dispersion is a linear effect and as such can be compensated by adding the complementary dispersion before any significant nonlinearities intervene. Nonlinearities do intervene in many of the systems previously discussed so that periodic dispersion mapping is required to manage them. Willner and Hoanca present a thorough taxonomy of techniques for compensating dispersion in transmission fiber. They cover fixed compensation by fibers and gratings, as well as tunable compensation by gratings and other novel devices. They also catalog the reasons for incorporating dynamic as well as k e d compensation in systems.

Polarization Mode Dispersion (Chapter 15)

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Polarization mode dispersion (PMD), like chromatic dispersion, is a linear effect that can be compensated in principle. However, fluctuationsin the polarization mode and fiber birefringence produced by the environment lead to a dispersion that varies statistically with time and frequency. The statistical nature makes PMD difficult to measure and compensate for. Nevertheless, it is an impairment that can kill a system, particularly when the bitrate is large (> 10 Gb/s) or the fiber has poor PMD performance. Nelson, Jopson, and Kogelnik offer an exhaustive survey of PMD covering the basic concepts, measurement techniques, PMD measurement, PMD statistics for first- and higher orders, PMD simulation and emulation, system impairments, and mitigation methods. Both optical and electrical PMD compensation (see Chapter 18) are considered.

16

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Ivan P. Kamhow

Bandwidth Efficient Formats for Digital Fiber Transmission Systems (Chapter 16)

Early lightwave systems employedNRZ modulation; newer long-haul systems are using RZ and chirped RZ to obtain better performance. One goal of system designersis to increase spectral efficiencyby reducing the RF spectrum required to transmit a given bitrate. Conradi examines a number of modulation formats well known to radio engineers to see if lightwave systems might benefit from their application. He reviews the theory and DWDM experiments for such formats as M-ary ASK, duo-binary, and optical single-sideband.He also examines RZ formats combined with various types of phase modulation, some of which are related to discussions of CRZ in the previous Chapters 4-7.

Error-Control Coding Techniques and Applications (Chapter 17)

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Error-correctingcodes axe widelyused in electronics, e.g., in compactdisc players, to radically improve system performance at modest cost. Similar forward error correcting codes (FEC) are used in undersea systems (see Chapter 4) and are planned for ULH systems (Chapter 5). Win, Georghiades, Kumar, and Lu give a tutorial introduction to coding theory and discuss its application to lightwave systems. They conclude with a critical survey of recent literature on FEC applications in lightwave systems, where FEC provides substantial system gains.

Equalization Techniques for Mitigating Transmission Impairments (Chapter 18) Chapters 14and 15describe optical means for compensatingthe linear impairments caused by chromatic dispersion and PMD. Chapters 16 and 17 describe two electronic means for reducing errors by novel modulation formats and by FEC. This chapter discusses a third electronic means for improvingperformance using equalizer circuits in the receiving terminal, which in principle can be added to upgrade an existing system. Equalization is widely used in telephony and other electronic applications. It is now on the verge of application in lightwave systems. Win, Vitetta, and Winters point out the challengesencounteredin lightwave applications and survey the mathematical techniques that can be employed to mitigate many of the impairments mentioned in previous chapters. They also describe some of the recent experimental implementations of equalizers. Additional discussion of PMD equalizers can be found in Chapter 15.

zyxwvut zyxwvu zyxw Duty Cycle

lOO%(Ng)

33%

50%

20%

10%

40 Gbls

2

Single channel

zyx

Distance of 80 km

TrueWave@

with D = 4 ps/(km nm)

zyx zyx

I

-250

-125

0

Pceromp Ipdnmm)

-250

-125

0

-250

-125

0

-250

k r o m p (pshml

k c a m p (p4nml

-125

-250

0

-2-1 0 I 2 3 Eye Closure Penalty (dB) -12J

0

k c o m p lpdnrnl

Prccomp lpdnrni

Plate 1 Eye closure penalties as a function of modulation formats and launch (average) power for 40-Gbh single-channel transmission over 80 km of TrueWaveTMfiber [TrueWaveTMparameters are given in Table 6.1 except for the value of D = 4ps/(km nm) here]. Full dispersion and dispersion slope compensation are assumed before the postcompensation. Each plot in the matrix of plots shows the color-coded eye closure penalties Ceyeas a function of pre- and postcompensation. Only a small improvement in eye opening (essentially the back-to-back difference in eye opening) can be seen when decreasing the duty cycle. Only when the duty cycle is reduced to a value as low as 10% is a significant improvement in transmission observed. Amplifier noise is not included.

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---

33%

I

5

RFrornp lpdnm)

F-omp lpdnml

20%

I

Rsomp

lpdnml

10% I

F-omp (~Jn,nm)

R-mp

Ipdoml

Plate 2 Identical to Plate 1 except for STD unshifted fiber (parameters given in Table 6.1). For large duty cycles (NRZ and 50% duty cycle), transmission is limited to lower powers than TrueWaveTMfiber but rapidly increases as the duty cycle decreases.

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40 Gb/s

Single channel

12 dBm

8 spans of 80 !un

TrueWaveTM/DSF with

D = 2 ps/(km nm)

- I O

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2

3

4

Eye Closure Penalty (dB)

Recomp. (pdnm)

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Reeomp. (pdnm)

Recomp. (pdnm)

Recomp. (pdnm)

Plate 3 Eye closure penalties after 8 spans of 80 km as a function of residual dispersion per span and modulation format. The transmission fiber has the same parameters as TrueWaveTM (Table 6.1) except we use here D = 2 ps/(km nm). The dashed lines are the points of zero net residual dispersion. Two regimes of transmission are present. A first regime (solitonic regime) has optimum transmission with a net positive residual dispersion. In this regime the solitonic effect is at play and is responsiblefor the compensationof dispersionby nonlinearity (even for NRZ!). The second regime (pseudo-linearregime) has its optimum transmission at zero net residualdispersion.

zyx zyxwvuts Residual DisDersion per Span

0

40 Gb/s

zyxwv Single channel

12 dBm

8 spans of 80 km

TrueWavem with

I

D = 4 pd&m nm)

-

1

0

1

2

3

4

zyxwvutsrqp zyxwvutsrqpon zyxwvutsrqpon Eye Closure Penalty (dB)

-la,

-200 -200

-100

zyxw zyxwvuts 0

Reeomp. (pdnm)

a

-100

0

Precomp. (pdnm)

-200 -100 0 Reeomp (plnm)

Precomp. (pdnm)

Plate 4 Same as Plate 3 except D = 4ps/(km nm).

0

Residual Dispersion per Span 8ps/m 16 ps/nm 24 pdnm

_____________ -_____________

40 Gb/s Single channel

12 dBm 8 spans of 80 km

TrueWavem with

D = 8 pd&m nm)

M,. .. .. , -1

0

1

2

3

1

Eye Closure Penalty (dB)

m

-100

o

Recomp. (jdnm)

-200

-100

o

PReomp (pdnm)

-200

-100

o

Reeomp. (pslnm)

Plate 5 Same as Plate 3 except D = 8 ps/(km nm).

zy

Residual Dispersion per Span

40 Gb/s

Single channel

12 dBm

zyx zy zy

8 spans of 80 km

STD Unshifted Fiber with D = 17 pd@m nm)

-

1

0

1

2

3

4

zyxw zyx Eye Closure Penalty (dB)

Rsomp. (pS/nrnl

Rsomp. (pslnml

F’recomp. ( g n m l

Pr~comp.(pdnm)

Plate 6 Same as Plate 3 except for STD unshifted fiber D = 17ps/(km nm) and A,ff = 80 km2.

zyxwvutsr Fiber 1

35

I

.-2 2 5 ‘ g 20 F

Fiber 2

15 10

15,J

1520

1530 1540 1550 Wavelength [nm]

1560

1510

1520

1530 1540 1550 Wavelength [nm]

1560

Plate 7 Contour plots of the simultaneous DGD measurements of two fibers in the same embedded cable over a 36-day period. The mean DGDs averaged over time and wavelength were 2.75 and 2.89 ps for fibers 1 and 2, respectively. Data is courtesy of Magnus Karlsson.

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Chapter 2

Growth of the Internet

Kerry G. Coffman

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AT&T Labs-Research, Middletown, New Jersey

Andrew M. Odlyzko

University of Minnesota, Minneapolis, Minnesota

Abstract The Internet is the main cause of the recent explosion of activity in opticalfiber telecommunications.The high growth rates observed on the Internet, and the popular perception that growth rates were even higher, led to an upsurge in research, development, and investment in telecommunications.The telecom crash of 2000 occurred when investors realized that transmission capacity in place and under construction greatly exceeded actual traffic demand. This chapter discussesthe growth of the Internet and compares it with that of other communication services. It also presents speculations about future developments. Internet traffic is growing, approximatelydoublingeach year. There are reasonable arguments that it will continue to grow at this rate for the rest of this decade. If this happens, then in a few years we may have a rough balance between supply and demand.

1. Introduction Optical fiber communication was initially developed for the voice phone system. The feverish level of activity that we have experienced since the late 199Os, though, was caused primarily by the rapidly rising demand for Internet connectivity. The Internet has been growing at unprecedented rates. Moreover, because it is versatile and penetrates deeply into the economy, it is affecting all of society, and therefore has attracted inordinate amounts of public attention. The aim of this chapter is to summarize the current state of knowledge about the growth rates of the Internet, with special attention paid to the implications for fiber optic transmission. We also attempt to put the growth rates of the Internet into the proper context by providing comparisons with other communications services. The overwhelmingly predominant view has been that Internet traffic (as measured in bytes received by customers) doubles every 3 or 4 months. 17 OPTICAL FIBER TELECOMMUNICATIONS, VOLUME TVB

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Copyright 0 2002, Elsevier Scienm (USA).

ALI rightsof reproduction in any form reserved.

ISBN &12-395173-9

18

Kerry G. Coffman and Andrew M. Odlyzko

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Such unprecedented rates (corresponding to traffic increasing by factors of between 8 and 16 each year) did prevail within the United States during the crucial 2-year period of 1995 and 1996, when the Internet first burst onto the scene as a major new factor with the potential to transform the economy. However, as we pointed out in [CoffmanOl] (written in early 1998, based on data through the end of 1997), by 1997those growth rates subsided to approximate the doubling of traffic each year that had been experienced in the early 1990s. A more recent study [CoffmanO2] provided much more evidence, and in particular more recent evidence, that traffic has about doubled each year since 1997. (We use a doubling of traffic each year to refer to growth rates between 70 and 150% per year, with the wide range reflecting the uncertainties in the estimates.) Other recent observers also found that Internet traffic is about doubling each year. The evidence was always plentiful, and the only thing lacking was the interest in investigatingthe question. By 2000, though, the myth of Internet traffic doubling every 3 or 4 months was getting hard to accept. Very simple arithmetic shows that such growth rates, had they been sustained throughout the period from 1995 (when they did hold) to the end of 2000, would have produced absurdly high tr&c volumes. For example, at the end of 1994, traffic on the NSFNet backbone, which was well instrumented, came to about 15TB/month. Had just that traffic grown at 1300% per year (which is what a doubling every 3 months corresponds to), by the end of 2000, there would have been about 250,000,000 TB/month of backbone traffic in the United States. If we assume there are 150million Internet users in the United States, that would produce a data flow of about 5Mb/s for each user around the clock. The assumption of a doubling of traffic every 4 months produces traffic volumes that are only slightly less absurd. Table 2.1 shows our estimates for traffic on the Internet. The data for 1990 through 1994 is that for the NSFNet backbone, and therefore is very precise. It is incomplete only to the extent of neglecting what is thought to have been small fractions of traffic that went completely through other backbones. The data for 1996 through 2000 are our estimates, and the wide ranges reflect the uncertainties caused by the lack of comprehensive data. Table 2.2 presents our estimates of the tr&c on various long-distance networks at the end of 2000. The voice network still dominated, but it will likely be surpassed by the public Internet within a year or two. (For details of the measurements used to convert voice traffic to terabytes and related issues, see [CoffmanOl].) In terms of bandwidth, the Internet is already dominant. However, it is hard to obtain good figures, since, as we discuss later, the bandwidth of Internet backbones jumps erratically. In terms of dollars, though, voice still provides the lion’s share (well over 80%) of total revenues. We concentrate in this chapter (as in our previous papers [CoffmanOl, CoffmanO21) on the growth rates in Internet tr&c, as measured in bytes. For many purposes, it is the other measures, namely bandwidth and revenues, that are more important.

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Table 2.1 Traffic on Internet Backbones in the United States. Data are estimated traffic in terabytes (TB) during December of that year

Year

TB/month

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

1.o 2.0 4.4 8.3 16.3 ? 1,500 2,5004,000 5,00&8,000 10,00&16,000 20,00&35,000

Tuble 2.2 Traffic on U.S. Long-Distance Networks, Year-End 2000

U.S. voice

Internet Other public data networks Private line

53,000 20,00&35,000 3,000 6,000-1 1,000

The reason we look at traffic is that we find more regularity there, and in the long run, we expect that there will be direct (although not linear) relations between traffic and the other measures. In particular, based on what we have observed so far, we expect capacity to grow somewhat faster than traffic. The studies of [CoffmanOl, Coffman021 led to the proposal of a new form of Moore’s Law, namely that a doubling of Internet tr&c each year is a natural growth rate. This hypothesis is supported by the estimates of Table 2.1, as well as by evidence presented in [CoffmanOl, CoffmanO2] of many institutions whose data traffic has been growing at about that rate for many years. This “law” is discussed further in Section 8. It is not a law of nature, but rather, like the Moore’s Law for semiconductors,a reflection of the complicated interactions of technology, economics, and sociology. Whether this “law” continues to hold or not will have important implications for the fiberoptic transmission industry.

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Much of this chapter, especially Sections6 8 , is based on our earlier studies [CoffmanOl,CoffmanO2]. In Section 2, we present yet more evidence of how often popular perception and subsequent technologyand investmentdecisions are colored by myths that are easy to disprove, but which nobody had bothered to disprove for an astonishingly long time. In Section 3, we look at historical growth rates of various communication services and how they compare to the much higher growth rate of the Internet. Section4 is a brief review of the history of the Internet. Section 5 discusses some of the various types of growth rates that are relevant in different contexts. Section 6 presents the evidence about Internet traffic growth rates we have been able to assemble. Section7 is devoted to new sources of traffic that might create sudden surges of demand, such as Napster. Section 8 discusses the conventional Moore’s Law and the analog we are proposing for data traffic. Section 9 suggests a way of thinking about data-traffic growth, based on an analogy with the computer industry. Finally, Section 10 presents our conclusions.

2. Growth Myths and Reality

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Internet growth is an unusual subject, in that it has been attracting enormous attention but very little serious study. In particular, the general consensus has been that Internet traffic is doubling every 3 or 4 months. Yet no real evidence of that astronomical rate of growth was ever presented. As we discuss later, Internet traffic did grow at such rates in 1995 and 1996, but before and since it has been about doubling each year. At this point, we would like to point out the need for careful quantitative data in evaluating any claims about growth rates. Some examples of public claims that do not match reality are presented in [Coffman02].Here we discuss another case, this one concerning the widely held belief that any capacity that is installed will be quickly saturated. The British JANET network, which provides connectivity to British academic and research institutions, will be discussed in more detail later. What is important is that it is large (with three OC3 links across the Atlantic at the end of 2000), and has traffic statisticsgoing back several years available at http://bill.ja.net/. A press release, available at http://~.ja.net/press_release/archive~nnounce/index.html as “Increase in Transatlantic Bandwidth-28 May 1998” (but actually dated 3 June 1998), describedwhat happened when JANET’Stransatlanticlink was increasedfrom a single T3 to two T3s: With effect from Thursday 28 May 1998, JANET has been running a second T3 (45 Mbit/s) link to the North American Internet, bringing the total transatlantic bandwidth available to JANET to 90 Mbit/s. . . . Usage of the new capacity has been brisk, with the afternoon usage levels reaching in excess of 80 Mbit/s This is of course evidence of the suppressed demand imposed by the single T3 link

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operating previously. The fact that usage has risen so quickly on this occasion is also indicative of the improved domestic infrastructures.. .that now exist.

This quote certainly appears to support the claim that demand for bandwidth is inexhaustible. One could easily conclude that traffic essentially doubled as soon as capacity doubled. The quote is imprecise, though, since it does not say how often those “afternoon usage levels” are “in excess of 80 Mbit/s,” nor does it say how those usage levels are measured. The usage statistics for JANET, available at http://bill.ja.net/, enable us to obtain precise information. Table 2.3 shows the transfer volumes on the more heavily utilized United States to United Kingdom part of the link for several days before and after the doubling of capacity of the link. (No data for May 27 is available, and the figures for May 28, the day the second T3 was put into operation, are suspiciously low, probably reflecting incomplete measurements, so those are not included.) Table 2.3 Traffic from the United States to the JANET Network during Late Spring 1998, When the Capacity Was Doubled Day

Wed 5/20 Thu 5/21

Fri 5/22 Sat 5/23 Sun 5/24 Mon 5/25 Tue 5/26 Wed 5/27 Thu 5/28 Fri 5/29 Sat 5130

Sun 5/31 Mon 6/01 Tue 6102 Wed 6/03 Thu 6/04

Fri 6/05 Sat 6/06

Sun 6/07 Mon 6/08 Tue 6/09

GB

UtiZizution (%)

272.7 275.5 265.1 202.7 189.8 211.2 267.2

58.8 59.4 57.1 43.7 40.9 45.5 57.6

286.6 209.7 199.9 318.1 319.2 295.9 343.2 322.4 208.3 202.7 338.0 307.2

30.9 22.6 21.5 34.3 34.4 31.9 37.0 34.7 22.4 21.8 36.4 33.1

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What we observe is that although there was substantial growth in traffic after the capacity increase, suggesting that the transatlantic link had been a bottleneck, this increase was far more moderate than the popular Internetgrowth mythology or the JANET press release would make one think. While capacity doubled, traffic increased by less than a third.

3. Growth Rates of Other Communication Services

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Telecommunicationshas been a growth industry for centuries, but growth rates have generally been modest, except for a few episodes, such as the beginnings of the electric telegraph (see [Odlyzko2]). For example, the number of pieces of mail delivered in the United States grew by a factor of over 50,000 between 1800 and 2000, but that was a growth rate of about 5.6% per year. (If we adjust for population increase, we find a growth rate of about 3.5% in the mail volume per capita.) The number of phone calls in the United Statesgrew by a factor of over 230 between 1900 and 2000, for a compound annual growth rate of 5.6%. (The per capita growth rate was 4.2% during this period.) Long-distance calls grew faster, about 12% per year between 1930 and 2000, and transatlantic calls faster yet. (There was just one voice circuit between the United States and Europe in 1927, when service was inaugurated. It used radio to span the ocean. This single low quality link grew to 23,000 voice circuits to Western Europe by 1995, for a compound annual growth rate of capacity of 16%.) One communications industry that has been growing very rapidly recently is wireless communication. Table 2.4 shows the growth of the U.S. cell phone industry, with the number of subscribers as of June of each year, and the revenue figures obtained by doubling those of the fmt 6 months of each year (and thus seriously understating the full-year figure). In many other countries, wireless communication has developed faster and plays a bigger role than it does in the United States. Still, even in the United States, at the end of 2000, there were close to 100 million cell phones in use, and the rate of growth was far higher than for traditional wired voice services. The cell phone example is worth keeping in mind, because it shows that volume of traffic or even the number of users has only a slight correlation to value. In the United States (unlike several other countries), there were more Internet users than cell phone subscribers at the end of 2000 (around 150 million vs. about 100 million). However, the revenues of the cell phone industry were far higher than those of the Internet. If we take a rough estimate of 60 million residential Internet users and assume they pay an average of $20 per month (both slight overestimates), we find that the total revenues from this segment come to about $15 billion. Business customers, with dedicated connections to the Internet, pay considerably less than that. For example, the 2000 revenues from business Internet connections of WorldCom (whose UUNet unit has the largest backbone in the world, often thought to carry over

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Table 2.4 Growth of the U.S.Cell Phone Industry Year

Number of Subscribers (miZlions)

Revenues (millions)

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

0.20 0.50 0.89 1.61 2.69 4.37 6.38 8.89 13.07 19.28 28.15 38.20 48.71 60.83 76.28 97.04

$352 721 959 1,772 2,813 4,253 5,307 7,267 9,639 13,038 17,499 22,388 26,270 30,573 38,737 49,291

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30% of the total backbone traffic) were just $2.5 billion (up from $1.6 billion in 1999). The conclusion of the previous paragraph is that even in the United States, basic Internet transport revenues are less than half those of cell phones. Yet volumes of traffic are far higher on the Internet. The average daily time spent by a subscriber on a cell phone in the United States is about 8 minutes. If we count wireless communicationas taking 8 Kb/s (since compression is used), we find that the total volume of traffic generated by cell phone users in the United States at the end of 2000 was only about 1500TB/month, a tiny fraction of the 20,000 to 35,000 TB/month traffic on United States Internet backbones. (Moreover, this comparison overestimates wireless traffic, since most of the mobile calls are local, whereas backbone traffic is by definition long distance.) The comparison of revenues from Internet connectivity to those of the cell phone industry leads naturally to the next topic, namely a comparison with the entire phone industry. As we saw earlier, Internet revenues were under $25 billion in the United States in 2000. On the other hand, the revenues of the entire telephone industry (including wireless communicationand data services such as private lines leased by corporations) were around $300 billion that year. Thus, in terms of revenues, the Internet is still small. Furthermore, it is so

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intimately tied to the phone industry that it is difficult to see what its roleis. The basic technologies (fiber transmission, SONET, and so on) that are used for Internet transport were developed initially for voice telephony, but were easily adopted for data. (Some, such as SONET, will likely turn out to be redundant, but are still widely used.) At the transport level, voice has been carried as bits for a long time. What happened is that during the late 1990s, the long-distance telecommunications infrastructure changed. It used to be dominated by the demands of voice transport, and data was a small part of what it carried. Now, however, its developmentis driven by data, especially Internet data. For quite a long time, the volume of data was extremely small, so that even though the growth rate was higher than for voice, this did not affect the overallgrowth rate of the infrastructure. That was one reason the telecommunications industry was repeatedly surprised by the demand for bandwidthin the 1990s. Moreover, the transition from voice to data domination was complicated by the presence of several types of data, with substantially different growth rates. We discuss this in more detail below. Another reason that the recent upsurge in demand for bandwidth was a surprise is that there had been several previous false predictions that data tralTic was about to explode. The excitement of the early 1990sabout the “telecommunications superhighway”and “500 channels to the home,” to be accomplished through technologies such as hybrid fiber-coax,certainly led to large financial losses and serious disappointments (see Woll21). However, there were even earlier periods of extremely rapid growth followed by sudden deceleration. For example, the number of modems in the United States grew between 1965 and 1970 at about 60% per year, to over 150,000 at the end of that period [WalkerM]. Had that growth rate been maintained, we would have had about 200 billion modems in the United States by the end of 2000, clearly an absurd number. Instead, it appears that growth in the 1970s followed the projections made around 1970 (p. 297 of [WalkerM]),which predicted annual increases of 25 to 30%. It is interestingto read the speculations in [DunnL]about the supposedly rosy prospects for electronic cash, distance education, and other data services (as well as for Picturephone) that were supposed to power the growth of networks. In general, predicting what communications services society will accept and how it will use them has been difficult (see [Luckyl, Odlyzko2]). In particular, even recent history is littered with technologies that seemed extremely promising at one point, such as ISDN (see meinrock3, WuL]) or SMDS (Switched Multimegabit Data Services-a high speed packet switched WAN technology), but never attained more than a marginal role. There are two aspects of the inability to forecast the prospects of communications technologies that are worth discussing at greater length. One goes back to the earlier discussion of wireless telephony and how the mobility offered by cell phones appears to be more important for many people than broadband Internet access. Sometimes, though, higher bandwidth did prevail. In the early days of telephony, there was widespread lack of appreciation of how attractive

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it would eventually prove to be. The telephone was used primarily for business purposes, and the telegraph appeared to be adequate for that to many. Yet it was the phone that won, even though it appeared to use bandwith very wastefully when compared to the telegraph, and even though it encouraged what was often dismissed as “idle chatter.” The attractions of instantaneous personal interactions turned out to be crucial in leading to an almost universal penetration of the telephone in industrialized countries. In the last four decades of the twentieth century though, the telecommunications industry attempted several times to extend its success with the voice telephone by introducing videotelephony. This service appeared to offer the attraction of an even deeper level of communication than voice. Yet prospective users have not only not embraced it, but have in many cases treated it with hostility. There is a growth of videoconferencing, but even that is far slower than its proponents had forecasted. For a variety of reasons that have not been completely explained, videotelephony does not appeal to people for person-to-person communication. On the other hand, mobile narrowband voice flourishes. The other aspect of the dismal record in forecasting the prospects of communications technologies that we now consider is that of the nature of traffic carried. Data networks, which in commercial settings go back about four decades, have spent essentially all this time in the shadow of the much larger voice telephone network. (They also benefited from being able to use the infrastructure of the phone network, and were also constrained by its limitations, but that is less relevant for us here.) It was therefore natural for networking experts to continuously think of voice traffic, and in particular of the possibility of eventually carrying it as data. Looking further out, to a stage where the progress of technology appeared to offer the possibility of data networks becoming much larger than the phone networks, it was also natural to think of enriching the communicationsmedium through the addition of video. (See the projections of Estill Green [Green, Lucky21 and Hough [Hough], for example.) Later, the huge volume of broadcast data (radio and especially television) offered further possibilities for traffic that could be carried on data networks. The key point is what was seen as eventually filling data network was streaming multimedia traffic. The Internet’s rise to dominance was a surprise for many reasons, but one of the main ones was that it did not fit this model. Although much current work on Internet technologies is devoted to streaming multimedia, there are good reasons, to be discussed later, why such traffic is not likely to dominate. Althoughit has proven difficult to forecast which technologieswill be widely adopted, once a service had been successfullyintroduced, it often showed regular growth rates for extended periods of time [Odlyzko2].The approximately 30% annual growth rate that had been projected in 1970 for data transmission (or, to be more precise, for the proxy for actual transmission that is offered by the number of modems) appears to have held not just in the 1970s, but in the 1980s and most of the 1990s as well. There are no comprehensive

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statistics (and there are measurement problems, in that private lines, whose bandwidth is often taken as a measure of the data traffic, can also be used for voice transmission). However, there are a few pieces of evidence supporting those growth rates around 1980 in [deSolaPITH]. Those same growth rates appeared to also hold for long-distance private line transmission in the mid 1990s [CoffmanOl] and for local data bandwidth in the late 1980s and most of the 1990s [Galbi]. The comprehensive data summarized in [Galbi] is especially interesting. During the late 1980s and most of the 199Os, installed computer power came close to doubling each year, and the new “Information Economy” was taking root, but this was not reflected in the volume of data traffic. This low rate of growth in data transmission may have come from the high cost and poor quality of data transmission or from other causes, such as lack of uniform standards that would enable easy data communication between companies. It may also have been caused to a large extent by the slow rate at which computation and communication technologies were adopted. Whatever the reasons, this low growth rate of approximately 30% a year (low by comparison to growth of computing power) in data transmission was higher than that of voice networks. Hence by the mid 199Os, the bandwidth of long-distance data networks (primarily private lines used for intracompany communication) was already comparable to that of the voice network [CoffmanOl]. The Internet has historically had a growth rate of close to 100% per year in the traffic it carried. As Table 2.1 shows, it was growing with striking regularity in the early 1990s at this rate. Then it experienced a period of astronomical growth in 1995 and 1996, and then reverted to an approximate doubling each year in 1997, and has continued growing at about that rate through the end of 2000. The big question is how fast it will grow in the future. While the overwhelming preponderance of opinion all through the end of 2000 was that Internet traffic was doubling every 3 or 4 months, by early 2001 the consensus started changing. Some analysts even began projecting declines in the growth rates to the 50% per year range by around 2005. And indeed, some sources of growth did dry up. With the crash of telecom stocks (caused largely by the realization that expected demand and revenues were not materializing), investments slowed, and many dot-coms that had been busily filling transmission pipes with their content disappeared. In a related development, corporate managements started asking for detailed justifications for new data networking expenditures instead of rushing to endorse any proposals that came along. At various enterprises, the growth rates of data traffic, which had been close to doubling every year in the late 199Os, began to slow down toward doubling every 18 or 24 months. It is not inconceivable that overall data traffic growth may be moving back to its historical rate of around 30% per year. We do not think this will occur, but before considering the reasons why (presented in detail in Sections 6 to 9), we look at the general history of the Internet and its growth rates.

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2. Growth of the Internet

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At this point we just remark that the dominant role of the Internet in communications, whether in terms of bandwidth of networks or popular consciousness, is a fairly recent phenomenon. There had been extensive discussions of the “Information Superhighway” and the “National Information Infrastructure” for a long time. Leading thinkers foresaw the possibilities for much improved communication offered by new technologies, and there was tremendous effort devoted to various systems. However, the general expectation was that the “Information Superhighway” would be composed of a very heterogeneous collection of (interconnected)networks. This was true even as late as the beginning of the Clinton presidency in 1993 and 1994 (see [NII]). It was only in the mid to late 1990s that the Internet was perceived as evolving toward an all-encompassing network, carrying all types of traffic.

4. Internet History Over the past 5 to 10 years, we have witnessed not only an explosion of activity, but the creation of entirely new sectors within the optical industry. As the concept of wavelength division multiplexing (WDM) began to emerge, many new companies developing WDM transport equipment came into existence. The newer enterprises pushed the older established equipment vendors to more aggressive deployment schedules, and a constant downward trend for the corresponding prices of WDM transport equipment followed. In what appeared to be an almost insatiable demand for more bandwidth, a situation arose that allowed the creation of the new companies and the accompanying innovation. Not only did new equipment vendors emerge, but also new national-scale carriers were created. This trend is continuing as the concept of optical layeringhetworking is gaining acceptance and new optical equipment companies are being formed on a regular basis. They deal not only with “traditional” WDM transport equipment, but also with terrestrial ultra long-haul systems, regional and metro optimized systems, and various incarnations of optical cross connects. There were hundreds of developments and contributions enabling this burst of activity. Many of the technical innovations are described in this book and its predecessors. However, perhaps the greatest single factor that fueled this phenomena was the belief and perception that traffic, and hence needed capacity, were growing at explosive rates. This is a remarkable fact, especially when one recalls that around 1990 both the traditional carriers and most of their equipment vendors still expected the traffic demands to not vary much from the voice demand growths (which historically was around 10% per year). In fact, both carriers and equipment vendors were arguing that WDM would not be needed and that going to individual channel rates of at most 10 Gb/s would be adequate. Also, around 1995, the conventional wisdom was that 8-channel WDM systems would suffice well into the foreseeable future. Now it almost

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appears as if the pendulum has swung the other way. Is too much capacity being deployed?Are many of the reported traffic growth rates correct? And if so, will they continue? As we explainedin the previous section, the early skepticism about the need for high-capacity optical transport was rooted in the reality of the telecommunications networks. Up until 1990, they were dominated by voice, which was growing slowly. Then, by the mid 1990s, they came to be dominated (in terms of capacity) by private lines, which were growing three or four times as fast. And then, in the late 1990s, they came to be dominated by the Internet, which was growing faster still. Before we go through the analyses for the tr&c growth on the Internet, we must first at least define the Internet and describe its history and structure. This is paramount in helping put much of the later described growth analyses into perspective. When one now speaks of the Internet, it is usually described as an evolution from ARPANET to NSFNet, and finally to the commercial Internet that now exists. Arguably, the phenomenal growth of the Internet started in 1986 (more than 17 years after its “birth”) with NSFNet. However, the path was very complicated and full of many twists and turns in its roughly 40-year history [Cerf, Hobbes, Leiner]. From the very early research in packet switching, academia, industry, and the U.S. government have been intertwined as partners. Ironically, the beginnings of the Internet can trace itself back to the Cold War and specihlly to the launch of Sputnik in 1957. The U.S. government formed the Advanced Research Project Agency (ARPA; the name was later changed to DARPA, Defense Advanced Research Project Agency, and later back to ARPA) the year after the launch with the stated goal of establishing a U.S. lead in technology and science (with emphasis on military applications). As ARPA was establishing itself, there were several pivotal works [Kleinrockl, Baran] in the early 1960s on packet switching and computer communications. These works and the efforts they spawned laid many of the foundations that enabled the deployment of distributed packet networks. J. C. R. Licklider (of MIT) [LickC] wrote a series of papers in 1962 in which he “envisioned a globally interconnected array of computers which would enable ‘everything’ to easily access data and programs from any of the sites.” Generically speaking, this idea is not much diflterent from what today’s Internet has become. Of importance is the fact the Licklider was the first head of the computer research program at DARPA (beginning in 1962), and in this role he was instrumental in pushing his concept of networks. Kleinrock published both the first paper on packet switching and the first book on the subject. In addition, Kleinrock convinced several key players of the theoretical feasibility of using packets instead of circuits for communications. One such person was Larry Roberts, one of the initial architects for the ARPANET. In the 1965 to 1966time frame, ARPA sponsoredstudies on a “cooperativenetwork of [users]

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sharing computers” [Leiner], and the first ARPANET plans were begun, with the first design papers on ARPANET being published in 1967. Concurrently, the National Physical Laboratory (NPL) in England deployed an experimental network called the NPL Network that made use of packet switching. It utilized 768 Kb/s lines. A year before the moon landing, in 1968, the first ARPANET requests for proposals were sent out, and the first ARPANET contracts were awarded.Two of the earliest contractswent to UCLA to develop the Network Measurement Center, and to Bolt, Beranek, and Newman (BBN) for the Packet Switch contract (to construct the Interface Message Processors or IMPs-effectively the routers). Kleinrock headed the Network Measurement Center at UCLA and it was selected as the first node on the ARPANET. The first IMP was installed at UCLA and the first host computer was connected in September of 1969. The second node was at Stanford Research Institution (SRI). Two other nodes were added at UC Santa Barbara and in Utah, so that by the second half of 1969,just months past the lkst moon landing, the initial four-node ARPANET became functional. This was truly the initial ARPANET, and thus a case can be made that this was when the Internet was born. The first message carried over the network went from Kleinrock’s lab to SRI. Supposedly the first packet sent over ARPANET was sent by Charley Kline, and as he was trying to log in the system crashed as the letter “ G of “LOGIN” was entered. One of the next major innovations for the fledgling Internet (i.e., ARPANET) was the introduction of the first host-to-host protocol, called Network Control Protocol, or NCP, which was first used in ARPANET in 1970. By 1972, all of the ARPANET sites had finished implementing NCP. Hence the users of ARPANET could finally begin to focus on the development of applications-another paramount driver for the phenomenal growth and sustained growth of the Internet. It was also in 1970 that the first crosscountry link was established for ARPANET by AT&T between UCLA and BBN (at the blinding rate of 56 Kbh). By 1971, the ARPANET had grown to 15 nodes and had 23 hosts. However, perhaps the most influential work that year was the creation of an e-mail program that could send messages across a distributed network. (E-mailwas not among the original design criteria for the ARPANET, and its success caught the creators of this network by surprise.) Ray Tomlinson of BBN developed this application, and his original program was based on two previous ones [Hobbes]. Tomlinson modified his program for ARPANET in 1972, and at that point its popularity quickly soared. In fact, it was at this time that the symbol “@,, was chosen. Arguably, Internet e-mail as we know it today can trace its origins directly to this work. Internet e-mail was clearly one of the key drivers for the popularity (and hence the phenomenal traffic-growthdemands) of the Internet and was the first “killer app” for the Net. It was every bit as critical to the Internet’s “success” as spreadsheet applications were to the popularization of the PC. Internet e-mail provided

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a new model of how people could communicate with each other and alter the very nature of collaborations. Although there was already considerable work being done on packet networks outside the United States, the first international connections to the ARPANET (to England via Norway) took place in 1973. To put the time frame in perspective, this was the same year that Robert Metcalfe did his PhD that described his idea for Ethernet. Also during this year, the number of ARPANET c‘users”was estimated to be 2,000 and that 75% of all the ARPANET t r a c (in terms of bytes) was e-mail. One needs to note that in only 1 to 2 years from its introduction onto the Internet, e-mail became the predominant type of traffic. The same behavior took place several years later for HTML (Hypertext Markup Language) (i.e., Web traffic), and to a somewhat lesser degree, this was seen for Napster-like traffic within many networks a few years later. Several other key developments began to take place in the mid 1970s. The initial design specification for TCP (Transfer Control Protocol) was published by Vint Cerf and Bob Kahn in 1974 [CerfK]. The NCP protocol, which was being utilized at the time, tended to act like a device driver, whereas the future TCP (later TCP/IP) would be much more like a communications protocol. As is discussed later, the evolution from ARPANET’s NCP protocol to TCP (which in 1978 was split into TCP and IP (Internet Protocol)) was critical in allowing the future growth and scalability of today’s Internet. DARPA had three contracts to implement TCPLIP (at the time still called TCP), at Stanford (led by Cerf), BBN (led by Ray Tomlinson), and UCLA (led by Kirsten). Stanford produced the detailed specification and within a year there were three independent implementations of TCP that could interoperate. It is noted that the basic reasons that led to the separation of TCP (which guaranteed reliable delivery) from IP actually came out of work that was done trying to encode and transport voice through a packet switch. It was found that a tremendous amount of bdering was needed in order to allow for the appropriate reassembly after transmission was completed. This in turn led to trying to find a way to deliver the packets without requiring a guaranteed level of reliability. In essence, the UDP (User Datagram Protocol) was created to allow users to make use of IP. In addition, it was also in 1978 that the first commercial version of ARPANET came into existence when BBN opened Telenet. In 1981-1982, the first plans were made to “migrate”from NCP to TCP. It is claimed by some that it was this event (TCP was establishedas the protocol suite for ARPANET) was truly the birth of the InternetAefined as a connected set of networks, specifically those with TCP/IP. A few years later (in 1983) another major development occurred, which later enabled the Internet to scale with the “explosive” growth and popularity of the future Internet. This was the development of the name server, which evolved into the DNS [Cerf, Leiner]. The name server was developed at the University of Wisconsin [Hobbes]. This made it easy for people to use the network because hosts were assigned names

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and it was not necessaryto remember numeric addresses. Much of the credit for the invention of the DNS (Domain Name Server) is given to Paul Mockapetris of USC/ISI [Cerfl. The year 1983 was also the date for two other key developments on ARPANET. The first one was the cutover from NCP to TCP on the ARPANET. Secondly, ARPANET was split into ARPANET and MILNET. Although the road was convoluted, this split was one of the key bifurcation points that later allowed NSFNet to come into existence. Soon thereafter (in 1984), the number of hosts on ARPANET had grown to 1,000, and the next year in 1985 the first registered domain was assigned in March. In 1985, NSFNet was created with a backbone speed of 56 Kb/s. Initially, there were five supercomputing centers that were interconnected. One of the paramount benefits of this was that it allowed an explosion of connections (most importantly from universities) to take place. Two years later in 1987, NSF agreed to work with MERIT Network to manage the NSFNet backbone. The next year (1988), the process of upgrading the NSFNet backbone to one based on T1 (Le., 1.5 Mb/s links) was begun. In 1987, the number of hosts on the Internet broke 10,000. Two years later in 1989, this had grown to around 100,000, and 3 years after that, in 1992, it reached the 1,000,000 value. It is noted that if you look at how the number of hosts had been growing from 1984 to 1992, that it was still pretty much tracking a growth curve that was less than tripling each year (i.e., doubling every 9 months). In the 1985-1986 time frame, a key decision was made that had very long-term impact: that TCP/IP would be mandatory for the NSFNet program. In the 1988-1990 time frame, a conscious decision was made to connect the Internet to electronicmail carriers, and by 1992,most of the commerciale-mail carriers in the United States were “like the Internet.” This was still another development that cemented e-mail as the single most important application to take advantage of the Internet. In 1990, the ARPANET ceased to exist, and arguably NSFNet was the essence of the Internet. The following year, commercial Internet Service Providers (ISPs) began to emerge (PSI, ANS, Sprint Link, to name a few), and the Commercial Internet Xchange (CIX) was organized in 1991 by commercial ISPs to provide transfer points for traffic. NSF’s lifting the restriction on the commercial use of the Net was again one of the pivotal decisions. This was again a key bifurcation point, in that this helped set the stage for the complete commercialization of the Net that would follow only a few years later. In 1991, the upgrading of the NSFNet backbone continued as the work to upgrade to a T3 (Le., 45 Mb/s links) began. It is also interesting to note that it was the next year, 1992, that the term “surfing the Internet” was first coined by Jean Armour Polly [Polly], only 2 years before the ARPANEThternet celebrated its 25th anniversary. It was in the 1993-1995 time period that several major events seemed to emerge that fueled an almost explosivegrowth in the popularity of the Internet.

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One of the key ones was the introduction of “browsers,” most notably Mosaic. This led to the creation of Netscape, which went public in 1995. Even as early as 1994, WWW (i.e., predominantly HTML) tr&c was increasing in volume on the Net. By then it was the second most popular type of traffic, surpassed only by FTP (File Transfer Protocol) tr&c. However, in 1995 WWW tra& surpassed FTP as the greatest amount of tr&c. In addition, the traditional online dial-up systems such as AOL (America Online), Prodigy, and CompuServe began to provide Internet access. In 1996, the Net truly became public with the NSFNet being phased out. Soon thereafter, major infrastructure improvements were made within the transport part of the Internet. The Internet began to upgrade much of its backbone to OC3-0C12 (up to 622Mb/s) links, and in 1999, upgrades began for much of the Net to OC48 (2.5 Gb/s) links.

5. The Many Internet Growth Rates The Internet is very hard to describe. By comparison, even the voice phone system, which is a huge enterprise, far larger in terms of revenues than the Internet, is much simpler. In the phone system, the basic service is well defined and simple to describe. The users have only limited ability to interact with the system. The Internet is completely different. Users interact with the system in a multiplicity of ways, on widely different time scales, and there are many complicated feedback loops. The paper [FloydP] is an excellent overview of the problems that arise in attempting to simulate the Internet. The problems of measuring the Internet are also formidable. There are many different measures that are relevant. In this chapter,just as in the papers [CoffmanOl,CoffmanO2], we will concentrate on traffic as measured in bytes. For the optical fiber telecommunications industry, it is capacity that is most relevant. Unfortunately, there are numerous problems in measuring capacity. Much of the fiber is not lit, and even when it is lit, often only a few wavelengths are lit. Finally, much of the potential capacity is used for restoration, through SONET or other methods. In addition, even at the levels of links used for providing IP traffic, it is hard to obtain accurate capacity measurements, because few carriers provide detailed data. Further, this type of capacity has a tendency to jump suddenly, as bandwidth is usually increased in large steps (such as going from OC3 to OC12, and then 0048, a phenomenon that contributes to the low utilization of data links [Odlyzkol]). Thus, there is little regularity in capacity growth figures. On the other hand, we do find astonishing regularity in traffic growth, which leads us to propose that a form of Moore’s Law applies. In the long run, we expect that capacity will grow slightly faster than traffic, as we explain later. For many purposes other measures are important, such as the number of users, how they spend their time, how many and what types of commercial

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transactions they engage in, and so on. There are many sources of such data, and useful references can be found at [Cyberspace, MeekerMJ, Nua].

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6. Internet Traffic and Bandwidth Growth Whether Internet traffic doubles every 3 months or just once a year has huge consequences for network design as well as the telecommunicationsequipment industry. Much of the excitement about and funding for novel technologies appears to be based on expectations of unrealistically high growth rates ([Bruno]). In this section we briefly examine avariety of examples in an attempt to understand the traffic-growth rates that the Internet has experiencedover its lifetime. There are places where the traffic is growing at rates that exceed 100% per year. One such example is LINX (London Internet Exchange). Its online data, available at http://ochre.linx.net/, clearly shows a growth rate of about 300% from early 1999 to early 2001. There are also examples of even higher growth rates, although those tend to be for much smaller links or exchange points. However, there are also numerous examples of much more slowly growing links. In this section we briefly present growth rates from avariety of sources and attempt to put them into context. In an earlier study [CoffmanOl] in 1997, we found that the evidence supported a traffic growth rate of about 100% per year (doubling annually). Four years later, the general conclusion is that Internet traffic still appears to be growing at about 100% per year. In other words, we have not found any substantial slowdown in the growth rate. Some recent reports and projections conclude that Internet traffic is only about doubling each year, but claim that it was growing much faster until recently, and that its growth rate will continue to slow down. In that view, the telecom crash of 2000 was associated with a sudden decline in the growth rate of traffic. As far as we can tell, that is not accurate. The general rate of growth of traffic appears to have been remarkably stable throughout the period 19972000. As one of the most convincing pieces confirming this claim, we cite the news story ([Cochrane]) based on official figures from Telstra, the dominant Australian telecommunications carrier. This story reports that Telstra’s IP traffic was almost exactly doubling each year between November 1997 and November 2000. (The printed version of this news story, but not the one available online at the URL listed in [Cochrane], shows a very regular growth, about 100% per year, from the beginning of 1997 to November 2000.) Hence our conclusion is that the problems the photonics industry is experiencingare not caused by any sudden slowdown in traffic, but rather by a realization that the astronomical growth rates that people had been assuming were fantasies. Most of this section is drawn from the more detailed account in [Coffman02]. There are only a few new pieces of information. For example, the China Internet Network Information Center has statistics (at www.cnnic.net.cn/develst./e-index.shtm1)of the Internet bandwidth between

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China and the rest of the world. It grew from 84.64Mb/s in June 1998 to 2,799 Mbls in December 2000, for a compound growth rate of 305% per year. Thus, even in a rapidly growing economy like that of China, where Internet penetration is low and is trying to catch up with the industrialized world, traffic is only doubling about every 6 months. The comparison of the international bandwidth for Australia and China is instructive. In December 2000, Telstra had about 1,000Mb/s to the rest of the world, about a third of Chinese bandwidth. Thus, making allowances for other Australian carriers, we can speculate that Australia may be exchanging half as much traffic with international destinations as China does, even though the latter has over 60 times the population. This shows the degree to which countries can differ in their intensity of Internet usage. The data in [Cochrane], showing that Telstra’s IP traffic in November 2000 reached about 270 TBlmonth, also shows that our general estimates for U.S. backbone traffic are reasonable, because the United Statesis not only larger than Australia, but also richer on aper capita basis and has a better developed telecommunications infrastructure. In the remainder of this section we examine some of the data and trends from ISPs, exchange points, and residential traffic patterns, along with traffic from “stable sources,” such as corporate, research, and academic networks. It is noted that the data for the first two sources (ISPs and exchange points) are not nearly as complete nor reliable as only a few years ago. However, much better data are available for the “stable sources,” and several are examined in much more detail later. As a brief note on conversion factors, traffic that averages 100Mb/s is equivalent to about 30 TB/month. (It is 32.4 TB for a 30-day month, but such precision is excessive given the uncertainties in the data we have.) Unfortunately, the largest ISPs do not release reliable statistics. This situation was better even a couple of years ago. Much of the older data was used in previous studies ([CoffmanOl]).For example, MCI used to publish precise data about the traffic volumes on their Internet backbone. Even though they were among the first ISPs to stop providing official network maps, one could obtain good estimates of the MCI Internet backbone capacity from public presentations. These sources dried up when MCI was acquired by WorldCom, and the backbone was sold to Cable &Wireless. As was noted in [CoffmanOl], the traffic-growthrate for that backbone had been in the range of 100% a year before the change. Today, one can obtain some idea of the sizes (but not trafEc) of various ISP networks through the backbone maps available from Boardwatch. However, even those are not too reliable. The only large ISP in the United States to provide detailed network statistics is AboveNet, at http:lluww.above.netltrafficl. Therefore, we looked at this ISP in moderate detail. We have recorded the MRTG (Multi-RouterTraffic Grapher)[MRTG]data for AboveNet for March 1999, June 1999, February 2000, June 2000, November 2000, and April 2001.

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The average utilizations of the links in the AboveNet long-haul backbone during those 4 months were 18, 16, 29, 12, 11, and lo%, respectively. (The large drop between February and June 2000 was caused by deployment of massive new capacity, including four OC48s. One of the reasons we concentrate on traffic and not network sizes in this chapter is that extensive new capacity is being deployed at an irregular schedule and is often lightly utilized. Thus, it is hard to obtain an accurate picture of the evolution of network capacity.) If one just adds up the volumes for each link separately, one finds that between March 1999 and April 2001, the total volumes of traffic increased at an annual growth rate of about 200%. However, this figure has to be treated with caution, as actual traffic almost surely increased less than 200%. During this period, AboveNet expanded geographically, with links to Japan and Europe, so that at the end it probably carried packets over more hops than before. Because we are interested in end-to-end traffic as seen by customers (which can be thought of as the ingress and/or egress traffic into and/or out of “the network”), we have to deflate the sum of traffic volumes seen on separate backbone links by the average number of hops that a packet makes over the backbones (perhaps around three). Even when there is reliable data for a single carrier, such as AboveNet, some of the growth seen may be coming from gains in market share, both from gains within a geographical region and from greater geographical reach, and not from general growth in the market. We next look at Internet exchangepoints. When the NSF Internet backbone was phased out in early 1995, it was widely claimed that most of the Internet backbone traffic was going through the Network Access Points (NAPs) (which are effectivelyinterconnectionvehicles), which tended to provide decent statistics on their traf3ic. Currently it is thought that only a small fraction of backbone traffic goes through the NAPs, while most goes through private peering connections. Furthermore, NAP statistics are either no longer available or not as reliable. This is in sharp contrast to the situation in 1998 [CoffmanOl]. As documented elsewhere [CoffmanO2], there is very little that can be reliably concluded about current growth rates of Internet traffic by examining the statistics of the public NAPs in the United States. However, the situation was slightly better when we examined a large number of international exchange points. These included LINX, AMS-IX (the Amsterdam Internet exchange), the Slovak Internet exchange, HKIX (a commercial exchange created by the Chinese University of Hong Kong, BNIX (located in Belgium), the INEX (an Irish exchange), and FICX (the Finish exchange). Some of these show growth rates of only about doubling per year while others show much faster growth rates. Trafiic interchange statistics are hard to interpret, unless one has data for most exchanges, which is virtually impossible to obtain. Much of the growth one sees can come from ISPs moving from one exchange to another, moving their traffic from one exchange to another, or coming to an exchange in preference to buying transit from another ISP. Consider the specific case of LINX. A large part of its growth

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is almost surely caused by more ISPs exchanging their traffic there. Between March 1999 and March 2000, the ranks of ISPs that are members of LINX have grown by about two-thirds, based on the data on the LINX home page. Hence the averageper-member traffic through LINX may have increased only around 120% during that year. The traffic from residential U.S. customers will probably begin to increase at a faster rate in the near future. The growth in the number of users is likely to diminish as we reach saturation. (You cannot doublethe ranks of subscribersif more than half the people are already signed up!) However, broadband access, in the shape of cable modems and DSL (and to a lesser extent fixed wireless links), will stimulate usage. The evidence so far is that users who switch to cable modem or DSL access increase their time online by 50 to loo%, and the total volume of data they download per month by factors of five to ten. A five- or tenfold growth in data traEic would correspond to a doubling of traffic every 4 months if everyone were to switch to such broadband access in a year. However, that is not going to happen. At the end of 1999, there were about 3 million households in the United States with broadband access. The most ambitious projections for cable modem and DSL access call for about 13 million households to have such links in 2003, and between 5 M O million in the year 2007. That is approximatelya doubling each year. (There was apparently almost a tripling in the ranks of households with broadband access in 2000, but the telecom crash that wiped out many of the ADSL providers has led to a slowdown in the pace of deployment in 2001.) The traffic from a typical residential broadband customer is likely to grow beyond the level we see today as more content becomes available and especially as more content that requires high bandwidth is produced. Still, it is hard to see average traffic per customer among those with broadband connections growing at more than 50% a year. Together with a doubling in the ranks of such customers, this might produce a tripling of traffic from this source. Because the ranks of customers with regular modems are unlikely to decrease much, if any, and because their traffic dominates, it appears that the most likely scenario will be for the total residential customer traffic to grow no faster than 200% per year, and probably closer to 100% per year. (Access from information appliances,which are forecast to proliferate, is unlikely to have a major impact on total traffic, since the mobile radio link will continue to have small bandwidth compared to wired connections.) We next consider traf€ic at various stableinstitutions-corporate, academic, and governmental. Growth in traffic can be broken down into growth in the number of traffic sources and growth in traffic per source. For LINX, much of the increase in traffic may be coming from an increase in member ISPs. For individual ISPs, much of the increase in traffic may also be coming from new customers. Yet in the end, that kind of growth is limited, as the market becomes saturated. The rest of this section focuses on rates of growth in traffic from stable sources. Now nothing is completely stable, as

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the number of devices per person is likely to continue growing, especially with the advent of information appliances and wireless data transmission. Hence we will consider growth in traffic from large institutions that are already well wired, such as corporations and universities. Most corporations do not publicize information about their network traffic, and many do not even collect it. However, there are some exceptions. For example, Lew Platt, the former CEO of Hewlett-Packard, used to regularly cite the HP intranet in his presentations.. The last such report, dated September 7, 1998, and available at http://www.hp.com/financials/textonly/personnel/ceo/~es.ht~, stated that this network carried 20 TB/month, and a comparison with previous reports shows that this volume of traffic had been doubling each year for at least the previous 2 years. (As an interesting point of comparison, the entire NSFNet Internet backbone carried 15TB/month at its peak at the end of 1994.) Several other corporations have provided data showing similar rates of growth for their Intranet trafllc, although some indicated their growth has slowed, and a few have had practically no recent growth. Internal corporate tr&c appears to be growing much more slowly than public Internet traffic. Data for retail private lines as well as for Frame Relay and ATM (Asynchronous Transfer Mode) services show aggregate growth in bandwidth (and therefore most likely also traffic) in a range of 3040% per year. The growth is slow for retail private lines and fast for Frame Relay and ATM. These rates are remarkably close to the growth rate observed in the late 1970s in the United States, which was around 30% per year [deSolaPITH]. Thus, it is the corporate traffic to the public Internet that is growing at 100% per year. It is also important to note that in the year 2000, over two-thirds of the volume on the public Internet appeared to be business to business. Thus, the accelerationof the overallgrowth rate of data trafficto about 100%per year from the old 30% or so a year appears to be a consequence of the advantages of the Internet, with its open standards and any-to-anyconnectivity. For the remainder of this section we concentrate on publicly available information, primarily about academic, research, and government networks. These might be thought of as unrepresentative of the corporate or private residential users. Our view is just the opposite, in that these are the institutions that are worth studyingthe most, since they normally alreadyhave broadband accessto the Internet, tend to be populated by technically sophisticated users, and tend to try out new technologies first. The spread of Napster through universities is a good example of the last point. We believe that Napster and related tools, such as Gnutella and Wrapster, are just the forerunners of other programs for sharing of general information, and not just for disseminating pirated MP3 files. As we explained elsewhere, there is already much more digital data on hard disks alone than shows up on today’s Internet. Further, this situation is likely to continue. The prevalent opinion appears to be that in data networks, “If you build it, they will fill it.” Our evidence supports this, but with the important

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qualiiication that “they” will not fill it immediately. That certainly has been the experience in local area networks, LANs. The prevalence of lightly utilized long-distance corporate links was noted in [Odlyzkol]. That paper also discussed the vBNS (very High Speed Backbone Network) research network, which was extremely lightly loaded. Here we cite another example of a large network with low utilizations and moderate growth rates. Abilene is the network created by the Internet2 consortium of U.S. universities. Its backbone consists of 13 OC48 (2.4 Gb/s) links. Moreover, most of the consortium members had OC3 links to it. The average utilization in June 2000 was about 1.5%, and by April 2001 it had grown to about 4.1%. Thus, in spite of the uncongested access and backbone links, tr&c did not explode. Even on more congested links, it often happens that an increase in capacity does not lead to a dramatic increase in traffic. This is supported by several examples. Such examples include the University of Waterloo, the SWITCH network, the NORDUNet network, the European TEN-155 network, the Merit network, the University of Toronto, Princeton University, and the University of California at Santa Cruz [CoffmanO2]. Later we go into moderate detail for these networks. Figure 2.1 shows statistics for the traffic from the public Internet to the University of Waterloo over the last 7 years. Detailed statistics for the Waterloo network are available at http://www.ist.uwaterloo.ca/cn/#Stats,but Fig. 2.1 is based on additional historical data provided to us by this institution. Just as for the JANET network discussed previously and the SWITCH network to be discussed later, as well as most access links, there is much more traffic from the public Internet to

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the institution than in the other direction. Hence we concentrate on this more congested link, because it offers more of a barrier. We see that even substantial jumps in link capacity did not affect the growth rate much. Traffic has been about doubling each year for the entire 7-year period. (Overall, the growth rate at the University of Waterloo has slowed, about 55% from early 1999 to early 2000. This was at least partially the result of official limits on individual users that were imposed, limits we will discuss later.) The same phenomenon of traffic doubling each year, no matter what happens to capacity, can be observed in the statistics for the SWITCH network, which provides connectivity for Swiss academic and research institutions. The history and operations of this network are described in [Harms, ReichlLS], and extensive current and historical data are available at http:// www.switch.ch/lan/stat/. The data used to prepare Fig. 2.2 was provided to us by SWITCH. As is noted in [ReichlLS], the transatlantic link has historically been the most expensive part of the SWITCH infrastructure, and at times was more expensive than the entire network within Switzerland. It is therefore not surprising that this link tends to be the most congested in the SWITCH network. Even so, increasing its capacity did not lead to a dramatic change in the growth rate of traffic. If we compare increases in volume of data received between November of one year and January of the following year, there was an unusually high jump (420/0)from November 1998to January 1999.This was in response to extreme congestion experienced at the end of 1998, congestion that produced extremely poor service, with packet loss rates during peak periods exceeding 20%. However, over longer periods of time, the growth rate has been rather steady at close to 100% per year and independent of the capacity

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Fig. 2.2 Capacity of link between the Swiss SWITCH network and the United States and traffic on it toward Switzerland.

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of the link. More detailed data about other types of SWITCH traffic can be found at http://www.switch.cMan/stat/ through the “Public access” link. The listings available there as of mid 2000, as well as those from previous years, show that various transmissions tended to grow at 100 to 150% per year. It is worth noting that capacity grew faster than traffic, but not too much faster. Merit Network is a nonprofit ISP that serves primarily Michigan educational institutions.It has data availableonline at http://www.merit.net/michnet/ statistics/direct.htmlthat goes back to January 1993. This data was used to construct the graph in Fig. 2.3. The data for January 1993 through June 1998 shows only the number of inbound IP packets. The data for months since July 1998 is more complete, but it is so complete, with details of so many interfaces, that we have not yet determined the best way to use it. Hence we have used only the earlier information for January 1993 through June 1998. The resulting time series is a reasonable, although imperfect, representation of a straight line, modulated by the periodic variations introduced by the academic calendar. The growth rate is almost exactly 100% per year. The research networks that were examined have low utilizations. It should be emphasized that this is not a sign of inefficiency. Many novel applications required high bandwidth to be effective. That, along with some additional factors, such as the high growth rate, lumpy capacity, and pricing structure, contributes to the much lower utilization of data networks than of the longdistance voice network [Odlyzkol]. The general conclusion that can be drawn from the examples listed in this section (along with numerous other examples) is that data traffic has a remarkable tendency to double each year. There are of course slower and faster growth rates. Overall though, they tend to cluster in the Vicinity of 100% per year.

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To date, the authors have not seen any large institutions with traffic doubling anywhere close to every 3 or even 4 months. The growth rates that are cited here are often affected strongly by restrictions imposed at various levels. As described elsewhere [CoffmanOl, CoffmanO2], some of the explicit limits are imposed by network administrators. The arrival of Napster (discussed in Section 7) led many institutions to either ban its use or else limit traffic rates to some parts of the campus (typically student dormitories). Push technologies were stifled at least partially because enterprise network administrators blocked them at their firewalls. E-mail often has size restrictions that block large attachments (and in some cases all attachments are still banned). Teleconferencing is only slowly being experimented with on corporate intranets, and even packetized voice sees very limited (although growing) use. Similar constraints apply to most of the content seen on the Web. As long as a large fraction of potential users have limited bandwidth, such as through dial modems, managers of Web servers will have an incentive to keep individual pages moderate in size. Thus, one can see that Internet traffic is subject to a variety of constraints at different levels. Some are applied by network managers, others by individual users, and the interaction of these constraints with the rising demands is fundamental in understanding what produces the growth rates observed. The ability to sustain the high growth rate of Internet traffic will require the creation of new applications that will generate huge volumes of traffic. At current growth rates, by 2005 there will be eight times as much Internet as voice traffic (on the U.S. long-haul networks). If voice were packetized, in all likelihood the voice traffic would only account for about 3% of the Internet traffic. Thus, voice traffic will not fiU the pipes that are likely to exist, and neither will traditional Web surfing. This will create a dilemma for service providers, network administrators, and equipment suppliers: To sustain the growth rates that the industry has come to depend on, and to accommodate the progress in technology, new technologies are needed. Such applications will appear disruptive to network operations today, and as such, they often have to be controlled. However, in the long run, they must be encouraged.

7. Disruptive Innovation It is often said that everything changes so rapidly on the Internet that it is impossible to forecast far into the future. The next “killer app” could disrupt any plans that one makes. Yet there have been just two “killer apps” in the history of the Internet: e-mail and the Web (or, more precisely, Web browsers, which made the Web usable by the masses). Many other technologies that had been widely touted as the next “killer app,” such as push technology have fizzled. (Push technology allows the sending of information directly to one’s

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computer instead of the computer needing to actively go out and obtain it.) Furthermore, only the Web can be said to have been truly disruptive. From the first release of the Mosaic visual browser around the middle of 1993, it apparently took under 18 months before Web trafKc became dominant on Internet backbones. It appears overwhelmingly likely that it was the appearance of browsers that then led, in combination with other developments, to that abnormal spurt of a doubling of Internet trafKc every 3 or 4 months in 1995 and 1996. What were the causes of the 100-fold explosion in Internet backbone traffic over the 2-year period of 1995 and 1996? We do not have precise data, but it appears that there were four main factors, all interrelated. Browsers passed some magic threshold of usability, so many more people were willing to use computers and online information services. Users of the established online services, primarily AOL, CompuServe, and Prodigy, started using the Internet. The text-based transmissions of those services, which probably averagedonly a few hundred bits per second per connected user, were replaced by the graphicsrich content of the Web, so transmission rates increased to a few thousand bits per second. Finally, flat rate access plans led to a tripling of the time that individual users spent online [Odlyzko3], as well as faster growth in number of users. The Internetwas able to support this explosionin use because it was utilizing the existinginfrastructure of the telephone network. At that time, the Internet was tiny compared to the voice network.It is likely that the data network that handles control and billing for the AT&T long-distance voice services by itself was carrying more traffic than the NSF Internet backbone did at its peak at the end of 1994. Today, by contrast, the public Internet is rapidly moving toward being the main network, so quantum jumps in traffic cannot be tolerated so easily. In late 1999, a new application appeared that attracted extensive attention and led to many predictions that network traffic would see a major impact. It was Napster. At the time, numerous articles in the press cited Napster’s ability to “overwhelm Internet lines,” and have claimed that it has forced numerous universities to ban or limit its use. The impression one got from those press reports was that Napster was causing a quantumjump in Internet traffic, and was driving the traffic growth rates well beyond the normal range. However, upon close examination this does not appear to be completely accurate, and the use of Napster has not increased growth rates much beyond the annual doubling or tripling rates, even within university environments,where Napster is most popular. That is not to say that it has not resulted in huge amounts of traffic, nor that it has not had serious impact on several major networks. Napster provides software that enables users connected to the Internet to exchange andor download MP3 music files. The Napster Web site matches users seeking certain music files with other users who have those files on their computer. The Napster system preferentially uses machines that have high

zy zyxwvu

2. Growth of the Internet

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bandwidth connections as sources of files. This means that universities are the primary sources, since other organizations with fast dedicated links, mainly corporations, do not allow such traffic. The result is that although college students are often cited as the greatest users of MP3 files, it is the traffic from universities that gets boosted the most. (Because that direction of traffic is typically much less heavily used than the reverse one, the impact of Napster is much less severe than if the dominant direction of traffic were reversed.) Regular modem users are usually not affected, because their connections are too slow. However, the proliferation of cable modems and DSL connections that have “always-onyy high-bandwidth connectivity is leading to problems for some residential users, especially since the uplink is the one that invariably has the more limited bandwidth. A key reason that Napster is of great interest to us is that similar types of sharing applications effectively turn consumers of information into providers of information. u h e World Wide Web was designed for such information sharing, but for some types of files Napster and its kin are preferable.) These applicationswill effectively turn traditional consumerPCs into Internet servers that will output large amounts of traffic to other users. In Napster’s case this has been predominantly MP3 musicfiles, but other programs, such as Gnutella, work with more general data. It is highly probable that such applicationscould be one of the key applications that fuel the continued annual doubling or tripling of data traffic. Napster first became noticeable in the summer of 1999. Its share of the total Internet traffic on many of the university networks has grown from essentially nothing to around 25% of the total traffic by mid to late 2000. In [CoffmanO2] the traffic generated by Napster and its impact on various networks was examined. The amount of Napster traffic that is reported by several university networks (such as University of California at Santa Cruz, University of Michigan, University of Indiana, University of California at Berkeley, Northwestern University, and Oregon State University to name a few) ranges from around 20 to 50%. However, the reported numbers are often very preliminary, and in some cases they compare Napster traffic to total traffic, whereas in others it appears that the high values may represent a comparison only to the out traffic. In any event, this is a phenomenal growth rate for any single application. Since it started from zero and our data only goes out to about a year from that time, it is risky to extrapolate this initial explosion out indefinitely. In most cases [CoffmanO2], Napster has had a noticeable effect on the growth rate of traffic on this campus, but not an outlandish one. Several networks, such as that of the University of Wisconsin-Madison that report Napster traflk making up as much as 30% of the total, are not doing anything to limit Napster because they claim that they still have plenty of bandwidth. Others have imposed limits on the total bandwidth available to the dormitories.

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Aside from Napster, occasionally even a large institution will experience a local perturbation in its data traffic patterns caused by one particular application. For example, the SETI@home distributed computing project (http://setiathome.ssl.berkeley.edu)uses idle time on about three million PCs (as of mid 2001) to search for signs of extraterrestrial intelligence in signals collected by radio telescopes. This project is run out of the Space SciencesInstitute at the University of California at Berkeley, and within a year of inception it accounted for about a third of the outgoing campus traffic [McCredie]. (Moreover, this was extremely asymmetrical traffic, with large sets of data to be analyzed going out to the participating PCs and small final results coming back. That most of the data went away from campus made this application less disruptive than it would have been otherwise.) Its disruptive effect is moderated by limiting its transmission rate to about 20 Mb/s. At the University of California at Santa Cruz, a complete copy of the available genome sequence was made available for public download in early July 2000. This, combined with coverage in the popular press and on Slashdot, led to an immediate surge in traffic, far exceeding the effects of Napster. If the interest in this database continues, it will require reengineering of the campus network. The SETI@home project is interesting for several reasons. It is cited in [McCredie] as a major new disruptive influence. Yet it contributes only about 20 Mb/s to the outgoing traffic. An increasing number of PCs and workstations are connected at 100Mb/s, and even Gigabit Ethernet (1,000 Mb/s) is coming to the desktop. This means that for the foreseeable future, a handful of workstations will, in principle, be capable of saturating any Internet link. Given the projections for bandwidth, a few thousand machines will continue to be capable of saturating all the links in the entire Internet. Thus control on user traffic will have to be exercised to prevent accidental as well as malicious disruptions of service. However, it seems likely that such control could be limited to the edges of the network. In fact, such control will pretty much have to be exercised at the edges of the network. QoS (Quality of Service) will not help by itself, since a malicious attacker who takes control of a machine will be able to subvert any automatic controls. Finally, after considering current disruptions from Napster and SETI@home, we go back and consider browsers and the Web again. They were cited as disruptive back in 1994 and 1995. (Mosaic was first released unofficially around the middle of 1993, officially in the fall of 1993, and took off in 1994.) However, when we consider the growth rates for the University of Waterloo, for MichNet [CoffmanOl], or for SWITCH (which apparently had regular growth throughout the 1990s according to [Harms]), we do not see anything anomalous, just the steady doubling of traffic each year or so. If we consider the composition of the traffic, there were major changes. For example, Fig. 2.4 shows the evolution of traffic between the University of Waterloo and the Internet. (It is based on analysis of traffic during the third week in each March, and more complete results

zyx zyx zyxwvu 2. Growth of the Internet

45

are available at http://www.ist.uwaterloo.ca/cn/Stats/ext-prot.html.) The Web did take over, but much more slowly than on Internet backbones. There are no good data sets, but it has been claimed that by the end of 1994, Web traffic was more than half of the volume of the commercial backbones. On the other hand, the data for the NSFNet backbone, available at http://www.merit.edu/merit/archive/nsfnet/statistics/index.html, show that Web traffic was only approaching 20% there by the end of 1994, a level similar to that for the University of Waterloo. Thus, at well-wired academic institutions such as the University of Waterloo and others that dominated NSFNet traffic, the impact of the Web was muted. Perhaps the main lesson to be drawn from the discussion in this section is that the most disruptive factor is simply rapid growth by itself. A doubling of traffic each year is very rapid, much more rapid than in other communication services. Figure 2.4 shows e-mail and netnews shrinking as fractions of the traffic at the University of Waterloo, from a quarter to about 5%. Yet the byte volume of these two applications grew by a factor of 12 during the 6 years covered by the graph, for a growth rate of over 50% per year, which is very rapid by most standards. If we are to continue the doubling of traffic each year, new applicationswill have to keep appearing and assuming dominant roles. An interesting data point is that even at the University of Wisconsin in Madison, which analyzes its data traffic very carefully, about 40% of the transmissions escape classification.That is consistent with information from a few corporate networks, where the managers report that upwards of half of their traffic is of unknown types. (A vast majority of network managers do not even attempt to perform such analyses.) This shows how difficult coping with rapid growth is.

zyx zyx

zyxwvu zyxw

internet traffic at the University of Waterloo

0 0

-

m

E

9

u - 0

o m

a

0, m c

p 0)

n 0

cu

1994

I

I

I

I

I

I

1995

1996

1997 year

1998

1999

2000

Fig. 2.4 Composition of traffic between the University of Waterloo and the Internet based on data collected in March of each year.

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zyxwvutsrq zyxw Kerry G. Coffman and Andrew M. Odlyzko

8. Moore’s Law for Data Traffic

The approximate doubling of transmission capacity of each fiber that is described in [CoffmanO2] is analogous to the famous Moore’s Law in the semiconductorindustry. In 1965, Gordon E. Moore, then in charge of R&D at Fairchild Semiconductor,made a simple extrapolation from three data points in his company’s product history. He predicted that the number of transistors per chip would about double each year for the next 10 years. This prediction was fulfilled, but when Moore revisited the subject in 1975, he modified his projection for further progress by predicting that the doubling period would be closer to 18 months. (For the history and fuller discussion of Moore’s Law, see [Schaller].) Remarkably enough, this growth rate has been sustained over the past 25 years. There have been many predictions that progress was about to come to a screeching halt (including some recent ones), but the most that can be said is that there may have been some slight slowdown recently. (For example, according to the calculations shown in FlderingSE], the number of transistors in leading-edge microprocessors doubles every 2.2 years. On the other hand, the doubling period is lower for commodity memories.) Experts in the semiconductor area are confident that Moore’s 1975 prediction for rate of improvement can be fulfilled for at least most of the next decade. Predictions similar to Moore’s had been made before in other areas, and in [Licklider]they were made for the entire spectrum of computing and communications. However, it is Moore’s Law that has entered the vernacular as a description of the steady and predictable progress of technology that improves at an exponential rate (in the precise mathematical sense). Moore’s Law results from a complex interaction of technology, sociology, and economics. No new laws of nature had to be discovered, and there have been no dramatic breakthroughs. On the other hand, an enormous amount of research had to be carried out to overcome the numerous obstacles that were encountered.It may have been incremental research, but it required increasing ranks of very clever people to undertake it. Furthermore, huge investments in manufacturing capacity had to be made to produce the hardware. Perhaps even more important, the resulting products had to be integrated into work and lifestyles of the institutions and individuals using them. For further discussions of the genesis, operations, and prospects of Moore’s Law, see [ElderingSE, Schaller]. The key point is that Moore’s Law is not a natural law, but depends on a variety of factors. Still, it has held with remarkable regularity over many decades. Although Moore’s Law does apply to a wide variety of technologies, the actual rates of progressvary tremendouslyamong Merent areas For example, battery storage is progressing at a snail‘s pace’ compared to microprocessor improvements. This has signscant implications for mobile Internet access, limiting processor power and display quality. Display advancesare more rapid than those in power storage, but nowhere near fast enough to replace paper

zyx

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as the preferred technology for general reading, at least not at any time in the next decade. (This implies, in particular, that the bandwidth required for a single video transmission will be growing slowly.) Dynamic Random Access Memories (DRAMS) is growing in size in accordance with Moore’s Law, but their speeds are improving slowly. Microprocessors are rapidly increasing their speed and size (which allows for faster execution through parallelism and other clever techniques), but memory buses are improving slowly. For some quantitative figures on recent progress, see [Grays]. From the standpoint of a decade ago, we have had tidal waves of just about everything: processing power, main memory, disk storage, and so on. For a typical user, the details of the PC on the desktop (MHz rating of the processor, disk capacity) do not matter too much. It is generally assumed that in a couple of years a nav and much more powerful machine will be required to run the new applications, and that it will be bought for about the same price as the current one. In the meantime, the average utilization of the processor is low (since it is provided for peak performance only), compression is not used, and wasteful encodings of information (such as 200 KB Word documents conveying a simple message of a few lines) are used. The stress is not on optimizing the utilization of the PC’s resources, but on making life easy for the user. To make life easy for the end user, though, clever engineering is employed. Because the tidal waves of different technologies are advancing at different rates, optimizing user experience requires careful architectural decisions [Grays, HennessyP]. In particular, since processing power and storage capacity are growing the fastest, while communication within a PC is improving much more slowly, elaborate memory hierarchies are built. They start with magnetic hard disks and proceed through several levels of caches, invisibly to the user. The resulting architecture has several interesting implications, which are explored in [Grays]. For example, mirroring disks is becoming preferable to RAID (Redundant Arrays of Inexpensive Disks) fault-tolerant schemes that are far more efficient but slower. The density of magnetic disk storage increased at about 30% per year from 1956 to 1991, doubling every 2; years [Economist]. (Total deployed storage capacity increased faster, as the number of disks shipped grew.) In the 1990s, the growth rate accelerated, and in the late 1990sincreased yet again. By some accounts, t h densities ~ in disk drives are about doubling each year. For our purposes, the most relevant figure will be total storage of disk drives. Table 2.5 shows data from an IDC study, which shows storagecapacity shippedeach year just about doubling through the year 2000, and then slowing down. However, that study was prepared in 1998, and since then IDC has revised upwards its estimatesfor disk storage systems toward a continuation of the doubling trend. Similar projections from Disk/Trend (http://www.disktrend.com/)also suggest that the total capacity of disk drives shipped will continue doubling through at least the year 2002. Given the advances in research on magnetic storage, it seems that a doubling each year until the year 2010 might be achievable (with

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zyxw

Table 2.5 Worldwide Hard Disk Drive Market (based on September 1998 and August 2000 IDC reports) Year

1995 1996 1997 1998 1999 2000 200 1 2002 2003 2004

Revenues (bizfions)

Storage Capacity (terabytes)

$21.593 24.655 27.339 26.969 29.143 32.519 36.219 40.683

76,243 147,200 334,791 695,140 1,463,109 3,222,153 7,239,972 15,424,824 30,239,756 56,558,700

some contributionfrom higher revenues, as shown in Table 2.5, but most coming from better technology).After about 2010, it appears that magnetic storage progress will face serious limits, but by then more exotic storage technologies may become competitive. It seems safest to assume that total magnetic disk storage capacity will be doubling each year for the next decade. However, even if there is a slowdown, say to a 70% annual growth rate, this will not affect our arguments too much. The key point is that storage capacity is likely to grow at rates not much slower than those of network capacity. Furthermore, total installed storage is already immense. Table 2.5 shows that at the beginning of the year 2000, there were about 3,000,000TB of magnetic disk storage. If we compare that with the estimates of Table 2.1 for network traffic, we see that it would take between 250 and 400 months to transmit all the bits on existing disks over the Internet backbones. This comparison is meant as just a thought exercise. The backbones considered in Table 2.1 arejust those in the United States, whereas disks counted in Table 2.5 are spread around the world. A large fraction of the disk space is spare, and much of the content is duplicated (such as those hundreds of millions of copies of Windows 98), so nobody would want to send them over the Internet. Still, this thought exercise is useful in showing that there is a huge amount of digital data that could potentially be sent over the Internet. Further, this pool of digital data is about doubling each year. An interesting estimate of the volume of information in the world is presented in [Lesk]. It shows that already in the year 1997we were on the threshold of being able to store all data that has ever been generated (meaning books, movies, music, and so on) in digital format on hard disks. By now we are well

2. Growth of the Internet

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past that threshold, so future growth in disk capacities will have to be devoted to other types of data that we have not dealt with before. Some of that capacity will surely be devoted to duplicate storage (such as a separate copy of an increasingly bloated operating system on each machine). Most of the storage, though, will have to be filled by new types of data. The same process that is yielding faster processors and larger memories is also leading to improved cameras and sensors These will yield huge amounts of new data that have not been available before. It appears impossible to predict precisely what type of data this will be. Much is likely to be video storage from cameras set up as security measures or ones that record our every movement. There could also be huge amounts of data from medical sensors on our bodies. What is clear, though, is that “[tlhe typical piece of information will never be looked at by a human being” [Lesk]. There will simply not be enough of the traditional “content” (books, movies, music) nor even enough of the less formal type of “content” that individuals will be generating on their own. Huge amounts of data that is machine generated for machine use suggests that data networks will also be dominated by transfers of such data. This was already predicted in [deSolaPITH],and more recently in [Odlyzko2,StArnaud, StArnaudCFM].Given an exponential growthrate in volume of data transfers, it was clear that at some point in the future most of the data flying through the networks would be neither seen nor heard by any human being. Thus, we can expect that streaming media with real-time quality requirements will be a decreasing fraction of total traffic at some point within the next decade. There will surely be an increase in the raw volume of streaming real-time traffic, as applications such as videoconferencing move onto the Internet. However, as a fraction of total trafiic, such transmissionswill not only decrease eventually, but may not grow much at all even in the intermediate future. (Recall that at the University of Waterloo over the last 6 years, the volume of e-mail grew about 50% a year, but as a fraction of total trafiic it is almost negligible now.) The huge imbalance in volume of storage and capacities of long-distance data networks means that even the majority of traditional “content” will be transmitted as files, and not in streaming form. For more detailed arguments supporting this prediction, see [Odlyzko2]. This development, in which “content”is sent around as files for local storage and playback, is already making its appearance with MP3, Napster, and related programs. The huge hard disk storagevolumes also mean that most data will have to be generated locally. There will surely also be much duplication (such as operating systems, movies, and so on that would be stored on millions of computers). Aside from that, there will surely be huge volumes of locally generated data (e.g., from security cameras and medical sensors) that will be used (if at all) only in highly digested form. The examples in [Coffman02] support the notion that there is a “Moore’s Law” for data traffic, with transmission volumes doubling each year. Even at large institutions that already have access to state-of-the art technology,

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data traffic to the public Internet tends to follow this rule of doubling each year. This is not a natural law, but, like all other versions of Moore’s Law, reflects a complicated process, the interaction of technology and the speed with which new technologies are absorbed. A Moore’s Law for data traffic is different from those in other areas, since it depends in a much more direct way on user behavior. In semiconductors, consumer willingness to pay drives the research, development, and investment decisions of the industry, but the effects are indirect. In data traffic, though, changes can potentially be much faster. A residential customer with dial-up modem access to the Internet could increase the volume of data transfer by a factor of about five very quickly. All it would take would be the installation of one of the software packages that prefetch Web sites that are of potentialinterest and that fill in the slack between transmissions initiated by the user. Similarly, a university’s T3 connection to the Internet could potentially be filled by a single workstation sending data to another institution. Thus any Moore’s Law for data traflic is by nature much more fragile than the standard Moore’s Law for semiconductors,for example. Thus it is remarkable that we see so much regularity in growth rates of data transfers. Links to the public Internet are usually the most expensive parts of a network, and are regarded as key choke points They are where congestion is seen most frequently at institutional networks. Yet the “mere” annual doubling of data traffic even at institutions that have plenty of spare capacity on their Internet links means that there are other barriers that matter. The obvious one is the public Internet itself. It is often (some would say usually) congested. A terabit pipe does not help if it is hooked up to a megabit link, and so providing a lightly utilized link to the Internet does not guarantee good end-to-end performance. Yet that is not the entire explanation either, since corporate Intranets, which tend to have adequate bandwidth and seldom run into congestion, tend to grow no faster than a doubling of traflic each year. There are other obstructions, such as servers, middleware, and, perhaps most important, services and user interfaces People do not care about getting many bits. What they care about are the applications. However, applications take time to be developed, deployed, and adopted. To quote J. Licklider (who probably deserves to be called “the grandfather of the Internet” for his role in setting up the research program that led to the Internet’s creation):

zy zyxwv zyx zyxwv

zyx

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A modern maxim says: “People tend to overestimate what can be done in one year and to underestimate what can be done in five or ten years.” Picklider]

“Internet time,” where everything changes in 18 months, has a grain of truth, but is largely a myth. Except for the ascendancy of browsers, most substantial changes take 5 to 10 years. As an example, it has been at least 4 years since voice over IP was first acclaimed as the ‘‘next big thing.” Yet its impact so far has been surprisinglymodest. It is coming, but it is not here today, and it won’t be here tomorrow. People take time to absorb new technologies.

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What is perhaps most remarkable is that even at institutions with congested links to the Internet, traffic doubles or almost doubles each year. Users appear to find the Internet attractive enough that they exert pressure on their administration to increase the capacity of the connection. Existing constraints, such as those on e-mail attachments, or on packetized voice or video, as well as the basic constraint of limited bandwidth, are gradually loosened. Note that this is similar to the process that produces the standard Moore’s Law for PCs. Intel, Micron, Toshiba, and the rest of the computer industry would surely produce faster advances if users bought new PCs every year. Instead, a typical PC is used for 3 to 4 years. On one hand there is pressure to keep expenditures on new equipment and software under control, and also to minimize the complexity of the computing and communicationssupportjob. On the other hand, there is pressure to upgrade, either to better support existing applications or to introduce new ones. Over the last three decades, the conflict between these two pressures has produced a steady progress in computers. Similar pressures appear to be in operation in data networking. In conclusion, we cannot be certain that Internet t r a c will continue doubling each year. All we can say is that historically it has tended to double each year. Still, trends in both transmission and in other information technologies appear to provide both the demand and the supply that will allow a continuing doubling each year. Since betting against such Moore’s laws in other areas has been a loser’s game for the last few decades, it appears safest to assume that data traffic will indeed follow the same pattern, and grow at close to 100% per year.

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9. Further Economic and Technical Considerations

A frequently asked question concerns the elasticity of demand for data transmission capacity. However, for long-range projections it might be more useful to think of analogies with the computer industry. In that industry, product managers clearly do think about elasticities in the short or intermediate terms. From a long-range perspective, though, what dominates are the effects of Moore’s Law. Table 2.6 (drawn from [FishburnO]) shows a dozen years from the history of Intel. The leading microprocessor sold for roughly a constant price all during this period. However, its power was increasing at the exponential rate given by Moore’s Law. Intel’s total revenues (and profits) grew, as more processors were being sold, but this growth rate was considerably more modest than that of the computing power. Users found the increasing computational power of new PCs sufficiently attractive that they not only bought new PCs, but increased their total spending. They did this even though most of that power was sitting idle, and it was only the occasional bursts of recomputing a spreadsheet or bringing up a presentation package that mattered. A similar

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Table 2.6 Intel and Its Microprocessors(each year lists the most powerful General Purpose Microprocessors Sold by Intel, Its Computing Power, Price at the End of the Year (in Dollars), and Intel’s Revenues and Profits for That Year (in Millions of Dollars)) Price (dollam)

Year

Processor

Mips

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

386 DX (16MHz) 386 DX (20 MHz) 386 DX (25 MHz) 486 DX (25 MHz) 486 DX (33 MHz) 486 DX (50 MHz) DX2 (66 MHz) Pentium (66 MHz) Pentium (100MHz) Pentium Pro (200 MHz)

5 6 8 20 27 41 54 112 166 400

950 950 644 600 898 935 1,325

Pentium I1 (300 MHz)

600

735

300

Revenue (millions of dollars)

Net Profit (millions of dollars)

1,265 1,907 2,875 3,127 3,922 4,779 5,844 8,782 11,521 16,202 20,847 25,070

- 173

248 453 391 650 819 1,067 2,295 2,266 3,566 5,157 8,945

zyxwv

evolution might take place in networking. Total spendingmay (subjectto business cycles) increase at a moderate pace, while the bandwidth and traffic grow at rates determined by technological progress. If that happens, we are likely to see traffic and capacity about doubling each year, with capacity growth faster than that of traffic.

10. Conclusions Much of the almost hyperactivitywithin the optical fiber telecommunications industry over the past few years can be traced to the perceived and real growth of the traffic on the Internet. We maintain that the overall growth rate of the Internet for most of its existence (despite some excursions) was remarkably close to “doubling every year,” and we anticipate that this rate will continue into the foreseeable future. In effect, we see a type of Moore’s Law associated with the growth of data traffic. This type of growth rate is in sharp contrast to the historical growth rates of various methods of communications (including conventional mail, telegraph service, and traditional voice phone service) that tended to be no greater (and typically much less) than about 10Y0per year. Still, even though a doubling each year represents very fast growth, it is only comparable to the rate of progress in transmission capacity. Hence we are

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unlikely to see the huge increases in spending on optical communication that many business plans had been based on. Throughout the history of the Internet there have only been two “killer applications”: e-mail and the Web (including Web browsers). Several events conspired that allowed an unprecedentedexplosion (roughly 100-fold increase) in Internet traffic in the 1995-1996 time frame, and the Internet was able to handle this because it made use of the existing telephone industry infrastructure. Because the Internet is quickly approaching the point at which it is the predominant network, it is very unlikely that such huge growth rates could be so easily supported in the future. It also appears that, aside from short-range perturbations, there will be neither a “bandwidth glut” nor a “bandwidth shortage” in the foreseeable future, in that supply and demand will be growing at comparable rates. As such, it is very likely that pricing will begin to play an even more important role in the evolution of traffic. Throughout most of the 1990s, data transmission prices were increasing. However, there are recent signs that they are beginning to decrease, and in some cases, especially across the Atlantic and on major transcontinental routes in the United States, they have decreased dramatically. If they begin to decrease rapidly in general, then many of the constraints on usage that exist today may very likely start to ease. We are likely to see capacity growing somewhat faster than traffic, a continuation of the trend we have already seen in the last few years. We also believe that “file” transfers, and not real-time streaming,will remain dominant on the network. Streaming real-time transmissionswill undoubtedly grow in absolute terms, and as a fraction of the total traffic it may increase for a while. However, in all likelihood it will eventually begin to decline as the demand for this type of traffic will not grow as fast as network capacity. We foresee sharing applications as a likely candidate to fuel traffic growth. One of the first major examples of this was Napster, because it effectively turned consumers of information into providers of information. It is extremely likely that such file sharing applications will be some of the key applications that continue to fuel the annual doubling of data traffic.

References [Abbate] [Baran] [Boardwatch] [Bruno]

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J. Abbate, Inventing the Internet, MIT Press, 1999.

I? Baran, On distributed communications network, IEEE Trans.

Comm. Systems, vol. 12, 1964, pp. 1-9. Boardwatch. Available at http://www.boardwatch.com. L. Bruno, Fiber optimism: Nortel, Lucent, and Cisco are battling to win the high-stakes fiber-optics game, Red Herring, June 2000. Available at http://www.herring.com/mag/issue79/mag-fiber79.html.

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1Cerf-I

[CerfKI

[Cochrane]

[CoffmanOl]

[Coffman02]

[CTIA]

[Cyberspace]

[deSolaPITH]

PWLI

[Economist] [ElderingSE]

[Fishburno]

FlOYdPI [Galbi]

V. G. Cerf, A brief history of the Internet and related networks. Available at http://www.isoc.org/internethistory/cerf html. V. G. Cerf and R. E. Kahn, A protocol for packet network interconnection, IEEE Trans. Comm. Tech., vol. COM-22, May 1974, pp. 627-641. N. Cochrane, We’re insatiable: Now it’s 20 million million bytes a day, Melbourne Age, January 15, 2001. Available at http:llwww .it.fairfax.com.au/networking/200 10115/A13694-2001Jan15.html. K. G. Coffman and A. M. Odlyzko, The size and growth rate of the Internet, First Monday, October 1998. Available at http://fkstmonday.org/. Also available at http://www.dtc.umn.edu/ -0dlyzko. K. G. Coffman and A. M. Odlyzko, Internet growth: Is there a “Moore’s Law” for data traffic?, Handbook of Massive Data Sets, J. Abello, P. M. Pardalos, and M. G. C. Resende, eds, Kluwer, 200 1, in press. Available at http://www.dtc.umn.edu/-odlyzko. CTIA (Cellular Telecommunications Industry Association), SemiAnnual FEreleSs Industry Survey, June 1985 to June 2000. Available at http:l/www.wow-com.codwirelesssurvey/. Geography of Cyberspace Directoiy: Internet Trafic and Demographic Statistics. Available at http://www.cybergeography.org/ statistics.html. I. de Sola Pool, H. Inose, N. Takasaki, and R. Hurwitz, Communications Flows: A Census in the Unitedstates andJapan, North-Holland, 1984. D. A. Dunn and A. J. Lipinski, Economic considerations in computer-communication systems, pp. 371- 422 in ComputerCommunication Networh, N. Abramson and F. F. Kuo, eda, Prentice-Hall, 1973. Not Moore’s Law, The Economist, July 12,1997. C . A. Eldering, M. L. Sylla, and J. A. Eisenach, Is there a Moore’s Law for bandwidth? IEEE Communications Magazine, October 1999, pp. 2-7. I? C . Fishburn and A. M. Odlyzko, Dynamic behavior of differential pricing and Quality of Service options for the Internet, pp. 128-139 in Proc. First Intern. Con$ on Information and Computation Economies (ICE-98), ACM Press, 1998. Available at http://www.dtc.umn.edu/-odlyzko. S. Floyd and V. Paxson, Dimculties in simulating the Internet, IEEE/ACM Damactions on Networking, in press. Available at ht tp://www.aciri.orglfloydpapers.html. D. Galbi, Bandwidth use and pricing trends in the U.S., Telecommunications Policy, vol. 24, no. 11, December 2000. Available at http://www.galbithink.org.

zyxw

2. Growth of the Internet

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J. Gray and P. Shenoy, Rules of thumb in data engineering,

[Green]

[Harms]

[HennessyP] [Hobbes] [Houghl [Kleinrockl]

Proc. 2000 ZEEE Intern. Con$ Data Engineering. Available at http://research.microsoft.com/-gray. E. E. Green, Communicationsspectra by the wholesage2012 A.D., Proc. IRE, vol. 50,1962, pp. 585-587. Reprinted in Proc. ZEEE, vol.

87,1999,1293-1295. J. Harms, From SWITCH to SWITCH*-extrapolating from a case study, Proc. INET '94, pp. 341-1 to 341-6. Available at http:l/ info.isoc.org/iso~whatis/conferences/ine~94lpapers/index. html. J. L. Hennessy and D. A. Patterson, Computer Architecture: A Quantitative Approach, Morgan Kaufmann, 1990. Hobbes Internet Emeline. Available at http:/lwww.zakon.org/ robert/internet/timeline/. R. W. Hough, Future data traffic volume, ZEEE Computer, September-October 1970, pp. 6-12. L. Kleinrock, Information flow in large communicationsnetworks, RLE Quarterly Progress Report, July 1961, pp. 1-35. Available at

zyx

http://www.lk.cs.ucla.edu/LK/Bib/REPORT/PhD. [Kleinrock2] [Kleinrock3]

L. Kleinrock, Communication Nets; Stochastic Message Flow and Delay, McGraw-Hill, 1964. L. Kleinrock, ISDN-The path to broadband networks, Proc. ZEEE, V O ~ .79,

[Leiner]

[Lesk] [Licklider] [LickC] [Lucky11 [Lucky21 [McCredie]

[MeekerMJ]

1991, pp. 112-117. B. M. Leiner, V. G. Cerf, D. D. Clark, R. E. Kahn, L. Kleinrock, D. C. Lynch, J. Postel, L. G. Roberts, and S. Wolf€, A Brief History of the Internet, Version 3.31, August 4, 2000. Available at http://www.isoc.org/internetlhistory/brief.html. M. Lesk, How much information is there in the world? 1997, unpublished paper. Available at http://www.lesk.com/mlesk/diglib.html. J. C. R. Licklider, Libraries of the Future, MIT Press, 1965. J. C . R. Licklider and W. Clark, On-Line Man Computer Communications, August 1962. R. W. Lucky, New communications services-What does society want? Proc. ZEEE, vol. 85, 1997, pp. 15361543. R. W. Lucky, Through a glass darkly-Viewing communicationsin 2012 from 1961, Proc. IEEE, vol. 87, 1999, pp. 1296-1300. J. McCredie, UC Berkeley must manage campus network growth, The Daily Californian, March 14, 2000. Available at http://www.dailycal.org/article.asp?id=1912&ref=news M. Meeker, M. Mahaney, and D. Joseph, The Internet userlusage ecosystem framework, Morgan Stanley Dean Witter report, January 24, 200 1. Available at http://www.msdw.com/techresearch/ index.htm1. The Multi-Router Traflc Grapher of Tobias Oetiker and Dave Rand,

information and links to sites using it at http://ee-staff.ethz.ch/ -oetiker/webtools/mrtg/mrtg.html.

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zyxw zyxwvutsr zyxw zyx zyxw zy zy Kerry G. Coffman and Andrew M. Odlyzko

U. S. Information Infrastructure Task Force, The NationalZnformation Znffastructure.Available at http://www.ibiblio.orglniiltoc.html. [Nolll] A. M. Noll, Znhoduction to Telephones and Telephone Traflc, 2nd ed., Artech House, 1991. A. M. Noll, Highway of Dreams: A Critical Appraisal of the Commu[No1121 nications Superhighway, Lawrence Erlbaum Associates, 1997. pol131 A. M. Noll, Does data traffic exceed voice traffic? Comm. ACM, June 1999, pp. 121-124. Nua Internet Surveys. Available at http://www.nua.com. [Nual A. M. Odlyzko, Data networks are lightly utilized, and will stay [OdlYZko11 that way. Available at http://m.dtc.umn.edu/-odlyzko. [Odlyzko2] A. M. Odlyzko, The history of communications and its implications for the Intenet. Available at http://www.dtc.umn.edu/-odlyzko. [Odlyzko3] A. M. Odlyzko, Internet pricing and the history of communications, Computer Networh, vol. 36, 2001, pp. 493-517. Also available at http://www.dtc.umn.edu/-odlyzko. J. A. Polly, Surfing the Internet: An introduction, Wilson Library Bulletin, June 1992, pp. 38-42. Available at http://www.netmom .com/about/surfing.shtml. [ReichlLS] P.Reichl, S. Leinen, and B. Stiller, A practical review of pricing and cost recovery for Internet services, Proc. 2nd Internet Economics Worhhop Berlin (IEW '99), Berlin, Germany, May 28-29, 1999. Available at http://www.tik.ee.ethz.ch/-cati/. R. R. Schaller, Moore's law: Past, present, and future, IEEE Spec[Schaller] trum, vol. 34: no. 6, June 1997, pp. 52-59. Available through Spectrum online search at http://www.spectrum.ieee.org. [StAmaud] B. St. Arnaud, The future of the Internet is NOT multimedia, Network World, November 1997. Available at http://www.canarie.ca/ -bstarn/publications. html . [StAmaudCFM] B. St. Arnaud, J. Coulter, J. Fitchett, and S. Mokbel, Architectural and engineering issues for building an optical Internet. Short version in Proc. SOC.Optical Engineering, 1998. Full version available at http://www.canet3.net. [Standage] T. Standage, n e Kctorian Internet: n e Remarkable Story of the Telegraph and the Nineteenth Century5. On-line Pioneers, Walker, 1998. S. Taggart, Telstra: The prices fight, Wired News, http://www.wired .com/news/politics/O,1283,32961,OO.html. €? M. Walker and S. L. Mathison, Regulatory policy and future data transmission services, pp. 295-370 in ComputerCommunication Networh, N. Abramson and F. E Kuo, eds, Prentice-Hall, 1973. W. W. Wu and A. Livne, ISDN A snapshot, Proc. ZEEE, vol. 79, 1 9 9 1 , ~103-111. ~. PI11

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Chapter 3

John Strand

Optical Network Architecture Evolution

AT&T Laboratories, Middletown, New Jersey

1. Introduction An Optical Transport Network (OTN) is composed of interconnectednetwork elements (NEs), plus software and operational processes that must function together to provide services. Ongoing advances in technology will cause significant changes in OTN architecture; however, equally important will be the growth and evolution of the services it transports, particularly the Internet. In addition, business changesin the telecommunicationsindustry will be very critical. This chapter tries to weave the technology, services, and business stories together to indicate how they are shaping the architecture of the emerging optical network. Because most of the readers of these volumes are primarily technologists, tutorial material has been included. 1.1. WHAT IS AN OPTICAL TRANSPORTNETWORK? The very definition of “Optical Transport Network” illustrates why these stones are interrelated. All would agree that optical fiber will be the physical layer of an OTN. There is less agreement on whether a network making extensive use of electronics for regeneration and switching should be called an OTN. Most of the audience for this volume are presumably most interested in all-optical OTNs; however, for a variety of business and service-related reasons that will be discussed later, many of the first generation “optical crossconnects” perform electronics-based functions like multiplexing DS-3s and slower speed SONET OC-ns into OC-48s and OC-192s. From this perspective, SONET is an “opaque one-wavelength”optical network, as Green [47]pointed out, even though much of its characteristic functionality is implemented in electronics. We will take a “broad church” approach to defining an OTN. Given the nature of this volume, we will concentrate primarily, when possible, on networks built from optical components; however, when necessary we will use the term to include networks transporting STS-1 (52 Mb/s) and larger connections that have an optical physical layer. When necessary to be precise, we will use the term “photonic” instead of “optical” to indicate that an all-optical

zyxw zyx

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The views expressed are those of the author and not necessarily those of AT&T.

57 OPTICAL FIBER TELECOMMUNICATIONS, VOLUME IVB

Copyright 0 2002, Elsevier Science (USA). AU rights of reproduction in any form reserved. ISBN: 0-12-395173-9

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situation is being discussed. Thus, a “PhotonicTransport Network” (PTN) will be an all-optical OTN, and “Photonic Cross-Connect” (PXC) and “Photonic Add/Drop Multiplexer” (PADM) will be used when all-optical equipment is under discussion. We will call a communications channel through an OTN a “circuit.” It is frequentlycalled a “wavelength”or a “lightpath,”but because of the possibility that a connection might be partially electronic,we will stick with “connection.” If it is all-optical,we will also use the term “optical channel” (OCh).

zyx zyxwvu zyxw zy

1.2. SCOPE OF THIS CHAPTER

Because other chapters in the current volume deal with submarine systems, metropolitan OTNs, and access OTNs, we will focus primarily on intercity networks. Because of the background of the author, most of the discussion will have a strong U.S.flavor: For example, I willuse SONET rather than SDH terminology, and I will frequently discuss issues of most interest to networks with diameters of thousands of kilometers, even though such large networks are only relevant to a handful of countries. To keep the material to be covered within bounds, only technology likely to be commercially available within the next few years is considered. Many interesting areas, such as optical packet switching, are therefore omitted. The reader should keep in mind the large error bars surrounding this whole enterprise. As an example, the architecture of actual OTNs even a few years in the future depends profoundly on the Internet: If its growth were to slow, the rate of introduction of new architectures would certainly slow, and the functionality desired (and hence the underlying technologies)might well change.

2. Technology Advances and Trends The important underlying optical technologiesare for the most part discussed elsewhere in this volume; the reader interested in the technologies per se should turn to the relevant sections. Our purpose here is twofold: (1) identify and define at a system level the building blocks on which the OTN architecture rests, and (2) point out major system-leveltrends we need to deal with in our later architecture development. 2.1. SONETBDH REFRESHER

SONET/SDHis important for optical networking for several reasons: (1) The overwhelming proportion of connections in long-haul OTNs are SONET or SDH formatted, and (2) many aspects of OTN architectures have been modeled on SONET/SDH concepts. This section gives a very brief overview of a few key aspects of these protocols that we will need later. For more complete overviews, see [18,72,73].

zyx zyx zyx zyxwvutsr zyxwvuts 3. Optical Network Architecture Evolution

59

Table 3.1 Selected SONET Signal Rates

SONET Name STS-1 STS-3 STS-12 STS-48 STS-192 STS-768

’

Name When Transported Optically

SDH Name

Signal Rate (Mbhec)

oc-1 OC-3 oc-12 OC-48 OC- 192 OC-768

STM-1 STM-4 STM-16 STM-64 STM-256

51.84 155.52 622.08 2,488.32 9,953.80 39,813.12

User Rate’ (IMb/sec)

49.54 148.61 594.43 2,377.73 9,510.91 38,043.65

The “User Rate” is the bandwidth actually available for user data. The difference between it and the “Signal Rate” is due to overhead information as discussed in the text.

Synchronous Optical NETwork (SONET) is a North American standard for networking developed in the mid-1980s primarily by Bellcore and standardized by ANSI [79,99, 1001. It defines the interface between two SONET network elements (NEs). More specifically, it defines a digital hierarchy of synchronous signals, including their formats and mappings of asynchronous signals (e.g., DS-1, DS-3) into these formats, and defines the electrical and optical characteristics of the interface. The Synchronous Digital Hierarchy (SDH) is a closely related standard developed by the ITU [78]. The basic SONET entity is the Synchronous Transport Signal-1 (STS-1). It operates at 51.84Mb/secondYof which 49.5 Mb/sec is usable payload and the rest overhead. The STS-1 frame structure is byte-oriented and has 9 rows and 90 columns, 4 of which are used for overhead purposes. The frame rate is 8000/second (125 ps/frame). Normally all SONET signals are bidirectional and run at the same rates in each direction. An STS-N signal (n > 1) is formed by byte-interleavingn STS-1s together. When an STS-N is transported electrically, it is called an “EC-n”; when transported optically, it is an c‘OC-n.y’ (EC stands for “Electrical Carrier,” OC for “Optical Carrier.”) SDH is virtually identical to SONET, except that its base frame is three times larger, corresponding to a SONET STS-3. It is called “STM-1,” where STM stands for “Synchronous Transfer Module.” The key SONET signal rates are summarized in Table 3.1. In their simplest form, the three basic SONET network elements are shown in Fig. 3.1. The Digital Cross-Connect System (DCS) is the most general of these NEs. In its simplest form, it has a fabric capable of cross-connecting STS-M and STS-N line-side2ports. Normally N is greater than the M , but it can be the

zyx zyxw

“Line-side” refers to the ports that are closest to the interoffice fibers; “drop-side” refers to those closest to the customer.

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Johnstrand

STS-N

I

I

k

-t

STS-N

STS-N

E S

STS-M Fabric (M M , an incoming STS-N is first demultiplexed into a number (N/M at most) of STS-Ms, which are switched through the STS-M fabric and reassembled into STS-N if they are continuing on or are dropped in the office as STS-Ms through the ports shown at the bottom. There could be many (thousands) of STS-N and STS-M ports on a single DCS. The Add-Drop Multiplexer (ADM), shown in the middle of Fig. 3.1, is a special case of a DCS. It has only two pair of bidirectional line-side ports, which are often designated “east” and “west.” Each pair has a service STS-N (“S” in the figure), and also a protection STS-N (“P”)that is normally in standby mode until needed to recover from a failure. The protection capacity may also be used for “extra traffic”--connections that will be preempted in the event of a failure. A basic multiplexer (see the right side of Fig. 3.1; often called an “end terminal”) is a further specialization. There is either a single line-side STS-N port (as shown) or a service/protection pair. It is used to multiplex a number of lower-speed signals into a single STS-N for transport through the network. All three of these types of NEs are very widely deployed today and continue to be deployed in large volumes (billions of dollars per year in the United States alone). In intercity networks, a typical ADM installed today would likely have STS-48 or STS-192 line-side ports and a mix of STS-3 and STS-12 drop-side ports. A number of specialized deployment configurations are also specified by the SONETEDH standards. The most important configuration is the Self-Healing Ring (SHR). One such SONET SHR configuration is called a “line-switched ring” for reasons that will become apparent shortly. In this configuration, up to 16 SONET ADMs are configured in a ring topology, as shown at the left in Fig. 3.2.

P=‘

!:?

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3. Optical Network Architecture Evolution

P O ................

61

P

@I---

I

S

0

S

ADM At Office F

Fig. 3.2 SONET line-switched ring example.

The ADMs are labeled “A” through “F,” with the service and protection STS-Ns interconnecting them labeled “S” and “P,” respectively. A connection is shown entering at A, then passing through F and E before exiting the ring at D. (Solid line is also labeled “1.”) The right side shows this connection passing through the fabric from one service port to the other. If the service connection between F and E fails, ADMs F and E would cooperate to reroute the connection over their protection connection. (Dashed line in the figure, also labeled “2.”) If there is a route failure that affects both S and P between F and E, the connection is rerouted the opposite way around the ring. (Dotted line, labeled “3.”) In both cases, the initial routing of the connection is reestablished at E. These recovery mechanisms are triggered by standardized signaling messages between F and E that are carried in the SONET overhead bytes mentioned earlier. The rerouting is done by the ADM switch fabrics as illustrated at the right in Fig. 3.2. The specialized structure of the configuration allows very rapid reaction (50 ms on rings under 1200km in circumference and with no extra traffic [79]. Sometimes 150-200 ms is used as a bound for an arbitrary ring.) In some cases the rigid restoration discipline generates convoluted restoration paths. For example, if for some reason an A-B connection was routed the long way around the ring (A-F-E-D-C-B) and E-F failed, then the restored connection would be routed A-F-A-B-C-D-E-D-C-B, even though A-B would have restored the failed connection! This is done to keep the protocol and implementations more manageable. The protection capacity is shared in this type of ring. This means that if a different link failed, the same protection capacity would be used for the connections affected. For this reason they are also called “Shared Protection Rings” (SPRING). Another important type of SONET ring is called a “path-switched ring,” for reasons discussed below. In this type of ring each connection has dedicated protection capacity. In Fig. 3.2, if the A-F-E-D connection were protected in this manner, there would have been dedicated protection capacity for the

62

zyxwvutsrq zyxwvut John Strand

zyx zyxwvut

connection that would be routed A-B-C-D. The ADMs at A and D (the entry and exit points) would monitor the health of the connection and switch the connection to the A-B-C-D path if necessary. For this type of ring there is no need to know exactly where the failure occurred, because the switch is between entry and exit points. A path-switched ring is closely related to what is called “1 1 protection.” As in the path-switched ring, the connection has two dedicated paths, but in the 1 1 case, copies of the signal are continuously sent along both paths and the better quality signal is selected (at D in our example for the A to D signal). This is extremely fast and has the added advantage that no signaling between nodes is required. The drawback of 1 + 1 protection is that no extra preemptible traffic is possible on the protection capacity. SONET functionality is divided into three layers, not all of which need to be implemented by every SONET NE. The layers and their principal functions are:

+

+

0

0

0

0

Path. Maps specific services into a SONET payload; end-to-end error

and status monitoring; path protection switching. Adds path overhead. Line. Multiplexing multiple paths into a STS-N; synchronization;error and status monitoring; line protection switching. Adds line overhead. Section. Framing, scrambling, other functions associated with the preparation for physical transport. Adds section overhead. Physical. Electrical-to-Opticalconversion; actual optical transmission.

Normally an ADM would be a line and section terminating NE, whereas a regenerator would terminate only the section. A path can ride on multiple lines in series, a line on multiple sections. See Fig. 3.3. Here, PTE, LTE, and STE stand for path, line, and section terminating equipment, respectively. SONET is a byte-structured protocol. An STS-1 frame is transmitted as a string of 810 bytes that are divided into 9 “rows” of 90 bytes each. The frame is

Fig. 3.3 SONET layering.

3. Optical Network Architecture Evolution

zyx zy 63

divided into payload and overhead sections. The resulting frame is illustrated in Fig. 3.4. POH stands for “payload overhead.” Each of the overhead areas contain parity information to allow error checking and data communication channels to allow peer NEs to communicate. In addition, the section overhead contains framing bytes to allow frame alignment to be verified, the line overhead contains fields to control protection switching, and the path overhead identifies the type of payload. Four columns are dedicated to overhead and 86 to payload. We mentioned earlier that STS-Ns are formed by byte interleaving N STS-1s. This fragments the payload into N pieces, which is undesirable for data communications (as discussed later). To deal with this, a “concatenated” frame is also deked. Denoted STS-Nc (e.g., STS-48c or 0 C - 4 8 ~ it) ~ has one large payload rather than N smaller ones. However, it still has 3N columns of overhead, which are mostly unused. SDH is virtually identical functionally to SONET,but unfortunately the two standards use different terminology. Table 3.2 gives their correspondences.

zy

-

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Overhead Section p

A

0

Line Overhead

,,

9

Payload

Rows

i Fig. 3.4 STS-1 frame structure.

Table 3.2 SONET and SDH TerminologyRelationship SONET Term

SDH Term

STS-N Path Line Section Line-switchedring Path-switched ring

STM-N/3 Transmission path Multiplex section Regenerator section Shared-protectionring (MSEPRING) Dedicated-protectionring (PaWDPRING)

64

zyxwvutsr John Strand

Frequency registered transmitters

Receivers

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Fig. 3.5 Basic Optical Transport System (OTrS).

2.1.1. Multivendor Interworking

One of the goals of SONET and SDH was to define standards that would let equipment from multiple vendors interwork. This has been achieved in simple point-to-point configurations, but in more complex configurations, such as shared protection rings, progress has been frustratingly slow. Hardware interoperability has by and large not been a serious problem; instead, software interworking has been limiting, particularly the exchange of state information between the ADMs and the handling of “operations, administration, and maintenance” functions. As a result, transport people tend to be suspicious of proposals for multivendor “mid-span meets.”

2.2. OPTICAL TRANSPORT SYSTEMS

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A basic Optical Transport System (OTrS) is shown in Fig. 3.5. In its most basic form, it consists of an optical multiplexer and demultiplexer and a number of optical amplifiers (OAs) between them.3 OAs in terrestrial systems usually have a nominal spacing (span length) of about 25dB (roughly 80km after allowance for splices, etc., and assuming a nominal span loss of 0.25 dB/km). Wider spacings can significantly reduce the first costs of a route, but cause difficulties for 10 Gb/sec and faster connections and also impose limits on the number of wavelengths that can be supported, therefore most operators appear to be sticking with 80 km or shorter spacings. Impairments force regeneration after about 5-7 spans (400-560 km). This is a wavelength rather than an OTrS constraint, so that if a wavelength traversed two such systems in series without regeneration between the systems, the span limit would apply to the sum of the spans on the systems.

2.2.1. Capacity Trends OTrS capacity has been increasing very rapidly. In fact, by some estimates the rate of increase is considerably faster than Moore’s Law for electronics The system shown (and the underlying technology, usually) is unidirectional; however, they are normally deployed in pairs so as to support bidirectional SONET/SDH circuits.

zyx zy zyxwvu zyxwvuts 3. Optical Network Architecture Evolution

Gbls

1996

1998

2000

2002

65

2004

Fig. 3.6 Capacity of a single fiber (derived from data in [SI).

(see [54]). The underlying trends are analyzed in [55], from which Fig. 3.6 is derived. The years given are for commercial deployment (actual and projected). Over the 10-year period shown, capacity doubles approximately eight times due to increasesin the bits per channel, reductions in wavelength spacing, and increases in the total usable fiber bandwidth. In a recent talk [104], Rick Barry of Sycamore used bandwidth times distance as a relevant metric. He traced the evolution of capacity from 120-160 Terabits/sec*km with conventional systems (e.g., 80 OC-48s over 600km or 40 OC-192s over 400km) to today's 160&2400Tb/sec*km (e.g., 80 OC-192 over 3000km) and projected a next generation providing 3200-4800 Tb/sec*km. Important architectural implications from these trends: 0

0

0

2.2.2.

The increase in wavelength counts make the introduction of some form of mechanized cross-connect a necessity if operations costs and complexity are to be kept under control. Total OTrS costs are rising significantly more slowly than capacity. Hence unit cost ($/Gigabit) is declining. The combination of these two trends-rapidly rising capacity and declining unit costs-have formed a synergistic relationship with the rapid growth of the Internet. Internet growth has allowed the new technologies to be economicallyjustified, while the rapid capacity increases and cost decreases have been essential enablers for the growth of the Internet.

Ultra-Long-Haul Systems

The OTrS just described requires each wavelength to be regenerated roughly every 500 km. The optical-electrical-optical(OEO) functionality required for regeneration is quite expensive; if a transponder is put on each wavelength of the OTS shown in Fig. 3.5, their cost could exceed the total costs of all the

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zyxwvutsr zyxwvut John Strand

MdDemux and OAs combined. Hence extending the regeneration distance is an appealing possibility. Raman amplification, strong forward error correction (FEC), and advances in dynamic power management are making this possible. The resulting “ultra-long-haul” technology can support OTrS with dozens of 80-km spans, leading to regeneration distances of 3000 km or more. However, this comes at a cost: To get longer regeneration distances, the perwavelengthmultiplexing, demultiplexing,and amplificationscosts are likely to significantlyexceed those of traditional systems. We can expect ultra-long-haul systems to be competitive, therefore, only for long systems where these perwavelength costs can be counterbalancedby regeneration savings. A strawman ultra-long system based on 2000-2001 products is shown in Fig. 3.7. This system shown in Fig. 3.7 illustrates a number of architecturally interesting features we shall return to in the architecture discussion. a

zyxwvutsrqp Adaptation. The boxes labeled “A” are adaptation functions. Using an OEO transponder function, they map one or more inputs (the a’s, typically standard short-reach signals) into a long-reach OCh or group of OCh‘s that will pass transparently to a distant adaptation function. Adaptation options include: a. Multiplexing. Either electrical or optical TDM may be used to combine the inputs into a single wavelength. This is done to increase effective capacity. After multiplexing, the combined signal must be routed as a group to the distant adaptation function. b. Adaptation grouping. In this technique, groups of k (e.g., 4) inputs are managed as a group (an “adaptation grouping,” increasingly called a “wave group”) within the system and normally must be addeddropped as a group. Tight spacing is used for wavelengths within a group, with larger guard bands between groups. Grouping is done to simplify power management. It may also be possible to largely contain nonlinear effects such as four-wave mixing within the groups. Wavelength spacing may vary between groups, as may the

zyxwvu zyxwvu X

Y

PADM

PADM

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D

........................ =a1

zyx 6 11

AN

T..............F IA

=Nl

=Nk

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Fig. 3.7 Strawman ultra-long-haul optical transport system (OAs not shown).

67

number of wavelengths in each group. Note that either option places limits on connectivity (which 0’s are delivered to which output port), because the inputs involved must be routed as a group to a compatible output adaptation function.

0

zy

zyxw zy zyxw

3. Optical Network Architecture Evolution

Photonic add-drop multiplexers (PADM). X and Y are “photonic add-drop multiplexers”-the all-optical analog to the SONET ADM discussed in Section 3.1. They allow economical dropping and insertion of limited numbers of adaptation groupings without requiring demultiplexing and remultiplexing all the other wavelengths. Depending on the filtering architecture, it may be possible to reuse frequencies so that, for instance, the same frequency could be used for a D to X grouping, an X to Y grouping, and a Y to E grouping. “Domain oftransparency.” The dotted line encloses an all-optical “domain of transparency,” an all-optical subnetwork. The adaptation functions just discussed optically isolate the domain.

2.2.3. More Complex Domains of Transparency

Since the PADMs in Fig. 3.7 are all-optical, it is possible to build more complex all-optical domains, as shown in Fig. 3.8. In Fig. 3.8, the basic ultra-long system D-X-Y-E from Fig. 3.7 has had branches added at the PADM’s X and Y, with further branching at PADM U. In this configuration, there is an all-optical path, A-Y-X-U-Z, connecting A to Z . Transponders to optically isolate the domain would need to be present on the boundary of the domain and would serve to define the boundary of the domain. There are no “loops” in Fig. 3.8. If a U-Y link were added, the domain would turn from a topological “tree” (only one path between any two points) into a more general “mesh.” The alternate paths that result might be useful for restoration, but they also might complicate considerably the management of impairments.

OPADM

Fig. 3.8 Larger domain of transparency (OAs not shown).

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2.3. RECONFIGURATION CAPABILITIES

2.3.1. Why Reconfigurability Is Important

Returning to the example given in Fig. 3.7, for fixed wavelengths, hk, and a fixed configuration of the PADMs, each input port is in effect hard-wired to some distant output port. The connectivity between ports is fixed. In fact, the set of transmitters and receivers that are tuned to a specific frequency can be thought of as a plane that cannot be interconnected within the domain to planes d e h e d by other frequencies. We will see later that this can be a serious problem in some situations. In addition, the lack of reconfigurability can make it difficult to effectively use the capacity of a complex domain of transparency such as that in Fig. 3.8. In this figure, for example, if a specific frequency is in use between D and E, then this frequency cannot be used for the path A-Y-X-U-Z connecting A to Z-it is blocked on the X-Y link. If it were possible to reconfigure this connectivity, the OTrS would in effect be turned into a distributed switch or cross-connect, which could be used for software controlled provisioning or for restoration after some types of failures. These types of functional capabilities are at the heart of the business rationale for deploying the optical network. There are a number of ways in which reconfigurability may be achieved: 0

0

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zy zyxwvutsrqp Laser/receiver tunability. The lasers producing the LR wavelengths (the Ai in Fig. 3.8) may have a fixed frequency, may be tunable over a limited range, or be tunable over the entire range of wavelengths supported by the DWDM. Tunability speeds may also vary. Tunability may give additional connectivity options, and allow ports that could not otherwise be connected to do so. Wavelengthconversion. Internal to a domain of transparency, it might be possible to change the frequency of a connection, thereby in effect interconnecting the planes described earlier. This could be done by converting to the electrical domain and then modulating a laser (fixed frequency or tunable) with the signal. However, this is apt to be quite expensive and may degrade the signal. Conversion in the optical domain has been the subject of considerable research but products with functionality, reliability, performance, and cost adequate to make them attractive are not yet available (see [5] and [13] for surveys). Switchfabrics. A switching fabric could be placed in the PADM in Fig. 3.7 or a cross-connect could be inside a domain of transparency or be placed between two domains. This technology is discussed next. Adaptation grouping adjustments. If the boundaries between groupings are dynamically adjustable, bandwidth could be moved between groupings.

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3. Optical Network Architecture Evolution

2.3.2. Optical Layer Cross-Connects (OLXC)

69

An OLXC is the optical layer’s equivalent of the Digital Cross-Connect (DCS) discussed in Section 2.1. OLXCs can be placed in a number of places, as the three options in Fig. 3.9 illustrate. The transponders are the demarcation point between the short-reach optical signals, all at the same frequency, that are often used for intraoffice connectivity and the proprietary frequency registered longreach OChs used interoffice. For simplicity, connectivity to routers and other services and TDM equipment is not shown; consider all signals as coming in from the right in the figure and then looping back to the right through one of the cross-connect options. Options B and C really only make sense if they are all-optical, whereas Option A could have either an electrical or optical fabric. Option C (often called a “fiber switch”) is switching the very wide-band proprietary multiwavelength signals produced by WDM multiplexers. This has the advantage that it handles many fewer signals and so needs many fewer ports and a much smaller fabric; however, transmission impairments and technology and vendor incompatibilities impose complex and potentially very restrictive limits on the connections that it can establish; at present, only single-vendor DWDM-DWDM connections can be made, and even with a single vendor, technology differences (e.g., different frequency grids) can prevent other connections. Consequently, Option C does not seem to be getting much attention at present, at least for long-haul applications. Option B (often called a “wavelength selective cross-connect”) also deals with wavelengths that must conform to the proprietary frequency grid and transmission constraints imposed by the DWDM equipment. Consequently, it is not really an option at present, except in the interior of a domain of SR

z zyxwvu LR

(1 frequency)

(N frequencies)

Multiplexed

I

U Transponders

Fig. 3.9 Optical Layer cross-connect (OLXC) options.

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transparency. Where feasible, however, it does offer the promise of substantial cost savings because it does eliminate transponders. If the domain implements adaptation groupings, this option could switch these groupings as an entity, thus reducing the number of ports and fabric cross-points required. Note also that in the absence of all-optical wavelength conversion only channels of the same color may be interconnected. Option A is optically isolated from the DWDM equipment and crossconnects wavelengths with a standard frequency. It thereforeprovidesthe most connectivity.It is insensitive to the optical architectures used by the DWDM vendors, and hence can sit between proprietary “domains of transparency.” It has two disadvantages, however: (1) It requires transponders on each port, these are expensive and also constrain the formats and bit rates that can be cross-connected; and (2) it may not scale as well as the other options because it requires a port per wavelength. Fault detection and localization can be done in Option A by the transponders, which have electrical access to the SONET/SDH overhead bytes. These functions are trickier in the all-optical environments of the other two options. In Option A, an important design choice is whether the transponders are functionally integrated into the DWDM, the OTS, or are stand-alone. Fast reaction to faults is really only possible if there is some level of integration; otherwise it is necessary for an alarm to be sent from the transponder through a time-consumingsequence of softwarelayersbefore restoration can be initiated. With the exception of all-optical network vendors, Option A has received the most attention to date.

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2.3.3. Optical Add-Drop Multiplexers (OADM)

The OADM’srole was mentioned in our discussion of ultra-long-haul OTrSs. The specifics of its rol+how many wavelengths need to be dropped, what constraints (if any) should be placed on which wavelengths can be dropped, what sort of rapid reconfiguration capabilities are needed-are not yet clear, and there are many technological choices to be made. Some of these choices are illustrated in Fig. 3.10.4 2.4. INTELLIGENT OPTICAL NETWORKS

Optical Transport Systems have been software intensive since their inception, but by and large this software has not been externally visible. This appears to be changing. The basic component technologies from which optical systems are built are usually availableto all systems integrators, so to differentiatetheir products they are turning to intelligent networking and management software. This software has the potential to allow network operators to reduce their operations costs and also to better customize their servicesfor their end users. Developed by Cedric Lam of ATBET Laboratories.

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3. Optical Network ArchitectureEvolution OADM I

completely flexible (any collection of wavelengths can be dropped)

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I wavelength selective (constraints on wavelengths dropped) I

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I

md rn”*n..r.hlm !.r

(tiwedlaser)

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Fig. 3.10 OADM architecture choices.

Intelligence is appearing in several areas: 0

0

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“Soft optics” internal to individual systems to allow things like dynamic power balancing and automatic discovery and reconfiguration of optical subsystems. “Network is the database” functionality that relieves the network operator of the expense of determining network state; instead, the network performs this function and makes the information available to queries. Automatic “point and click” provisioning of new connections using vendor provided software and Graphical User Interface (GUI).

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These developments are potentially very attractive to network operators and are receiving a lot of attention. We will return to this topic later (Section 5).

2.5. OPTICAL FAULT MANAGEMENT

SONET/SDH has very mature and time-tested methods for detecting faults and isolating the source of the problem, primarily based on electronic detection of bit errors using CRCs carried at each level of the frame overhead. A significant concern of network operators has been the possible existence

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of failure modes that are difficult or perhaps impossible to isolate by optical means alone. One can envision monitoring optical power or signal-to-noise ratio, but these analog measurements will not detect pulse distortion arising from nonlinearity and dispersion, for example. Maeda [121gives as an example an OLXC failure that resulted in the delivery to the proper port of a signal with the correct optical characteristics but incorrect digital content. This is a serious matter, perhaps even a show-stopper, for network operators, particularly as network growth and cost pressures continue to stretch operations resources ever thinner. A number of approaches are being tried to deal with the issue: 0

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zyxwvutsrqp Persuasion. Green [47l points out that this issue was encountered when all-optical OAs replaced OEO regenerators that did electronic fault monitoring approximately every 40 miles. Anxious to realize the enormous economic and capacity benefits offered by OAs, operators were persuaded that pump power level and other optical parameters were adequate. Green hopes that history will repeat itself and make looking at the bits unnecessary. SignaZ splitting. A small amount of the optical signal could be diverted and examined electronically. Containment. All-optical subnetworks could be kept small and optically contained, with electronic monitoring of all connections entering/ leaving such a subnetwork. A related step would be to keep the topology of all-optical subnetworks simple-for example, require them to be topological “trees” without loops. (Fig. 3.8 is such a tree.)

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2.6. FUNCTIONAL CONSOLIDATION Advances in silicon technology have created the possibility of integrating transport functions that traditionally had been in discrete boxes. For example, in SONET/SDH networks cross-connects and add-drop multiplexers have traditionally been physically separate network elements (NEs), as have DWDM terminals. However, it is now possible to implement a full ADM on a DCS line card. In the intercity network, so-called “optical layer cross-connects” have appeared: They have a large number (thousands) of OC-48/192 ports but an STS-1 fabric and the ability to do all the traditional ADM functions as well as provide an OC-48/192 cross-connect capability. In the metropolitan market, products (often called “multi-service provisioning platforms”) are appearing that carry this trend further, with optical ring functionality and the ability to groom individual DS-1 (1.5 Mb/sec) signals and even ATM switch and IP router capabilities added to the functionality mix in a single NE. The drivers for this trend are compelling: Significantcost, power, and floorspace savings result from the eliminationof the line cards and cabling necessary to interconnect network elements. In addition, maintenance costs tend to be

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proportional to the number of NEs, and would therefore benefit from this trend. When functions are integrated in the same NE, layer boundaries get blurred. In the case of the OTN, it is likely that it will be difficult to cleanly separate the management of the OTN from the other transport networks residing in the same NE. If OTN software and operations cannot be cleanly separated from the massive and complex multilayer legacy transport network, the introduction of new OTN technology and functionality will be significantly impeded.

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3. Service and Business Trends

Changes and trends in the telecommunications services mix and also in the structure of the telecom industry will be critically important determinants of tomorrow's OTN architecture. In this section we will look at a few of the most important trends and their architectural implications.

3.1. SERVICE BASICS

The breakdown of bytes of U.S. long-distance traffic by major service grouping is summarized in Fig. 3.1 1. The two bars on the left show the service breakdown at the end of 1997 and 1999, respectively. The bar on the right shows the breakdown of the growth in this period. The predominance of voice traffic even at the end of 1999 may seem surprising to some; much of this is due to differences in utilization, which are discussed later. The Internet segment is clearly growing more rapidly; in [55] it is estimated that average annual growth rates for voice are about 109'0, for the Internet about loo%, and for private line about 30%. Because of this, Internet traffic is expected to exceed voice traffic by early 2002. Note that even in the 1997-1999 period, network growth was driven by the Internet segment. After 1999, Internet growth is expected to become increasingly dominant. From an architectural perspective, this means

DataNetworks

EOY 1997

EOY 1999

1997-99 Growth

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Fig. 3.11 Traffic on U.S. long-distance networks, 1997-1999 (from [SI).

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that new investmentwill need to be pointed increasingly to the needs of Internet trfic. The revenue perspective is quite different. A leading industry consulting group (RHK) estimates that voice revenue per megabit is seven times that for a T1 Internet connection; for the telecommunications industry as a whole, total voice revenues are projected to be much larger than data revenues for many years. Much of the voice revenue comes from a small number of very large corporate customers who are dependent on very sophisticated and complex software-based functionality in the legacy voice network, and therefore very hard to migrate to a new IP-based infrastructure without the same level of f~nctionality.~ This introduces conflicts into the strategic planning process, particularly for carriers with a large embedded base of voice customers, because there is a constant tension between investing in the future and satisfying the current customer base.

3.1.1. Ethernet We are focused on intercity transport, and so Local Area Networks (LANs) are out of scope. However, we should not lose sight of the fact that Ethernet is the dominant protocol in buildings and campuses, and that a large portion of data traffic is carried at least partly on Ethernet. Ethernet is a very rapidly evolving technology.6 It has benefited from enormous volumes and achieved unsurpassedfiber-porteconomies and is steadilyextendingits reach into metro and even long-haul networks, and therefore it bears careful watching as a potential service driver in the long-haul network in its own right, and even a technological competitor for some long-haul applications.

3.2. INTERNET TRAFFIC CHARACTERISTICS

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Since Internet traffic will be the driver for network growth and architectural change, it is important to understand the nature of this t r f i c . In this section we will look at some of its important characteristics.

3.2.1. Connection Bandwidth

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The size of the connections between routers will impact a number of aspects of the OTN architecture. For example, the necessity for leaving the optical

IBM, for example, has thousands of call center agents averaging 95 sales calls and revenues of $63,000 a minute [107]. Such an operation depends heavily on sophisticated network call-management software to balance loads between call centers, among other functions. This softwm works in coordination with IBM’s internal computer telephony integration product, which provides a customer history screen-popwhen an incoming customer number is transferred to an mailable agent’s phone. See Chapter 11 on Ethernet in this volume.

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layer at intermediate points to do TDM multiplexing at sub OC-48 rates will be eliminated if these connections are all at OC-48 or higher rates. The interfaces to voice-service switches normally are (1.5 Mb/s) DS-1 or channelized (45 Mb/s) DS-3. If there is a large community of interest between two such switches, there will be a large number of independent links. This is not the case for large routers, where a singlehigh-speed port normally is much more efficient than a number of lower-speed ports with the same aggregate capacity as the high-speed port. There are a number of reasons for this: (1) There is a significantgain in statisticalmultiplexingefficiencyin the one-port case; (2) the hardware design of routers has normally put a hard upper limit on the total number of interfaces that it can support. The effect of this on the service-providingfacilities7offered to today’s transport network has been dramatic. As recently as the late 1990s, the great bulk of demand growth was for DS-1s. By 2001, the bandwidth-weighted growth in most intercity networks is overwhelminglyfor unchannelized DS-3s and larger facilities; indeed, it is expected that the dominant size of service-providing facilities will become OC-48 (2.5 Gb/sec) and OC-192 as IP traffic starts to predominate.

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3.2.2. Connection Length Connection-lengthdistributions have a subtle but profound effect on transport network architectures. For example, if lengths are short, the market opportunities for ultra-long DWDM systems (see Sections 2.2 and 4.2) and their enabling technologies such as Raman amplification are limited. The volume of voice traffic between two cities is determined by their “community of interest,” the propensity of people in them to want to communicate. This can be roughly modeled using a “gravity model,” which predicts that call volume between two cities is proportional to the product of their sizes (measured in people or total income, for example) divided by the square of the distance between them. This results in relatively short connections-the median length of an intercity DS3 carrying voice traffic, for example, is just a few hundred miles. Internet traffic, and particularly Web traffic, is quite different. Normally one has no idea or interest in the physical location of the server involved in a Web session. Furthermore, the determinants of server location are different, for example, Silicon Valley has an enormous concentration of servers because so many Web-based services were developed there. The net effect of this has been to lengthen average intercity Internet-related facility lengths by an order of magnitude compared to those deployed for voice services.

A “service-providingfacility” is a circuit that terminates on a service-providing NE, such as a voice switch or a router.

zy

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(a) Toll Switching Hierarchy

(b) Internet ISP Hierarchy

Fig. 3.12 Hierarchical and nonhierarchical routing.

There are a number of other more speculative trends that may affect connection length. One is based on an analogy to the growth of the long-distance voice network. Originally, “toll” voice switches were hierarchically structured into a four-layer “tree.” This was done on a geographic basis, with parent and sibling switches connected together by relatively short trunks (called “final” trunks). This is illustrated in Fig. 3.12a. Calls were passed up the tree until a switch above both caller and called party was reached. In Fig. 3.12a, an A-Z call was routed A-B-C-R-X-Y-Z. However, if there was sufficient calling volume between two lower-level switches, some “high-usage trunks” (B-Y in the figure)would be built between them to avoid the cost and delay of followingthe rigid hierarchy. These trunks tended to be much longer than the final trunks. As this network scaled, the proportion of calls handled on these trunks rose, and the higher-level switches in the hierarchy lost their importance. Eventually they were not needed, and the hierarchical structure was replaced by a flat nonhierarchical arrangement. In this process, connection (trunk) lengths increased substantially. The Internet Service Providers (ISPs) that compose the Internet are today also structured hierarchically into local, regional, and national (nondefault) ISPs (Fig. 3.12b). As the Internet rapidly grows, it would be natural if lowerlevel ISPs would discover opportunities to build the optical equivalent of high-usage trunks that would avoid the expense and delay associated with the current structure. If this occurs, one would expect the net effect to be the further lengthening of Internet facilities.8

3.2.3.

Tkaffic Symmetry

zy zy zyx zyx

A fundamental element of current TDM-based architectures is the symmetry of the connections supported: There is always the same unidirectional

*

The drivers for “direct peering,” as this process is called, are discussed in [59], and its sigmficance is discussed in [58]. Currently a Web fetch requires two to seven round-trips to the server, each of which goes through a large number of routers (17 is the number given in [60]). By reducing the number of ISPs and routers in series, direct peering also has performance and reliability benefits that are encouraging this trend [60].

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bandwidth dedicated to A to Z traffic as there is no traffic in the reverse direction. This originates in the design of traditional voice circuits, which are 64-kb/sec full-duplex connections. If this were to change, there would be opportunities to build more economical networks if asymmetry were better supported. There is no need for data traffic to be symmetric. A file transfer is unidirectional; on the Internet, the prevalent client-server architecture leads to large amounts of data sent from servers in response to small requests. Various studies have found twice as much traffic flowing from the United States to other countries, and much larger imbalances in flows from ISPs that specialize in supporting servers to those that are residentially oriented (see [48] and [29]). 3.2.4.

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Utilization

By utilization, we mean the proportion of bandwidth that is actually used. Because there is hourly, daily, and seasonal variation in traffic intensity, it is appropriate to look at a time-averaged utilization. Odlyzko [40, 571 estimates that Internet backbones are about one-third as utilized as U.S. long-distance switched voice networks, and that private line data networks are only about 10% as utilized. There are many reasons for this that are discussed in the references; two of these provide opportunities for the OTN architecture to add value: 0

0

If it is possible to add capacity very rapidly, there is little reason for an ISP to keep a spare capacity buffer. However, if additions take a long time, it is prudent to order capacity so it is available well before it is likely to be needed to guard against unexpectedly rapid demand growth or unexpected delays in getting the capacity online. The higher the demand volatility or the more uncertain the capacity delivery process, the earlier a prudent manager will order new capacity. The Internet is noted for wild demand surges, and the time it takes to get an additional large (multi-megabidsecond) connection installed today is frequently measured in months, and there can be significant uncertainties, particularly when multiple operators are involved (e.g., a local telco and a long-distance telco). Hence early capacity ordering, which leads to low utilization on average, is standard operations procedure for many data network managers. Intranets and other business-oriented private data networks have usage concentrated during business hours. Because these networks use dedicated private lines, there is little ability to use the idle bandwidth for other purposes during off hours. Conversely, ISPs catering to residential customers are likely to see their usage higher in the evenings and on weekends.

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3.3. INDUSTRY STRUCTURE

The US. telecommunicationsindustry is changing in ways that are profoundly affecting OTN architecture. This section identifies a few of the changes that affect network architecture. 3.3.1. Additional Intercity Optical Networks

In the mid-1990s, there were basically three national scale OTNs in the United States, each vertically integrated into one of the major intercity service providers (AT&T, MCI, and Sprint). They accounted for about three-quarters of total intercity fiber deployment. By the end of the decade, however, they accounted for less than a third, with 39 new national carriers accounting for an equal amount [61]. This same source estimates that in 1999 there was a total of 400K route miles in long-haul networks, with an average of 46 fibers per cable. This trend has a number of architectural implications: 0

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The new OTNs can provide a facility underpinning for nonfacility based ISPs and other service providers. The resulting service competition puts pressure on vertically integrated service providers to keep the unit cost of their OTNs competitive,for example, by introducing new technologies faster than they would otherwise have done. There are many opportunities for buying, selling, or swapping fiber, leading to a situation where competing OTN operators may share fiber in the same right of way or even the same fiber cable.

3.3.2. Additional Local Networks Hundreds of so-called “Competitive Local Exchange Companies” (CLECs) provide competition for the “Baby Bells.” Particularly in areas with a high density of telecom-intensivebusinesses such as lower Manhattan, these companies provide optical connectivity to many key customerlocations. They have more incentive to introducenew architecturesthan the incumbentcarriers. The long-termeconomicviability of many CLECs is hostage to politicdregulatory developments affecting their complex relationships with the “Baby Bells”

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3.3.3. Web Hosting and Carrier Hotels

Facilitiesto meet the need of carriers, ISPs, and Internet content providers are changing the geographic structure of the industry: 0

“Carrier hotels” are buildings run by third parties that meet the needs of new carriers for a physical presence in some city. They provide a

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telco-grade infrastructure, so all conduit, power, environmental, and security requirements are satisfied; provide an opportunity to share costs; and facilitate interconnection between CLECs, ISPs, and intercity carriers. Web hosting sites provide similar facilities for the enormous number of servers and routers deployed by Internet content providers.

These sites provide enormous concentrations of potential business and potentially make it easier for start-up OTNs to find the service volumes they need. The “dot-com” downturn in 2001 has hit a number of them very severely, however.

3.3.4. Bandwidth Trading We mentioned earlier that carriers frequently lease dark fiber from each other. These deals are each separately negotiated by the parties to specify quality of service, any penalties for contract nonfulfillment, and other details, and the physical implementation typically requires engineering and construction to establish the physical connection. This process is time consuming and expensive. This is in marked contrast with the situation in energy markets like gas, oil, and electricity where there are enormous markets to facilitate trading. These markets are based on standardizing the product’s physical characteristics and quality, specifyinga clearing and settlement process for payments, and defining penalties for nonperformance. To facilitate trading, a “benchmark” product delivered at a specified location is used as a basis for establishing a price, and conversion factors are established to establish prices for other grades and physical delivery points. Once this is done, it is possible to establish forward markets that allow buyers and sellers to do financial risk management and also allow speculation. Markets that have been through this ‘ccommodification’y process have been profoundly changed, as anyone following the deregulation of the U.S. electricity industry is aware. Many sophisticatedand very well financed players are trying to commodify the bandwidth market: A Web search for “bandwidth trading” in January 2001 got 95,800 hits. A number of intermediaries have sprung up to help buyers and sellers of bandwidth to trade with each other efficiently. One approach is to act as a “matchmaker.” Many of these companies have Web sites where owners of underutilized capacity can post their offering^.^ A smaller number of players are actually deploying equipment to facilitatethe process. A possible architecture is shown in Fig. 3.13.

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An offering typically identifies the two end points, the type of circuit (OC-3, STM-1, etc.), and the price and availability date. Offerings can be either “IrrevocableRight to Use” (long-term or permanent) or on some sort of leasing arrangement, e.g., on a monthly basis.

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Pooling Point Carrier F

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CarrierK

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Fig. 3.13 Pooling points for OC-n connections.

A “pooling point” with a DCS and/or an OLXC provides the necessary connectivity. It might be located at a carrier hotel or a Web hosting site where colocated routers require a high volume of OC-n connections. It also could be connected by CLEC or ILEC facilities to remote customer locations. Carriers might be invited to connect together pooling points in different cities. The pooling point operator could then establish a trading operation to match buyers with sellers. In Fig. 3.13, a customer wanting an OC-n from A to Z could then use one carrier from A to B and another from B to Z . The bandwidth buyers would hope to gain lower prices through vendor competition. Colocated buyers especially could then hope for more rapid provisioning of their capacity. Among the carriers, start-ups with lots of unused capacity could be expected to gain customers. New ways to use the OTNmight also arise: A large private line network that had very low utilization at night and weekends could try to sell this bandwidth at off-peak periods to someone needing bandwidth to do computer back-ups, for example. Carriers might be able to reduce their sales and marketing expenses significantly. There are a number of issues regarding this: Competition would be increasingly price driven, and there would be pressure to provide a basic standardized product. This could make it difficult to introduce technologies and products differentiated by reliability, security, or customer service. The vertical integration of network with services currently prevalent in the telecom industry would come under pressure and new business models might be needed. Many of the criteria associated with successful commodity markets are not present. A study by the Boston Consulting Group [loll identified six critical criteria: (1) Vertical deconstruction. Vertically integrated industries are poor candidates. (2) Fragmented supplier base. Suppliers with market power can refuse to participate.

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(3) Fragmented customer base. If there are few buyers, they can be targeted by suppliers, eliminating the need for a market. (4) Price volatility. Predictable prices reduce the need to hedge risk and reduce the incentives of market makers. (5) Common unit ofexchange. Efficient trading environments require common units of exchange and settlement contracts to fuel liquidity. (6) Delivery mechanism. A physical delivery mechanism is required to efficiently and quickly move commodities between buyers and sellers.

This study concluded that in most of these areas, the bandwidth market was not yet ripe for commodification but might be in a few years. They did see immediate opportunities in a few specific areas, especially for private lines on high-volume, capacity constrained routes. In summary, bandwidth trading is not yet a significant factor for 0 7 3 s . However, it does appear that there are short-term opportunities and incentives for companies running carrier hotels and server farms, and also for some start-up carriers, to move in this direction. In the longer term, the prospects appear rosier.lo There are also significant architectural implications: Bandwidth trading would make rapid provisioning an essential network capability, would make it harder for both equipment vendors and carriers to establish proprietary product and service improvements not incorporated in the definition of the standard traded product, and would make network interworking much more important.

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3.4. OPTICAL NETWORK SERVICES 3.4.1. Services Overview

It should be clear from the discussion in Section 3.1, that OTN services in the future will be targeted primarily at meeting the needs of public and private data services, and particularly IP-based services. We will generically refer to the providers of these services as “ISPs.” From an architectural perspective, an OTN architect must make a choice: (1) Build a network with premium features such as very fast restoration in the hope that it will command a premium price and profit margin; (2) build a network offering only the functionality required for “commodity” bandwidth and hope to get higher volumes and efficiencies; or (3) build a network that

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lo The Web is the best place to do further research on bandwidth trading. Some market participants whose Web sites might be of interest are Band-X, Interxion, AIG, and Arbinet (all facilitiesbased) and Ratexchange, Bandwidth Market, and Bandwidth.com(nonfacilitiesbased).

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can offer both commodity and premium services. We expect that there will be network operators opting for each of these options. A fruitful way to start thinking about the service/architectureinterrelationship is to identify ISP needs, identify the functionalitiesthat might possibly be provided by the network, and then match functionalitiesto needs. 3.4.2.

ISP Needs

ISP needs axe as follows: 0 0

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0

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Price. The most important need is undoubtedly low price. Availability. ISPs are struggling to keep up with exponential growth. Therefore, the availability of bandwidth is a key need-whether it can be provided at all between the desired locations, and if so, how quickly. ISP cost displacement. Displacement of internal ISP costs is also desirable. By this we mean functionality provided by the OTN that will allow the ISP to reduce their internal costs. Some potential areas for this are: a. Reduce the cost of physical interfaces on routers. b. Provide bandwidth at the speeds optimal for the router. c. Assume some of the costs of reliability and failure recovery. d. Assume the responsibility for providing exactly the capacity required when it is required. e. Allow flexible peering with other ISPs. f. Provide network management capabilities that allow the ISP to be aware of the state of their connections at all time and to reconfigure them as appropriate. Additional revenue opportunities. Provision of capabilities that enable new services. For example, a highly reliable Virtual Private Network (VPN) offering conceivably might be based on an optical layer restoration capability. Coverage of special events might be facilitated by rapid OTN provisioning of extra bandwidth.

3.4.3. Possible Functionality Areas Possible areas of functionality include the following: 0

0

Additional connection oflerings. Higher bit rates (e.g., OC-768); different formats (Ethernet, Digital Wrapper); more flexible bandwidth configurations, such as asymmetric or unidirectional connections; flexible concatenation of standard SDHBONET connectionsto provide additional bandwidth options; and inverse multiplexing. More rupidprovisioning. Software control of optical cross-connects and other reconfigurableONES.User-Network Interface (UNI) allowing

zy zyxwv

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83

direct signaling by a router or customer controller requesting immediate additional connections. Larger networkfootprint. More ubiquitous connectivity can be provided by interworking between networks and by providing OTN access from more locations. Additional restoration options. A range of restoration speeds and threat coverage; assistance in dealing with service layer failures such as router or service outages.

3.4.4. Relating Needs and Possible Functionality Table 3.3 attempts to identify possible relationships between needs and functionality. The justification for many of the entries can be found in the subsections of Section 3.4.

3.4.5. A Carrier Perspective on Service Functionality The Carrier Working Group within the Optical Interworking Forum (OIF) recently produced an “Optical Services Framework and Associated Requirements” document [43] that provides a good snapshot of current services thinking in the carrier community as it relates to optical networking and software control. What follows is excerpted from this document.’*

3.4.6. Value Statement Optical networkingpermits camers to provide new types of network services not available with other technologies, enabling sophisticated transport applications of (D)WDM based networks (featuring a variety of topologies such as pointto-point, ring and mesh). These new generation networks provide means for the improved use of network resources and the support of high-bandwidth services. Dynamic bandwidth allocation, fast restoration techniques and flow-through provisioning give birth to an assortment of services. Intelligent OTNs contain distributedmanagement capabilityand subsume many provisioning and data basing functions currently performed by carrier Operations Systems (OS). This allows the rapid establishment and reconfiguration of connections, potentially reducing provisioning times from months to seconds, thus lowering operating costs and providing the means to set and guarantee SLAs12 and QoS configured on a per-connection basis to better meet customer’s specificneeds.

zyxwvut

I I The current author was the chair of the OIF group producing this report. It is a working text and not an official OIF Technical Report, and is not binding on the OIF or its members. l2 SLA Service Level Agreement. Defines the details of the service to be provided, particularly its availability and reliability.

zyxwvutsr zyxwvutsrqpon zyxw Table 3.3 Relations Between Needs and Potential OTN Functionality Additional Connection Offerings

Price

0

0

Asymmetric connections

Rapid Provisioning

Additional Restoration Options

Larger Footprint

Reduced network operations expense

Lower internetwork coordination costs

Shortened provisioning interval

More optically reachable locations 0 Faster multinetwork provisioning

Concatenation (e.g., OC-15)

Availability

Less expensive router line cards 0 Higher utilization

0

cost displacement

0

Higher utilization

Higher utilization

Revenue opportunities

Lower delay

0

Reconfigure for special events 0 Add temporary busy hour bandwidth

0

Higher availability 0 Lower MTBF

3. Optical Network Architecture Evolution

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The large capacity and great flexibility of such networks enables the support of several degrees of transparency to user traffic at lower cost to the end customer. The new services expectedto be enabled as aminimumare bandwidth on demand, point and click provisioning of optical connections, and optical virtual private networks. The standardized interface between the optical layer and the higher layer data service layers such as IP, ATM, SONET/SDH enables the end-to-end internetworking of the optical channels for conveying user information of varying formats. The use of standardized protocols will make the benefits of the intelligent OTNs available end-to-end, even if several networks are involved.

zyxwv zyxw

This document also defined business models for three types of service offerings they hoped to see supported. These were: Provisioned Bandwidth Service: Enhanced leaseaprivate line services. Provisioning is done at the customer request by the network operator. . . . This is basically the “point and click” type of service currently proposed by many vendors.. . . Billing will be based on the bandwidth, restoration and diversity provided, service duration, quality of service, and other characteristics of the connection.. . . No customer visibility into the interior of the OTN is required; however, information on the health of provisioned connection and other technical aspects of the connection may in some circumstances be provided to the user network as a part of the service agreement. . .may involve multiple networks, e.g., both access networks and an intercity network. In this case provisioning may be initiated by whichever network has primary service responsibility. . .

Bandwidth-&-Demand Service: OC-n/STM-n and other facility connections are established and reconfigured in real time. Signalingbetween the user NE and the optical layer control plane initiates all necessary network activities. A real-time commitment for a future connection may also be established.A standard set of “branded” service options is available. . . . Optical Ertual Private Network The customer contracts for specific network resources (capacity between OLXCs, OLXC ports, OLXC switching resources) and is able to control these resowces to establish, disconnect, and reconfigure opticalconnection connections.In effect they would have a dedicatedoptical subnetwork under their control.. . . Billing will be based on the network resources contracted. Network connection acceptancewould involve only a check to ensure that the request is in conformance with capacities and constraints specified in the OWN service agreement.. .. Real-time information about the state of all resources contracted for would be made availableto the customer. Depending on the service agreement,this may includeinformationon both in-effectconnections and spare resources accessible to the customer.

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zyxwvutsr zyxw zyxwvuts Johnstrand

4. Optical Network Architectures 4.1. INTRODUCTION 4.1.1.

Unit Costs

zyxw zyx

Architecture is basically about achieving a proper balance between costs and capabilities.A common mistake is to equate “cost” with equipment cost. This is far from the truth. For a typical traditional long-distance voice service, for example, a typical cost breakdown is as follows: Access (paid to the local exchange carrier) Network-related costs Customer care, billing, miscellaneous

35% 15% 50%

The network-related costs typically divide roughly equally between the actual carrying costs associated with the equipment and the expenses associated with running the network. It is not unusual for the hardware cost of the NEs to be 10% or less of the total costs that need to be recovered. Thus it is crucial to always consider the non-hardware-cost implications of all architecture decisions. The revenue implications are also crucial. 4.2. TRANSPARENCY In an optical network, “transparency” refers to whether, or to what degree, an optical signal passes through the network optically. In today’s (2001) socalled “optical” networks, there are actuallymany OEO conversionsand a high degree of reliance on electronicprocessing. However,the vision of many optical networking researchersincludes a much larger role for all-opticalfunctionality. In this section we will explore this issue, the outcome of which will have a large role in shaping the use of optical technologyin future OTN architectures. 4.2.1.

zyxwvut

m e s of Transparency

There are many shades of transparency. A categorizationused in the MONET project13was: Digital transparency. Transparency to intensity-modulated digital

signals of arbitrary bit rate, frame format, and protocol.

Amplitude transparency. Transparency to intensity-modulated digital or

analog signals. Strict transparency. Transparency to any optical signal. l3 MONET w a s an ARPA-sponsored project established to define and demonstrate how best achieve multiwavelength optical networking of national scale. See www.bell-Iabs.com/ project/MONET or www.darpa.mil.

to

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87

Even if there is optoelectronic regeneration, there are a number of levels of transparency possible [11: 0

a

0

Regeneration with retiming and reshaping (3R). This involves acquiring the clock of the regenerated signal, and thus makes it quite difficult to handle multiple frame formats. Regeneration with reshaping but without retiming (2R). This offers bit rate and format transparency, but allows jitter to accumulate, thus limiting the number of regenerations that can be done. Regeneration without retiming or reshaping (IR). This has the worst performance but can handle a wide variety of signals, both analog and digital.

We will use the word transparency to mean no optoelectronic conversions of any kind.

4.2.2. Potential Advantages of Transparency The potential advantages of transparency fall into two major categories: a

0

Format independence. A transparent network is largely indifferent to the details of the signal being transported so long as the power levels and other optical characteristics are within bounds. This has the major advantage of allowing new protocols (and also legacy protocols such as PDH) to be easily handled.I4 Without this independence, potentially each new format or bit rate requires standards changes and hardware and software to be developed and deployed. Less expense at intermediate nodes. A transparent network does not require expensive OEO functionality at intermediate nodes; electronics is bypassed by through wavelengths.

4.2.3. Limitations on Transparency [30,45,46] Unfortunately, transparency also has some serious problems:

zy

Impairments accumulate. Various forms of dispersion, nonlinearities, polarization-dependent loss, multipath interference, misalignment of lasers and WDM filters all degrade optical signals, and many of them pose increasingly serious performance limitations as bit rates increases channel spacing gets tighter, and the number of channels increases. Individually, these limitations constrain the distance a wavelength can

l4 A thought-provoking example of this is quantum cryptography, an unbreakable form of cryptography that exploits the uncertainty principle of quantum theory, but requires the polarization of individual photons to be preserved. It has been demonstrated over 23 km of fiber [62].

John Strand

88

e

e

zyxwvu zy

zyxwvutsrq travel without regeneration and/or lead to a relentless tightening of component and fiber requirements. Furthermore they may combine to provide unexpectedly severe impairments. (See also [64].) All-optical interoperability is problematic. This problem has several dimensions. First, performance monitoring and fault location is problematic. As discussed in Section 2.5, our optical monitoring ability is limited. In a large network, particularly one involving multiple vendors or network operators, it is essential that faults be quickly detectable and the source of the problem be quickly identifiable. Second, it is unclear how to introduce new technology, such as an upgrade from 100 to 50 GHz wavelength spacing, incrementally. It appears that the technical specifications of an all-optical network must be fixed at the time it is first deployed if costly and difficult in-service upgrades of equipment are to be avoided. Wavelength interconnection is restricted. As discussed in Section 2.3, our ability to do wavelength translation in the optical domain is inadequate at present. As we shall see later in this section, this can make it difficult to use some of the capacity of the system.

4.2.4.

Opaque Optical Networks

An opaque OTN is one where each cross-connect and each OTrS is optically isolated by transponders. In its simplest form, an opaque network is formed by adding transponders at the interfaces to the OTrS shown in Fig. 3.5 (see Fig. 3.14). Figure 3.15 shows a cross-connect in an opaque network. Typically the optical signalsbetween the transponders and the OLXC would be short-reach or intermediate-reach, depending on the loss characteristics of the cross-connect, and would all be operating at the same frequency. Note that the OLXC could have either an electrical or optical fabric.

Standard SRh

zyxwvuts :

Frequency Registered LRh

Frequency Registered

LRh

Standard SRh

4--+-- +

4---;--+

Transponders

El El

Span Mux Trai

Receivers

Fig. 3.14 Optical Transport System (OTrS) with transponders.

3. Optical Network Architecture Evolution

89

zy

0 Transponders

zyxwvu zyxwvuts

Fig. 3.15 Opaque node showing transponders and cross-connect.

The strengths and weaknesses of opaque and transparent OTNs are mirror images of each other. An opaque OTN is very limited in the formats and bit rates of the signals it can carry, and it incurs significant costs for OEO functionality for each wavelength at each node. On the other hand, in an opaque network, impairments do not accumulate, interoperability is guaranteed, and wavelength translation is obtained as a by-product. All the large OTNs known to the author have found the case for opacity compelling to date. 4.2.5.

Domains of Transparency

The choice between opacity and transparency is not really black and white. The concept of a “domain of transparency”-a transparent subnetwork, optically isolated from the rest of the network by transponders-provides a means to control the drawbacks of transparency discussed above. This technique offers us the possibility of limiting the size of each domain, thereby keeping impairment-related problems in check. New technologies might be put in separate domains, thereby avoiding technology interworking problems. Organizational boundaries, such as those between network operators, can be aligned with domain boundaries. A DWDM system such as that shown in Fig. 3.14 is an example of a domain of transparency. If transponders are put on all the q, in the ultra-long OTrS shown in Figs. 3.7 or 3.8, a more interesting domain would be defined. In effect, this is what vendors of such systems are proposing. The technological trends enabling longer wavelengths and all-optical reconfigurability should make ever larger and more complex domains of transparency feasible. However, there are costs associated with introducing multiple domains of transparency. On each boundary, costly transponders must be installed. In addition, as we shall see later when we discuss control planes, additional complexity can be added to the processes that route and manage wavelengths.

zyx

90

John Strand

4.2.6. Economics of Transparency

zyxw

The economic attractiveness of a domain of transparency arises largely from the opportunity to reduce transponder (OEO) costs. These per-wavelength costs can be the largest single cost in an OTN, as is shown in Fig. 3.16. The cost breakdown is for an OTrS such as that in Fig. 3.14 that is bounded by transponders. The costs are based on typical vendor prices in 2000; they could vary considerably based on the vendor’s pricing strategy and the specific size and capabilities of the OTrS. The transponder costs are linear in the number of working wavelengths (utilization), but independent of the number of spans, whereas the other costs are independent of the utilization and linear in the number of spans (except for the MudDemux), hence the relationships shown in Fig. 3.16. In an opaque OTN, transponders need to be placed on the ports of each OTrS. OTrS lengths are limited by (1) technology (the maximum number of spans before regeneration is needed), and also (2) by the need for wavelengths to be added or dropped from the OTrS. To get some insight into the economic trade-offs involved in transparency, we will give an example related to (1). Consider the example given in Fig. 3.17. Figure 3.17a shows a sequence of standard OTrS and an ultra-long-haul OTrS. Both are assumed to have the same OA spacing and the same wavelength capacity. The standard OTrS we assume to be limited to a five-span configuration before transponders are required for regeneration; in (a) this happens at offices B and C. The ULH system merely needs an OA at these locations. To go further, the ULH has presumably been designed using additional costly technology (see Section 2.2). We model this parametrically by use of

z

n zyxwvut zyxwvuts zyxw Transponder

Optical Amplifier

I

h Utilization (%) # Spans (80 km)

50

100

3

3

I

50 7

100 7

Fig. 3.16 Cost breakdown, OTrS bounded by transponders.

zy zyxwvutsr zyxwv zyxwvutsrq zyxwvu 3. Optical Network Architecture Evolution

OTS Type

100

Transponder

0

b

91

ULHlStandard Cost Ratio

Y

C

._

Standard

0

ULH

1 3 5 7 9 No. Of Standard OTS Systems (5 span) In Series

(a) Reference Systems

(b) Domains Of Application

Fig. 3.17 Ultra-long-haul economics.

zyxwv

a cost ratio (assumed the same for DWDMs and for OAs). The additional ULH costs are system costs, which are independent of the number of wavelengths that are actually equipped. The penalty for opaqueness incurred by the five-span configuration is partially per-system (the additional back-toback DWDMs required) but primarily per-wavelength (the transponders at intermediate nodes like B and C in Fig. 3.17). Therefore, the ULH system would be expected to become more competitive as the number of systems increases (more DWDMs for the competing solution) and also as the utilization increases (more transponders). This is quantified in Fig. 3.17b, which shows for various cost ratios15 the frontier between the regions where each alternative has an economic advantage. The ULH system is economically preferred above and to the right of the appropriate curve. For example, if the ULH system is 75% more expensive, the arrows indicate that ULH is preferred for fills above about 45% if 5 systems (25 spans) are needed. If the topology of the subnetwork is more complex, as in Fig. 3.8, an alloptical solution has the additional advantage that transponders are not needed at the branch points. Evaluation of this benefit is more complex and will not be discussed further here. Unfortunately, we are not aware of any efforts to systematically look at this effect. In metro areas, the economic issues are quite different. Normally OEO is not needed for transmission reasons, because the distances involved are relatively short. Instead, the ability to carry a wide variety of bit rates and formats becomes more important. 4.2.7.

Incorporating Domains of Transparency in a Network

Domains of transparency will be limited in size by transmission constraints, the inability until standards evolve significantly to have optical interworking l5

Representative year 2000 list costs for the "standard system" were used in this exercise.

92

John Strand

zyxwvu

Fig. 3.18 Express domain of transparency example.

between vendors, and by economics. In a long-haul network, a likely initial use of a domain of transparency would be to provide an express backbone on which longer connections would be routed. Shorter connections would be routed on an opaque technology that is more economic over shorter distances. This situation is illustrated in Fig. 3.18. In this mesh network, two technologies are used, one all-optical (shown by dashed lines with squares showing offices with DWDMs or OADMs), the other one an opaque technology with electrical fabric OLXCs (circles) and with solid lines showing connectivity. On the left, the two technologies are shown with the topologies separate, and on the right, they are laid onto the conduit network used for both. As just discussed, the all-optical technology is most cost-effective for longer distances. In this case, if we wished to route a connection from A to Z, the best route might be to go from A to J using the opaque technology (top plane in Fig. 3.18a), then go J-N-P-Q-L using the all-optical technology, and complete the route from L to Z using the opaque technology. This example suggests that introducing such a domain of transparency will raise new issues for routing and probably for other operational areas. We consider routing next. 4.2.8.

Routing and Wavelength Assignment in a Domain of Transparency

zy

Within an all-optical domain, “wavelength conversion” (changing the wavelength of a connection) is still expensive and not yet practical without an OEO conversion. Therefore, it is important to understand the architectural implications of limited (or no) wavelength conversion. This requires us to look at what is called the “Routing and Wavelength Assignment (RWA) Problem” [l]: Given one or more connections that need to be established in an all-optical domain, determine the routes over which each connection should be routed and also assign each connection a color. If the routes are already known, the problem is called the “Wavelength Assignment (WA) Problem.” The RWA problem has received extensive attention in the literature, mostly from a mathematical perspective. This literature is best approached through

zy zyxwv

3. Optical Network Architecture Evolution

93

zyxwvu zyxwv

a survey article (e.g., [l, 2, 14, 741). The underlying mathematical problem is very hard in general. The WA problem is easily seen to be equivalent to the problem of coloring the nodes of a graph so that no two nodes connected by an arc of the graph have the same color: Simply represent each connection by a node, and connect every pair of nodes whose corresponding connections ride on the same link (and so need to be assigned different wavelengths). This coloring problem is known to be NP-complete [75], which means that, in general, it is computationally intractable, but there are many fast but approximate (heuristic) algorithms for solving it. Before discussing some of the architectural implications of this problem, it should be emphasized that the results in the literature frequently depend crucially on subtle points of the problem definition. The followingdefinitional choices are particularly important: 0

0

0

Is there an accurate forecast of future connection requirements? If so the RWA process can take a more global approach to decision making. What is the expected holding time of a connection? Some analyses assume that connections are permanent, while others assume that holding times are quite short. Is it possible to rearrange connections?In situations where unexpected demands are likely, this makes a major difference.

We feel that the most appropriate assumption at the present time is to assume that (1) we have minimal knowledge about future demands, therefore each demand must be routed and assigned a wavelength when it appears without knowledge of future demands, and (2) that holding times are very long. With these assumptions, we simulated a number of RWA algorithms on a realistic model of the U.S. intercity network [76] without rearrangement or wavelength conversion and reached the following conclusions: 0

0

0

It is important to choose the route and do the wavelength assignment simultaneously.If routing is done first and then a wavelength is assigned, significantly suboptimal results are obtained (e.g., low utilization). Even with simultaneous route and wavelength selection, a significant capacity penalty can be incurred if wavelength conversion is not available. This penalty can be significantly mitigated if wavelength conversion is available at a small subset of nodes. In particular, half of the lack-of-wavelength-conversionpenalty is removed if 21% of the nodes have conversion capabilities; 75% was removed if 35% of the nodes have conversion capabilities.

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zyxwvutsr zyxwvutsrq John Strand

e

Dual-OTrS scenarios, which provide two instances of each wavelength on each link, reduced this penalty by only 6%.

A recent survey of the value of wavelength conversion [74] concluded that the performance improvementsit offered depended on a number of factors, including the network topology and size. It further concluded that in networks with tunable transmitters and receivers, limited wavelength conversion provides improvements close to that achieved with ideal wavelength conversion. 4.2.9.

zyxwvu zyx

Effect of Impairments on Routing in a Domain of Transparency [19,95]

As domains of transparency get larger, optical impairments such as amplifier spontaneous emission (ASE) and various types of dispersion may become an issue. Specifically:

(PMD). PMD imposes a limit on the maximum wavelength length that is inversely proportional to the square of the bit rate of the signal. For typical installed fibers, the limits are 400 km and 25 km for bit rates of 10 Gb/s and 40 Gb/s, respectively. With newer fibers assuming PMD of 0.1 ps/,/km, the limits are 10,000km and 625 km, respectively. e AmpIiJierSpontaneous Emission (ASE). ASE imposes a constraint on the number of spans that is inversely proportional to its optical bandwidth. e other polarization-dependent impairments. For example, many components have polarization-dependentloss (PDL) [11 that accumulates in a system with many components on the transmission path. The state of polarization fluctuates with time, and it is generally required to maintain the total PDL on the path to be within some acceptable limit. a Nonlinear impairments. As wavelengths get longer, nonlinear impairments such as four-wave mixing cause more problems at a given launch power.

e Polarization Mode Dispersion

These constraints are summarized in Fig. 3.19. The specific constraints required in a given situation will depend on the design and engineering of the domain of transparency. For example: e

e

The effect of nonlinear impairments depends on complex factors, e.g., on the order in which specific fiber types are traversed, the specific types of fiber involved, and the characteristics of the other active wavelengths (see, e.g., [46] or [64]). The impact of chromatic dispersion may depend on whether it has been dealt with on a per-link basis, and whether the domain is operating in a linear or nonlinear regime.

3. Optical Network Architecture Evolution

zyx zyx 95

zyxwvutsrq zyx \

PMD Constraint

Launch Power (PL)

Bit Rate PMD Parameter Optical Bandwidth Minimum acceptable SNR at receiver

**

L6ther System Parameters

Length Of All-Optical Path

Fig. 3.19 Effect of impairments on wavelength muting.

4.2.10. Connectivity Limitations Associated with a Domain of Transparency The strawman ultra-long-haul system shown in Fig. 3.7 may be thought of as a large distributed switch. Depending on the configuration of the OADMs and the tunable lasersh-eceivers, the port-to-port connectivity of the a's will change. However, the connectivity is limited: 0

0

0

The adaptation function forces groups of input channels to be delivered together to the same distant adaptation function. Only adaptation functions whose laserdreceivers are tunable to compatible frequencies can be connected. The switching capability of the OADMs may also be constrained. For example: a. There may be some wavelengths that cannot be dropped at all. b. There may be a fixed relationship between the wavelength dropped and the physical port on the OADM to which it is dropped. c. OADM physical design may put an upper bound on the number of adaptation groupings dropped at any single OADM.

For a fixed configuration of the OADMs and adaptation functions, connectivity will be fixed: Each input port will essentially be hard-wired to some specific distant port. However, this connectivity can be changed by changing the configurations of the OADMs and adaptation functions. For example, an additional adaptation grouping might be dropped at an OADM or a tunable laser retuned. In each case, the port-to-port connectivityis changed. This capability can be expected to be under software control. Today the control would rest in the vendor-supplied Element Management System (EMS), which in turn would be controlled by the operator's 0%.

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zyxwvutsr zyxwvu zyxwvut John Strand

4.3. LAYERING AND THE OPTICAL LAYER

The term “optical layer” is frequently used in architecture discussions. The term “layer” is taken from a modeling methodology that must be understood if one wants to read the technical literature on this subject or work on network architecture problems. This section gives a very brief overview of the methodology and then applies it to optical networks. The methodology described in this section was developed by the International Telecommunication Union (ITU), the international governmentsanctioned international standards organization. Reference [65] defines the basic approach, and [66] and [67] apply the approach to SDH and OTNs, respectively.

zyx

4.3.1. Layering Concept A transport network may be vertically decomposed into a number of layers that are related by a client-server relationship as shown in Fig. 3.20. Only two layers are shown. The upper layer is the client: It requests services from the lower layer, where a “service” is defined by its protocol, bandwidth, service quality, and perhaps other functionality. The lower server layer, in turn, provides capacity and the other aspects of the desired service. A couple of caveats about layering: 0

0

zy

There is no single way to define layers. For example, layered views of the Internet normally collapse all the transport layers into one, whereas transport-oriented layerings normally collapse the multiple protocol levels describing the various Internet protocols into a single layer but show many transport layers. There is no necessary relationship between layers and hardware. A single box may perform the functions of several layers or a single layer may be implemented in a set of boxes.

Well-Defined Interface Protocol Service Quality Functionality

-

Requested

Capacity Layer N

Fig. 3.20 Layering concept.

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3. Optical Network Architecture Evolution

4.3.2. Transport Layering

97

The layers in today’s transport network are shown in Fig. 3.21 and Table 3.4. The relationship between these layers is illustrated in Fig. 3.21.

4.3.3.

zyxw

Layers and Planes

To function, a transport network needs a signaling and control infrastructure. These infrastructures are also layered, as illustrated in Fig. 3.22. The shaded stack labeled “User Plane” corresponds to the layers we have been discussing. Two additional “planes” are shown in the figure: Control plane. Responsible for activities such as connection set-up or tear down and restoration. Operates in a dynamic “real-time” environment that directly responds to user activities or network state changes such as failures or maintenance activities. Increasingly its functionality is distributed and implemented in software resident on each ONE or directly connected to it. It has its own infrastructure for signaling to other systems within the network or to users or other networks. It is important to note that there may be separate control planes for each layer, as shown in Fig. 3.22. Management plane. Gives the network operator visibility into and control of the other two planes. Normally implemented in centralized OSs with information exchange carried over operations communications channels. This results in a static control environment characterized by scheduled activities and delayed response to network state changes.

DSl(1SMbls)

zyxwvut

DS3 (45 Mbk) STS-3 (155 Mbk) STS-12 (622 Mb/S)

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STS-48~(2.5 Gb/S)PTP 1 n?- fin P . I . L \ *,*-,7LL (‘VU”,>,

igital Transmissio

Proprietary (20 Gbk -400+ GbA)

Fig. 3.21 Transport layering.

zyxwvut zy zyxwvutsrqpon zyxwvuts Table 3.4 Transport Layers

Layer Services

Sublayer

Digital Transmission

Typical Demand

Typical Nodes

Typical Links

Voice services

calls

DSO

Circuit switch (4E)

Data services

Data transfer

Packets

Packet, frame, cell switches

Private line DSO Private line DS 1

DSOs DSls

DCS-1/0 W-DCS

DS 1 DS3, STS-I, STS-3

Private line DS3/STS3/STS12 Switch access lines, private lines Switch access lines, private lines

DS3s

B-DCS

DS3, STS-N

Digital Cross-Connect DCS 110

WS)

Service Requests Originatingat Layer

Wideband DCS (W-DCS) Broadband DCS (B-DCS)

Self-healing rings Linear add/drop or point-to point systems

Optical

See text

Private line STS-48/STS-192

Media

Fiber

Dark fiber

DS3, STS-N Add-drop multiplexer

DSO “trunks” (Modulo DS1) DS0/1/3, STS-N(c)

DS3, STS-N Terminal multiplexer, add-drop multiplexer

OC-12,OC-48, OC- 192 OC-3,OG12,OC-48, OC-192

Optical ADM, optical STS-48c, STS-1 9 2 ~ cross-connect DWDM OTS

Optical transport systems (OTrS) Fiber pairs

zyx zyxwvuts 3. Optical Network Architecture Evolution

N Layers 3

2

99

zyxwvuts zyxwvu .: * ‘
.e

;- 6 rY

t-compensation to 100 pslnmlkm

A - A 0 =-6nm

-8

I

I

I

Fig. 4.19 Relative eye opening versus phase modulation index for a channel located 6 nm lower than the system's average zero dispersion wavelength. The values of residual end-to-end dispersion are given in the legend.

22

m

18

D

v

14 10

1000 3000

5000

7000

Distance (km)

9000

11.5

I (b) 0.5

1

1.5

2

Phase Modulation Index (RAD)

Fig. 4.20 (a) Q-factor versus distance for channel 2 of 64 with different modulation formats (CRZ with one RAD phasemodulation). (b) Q-factorversus phase modulation index for channel 2 at 7900 km measured for different phase modulations.

nonlinear ISI, it also increases the signal spectral width and with that the interchannel linear cross-talk. The optimum amount of phase modulation for CRZ is thus a compromise between the signal power and the accumulated dispersion on one side and the channel spacing on the other. As an example, Fig. 4.20b shows Q-factor versus phase modulation for channel 2 at 7900 km. As is clear in this figure, the optimum phase modulation for this case is in fact 1.5RAD, resulting in 1.3 dB higher Q-factor compared to RZ. However, for an increased signal power and/or channel spacing, the optimum amount of phase modulation and the corresponding improvement will also increase. Many in the optics and physics communities often wonder if optical solitons are used in undersea cable systems. The optical soliton is another pulse waveform that has been widely studied for long-distancedata transmis~ion.~~ There

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was an active debate in the early 1990s between using NRZ or solitons for the first single channel EDFA-based transmission systems. NRZ had the advantage of compatibility with existing systems, and solitons were thought to have the advantage of higher single channel bit rates. At that time it was decided to use the NRZ format for the first systems then switch to the “higher” capacity format for the next generation systems. When WDM techniques became available, new dispersion maps were invented that strongly reduced the four-wave mixing between NRZ channels, thus eliminating one of the big advantages of solitons. This made adding NRZ wavelength channels the preferred path for greatly increasing capacity, rather than making incremental improvements by increasing the bit rate per channel. In the intervening years a few eventschanged the debate. The understanding of the basic physics of optical propagation has increased, driving the evolution of both the NRZ and soliton transmission formats. The NRZ format evolved into RZ and CRZ, and soliton transmission evolved into dispersion-managed solitons.31The modulation format debate changed to a question of, on the one hand, purposely using the fiber’s nonlinearity to help guide data pulses, or on the other hand, to reduce the system’s nonlinear behavior and operate the system in a quasi-linear region. Clearly, designers working at multiples of 10 Gbls have chosen the quasi-linear approach of managing the fiber’s nonlinearity. Many variants of the simple NRZ and RZ formats have appeared, such as CRZ, alternating-phase RZ, duo-binary, vestigial side band, etc. All of these formats attempt to optimize some aspect of the transmission system. For example, some of the formats attempt to optimize spectral efficiency by transmitting a small optical bandwidth.

4.6 Measures of System Performance The performance of a digital lightwave system is specifiedusing the Q-fa~tor.~* The Q-factor (adapted from Personick’s work on calculating the performance of receivers in lightwave links33)is the electrical signal-to-noise ratio at the input of the decision circuit in the receiver’s terminal. This is shown schematically in Fig. 4.21 using a typical RZ eye diagram. For the purpose of calculation, the signal level is interpreted as the difference in the mean values, and the noise level is the sum of the standard deviations. The Q-factor is formed by the following ratio:

zyxw zy zyxwv

zyxwvu 4

lPl - Pol

a1+a0)

where POand p1 are the mean values of the “zeros” and the “ones,” and a0 and a1 are their standard deviations at the sampling time.

Eye Diagram

............

”

’

s I3

Q

5

zyx

zyx P1

.. Po

zyxwvu

I

w

173

Decision Level

a,

... =gJ.. Sampling time

zy

z

4. Undersea Communication Systems

Fig. 4.21 A typical received RZ eye diagram for a lightwave system. A voltage histogram is schematically shown to indicate the parameters that are included in the definition of Q-factor.

The Q-factor is related to the system’s bit error ratio through the complementary error function, given by:*

where

zyxw zyxwvut M

or in terms of the more standard error function erf( . ):

(4.10)

where

The Q-factor given in Eq. 4.8 is a unitless quantity expressed as a linear ratio, or it can be expressed in decibels as 20log(q). The factor of 20 (or 10log (q2))is used to maintain consistency with the linear noise accumulation model. For example, a 3-dB increase in the average launch power in all of the spans results in a 3-dB increase in Q-factor (assuming signal-spontaneous beat noise dominates and ignoring signal decay and fiber nonlinearity). The *Here I use the definition of erfC(n) as given in MATLAB@ rather than the definition originally given in reference [32]. (MATLAB@is a product of The Mathworks Inc.)

174

zyxwvutsr zyxwv Neal S. Bergano

Q-Factor (linear) 2 3 4

1

5 6 7

zyxwvuts 0-

-4-

Log (BER)

-8-

-10-

zyxwvut

-1 2-_

5 10 Q-Factor (dB)

0

15

zyxwv zyxwvuts Fig. 4.22 Bit-error ratio as a function of Q-factor.

relationship between the Q-factor and bit-error ratio is shown in Fig. 4.22. A convenient relationship to bear in mind is that a BER of requires a Qfactor of 15.6 dB (or a linear ratio of 6). A useful approximation for converting BER back into Q - f a ~ t o is r ~given ~ by: Let t = J-2 log, (BER)

[

2.307

+ 0.2706t

System margin is the amount that the Q-factor (measured in dB) exceeds the required value for a given bit-error ratio. In long-haul lightwave systems the BER is set by a combination of the electrical signal-to-noise ratio of the data signal at the decision circuit and any distortions in the data’s waveform. Optical noise, fiber chromatic dispersion, polarization mode dispersion, fiber nonlinearities, and nonideal settings in the transmitter and receiver degrade the BER. Also, the BER can fluctuate with time due to polarization effects in the transmission fiber and the amplifier’s components (see Section 1.8). The most accurate methods of measuring margin are based on bit-error ratio measurements. When practical, the simplest method is to measure the BER on the ampliiied line, convert it to a Q-factor using Eq. 4.1 1, and state the margin as the difference between the measured Q-factor and the requirement. This technique is possible in some systems that use forward error correcting codes in the terminals (see next section). However, if the line bit-error ratio is below the practical measurement limit (about 10-13), then other methods are needed. For systems operating in this “error free” region, the most accurate method is the decision-circuit method of measuring the Q - f a c t ~ r . ~ ~ This measurement technique includes the intersymbol interference present in the regenerator’s linear channel, as well as that generated in the system from dispersion and fiber nonlinearity.

4. Undersea Communication Systems

175

zyx

zyx zyxwvut * v

-0.4

-0.2

0.0

0.2

0.4

Decision Level (volts)

Fig. 4.23 Typical Q-factor measurement for 5-Gb/s, 9000-kmoperation. The data shows the bit-error ratio vs the decision threshold. The solid lines show the fit of Eq. 4.12 to the data.

The decision-circuit method of measuring Q-factor involves three steps. First, the system’s BER is measured as a function of the decision circuit’s threshold voltage (this voltage is shown on the vertical axis in Fig. 4.21). Figure 4.23 shows data for a typical Q-factor measurement for a 9OOO-km, 5-Gb/s transmission system operating at a Q-factor 7.2: 1 (linear ratio) or 17.2dB. Second, the measured data is fit to the ideal curve of BER as a function of threshold voltage, as given by:

zyxw

The form of Eq. 4.12 assumes Gaussian noise statistics, and the curve-fitting operation results in calculating values for PO,ply00, and q.In the third and final step, the Q-factor is formed using the fitted values for p and CJ in Eq. 4.8. It is well known that the electrical noise at the decision circuit is not exactly Gaussian,35however, the Gaussian approximation can lead to close BER estimates36Figure 4.24 shows the measured voltage histogram of a detected optical signal emerging from a long lightwave system operating at 5 Gb/s. For this measurement, 1 million voltage samples were recorded for a zero bit and a one bit in a 27-1data pattern. The non-Gaussian probability density function is apparent when the actual density is compared with a best-fit Gaussian. The measurement of Q-factor as described previously measures only a subset of the distributions located near “inside” rails of the received eye or the voltages that are close to the decision circuit. Thus, the insides of the edges of the eye are fitted with an equivalent Gaussian function, and the underlying SNR is extrapolated from the fit. Mazurczyk and Duff have identified the inability of the decision circuit Q-factor measurement to measure large margins using long data Pattern-dependent effects cause the Q-factor measurement to underestimate

176

zyxwvutsr zyxwvu Neal S. Bergano

zyxwvuts z

P -1

a,

I

-3

r

:

t

a/+ Gaussian Fit

-4

-1

.o

-0.5

0 Voltage

0.5

*

1.o

Fig. 4.24 Typical voltage histograms of a 5-Gb/s NRZ data signal for the “ones” and “zeros” rails. One million voltage samples are recorded in each bit using a digital oscilloscope. Eye Diagram -5

‘..,

’

-1 0

%

Decision Point Fig. 4.25 An expanded view of the upper rail of an eye diagram showing ISI. The resulting BER vs decision level can have a slope change causing the Q-factor measurement to underestimate the actual value.

the actual Q-factor for long pseudorandom data patterns with large margins. The root cause of the effect is shown schematicallyin Fig. 4.25. In the figure, the upper part of the received eye diagram is expanded to show the intersymbo1 interference (ISI). Here the pattern dependenceof the data causes different bits to have different mean voltages at the decision circuit’s timing point. The resulting BER vs decision voltage does not followa simple Gaussian characteristic, rather it follows the rules of total probability given each bit’s probability density function. For large margins, the resulting curve can exhibit a slope

zyxwvu zy

4. Undersea Communication Systems

177

change at BERs less than what is practical to measure, and the extrapolated BER (and Q-factor) is then underestimated. In practice, this is not a serious limitation to characterizinga working system, because typical values of beginning of life optical margins are less than 5 or 6 dB. A practical engineering fix to this problem is to measure the Q-factor for a series of word lengths. It is often useful to know the ideal Q-factor as a starting place for system calculations. Marcuse describedthe ideal Q - f a ~ t oconsidering r~~ only accumulated noise impairments in terms of the optical SNR. This formalism can be embellished to include other effects such as finite extinction ratio in the transmitter and other pulse shapes. For example, assuminga NRZ data format with extinction ratio (I), the ideal Q-factor is given as:

where

zyxwvu zyxw zy zyxwvu [d], 2(1 -

y=

where& andBE are the optical and electricalbandwidths in the receiver. Later in the section on system design (Section 4.9) we will use Eq. 4.13 to calculate the expected Q-factor using the SNR given by Eq. 4.3 as a starting point for the impairment budget.

4.7 Error Correcting Codes Up to this point our discussion has focused on the generation of optical signals, propagating them over fiber cables, and detecting them at the far end; that is to say the physics of getting optical data bits across the system. The topic of forward error correction (FEC) codes approaches the subject of data transmission from a more classical communications channel perspective, where information is transmitted over a nonideal noisy channel. FEC adds redundancy or extra information to the original input data before it is converted to an optical signal (Fig. 4.26). The decoder in the receiver uses this redundant information to identify and correct bit errors caused by the transmission channel. The result of this added information is that the actual transmitted bit rate is larger than the rate of the input data. For example, a 10-Gb/s system employing a 23% FEC overhead has a transmitted data rate of 12.3Gb/s.

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Neal S. Bergano

Data In

4 FEC Encoder

,-I

Transiitter

.........................................................................

Transmit Terminal

Channel: Added Noise Chromatic Dispersion Fiber's nonlinear index

.........................................................................

I

Data Out

........................................................................

:

;

Receive Terminal

Fig. 4.26 A transmission system using FEC codes in the terminals. Redundancy or extra bits are added at the transmit end before the data is transmitted into the system. The FEC-enabled receiver identifies and corrects bit errors.

FEC codes can dramatically improve the performance of lightwave transmission systems by adding system margin.39 For example, a BER of lo-" requires a Q-factor of 17dB (calculated from Eq. 4.1 1). Figure 4.27 shows the output bit-error ratio as a function of input Q-factor for 7% and 23% FEC codesa For the 23% code shown in the figure, an output BER of 1O-I' is achieved with input Q-factor of about 8.4 dB, or a gross coding gain of 8.6 dB (i.e., 17dB - 8.4 dB)! The net coding gain will be reduced because the bit rate of the system increased. We can estimate the penalty of increasing the bit rate assuming an increased noise bandwidth of the receiver by 10 log (1.23)' or about 0.9 dB (assuming that the penalty scales linearly with the bit rate). This gives a net coding gain of about 7.7 dB. The FEC coding gain allows the target Q-factor (or line bit-error ratio) to be greatly relaxed, which can be used to improve the transmission system in several ways. For example, the system can be made more linear by operating the WDM channels at a lower average power. The resulting degraded error ratio (caused by the lower SNR) can be removed with the FEC. This more linear system could be used to transmit higher capacity by placing WDM channels closer together and/or using wavelengths that are farther away from the fiber's zero dispersion wavelength. Other benefits could be increased repeater spacing, longer transmission distances, or a relaxed tolerance on component specifications. The solid lines in Fig. 4.27 are theoretical calculations of the FEC code's performance assuming additive white Gaussian noise and ideal data streams without any intersymbol interference. Although these assumptions are not completely true, the measured data points are in good agreement with the theory. Figure 4.28 shows the results of a study that was performed to test the ~ study the error correction capability validity of the ideal c a l ~ u l a t i o n sIn~this

zy zyxw zy zyxwvutsrqp 4. Undersea Communication Systems

179

Input BER

2.7e-002

2.7e-003

3.6e-005

I

I

IO-‘

I 0-3 Output BER

I 0-5 I 0-7 I 0-9 IO-”

6

7

8

9 10 Input Q-Factor (dB)

11

12

Fig. 4.27 Output bit-error ratio as a function of input Q-factor for three cases: (1) No FEC, (2) 7% single-stage Read-Solomon code, and (3) 23% concatenated Reed-Solomon code. The solid lines are theoretical calculations and the symbols are measured points.

6

7

8 9 10 Input Q (dB)

11

12

6

7

8 9 10 Input Q (dB)

11

12

Fig. 4.28 Output BER vs input Q-factor for two different forms of distortion: (A) BER is degraded by added noise, (B) BER is degraded by waveform distortion caused by the fiber’s nonlinear index. Eye diagrams are shown in the inserts.

for a 14% Reed-Solomon code was measured under two different conditions. In the first, data were collected for a noise-loaded system, and as expected, the measured data points fit the theoretical prediction. In the second experiment, waveform distortion arising from chromatic dispersion and the nonlinear behavior in the transmission line degraded the input BER. Even in this case the measured data points are in agreement with the simple theory. FEC codes have the added benefit of simplifyingthe measurement of margin in an operating system. Many FEC decoders can report how many errors have

180

Neal S. Bergano

zyxwvu

zyx zyx

been corrected. This can give an accurate measurement of the actual bit-error ratio on the line. As stated in the previous section, the most accurate way of measuring margin is to know the BER on the line (thus knowing the received Q-factor). Alternatively, if the FEC decoder reports error-free operation on the line, then it is known with a high degree of confidence that the system is operating with a minimum margin equal to the FEC coding gain.

4.8

Polarization Effects

Several polarization effects in lightwave systems can combine to degrade the performance of long-haul lightwave systems42(see Table 4.1). These effects can both reduce the mean received SNR43344and cause the S N R to fluctuate with time.45Standard telecommunication optical fibers do not maintain the state-of-polarization of the transmitted signal. Random perturbations along the fiber’s length can couple the transmitted signal between the two polarization modes and give rise to the time-varying state-of-p~larization.~~ The unstable state of polarization interacting with the polarization dependence in the transmission line can lead to a fluctuating Q-factor at the receive-terminal. To accommodate this fluctuating performance, additional margin needs to be designed into the system (see Section 4.9 on system design). Figure 4.29 gives a graphical representation of how polarization dependence can result in a time-varying SNR. Consider an amplifier chain where each amplifier has some PDL. During a favorable time, the states of polarization at the inputs to the amplifiers could drift to coincide with a majority of the low-loss axes of the PDL in the amplifiers. At these times the SNR will be high. Alternatively, at unfavorable times, a majority of the input polarizations could coincide with the high-loss axes, producing lower SNR. The same type of effect is true for polarization mode dispersion in the transmission fiber

zy zyxwvu

Table 4.1 Important Polarization Effects Found in Lightwave Systems ~

~~~~~~~

SOP (State Of Polarization) drift

The state of polarization evolves over time, caused by temperature and stress changes of the transmission fiber.

PDL (Polarization Dependent Loss)

A component’s attenuation has a small dependence on the signal‘s polarization.

PMD (Polarization Mode Dispersion)

The group delay through the transmission fiber or component is polarization dependent.

PHB (Polarization Hole-Burning)

The amplifier’s saturated output power is slightly larger for light in the orthogonal polarization from the saturating signal.

zyxwvut

zy zyxwv

4. Undersea Communication Systems

zyxwvutsrq Time Varying Birefringence (PMD)

:

:

181

IzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 'uL F H SNR Low

+

~~

H

Input

rl'

Signal

A

-

A

T

H

-

L

.,.

,

~ow-Loss~xis of PDL

Fig. 4.29 A transmission line containing polarization-dependent elements, such as polarization-dependent loss and polarization mode dispersion. The unstable state of polarization caused the received SNR to fluctuate with time.

I

0

I

1

I

I

I

1

2

3

4

5

Time (hours)

Fig. 4.30 Q-factor vs time for a 5-Gb/s signal transmitted over 7200 km. The insert shows a histogram of the Q-factor data.

and the amplifier's components, only in this case we are more concerned with waveform distortions than SNR. Figure 4.30 shows a measurement of the Q-factor fluctuations in a WDM transmission experiment for 1 of 16 5-Gb/s channels after 7200 km. Polarization hole-burning results from an anisotropic saturation created when a polarized saturating signal is launched into the erbium doped fiber. The PHB effect was first observed as an excess noise accumulation in a chain

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Neal S. Bergano

of saturated E D F A s , ~and ~ was later isolated in a single amplifier and identified as PHB.48The gain difference caused by PHB is quite small in a single amplifier, with a typical value of about 0.07 dB for an amplifier with 3 dB of gain compression. Although PHB is a very small effect in a single EDFA, its effect on the overall performance of an optical amplifier transmission line can be several dBs in received Q-factor. PHB can cause the amplified spontaneous emission noise to accumulate in the polarization orthogonal to the signal faster than along the parallel axis (Fig. 4.31). Noise accumulates faster than would be predicted by simple noise accumulation theory, and as a result, the signal decays at the expense of the noise. Fortunately, the deleterious effects of PHB can be avoided by depolarizing the total signal propagating in the amplifier chain at a rate faster than the EDFA’s gain recovery time. When the signal’s degree of polarization is low, there is no preferred polarization axis for the gain to be depleted, and the transmission performance returns to the expected value. Depolarizing the total signal in a WDM system can be performed passively by allowingchannels to take on random SOPSor actively by modulating the channel’s polarizations. In a WDM system with many optical channels, the unavoidable PMD in the amplified line causes the different channels to disperse in polarization, which leads to a natural decrease in the degree of polarization. This process can be accelerated by purposely launching the channels in a “pair-wise” orthogonal manner.23

zyxw Actual Signal Decay with

Distance (km)

Rg. 4.31 PHB causes the noise in the orthogonal polarization to have an excess gain. If left unchecked, this could lead to noise accumulation faster than would be predicted with simple noise accumulationtheory.

zyxwvut zyx

4. Undersea Communication Systems

183

Alternatively,the state of polarization can be activelymodulated or “scrambled” at the transmit end of the system. Because the dynamics of the EDFA gain are relatively polarization scrambling the signal at a rate faster than the EDFA can respond to eliminates any excess noise accumulation caused by PHB. The characteristic time constant associated with PHB is similar to the time contents that govern the large signal response of the EDFA, or about 130-200 ~ s e c . ~To O reduce the negative effects of PHB on transmissionsystems, the SOP of the transmitted optical data signal should be scrambled at a rate that is high compared to the amplifier’sresponse time. Therefore, polarization scrambling should interchange the optical signal between orthogonal polarizations at a frequency higher than 1/ 130 sec, or about 7 kHz. Polarization scrambling techniques were particularly important for the first single-channel optical amplifier systems where the degree of polarization launched into the system was potentially large. Performance improvements have been reported for slow-speed ~crambling~lg~~ (i.e., much lower than the bit rate), synchronous scrambling53(equal to the bit rate), and high-speed ~ c r a m b l i n g(faster ~ ~ . ~than ~ the bit rate).

zyxw

4.9

System Design

Thus far, we have reviewed several aspects of optical amplifier transmission technology used in undersea cable systems. This section attempts to put the pieces together by reviewing the design of a 32-channel by lO-Gb/s transatlantic 6000-km system. The goal of the system design is to have adequate end-of-life margin considering many of the factors presented thus far, such as degradations caused by optical noise, waveform distortions, Q-factor fluctuations, and system aging. Key design parameters are the repeater spacing, launch power, and the dispersion management of the amplified line (Table 4.2). A 6000-km system will require about 120repeaters spaced every 50 km.The term repeater is taken from the nomenclature of analog transmission systems. For our purposes, a repeater is the pressure vessel that houses the erbiumdoped fiber amplifiers. In ow example the repeater’s EDFA will have a net gain of 10 dB, assuming an average cable attenuation of 0.2 dB/km. A total launch power of about 11dBm (-4 dBm per channel) is required to produce enough margin. A systembandwidth of about 19nm is required for 32 channels spaced every 75 GHz (-0.6nm at 1550nm). The dispersion map shown in Fig. 4.10 is used to limit the negative effects of the fiber’s nonlinear index, and each transmitter will use the chirped return to zero format. The impairment budget (Table 4.3) is a design tool used to account for all of the expected impairments over the system’s lifetime. The starting point is the ideal Q-factor that is calculated considering only the received SNR, calculated for example using Eq. 4.3 and Eq. 4.13. From this starting point the

zyx

184

zyxwvu zyxw zyxw zyxwvu zyxw

Neal S. Bergano

Table 4.2 Key Design Parameters Parameter

Length Repeater spacing Repeater count Repeater gain Total launch power Repeater noise figure Channel spacing Amplifier bandwidth Dispersion period dispersion map (see Fig. 4.10) Dispersion slope Line rate (23% FEC overhead) Transmitter extinction ratio Receiver optical bandwidth Receiver electrical bandwidth

Value

6000 km 50 km

120 10dB 11dBm 4.5 dB 75 GHz 19nm 500 km

0.075 ps/km-nm2 12.3Gbls 13.7dB 50 GHZ 8.6GHz

Table 4.3 Impairment Budget for a 32-Channel, 10-Gb/s, 6000-kmSystem ~

Line 1 2 3

4 5 6

7 8

~~~

Parameter

Mean Q value (from simple SNR calculation) Propagation impairment Manufacturing variations and impairments Q-factor time variations Aging End-of-life Q-factor (1 - 2 - 3 - 4 - 5) Required Q-factor End-of-lifemargin (6 - 7)

dB Value 17.8 4.3 2.0 1.o 1.o 9.5 8.5 1.o

values of all expected degradations are subtracted. For example, the 4.3-dB value in line 2 includes effects arising from propagation impairments such as the fiber’s nonlinear index, added noise from optical reflections, and nonideal dispersion compensation. This value is obtained using very detailed computer modeling of the optical propagation in a transmission system56(which unfortunately is beyond the scope of this chapter). Line 3 gives a 2-dB allotment for manufacturing variations, which covers all of the realistic population distributions of the components, and the imperfect system assembly process. Line 4 gives 1dB for Q-factor fluctuation, and line 5 allots 1dB for system aging.

4. Undersea CommunicationSystems

185

The Q-factor target of 8.5 dB represents the FEC threshold value shown in Fig. 4.27. The values in the table were recalculated for different launch powers and span lengths until the 1 dB end-of-life figure was reached. Much of the terminal transmission equipment for undersea systems differs significantly from equipment for terrestrial applications because of the large system-length differences. The transmission terminals include equipment to condition digital data for transmission undersea, power feed equipment to provide DC power to the undersea equipment,and line monitoring equipment to diagnose the location of undersea cable cuts and other undersea faults. An important part of the undersea cable network's terminal is the power feed equipment used to supply electricalpower to the optical amplifierslocated in the undersea repeaters. The active components (such as pump lasers) are powered by running a DC current through the copper conductor in the cable. The power feed equipment at the shore terminals supply a constant current of about 1 Ampere at -lO,OOOvolts, where one side of the cable is biased with positive voltage and the other with negative voltage. Interestingly, having a cable conductor across the ocean allows one to determinethe ground potential difference between continents, which is typically tens of volts, but can increase significantly during electrical or solar storms. Figure 4.32 shows a diagram of a typical amplifier pair that is located in an undersea system. A maintenance system is used to identify the location of faults andor degraded components by monitoring the undersea equipment from the shore terminals. An optical monitoring signal is coupled back into the fiber in the reverse direction at a low optical power. The signal-to-noise ratio of this low-level signal is enhanced using signal correlation techniques to provide data on repeater gain, gain tilt, and span attenuation. This approach

zy

zyxwvu zyxw WDM

Erbium Doped Fiber

Isolator

zyxwvut U '

b

186

zyxwvutsr zyxwvu zyxwvu Neal S. Bergano

also is synergistic with the use of COTDR (Coherent Optical Time Domain Reflectometer) techniques to identify the location of a cable cut or other fault between repeaters.

4.10 Transmission Experiments Most long-haul transmission experiments using optical amplifiers fall into one of three categories: circulating test bed^,^^ and special measurements performed on installed systems.59 Circulating-loop transmission measurements are by far the most important experimentaltechnique. Circulating-loop techniques applied to an amplifier chain of modest length can provide an experimentalplatform to study a broad range of transmission phenomena for EDFA-based transmission systems.60 A loop experiment attempts to simulate the transmission performance of a multithousand-kilometer-longsystem by making multiple passes through an amplifier chain of modest length (Le., hundreds of kilometers). The loop transmission experiment (Fig. 4.33) contains most of the elements found in conventionalexperiments, such as an opticaldata transmitterlregeneratorpair, a chain of amplifiedfibersections, and diagnosticequipment such as a bit-error ratio test set (BERTS). In the loop experiment, optical switching is added to allow data to flow into the loop (the load state) and then to circulate (the loop state, Fig. 4.34). The data circuIates for a specified time, after which the state of the experiment toggles, and the Ioacfnoop cycle is repeated. Load Switch

zyx zyx

3dB Coupler

BERTS

Clock

Gate

Load

J aitchL-1 State

hl

Measurement Gate

,

:>

,

-2.4 msec trip time

/round

I:

,

I

+ -,.

Jnl

,

,)

Fig. 4.33 Top: Block diagram for a circulating-loop transmission experiment. Bottom: Timing diagram for the experiment showing the optical switch states and the time gate for making measurements.

zy zyxwvuts zyxw zyxwvuts zyx 4. Undersea Communication Systems

A) Load

187

B) Loop

Fig. 4.34 Simplified block diagram of a loop transmission experiment, showing: (A) the load state and (B) the loop state.

The basic unit of time for the loop experiment is the time of flight for an optical signal around the closed loop, which is about 4.89 wsec per kilometer of fiber. With reference to the timing diagram of Fig. 4.33, the experiment starts with the load switch on (or transmitting light) and the loop switch off (or blocking light). The two switchesare held in this load condition (Fig. 4.34a) for at least one loop time to fill the loop with the optical data signal. Once the loop is loaded with data, the switches change state to the loop configuration (Fig. 4.34b), and the data is allowed to circulate around the loop for some specified number of revolutions.A portion of the data signal is coupled to the receiver or other diagnostic equipment for analysis. The data signal is received and retimed by the regenerator and compared to the transmitted signal in the BERTS for error detection. The measurement continues, switchingbetween the load and the loop states so that errors can be accumulated over long intervals of time. Since errors are counted only during the measurement gate period, the effective bit rate for the experimentis diminished by the duty cycle of the gate signal; thus, the real time for demonstrating a particular BER might be increased by 50 or 100 times over conventional measurements. In addition to bit-error ratio, many other measurements are possible, such as optical spectra, eye diagrams, and Q-factor. For example, Fig. 4.35 shows the optical spectra of a 16-channel WDM experiment as a function of distance. One of the advantages of a circulating loop is that length dependencemeasurements are easily made. From this measurement, the nonideal gain equalization of the amplifier chain is clearly observed; the inner channels gain power, and the outer channels lose power as they propagate into the system. The length of the amplifier chain used in the loop experiment is an engineering tradeoff between cost and performance. To perform meaningful experiments, many in the lightwave community have settled on a minimum amplifier chain of about 500 km. The benefits of having a long amplifier chain are:

zyxw zyx

0

As the loop length is increased, the round-trip time becomes long compared to the optical amplifier’s recovery time.

188

zyxwvu zyxwvu

Neal S. Bergano -

Intensity (dB)

i

62

zyxw 1558

Distance (krn) 0

‘

i556

1554

1552

Wavelength (nrn)

Fig. 4.35 Optical spectrum of 16, 5-Gbls channels measured for different transmission distances in a circulating loop.

0

0 0

Long amplifier chains have more accurate dispersion maps and/or more map periods. The statistics of the performance fluctuations become more realistic. Any attenuation that is added by the “loop specific” equipment becomes less significant.

The benefits of having a short amplifier chain are: 0 0

0

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Circulating-loop experimentshave been used to demonstrate massive transmission capacity over long distances. For example, Fig. 4.36 and Fig. 4.37 show the results of a 2400-Gb/s transmission experiment, where 120 channels, each carrying 20 Gb/s, were transmitted over 6200 km.61This experiment used many of the techniques described in the previous sections, such as gain equalization, dispersion management, FEC, RZ pulses, and orthogonal polarization launch. This massive capacity and high spectral efficiencywas achieved by using an optimum FEC code, a carefully engineered dispersion map with ultra-low dispersion slope, and full C-band EDFAs.

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4.11 Future Trends in Long-Haul Optical Transmission Systems The capacity of undersea fiber-optic systems will increase by using more optical bandwidth and by using the available bandwidth more efficiently. The conventional pass-band of the EDFA (C-band) is about 40nm wide, in the wavelength range of roughly 1526 to 1566nm, corresponding to optical frequencies of 196.5 to 191.4THz. Thus, the conventional erbium band has about 5 THz of bandwidth available for data transmission. The ultimate digital capacity that can be “fit” into the EDFA’s C-band will depend on how efficientlythis bandwidth can be used for data transmission. This spectral efficiency, expressed in (Bits/second)/Hz,is defined as the system’s average digital

Neal S. Bergano

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capacity divided by the average optical bandwidth of the system. The bestreported spectral efficiencies in WDM transmission range from 1.Obits/sec/Hz for very short (-100 km) distances, to roughly 0.5 bits/sec/Hz for transoceanic distance (Fig. 4.38). For example, the data shown in Fig. 4.36 represents a spectral efficiency of about 0.48 bits/sec/Hz. Assuming that this spectral efficiency could be achieved (with realistic margin) gives an upper limit on the C-band capacity of about 2.5TB/s on a single fiber. Table 4.4 gives some representative values for the optical bandwidth required to achieve a total transmission capacity for different spectral efficiencies.

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Table 4.4 The Relationship between Total Capacity, Spectral Efficiency, and Required Optical Bandwidth (The required optical bandwidth is calculated assuming a center wavelength of 1545 nm. The missing entries calculate to a bandwidth that is much larger than 80 nm.)

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Fig. 4.39 An amplifier chain with both EDFAs and Raman gain.

The performance of the C-band could also be improved by using a combination of Raman gain with the EDFA as shown in Fig. 4.39. Here Raman gain in the transmission fiber is used to “assist” the EDFA gain, which lowers the accumulated noise, thus increasing the SNR. Alternatively, the same SNR could be achieved while lowering the signal power, thus reducing the nonlinear effects.62 The system’stotal capacity could also be improved by increasing the number of optical fibers in the cable. This becomes an engineering challenge to make the optical amplifiers more efficient in physical space, given the limited amount of space in the pressure vessels, and require less electrical power, given the practical limits of electrical power transmission in the cable. We can continue to use this bandwidthhpectral efficiency idea to estimate the ultimate capacity of a transoceanic-length system (practicality notwithstanding). The low attenuation window of typical telecommunications-grade optical fibers is about 120 nm wide and extends from approximately 1500 to 1620 nm, corresponding to -1 5 THz. Assuming the same 0.5 bits/sec/Hz spectral efficiency yields a potential capacity of about 7.5 TB/s. Erbium amplifiers can cover about 2/3 of this bandwidth by using both the C-band and the newer “Long” wavelength band (or L-band) in the wavelength range of about 1570 to 1610nm. The leading optical amplifier candidate for the remaining short wavelength band (S-band) is stimulated Raman gain, which would be accomplished by pumping the transmission fiber at 1430 nm. Commensurate with the required wide-band optical amplifier, is the need for wide-band transmission fibers that have a “flattened” chromatic dispersion characteristic. Such fibers have been reported recently that extend the concept of dispersion mapping by alternating both the sign and the slope of the d i s p e r s i ~ n .The ~ ~ ,resulting ~ fiber spans have relatively constant dispersion value over a broad bandwidth (Fig. 4.40). Ultimately, one could envision using the entire pass-band of the transmission fiber from 1300to 1700 nm, corresponding to 55 THz. This would pose many challenges to fiber and system designers. For example, a very broadband optical amplifier would be needed (or combinations of amplifiers), and the added attenuation of the fiber at the shorter wavelengths would decrease the signal-to-noise ratios for WDM channels in that region.

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As stated previously, the transmission performance of a lightwave system can be improved using FEC coding. Figure 4.41 shows a calculation for bit error ratio as a function of input Q-factor for different FEC code rates.65This calculation recasts Shannon’s capacity limit66,67 in terms of a lightwave system assuming a binary asymmetric channel. For example, the theoretical BER

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threshold for a code rate of 0.8 (or a 20% FEC overhead) is approximately 5 dB. This represents an improvement of 3.5 dB over the performance shown in Fig. 4.27 for a 23% FEC overhead. Thus, there is room for improvement in terms of the quality of FEC encoders and decoders. Some of the promising techniques to improving FEC performance are iterative concatenated codesY6* turbo product codes,69and low-densityparity check codes.70

4.12 Summary We have come a long way since the 1980s and the first undersea fiber-optic cables that revolutionized international telecommunications. Optical fiber cable networks now provide the bulk of the long-haul telecommunicationsfor voice and data over land and across seas. Today, transoceanic cable networks are being built with multi-Terabitcapacities.Ultimately, another order of magnitude increase in the data transmission capacity of single-mode fiber will occur given wider bandwidth amplifiers and improvements in spectral efficiency. These improvementswill foster unprecedented capacity improvements for international telecommunications.

References

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Neal S. Bergano, “Undersea Fiberoptic Cable Systems: High-Tech Telecomunications Tempered By a Century of Ocean Cable Experience,” Optics and Photonics News Magazine, Vol. 11, No. 3, March 2000. Neal S. Bergano and Howard Kidorf, “Global Undersea Cable Networks,” Optics and Photonics News Magazine, Vol. 22, No. 3, March 2001. F! R. Trischitta and W. C. Marra, “Global Undersea CommunicationsNetworks,” IEEE CommunicationsMagazine, Vol. 34, No. 2, February 1996. Bern Dibner, The Atlantic Cable, Burndy Library, Norwalk, CT, 1959. R. D. Ehrbar, “Undersea Cables for Telephony,” Chapter 1 in Undersea Lightwave Communications, edited by Peter K. Runge and Patrick R. Trischitta, IEEE Press, New York, 1986. P. K. Runge and P. R. Trischitta, “The SL Undersea Lightwave System,” Chapter 4 in Undersea Lightwave Communications, edited by Peter K. Runge and Patrick R. Trischitta, IEEE Press, New York, 1986. P. Trischitta, et al., “The TAT-12/13 Cable Network,” IEEE Communications Magazine, Vol. 34, No. 2, p. 24, February 1996. T. Li, “The Impact of Optical Amplifiers on Long-Distance Lightwave Telecommunications,’’Proceedings ofthe IEEE, Vol. 18, No. 11, p. 1568, 1993. A. M. Vengsarkar, et al., “Long-Period Fiber-GratingBased Gain Equalizers,” Opt. Lett., Vol. 21, No. 5, pp. 336-338, 1996. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplijiers Fundamentals and Technology,p. 206, Academic Press, Boston, 1999.

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J. P. Gordon and L. F. Mollenauer, “Effects on Fiber Nonlinearities and Amplifier Spacing on Ultra-Long Distance Transmission,” Journal of Lightwave Communication, Vol. 9, No. 2, p. 170, 1991. E. Lichtman, “Optimal Amplifier Spacing in Ultra-Long Lightwave Systems,” Electronics Letters, Vol. 29, p. 2058, 1993. C. R. a l e s and E. Desurvire, “Propagation of Signal and Noise in Concatenated Erbium-Doped Fiber Amplifiers,” Journal of Lightwave Technology, Vol. 9, No. 2, p. 147, 1991. A. K. Srivastava, et al., “Room Temperature Spectral Hole-Burning in ErbiumDoped Fiber Amplifiers,” in Proc. Optical Fiber Con$, p. 33, San Jose, CA, 1996. A. R. Chraplyvy, J. A. Nagel, and R. W. Tkach, “Equalization in Amplified WDM Lightwave Transmission Systems,” IEEE Photonics Technology Letters, Vol. 4, No. 8, August 1992. G. P. Agrawal, “Group-Velocity Dispersion,” Chapter 3 in NonlinearFiber Optics, edited by Ivan P. Kaminow and Thomas L. Koch, Academic Press, Boston, 1989. A. H. Gnauck and R. M. Jopson, “Dispersion Compensation for Optical Fiber Systems,” Chapter 7 in Optical Fiber Telecommunications IIU, edited by Ivan F? Kaminow and Thomas L. Koch, Academic Press, Boston, 1997. G. P. Agrawal, NonlinearFiber Optics, Academic Press, Boston, 1989. D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Effects of Fiber Nonlinearity on Long-Distance Transmission,” Journal of Lightwave Technology, Vol. 9, No. 1, pp. 121-128,1991. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Fiber Nonlinearities and Their Impact on Transmission Systems,” Chapter 8 in Optical Fiber Telecommunications IIIA, edited by Ivan P. Kaminow and Thomas L. Koch, Academic Press, Boston, 1997. T. Naito, T. Terahara, T. Chikama, and M. Suyama, “Four 5-Gbith WDM Transmission Over 4760-km Straight-Line Using Pre- and Post-Dispersion Compensation and FWM Cross-Talk Reduction,” Optical Fiber Communications,OFC ’96, pp. 182-183, 1996. A. Puc, F. W Kerfoot, A. Simons, and D. L. Wilson, “Concatenated FEC Experiment Over 5000-km-long Straight Line WDM Test Bed,” OFC ’99 Paper ThQ6, San Diego, CA. Neal S. Bergano and C. R. Davidson, “Method and Apparatus for Improving Spectral Efficiency in Wavelength Division Multiplexed Transmission Systems,” United States Patent 6,134,033, issued October 17,2000. Neal S. Bergano, et al., “320 Gb/s WDM Transmission (64 x 5 Gb/s) over 7,200 km using Large Mode Fiber Spans and Chirped Return-to-Zero Signals,” OFC ’98, paper PD12, San Jose, CA, February 1998. E. A. Golovchenko, Neal S. Bergano, and C. R. Davidson, “Four-WaveMixing in Multispan Dispersion-Managed Transmission Links,” IEEE Photonics Technology Letters, Vol. 10, No. 10, October 1998. Bell Telephone Laboratories, Transmission Systems for Communications, Fifth Edition, Chapter 30, p. 741, Bell Telephone Laboratories, Inc., 1982.

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Bell Telephone Laboratories, Transmission Systems for Communications, Fifth Edition, Chapter 30, p. 741, Bell Telephone Laboratories, Inc., 1982. Ekaterina A. Golovchenko, Alexei N. Pilipetskii, and Neal S. Bergano, “Transmission Properties of Chirped Return-to-Zero Pulses and Nonlinear Intersymbol Interference in 10 Gbls WDM Transmission,” OFC 2000, paper FC3, Baltimore, MD, March 2000. B. Bakhshi, M. Vaa, E. A. Golovchenko, W. W. Patterson, R. L. Maybach, and Neal S. Bergano, “Comparison of CRZ, RZ, and NRZ Modulation Formats in a 64 x 12.3 Gbls WDM Transmission Experiment Over 9000 km,”OFC 2001, paper WF4, Anaheim, CA, March 2001. L. F. Mollenauer, J. P. Gordon, and P. V, Mamyshev, “Solitons in High Bit-Rate Long-DistanceTransmission,”Chapter 12in Optical Fiber TelecommunicationsIIIA, edited by Ivan P. Kaminow and T. L. Koch, Academic Press, Boston, 1997. M. I. Suzuki, et al., “Reduction of Gordon-Haus Timing Jitter by Periodic Dispersion Compensation in Soliton Transmission,”Electronics Letters, Vol. 31, No. 23, p. 2027, 1995. Neal S. Bergano, E W. Kerfoot, and C. R. Davidson, “Margin Measurements in Optical Amplifier Systems,” IEEE Photonics TechnologyLetters, Vol. 5, No. 3, March 1993. S. D. Personick, “Receiver Design for Digital Fiber Optic Communications Systems,” Bell System TechnicalJournal, Vol. 52, No. 6, pp. 843-886, 1973. Cecil Hastings, Jr., Approximations for Digital Computers, Princeton University Press, Princeton, p. 191, 1955. D. Marcuse, “Derivation of Analytical Expressions for the Bit-Error Probability in Lightwave Systems with Optical Amplifiers,” Journal of Lightwave Technology, Vol. 8, pp. 18161823, 1990. P. A. Humblet and M. Azizoglu, “On the Bit Error Rate of Lightwave Systems with Optical Amplifiers,” JournaZ of Lightwave Technology,Vol. 9, pp. 15761582, 1991. V, J. Mamczyk and D. G. Duf, “Effect of Intersymbol Interference on Signal-toNoise Measurements,’’ Conference on Optical Fiber Communications, paper WQ1, 1995. D. Marcuse, “Derivation of Analytical Expressions for the Bit-Error Probability in Lightwave Systems with Optical Amplifiers,’’ Journal of Lightwave Technology, Vol. 8, pp. 18161823, December 1990. N. Ramanujam, et al., “Forward Error Correction (FEC) Techniques in LongHaul Optical Transmission Systems,” Paper WE1 presented at the LEOS Annual Meeting, Vol. 2, p. 405,2000. C. R. Davidson, et al., “1800Gbls Transmission of One Hundred and Eighty 10 Gbls WDM Channels over 7,000 km using the Full EDFA C-Band,” Paper PD25 at the conference on Optical Fiber CommunicationsOFC 2000, March 2000. H. Kidorf, et al., “Performance Improvement in High-Capacity, Ultra-Long Distance, WDM Systems using Forward Error Correction Codes,” Paper ThS3 presented at the conference on Optical Fiber CommunicationsOFC 2000, p. 274, March 2000.

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C. D. Poole and J. Nagel, “Polarization Effects in Lightwave Systems,” Chapter 6 in OpticalFiber TelecommunicationsIIIa, edited by I. Kaminowand T. Koch, Academic Press, Boston, 1997. E. Lichtmann, “Performance Degradation Due to Polarization Dependent Gain and Loss in Lightwave Systems with Optical Amplifiers,” Electronics Letters, Vol. 29, NO.22, pp. 1971-1972,1993. F. Bruyere and 0. Audouin, “Penalties in Long-Haul Optical Amplifier Systems Due to Polarization Dependent Loss and Gain,” IEEE Photon. Tech. Lett., Vol. 6, No. 5, pp. 654-656, 1994. S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, “Observation of BER Degradation Due to Fading in Long-Distance Optical Amplifier System,” Electronics Letters, Vol. 29, No. 2, pp. 209-210, 1993. R. E. Wagner, C. D. Poole, H. J. Schulte, N. S. Bergano, V. P.Nathu, J. M. Amon, R. L. Rosenberg, and R. C. Alferness, “Polarization Measurements on a 147-km Lightwave Undersea Cable,” in Technical Digest of OFC ’86,Paper PDP7, Atlanta, GA, February 24-26,1986. M. G. Taylor, “Observation of New Polarization Dependence Effect in Long-Haul Optically AmpUied System,” OFC ’93, Post-deadline paper, PDS, San Jose, CA, 1993. V. J. Mazurczyk and J. L. Zyskind, “Polarization Hole-Burning in Erbium-Doped Fiber Amplifiers,” CLEO ’93, Post-deadline paper, CPD26, Baltimore, MD, 1993. E. Desurvire, C. R. Giles, and J. R. Simpson, “Gain Saturation Effects in HighSpeed, Multichannel Erbium-doped Fiber Amplifiers at h = 1.53 pm,” Journal of Lightwave Technology, Vol. 7, No. 7, pp. 2095-2104, December 12,1989. Neal S. Bergano, “The Time Dynamics of Polarization Hole Burning in ErbiumDoped Fiber Amplifiers,” OFC ’94, San Jose, CA, 1994. Neal S. Bergano, V. J. Mazurczyk, and C. R. Davidson, “Polarization Scrambling Improves SNR Performance in a Chain of EDFAs,” OFC ’94, San Jose, CA, 1994. M. G. Taylor, “Improvement in Q with Low-Frequency Polarization Modulation on Transoceanic EDFA Link,” IEEE Photonics Technology Letters, Vol. 6, No. 7, pp. 860-862, July 1994. Neal S. Bergano, C. R. Davidson, and F. Heismann, “Bit-SynchronousPolarization and Phase Modulation Scheme for Improving the Transmission Performance of Optical Amplifier Transmission System,” Electronic Letters, Vol. 32, No. 1, pp. 52-54, January 4,1996. M. G. Taylor and S. J. Penticost, “Improvement in Performance of Long Haul EDFA Link Using High Frequency Polarization Modulation,” Electronics Letters, Vol. 30, No. 10, pp. 805-806, 1994. Y. Fukada, T. Imai, and A. Mamoru, “BER Fluctuation Suppression in Optical In-Line Amplifier Systems Using Polarization Scrambling Technique,” Electronics Letters, Vol. 30, No. 5, pp. 432433, 1994. E. A. Golovchenko, et al., “Modeling of Transoceanic Fiber-optic WDM Communications Systems,” IEEE Journal of Selected Topics in Quantum Electronics, Vol. 6, No. 2, pp. 337-347, March/April2000.

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Neal S. Bergano, Jennifer Aspell, C. R. Davidson, P. R. Trischitta, B. M. Nyman, and F. W. Kerfoot, “A 9000-km 5 Gb/s and 21,000-km 2.4 Gb/s Feasibility Demonstration of Transoceanic EDFA Systems Using a Circulating Loop,” Optical Fiber Communications Conference, PD-13, San Diego, CA, February 18-22,1991. H. Taga, N. Edagawa, H. Tanaka, M. Suzuki, S. Yamamoto, H. Wakabayashi, N. Bergano, C. Davidson, G. Homsey, D. Kalmus, P. Trischitta, D. Gray, and R. Maybach, “10-Gb/s, 9,000-km IM-DD Transmission Experiments Using 274 Er-Doped Fiber Amplifier Repeaters,” Post-deadlinePaper, OFC ’93. J. C. Feggeler, et al., “10-Gb/s WDM Transmission Measurements on an Installed Optical Amplifier Undersea Cable System,” Electronics Letters, Vol. 31, No. 19, p. 1676, September 14,1995. Neal S. Bergano and C. R. Davidson, “CirculatingLoop Transmission Experiments for the Study of Long-Haul Transmission Systems Using Erbium-Doped FiberAmplifiers,” IEEEJournalofLightwave Technology,Vol. 13, No. 5, p. 879, May 1995. J.-X. Cai, M. Nissov, A. N. Pilipetskii, A. J. Lucero, C. R. Davidson, D. Foursa, H. Kidorf, M. A. Mills, R. Menges, P. C. Corbett, D. Sutton, and N. S. Bergano, “2.4 Tb/s (120 x 20 Gb/s) Transmission over Transoceanic Distance with Optimum FEC Overhead and 48% Spectral Efficiency,” OFC 2001, PD-20, March 2001. Balslev C. Clausen, et al., “Modeling and Experiments of Raman Assisted Ultra Long-haul Terrestrial Transmission Over 7500 km,” Paper We.F. 1.2 presented at the 27th European Conference on Optical Communications, Amsterdam, The Netherlands, 2001. Stig Nissen Knudsen and Torben Veng, “Large Effective Area Dispersion Compensating Fiber for Cabled Compensation of Standard Single Mode Fiber,” OFC 2000, Paper TUGS,Baltimore, MD, March 2000. M. Tsukitani, et al., “LOW-LossDispersion-Flattened Hybrid Transmission Lines Consisting of Low-NonlinearityPure Silica Core Fibres and Dispersion Compensating Fibers,” Electronics Letters, Vol. 36, No. 1,2000. Y Cai, et al., “Performance Limit of Forward Error Correction Codes in Optical Fiber Communications,” Paper TuF2, presented at the Optical Fiber Communications Conference, Anaheim, CA, 2001. C. E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, Vol. 27, pp. 379423 and 623-656, July and October, 1948. W Weaver and C. E. Shannon, n e Mathematical Theory of Communication, University of Illinois Press, Urbana, Illinois: 1949, republished in paperback, 1963. 0. Ait Sab, “FEC Techniques in Submarine Transmission Systems,” Paper TuF1, presented at the Optical Fiber Communications Conference, Anaheim, CA, 2001. R. M. Pyndiah, “Near-optimum decoding of product codes: block turbo codes,” IEEE Trans. on Communications,Vol. 46, No. 8, pp. 1003-1010, August 1998. D. J. C. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” Electronics Letters, Vol. 32, No. 18, pp. 1645-1646, August 1996.

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Chapter 5

High-Capacity, Ultra-Long-Haul Networks

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John Zyskind, Rick Barry, Graeme Pendock, Michael Cahill, and Jinendra Ranka Sycamore NetworkF, Chelmsford,Massachusetts

I. Introduction

The advent of optically amplified transmission and of Dense Wavelength Division Multiplexing (DWDM) technology has transformed the technology and also the economics of optical network deployments. In less than 10 years, the capacity of a single optical fiber equipped with commercial transmission equipment has increased from a single OC-48 signal, transmitting at a rate of 2.488 Gb/s, to 160 OC-192s signals, totaling 1600Gb/s, a factor of close to 1000. The economics of DWDM are driving the development and deployment of a new generation of ultra-long-haul DWDM systems for terrestrial networks that can carry these high-capacity data streams over thousands of kilometers. During the same period, driven by the growth of the Internet and other data-based services, the demand for new capacity has exploded and the requirements for the public network have changed dramatically. This chapter will discuss the challenges of high-capacity, ultra-long-haul terrestrial transmission systems, the advanced technologies required for such systems, and the architectures of optical networks based on ultra-long-haul transmission capability designed to meet these new demands. In conventional time-division multiplexed (TDM) regenerated transmission, prevalent until the mid-l990s, one signal was transmitted over its own fiber and, because of the attenuation of the fiber, the signal had to be optoelectronicallyregenerated approximately every 50 km by a dedicated, 13 IO-nm optoelectronic regenerator, comprising expensive, complex, and bit-rate specific high-speed optical and electronic components, the bandwidth of which limited the capacity of the TDM signal. On the other hand, modern day DWDM systems can carry simultaneously on a single fiber numerous signals, each at the same bit rate as the aforementionedTDM signal, and each carried on a distinct optical wavelength. A single optical amplifier, which amplifies all the signal wavelengths simultaneously,is used periodically to overcome the fiber attenuation in place of the multitude of more complicated regenerators that would be required, one for each signal, in a regenerated TDM system. These technologies dramatically reduce the cost of long-haul transmission capacity, and this dramatic cost reduction has driven the development and 198 OPTICAL FIBER TELECOMMUNICATIONS, VOLUME N B

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widespread deployment of DWDM as the technology of choice for long-haul telecommunicationsnetworks. Since the introduction of the first commercial DWDM systems in 1995, the capacity of such systems has grown explosively from 8 channels each carrying a DWDM OC-48 signal in the first systems to 160 DWDM channels or more each carrying an OC-192 channel in some recently announced systems. Until recently, these systemswere typically able to carry the DWDM signals over distances of 300-600 km without optoelectronic regeneration. As the capacity of such systems has exploded, the cost of terminals and regenerators has become an ever larger fraction of total system cost. Minimizingthe number and the cost of regenerators is now a major economic driver in the design of new equipment and the design of carriers’ fiber networks. These economic factors are driving increased channel bit rates from OC-48 (2.488 Gb/s) to OC-192 (9.953 Gb/s) and, in the near future, to OC-768 (39.813 Gb/s) to minimize the number of regenerators, transmitters, and receivers. The demand to reduce system cost is also driving the demand for, and development of, ultra-long-haul terrestrial DWDM systems with reach between regenerators exceeding 2000 km. A hypothetical national-scale fiber network connecting major urban centers of the United States is shown in Fig. 5.1. A backbone network would connect such centers, and much of the traffic arriving at these network nodes would pass through destined for other nodes. The cost benefit lies in avoiding the necessity for expensive optoelectronic regenerators between these nodes and permitting optical pass through of express traffic destined for another node.

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Managing the large bandwith and the large number of channels carried by high capacity DWDM systems represents an unprecedented challenge both for equipment suppliers and for carriers. Applying the conventional technology of switchingand routing low-bit-ratetributaries, for example, at the STS-1 speed, requires very large and expensive switches, and the optical-to-electronicto-optical (OEO) conversions required for such electronic switching is also increasingly expensive. Optical networking promises a solution to the challenge of managing the immense bandwidth carried by such DWDM systems. The fact that the different signals are encoded on distinct optical wavelengths opens the possibility of optical manipulation, switching, and routing of each individual signal channel using optical filtering and switching technologies to which optics is naturally well suited. For such optical networking to be useful, it will be necessary to extend the unregenerated reach of DWDM optical transmission to support the extended optical path lengths that will result. Transmission of high data rate channels (presently at lOGb/s as in the future at 40 Gbls) over unregenerated links with lengths of 1000 to 5000 km poses major challenges that cannot be met with conventional DWDM technology. Foremost among these problems are the accumulation of optical noise and spectral gain nonuniformity arising from optical amplification, as well as distortion due to transmission effects (including chromatic dispersion, polarization mode dispersion, and optical nonlinearities). These challenges were first addressed for undersea systems in which both fiber and optical amplifiers are placed under the water while terminals and regenerators are restricted to the shores at the ends of transoceanic links spanning thousands of kilometers (see, for example, Bergano 1997). The undersea elements of transoceanic systems must meet much more stringent reliability requirements than terrestrial systems because of the great expense that deep water ship repairs entail; the range of technologies that can be deployed is thereby strictly limited. However, each undersea deployment is a “green field” system in which the fiber spans, fiber type, and optical amplifier spacing can be specially tailored to the link length and designed capacity of that particular system. As a result, there is a great deal of latitude for optimization of each system’s design to meet the challenges of ultra-long-haul transmission. In terrestrial systems, on the other hand, the fiber network is typically already installed, often with a very different system in mind, well before the ultra-long-haul system designer begins. The fiber type is usually already defined and is one of a number of widely deployed, distinct fiber types. The locations of optical amplifiers are predetermined by the locations of hut sites, selected based on the availability of rights of way and the economic incentive to support as few amplifier sites as possible, which as we shall see, is not conducive to overcoming the challenges of ultra-long-haul transmission. While terrestrial ultra-long-haul systems certainly have strong similarities to undersea systems, the differences are significant, and the solutions to the problems

zy zyxwvuts zy zyxwvu 5. High-Capacity, Ultra-Long-Haul Networks

FEC

Deriodic channel Dower manaoement & optional dispersion slope management

encoder OC192 Tx’s

FEC decoder

dispersion

Raman pump

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Raman pump

Fig. 5.2 Schematic of an ultra-long-haultransmission system illustratingthe use of Raman amplification, FEC, and periodic dispersion slope compensation and power

management with a reconfigurable gain-flattening filter.

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of ultra-long-haul transmission are quite distinct. Figure 5.2 depicts some of the key features of a high-capacity, ultra-long-haul transmission system which will be discussed in this chapter.

11. Noise and Optical Amplification A. NOISE IN OPTICALLYAMPLIFIED ULTRA-LONG-HAUL SYSTEMS

The management of optical amplifier noise and the management of transmission distortions of the high-speed optical signals are the two most important considerations in the design of high-capacity, ultra-long-haul transmission systems. This section will focus on the management of amplifier noise, and in Section I11 we will turn to sources of distortion. The advent of practical optical amplifiers capable of simultaneously amplifying multiple signal wavelengths that occupy an appreciable range of the optical spectrum was the key technological advance that ushered in the DWDM revolution. Optical amplifiers are used at the end of each fiber span to boost the power of the DWDM signal channels to compensate for fiber attenuation in the span. EDFAs designed to operate with high inversion provide gain over a spectral range about 30 nm in width, from about 1530 nm to about 1560nm. This spectral range can support roughly 40 DWDM signal channels with a separation of 100GHz and 80 channels with a separation of 50 GHz, corresponding to 400 or 800 Gb/s, respectively, for 10 Gb/s OC-192 or STM-64 channels, and in the future, with 40-Gb/s channels, capacities of 1.6Tb/s (1600 Gb/s) for 100-GHz spaced channels. EDFAs designed to operate with lower inversion can provide gain over an even wider spectral range, including the so-called L-band, starting at about 1570nm, thus offering the opportunity to double the capacity on a single fiber through addition of an L-band EDFA. For a system transmitting over both the C- and L-bands, the

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capacity can reach 1.6 Tb/s or more for lO-Gb/schannels spaced at 50 GHz or 3.2 Tb/s or more for 40-Gb/s channels spaced at 100GHz. Unfortunately, optical amplification is not possible without the generation of amplified spontaneous emission (ASE), and the noise resulting from this ASE constitutes perhaps the most severe impairment that limits the reach and capacity of such systems. Each optical ampljjier contributes ASE, and these contributions add cumulatively along the amplifier chain. This accumulated ASE gives rise to signal-spontaneousbeat noise at the receiver, which is the fundamental noise limit in an optically amplified transmission system. Each EDFA contributes an amount of ASE:

zyxwvuts zyx

where PME is the ASE power in an optical bandwidth Av, h is Planck’s constant, v is the optical frequency, nsp is the spontaneous emission factor, and G is the optical amplifier gain. The spontaneous emission factor, nsp, is determined by the inversion of the amplifier’s Er ions. The contribution of each amplifier’s ASE to the accumulated ASE is characterized by the amplifier’s noise figure, which at high gain is well approximated by NF rz 2nsp. The signal-spontaneousnoise impairment can be characterizedin terms of the Optical Signal to Noise Ratio (OSNR), defined as the ratio of the signal channel power to the power of the ASE in a specified optical bandwidth, usually taken by convention to be 0.1 nm. This OSNR target must be sufficient to achieve the required system performance, which for commercial systems is today most often a bit-error rate (BER) of Le., effectivelyerror free. The OSNR target must include s a c i e n t margin to provide for any impairments that may be encountered. These include transmission impairmentsarising, for example, from chromatic dispersion, nonlinearities, and PMD discussed in the following sections; distortions introduced by the transmitter and receiver; amplser gain ripple; manufacturingmargin to provide for variances in performance of parts such as transmitters and receivers produced in a commercial manufacturing environment; and aging both of the system equipment and fiber plant during the expected life of the system. The target OSNR must theoretically increase by 6 dB for each factor of 4 increase in the channel bit rate in order to maintain equivalent noise performance. The actual increase in required OSNR with channel bit rate may be greater than this value due to the greater difficulty in achieving comparable transmitter and receiver performance at higher bit rates, and because of the greater severity of transmission impairments at higher bit rates, especially for rates as high as 40 Gb/s. As the length of a system increases, and the number of amplifiers contributing ASE increases, the OSNR at the end of the system decreases. The maximum unregenerated reach of an optically amplified system is the length of the system at which the OSNR at its end equals the target OSNR for acceptable system performance. However, the realization of this maximum length is contingent

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on successful management of transmission impairments that generate signal distortion. The length of the system that results in this OSNR is determined by the characteristics of the fiber network and of the optical amplifiers. For a system consisting of NaW fiber spans, each of loss LsPM(in dB) followed by an optical amplifier with output power Pout(in dBm) per channel launched into the span and noise figure NF (in dB), the OSNR (in dB) of a signal channel at the end of the system is approximately (Zyskind et al. 1997): OSNR (in dB) = 58

+ Pout - LsPw - NF - 10log (Namp).

(5.2)

Although the fiber spans of actual commercial fiber networks are typically not uniform in length, Eq. 5.2 can be used to illustrate some of the constraints placed on ultra-long-haul system design as a result of amplifier noise. The first thing to note is that if the amplifier spacing is fixed, for each dB that the available OSNR is increased (or the target OSNR can be reduced), the unregenerated reach of the system can be increased by about 25% (i.e., 1 dB). If the OSNR is increased by 3 dB, the length of the system can be doubled. The OSNR can be increased dB for dB by increasing Pout,by decreasing noise figure, or by decreasing span loss. The OSNR can also be increased by reducing the number of spans, but the dependence is much weaker. The system reach (in dB of loss) can be represented as the product of the span loss, L, in dB, which is proportional to span length in kilometers, and the number of spans, Namp.Equation 5.2 shows that, if the system reach Lspan. Nampis kept constant, the OSNR increases as the span length is reduced, and the number of spans is increased in the same proportion, because the OSNR depends only logarithmically on the number of spans. Figure 5.3 shows the OSNR as a

0

zyxwvu zyxwv

500 1000 1500 Aggregate Fiber Loss (dB)

2000

Fig. 5.3 OSNR of systems with the indicated span losses (15, 20, 25, and 30dB) as a function of the aggregate fiber loss, which is the span loss multiplied by the number of spans The amplifier noise figure is taken to be 5 dB, and the launched power per channel is 0 dBm.

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function of system reach for systems with span losses of 15,20,25, and 30 dB, correspondingto spans of approximately60,80,100, and 120km, respectively, in practical fiber networks. A noise figure of 5 dB, typical of an EDFA, and launched channel power of 0 dBm per channel have been assumed. No margin has been allowed that would shorten the reach of a practical system. These parameters are typical of systems capable of transmitting DWDM signals several hundred km without regeneration. For longer systems and higher bit rates, the availableOSNR must be increased and/or the target OSNR must be reduced. An ultra-long-haul system with an unregenerated reach of several thousand kilometers, for example, would require an OSNR increase on the order of 10dB. For ultra-long-haul systems with 4O-Gb/s DWDM channels, the OSNR would need to increase by at least an additional 6 dB to achieve the same system reach. The OSNR could be improved by reducing the span loss, Lspan,and this is done in commercial undersea systems where span lengths for transoceanic systems can be 50 km or less, corresponding to span losses of about 10dB. However, for terrestrial systems,reducing the span loss by reducing the separation between amplifier sitesis expensive and commerciallyunattractivebecause more optical amplifiers are required and additional amplifier sites are needed to accommodate them. In addition, the amplifier sites in terrestrial systems must often be placed in pre-existing equipment huts, the locations of which cannot be changed. The OSNR could also be improved by increasing Pout. Increasing Pouris possible only to a certain extent, because as Pourincreases, impairmentsarising from optical nonlinearitiesbecome more severe, especially for very long transmission distances. The remaining alternativeis to reduce the noise figure of the optical amplifiers. For each 1dB decrease in the noise figure, the accumulated ASE will be reduced by 1dB. For high-gain EDFAs, the noise figure is in principle limited to values above 3 dB. For practical designs this is generally a few dB higher, and there is little opportunity to reduce the noise figure of EDFAs.

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B. DISTRIBUTED RAlMAN AMPLIFICATION

Distributed Raman ampliiication is a new technology that offers the promise of effective noise figures that break the 3-dB barrier; this w ill increase system OSNR and enable extended transmission distances (Hansen et al. 1997). Raman amplification makes use of high power laser light, or Raman pump light traveling in the transmission fiber, as illustrated in Fig. 5 . 3 to ~ produce amplification in the transmission fiber over an appreciable distance due to the stimulated Raman scattering effect. The Raman pump typically has a wavelength approximately 100nm shorter than that of the signals to be amplified. Raman pumping requires relatively high pump powers; approximately a few hundred milliwatts are needed to provide gains of 10-15dB in commonly deployed transmission fibers. Early Raman pump units were based

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on high-power, double-clad fiber lasers pumping cascaded Raman fiber resonators. Due to their cost, these units were used primarily for specialized applications such as repeaterless transmission. However, the recent availability of pumps with adequate power has made the deployment of Raman amplification in commercial transmission systems possible. The units most likely to see widespread deployment will use multiplexed, single-transverse mode 14xxs-nm semiconductor pump diodes, i.e., diodes with various wavelengths within several 10s of nm of 1450nm depending on the range of signal wavelengths to be amplified. The technology for 14xx-nm diode lasers used in such pump modules is similar to that for 1480-nmpumps used to pump erbium-doped fiber amplifiers, and there has been dramatic progress in the technology of such pumps during the last decade. Presently 14xx-pumpdiodes are available with pump powers exceeding200 mW of fiberpigtailed power, and vendors are working on development of diodes with even higher power. These diodes are suitable for use in modules that employ several such diodes multiplexed in both polarization and wavelength. Multiplexing multiple pumps delivers greater Raman pump powers than possible from a single diode. In addition, multiplexingin polarization minimizes polarizationdependent Raman gain, whilst using pumps at different wavelengths broadens and flattens the Raman spectral-gain profile (Emori and Namiki 1999). For Raman-enhanced systemswith very wide optical bandwidth, for examplethose employing both the C- and L-bands, the Raman pumps must employ multiple pump wavelengths to deliver flat gain over a bandwidth of 70nm or more, and the various pump wavelengths and powers must be carefully selected to take into account not only the Raman gain spectra produced by the various wavelengths,but also the Raman interactions among the various Raman pump wavelengths as they propagate down the fiber. The distributed Raman gain induced in the fiber can dramatically improve the OSNR. This is because the distributed Raman amplification overcomes the attenuation in the latter part of the span and the minimum signal power is increased roughly by the loss of the fiber over that portion of the span where the Raman amplification exceeds the fiber attenuation as shown in Fig. 5.3. This improvement in performance is typically represented by an “equivalent”noise figure,which is the noise figure of a hypothetical lumped amplifier located at the end of the span that would produce the same gain and the same contribution to the accumulated ASE. The equivalent noise figure for a counter-pumped distributed Raman pump is:

zy

zyxw zyx zyxwvu %-

zyxwvu zyxwvu zyxw

2

(5.3)

In GR

where NFeqis the equivalent noise figure in linear units, GRis the Raman gain in linear units at the signal wavelength, asis the fiber attenuation at the signal

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wavelength, and olP is the attenuation at the Raman pump wavelength. The approximation for NF,, holds for large gain G >> 1 and in the approximation that as x 9. Figure 5.4b shows the measured gain and effective NF from a Raman pump with a single pump wavelength. The figure also shows the a m rate agreement obtained with simulated performance using a model of pump propagation and distributed Raman gain. Wavelength multiplexing pumps of different wavelengths are often used in commercial practice to produce a broader and flatter gain profile. The theoretical limit, often termed the quantum limit, to the noise figure of a discrete optical amplifier located at the end of the span is 3 dB, and the noise figures of commercialEDFAs are typically a few dB higher. If the gain of a distributed Raman amplifier is, for example, 15dB or approximately 30 in linear units, then the equivalent noise figure is approximately 0.7, or -1.5 dB, an improvementof 6 dB or more over a discrete EDFA. This is possible because the equivalent noise figure is referenced to the end of the span. However, the distributed Raman amplifier is not actually located at the end of the span, but provides distributed amplification over an appreciable part of the preceding fiber span. Thus distributed Raman amplification delivers a substantial improvement in OSNR as illustrated in Fig. 5.5. At gains above 20dB, the improvement in noise figure is significantly degraded by the onset of Rayleigh scattering, which places an upper limit on the usable Raman gain (Hansen et al. 1997). Because of the logarithmic dependence of NF,, on GR, the Raman noise figure is not significantly impacted by this limit. However, it does mean that the gain available from a distributed Raman amplifier is insufficient to compensate fully the loss of a typical terrestrial transmission span. This is all the more so when the extra loss of dispersion compensation and possible adddrop multiplexing are included.

Raman On

I a

distance [km] Raman-Signal WDM

3 Raman Pump

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.

1530

.

.

1540

-

1-2

1550

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wavelength [nm]

Fig. 5.4 (a) Raman amplification showing evolution of signal gain. The distributed gain provides improvement in OSNR. (b) Spectral gain and equivalent noise figure (NF) obtained with Raman pump. Experimental data (solid line) agrees closely with simulated results (dotted).

5. High-Capacity, Ultra-Long-Haul Networks

0

5

207

zy

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10 15 Distributed Raman Gain (dB)

20

Fig. 5.5 Discrete EDFA quantum-limited noise figure compared to equivalent noise figure for distributed Raman amplification.

Thus in commercial systems, it is most common to follow a backward-pumped distributed Raman amplifier with a relatively low-gain EDFA. The noise figure of the hybrid Raman-EDFA combination is determined primarily by that of the distributed Raman amplifier because of the higher power it delivers to the input of the EDFA, hence the additional noise is negligible. The improvement in OSNR performance offered by Raman amplification can be used to improve systemperformance in a number of ways. First, Raman amplification can be used to extend the reach of an unregenerated link. Referring to Fig. 5.3, if the span losses and channel launch powers are kept constant and the link length is limited by ASE accumulation, and if the Raman amplification delivers 6 dB improvement in OSNR, it will be possible to quadruple the length of the link. Alternatively,if the number of spans is kept constant, it will be possible to increase the span loss by about 6 dB, which would correspond to about 25-30% of a typical terrestrial span. For fiber networks with relatively short hut spacings, distributed Raman amplification may make it possible to skip huts and totally eliminate amplifier sites that would be necessary for systems relying only on EDFAs or other discrete amplifiers. This represents a substantial savings to carriers, both in terms of equipment costs and in terms of the costs associated with maintaining the site where the amplifier would have been located. Raman amplification can also assist systems that employ channels closely spaced in wavelength. With closely spaced channels, the nonlinear interactions among the channels, particularly four-wave mixing and cross-phase modulation, become more severe. With distributed Raman amplification it is

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possible to reduce launched channel powers in order to mitigate the nonlinear interactions while maintaining the link‘s OSNR performance. CounterpropagatingRaman pumping is preferred to copropagatingRaman pumping, as this reduces the transfer of pump noise to the signal, as well as pump mediated cross-talk between the signals. Further improvements in OSNR may also be possible through the use of copropagating Raman amplification, and the development of Raman pump sources suitable for copumped distributed Raman amplifiers is an area of active research. The use of second-orderRaman pumping in conjunction with first-order counterpumping (Rottwitt et al. 2000; Dominic et al. 2001) has been proposed, as has the use of low-noise pump sources with a low degree of polarization (Dominic et al. 2001b).

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C. FORWARD ERROR CORRECTION An additional way of improving the system bit error rate without requiring an increase in the OSNR, is by making use of forward error correcting (FEC) codes. With FEC, extra bits are appended to the data by the FEC encoder at the transmitter. These extra bits help the FEC decoder at the receiver to detect and correct bits that become corrupted through transmission. Consequently, FEC enables the system to operate at a far lower received OSNR than would be possible without FEC, whilst maintaining an acceptable BER. The system’s target OSNR can be correspondingly reduced, which makes extended transmission distances possible. The strength of the FEC in correctingerrors is characterized in terms of the coding gain, which is the difference in the OSNR at which the system operates with a specified bit error rate (BER) without and with FEC. The coding gain is usually defined at the system’s target BER, for example for many 10-Gb/s-based and 40-Gbh-based terrestrial systems. The serial addition of the extra bits with FEC increases the bit rate. There are penalties associated with the expanded serial bit rate of FEC-encoded signals. To maintain the same noise performance, the required OSNR increases by the ratio of the rate expansion, for example a 7% rate expansion requires a 0.3 dB increase in OSNR. Thus the coding gain is often quoted as a Net Equivalent Coding Gain, which is obtained by subtracting the linear noise penalty associated with the expanded serial rate from the raw coding gain. In addition, higher transmission rates may, depending on the channel bit rate and the system design, entail greater transmission penalties from nonlinearities, dispersion, and PMD, and from limitations in transmitters and receivers. The higher bandwidth components required for the expanded rate may also be more expensive. Typically, for a given type of error correcting code, the stronger the FEC coding gain, the higher this overhead will be, but the better the FEC will be at correcting a severely corrupted signal. The most advantageousFEC encoding is that which requires the least rate expansion and delivers the greatest coding gain.

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In fact, coding schemes have been found and implemented commercially that deliver very substantial coding gains with acceptable overhead. FEC is typically implemented on one or more integrated circuits specially designed for this purpose. Beyond the rate expansion and the coding gain, the complexity of the encoding algorithm and the feasibility of implementing it on an integrated circuit (IC) are critical considerations in designing a FEC code for ultra-long-haul systems. Some commercial optical communications systems placed the extra bits in the SONET overhead. This has the advantage that the aggregate bit rate transmitted is not increased, but the available overhead rate is relatively small and the FEC coding gain is correspondingly weak. In so-called “out of band of band” FEC, the serial bit rate carried on a wavelength is expanded above the rate required to carry the data. The most widely used FEC code is the ITU G.975 standard (ITU 1999), which is a Reed-Solomon (255,239). The RS(255,239) code increases the bit rate by 7%, from 9.95 Gb/s to 10.66Gb/s, but is able to correct a BER of IO-’ down to a BER below lo-’’, corresponding to a coding gain of approximately 6 dB. This code was first adopted for commercial undersea systems where it was widely used. Single-chip codecs capable of providing G.975 FEC for terrestrial systems are now offered for OC-192 lO-Gb/s transmission by a number of commercial vendors of telecommunications ICs, and codecs for 4O-Gb/s OC-768 transmission are currently under development. The ability to reduce OSNR requirements by up to 6 dB has a dramatic impact on system capabilities similar to that delivered by the OSNR improvement achieved with distributed Raman amplification. In a system limited by noise accumulation and not by transmission impairments, 6 dB of coding gain results in a quadrupling in the length of an unregenerated link. Advanced FEC schemes that deliver even greater coding gain will be critically important for future ultra-long-haul systems, and are the object of a great deal of work by equipment manufacturers and companies specializing in integrated circuits for the telecommunications industry. The most straightforward improvement would be to use a stronger Reed-Solomon code, and Kidorf et al. (2000) have reported a further 1.2dB increase in coding gain for a RS (255,223) code, but at the cost of increasing the rate expansion from 7% for the G.975 RS code to 14% for the RS(255,223) code. More powerful FEC schemes can be designed by using other coding approaches. Concatenated FEC codes use two FEC codes, an inner code and an outer code, and at the transmitter the data is sequentially encoded with the outer code and then the inner code, and at the receiver sequentially decoded with the inner code and then the outer code. Concatenated codes can significantly increase the coding gain, but at the cost of greater complexity and, in many cases, greater rate expansion to support the FEC overhead. Ait et al. (1999) proposed concatenation of the RS(255,223) with the RS(255,239) code, which provides an additional 2 dB of coding gain relative to the RS(255,239) code alone with a rate expansion of about 25%. This approach, based as it is

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on concatenation of the already commerciallydeployed Reed-Solomoncodes, appears very attractive. PUCet al. (1999) reported use of a Reed Solomon (255,239) code concatenated with a soft-decision Viterbi convolutionalcode to produce a net coding gain of 10dB. However, this coding scheme requires an overhead of 113% or an expanded rate 2.13 times greater than the rate of the payload data. For high-speed fiber-optics systems where rate expansion entails not only proportionatelygreater OSNR requirements for an ideal receiver, but also more severe nonlinear transmission impairments and bandwidth limitations of optoelectronic components, such dramatic rate expansion is likely not practical. Sab and Lemaire (2001) have reported results of the performance calculated for a block turbo-code, which is an interative, soft-decision code. This code should deliver a net coding gain of 10dB with a more feasible rate expansion of 28%, but its implementation is likely to be complex. Keeton et al. (2001) have proposed the use of BCH both in conjunction with Reed-Solomoncodes in a concatenated scheme and for even greater coding gain in a two-dimensional product code. In the product code the data are encoded with the BCH code in each dimension of a two-dimensional array. The product code can be decoded iteratively by iterating alternately on the product code in each dimension, resulting in higher coding gain while materially increasing the overhead. Simulated results for these schemes indicate that they offer high net coding gain with modest rate expansion. Figure 5.6 shows

zyxwvut 3

4

5

6

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8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Q factor per information bit (dB)

Fig. 5.6 Simulated coding gains for three coding schemes: a RS(255,239) code, a BCH(239,223)-RS(255,239)concatenated code, and a BCH(255,239) product code. In each case the raw coding gain (dotted curve) and the Net Equivalent Coding Gain (solid curve) are shown. (From Keeton et al. 2001.)

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the simulated results for three coding schemes, the widely used G.975 ReedSolomon (255,239) coding scheme, concatenated FEC with a BCH(239,223) code and an RS(255,239) code, and finally a BCH(255,239) product code. In each case the raw coding gain and the Net Equivalent Coding Gain are shown as a function of the Q-factor per information bit, which scales dB for dB as the OSNR in a noise limited system. The RS(255,239) code has a raw gain and a NECG of 6.1 dB with a rate expansion of of 6.4dB at a BER of 6.7%. The BCH(239,223)-RS(225,239) concatenated code has a raw coding gain of 8.5dB and a NECG of 7.9dB with a rate expansion of 14.3%. The BCH(255,239) product code has a rate expansion only slightly greater, 14.7%, but has a raw coding gain of 10.1 dB and NECG of 9.5 dB. For 4O-Gb/s transmission, FEC will be even more critical because of the extremelyhigh OSNR that would otherwise be required at the receiver. Because the transmission penalties and transceiver penalties increase dramatically with bit rate at this very high transmission rate, there will be much more pressure to deliver greater coding gain with less rate expansion. FEC with 7% overhead will be used in long-haul and ultra-long-haul applications, but any additional rate expansion may not be attractive at 40 Gb/s.

D. P O n R MANAGEMENT

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A major limitation in long transmission systems is the deviation in power amongst the channels that results from the accumulation of optical amplifier gain nonuniformities. This impacts the system in two ways: those channels that decrease in power sufTer a penalty from reduced OSNR, while those channels that increase in power may degrade due to fiber nonlinearity. Figure 5 . 7 ~ input Spectrum

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illustrates the impact that a 0.8 dB EDFA gain ripple has on a flat input spectrum after only five spans. There is significant variation in both the output power and OSNR of the channels. Consequently, there will be substantial variation in error rate among the channels. For systems with sufliciently few concatenated optical amplifiers(or sufficientlyflat amplifiers)resultingin accumulated ripple less than about 10 dB, the effect of accumulated gain ripple can be successfully managed by pre-emphasizing the input spectrum to obtain an equal OSNR for all the channels at the output (Chraplyvy et al. 1993), as illustrated in Fig. 5.7b. This is done by redistributing the power at the booster amplifier among the various channels so that the total launched output power is still constant, but the OSNR at the end of the system is uniform among the channels. This improves the OSNR of the worst channels and helps to achieve uniform performance across the band. As the system must deliver error-free performance in all channels, it is the channel with the lowest OSNR that will impose the noise limit on the system’s engineering rules. The case illustrated, with only five spans and fairly flat amplifiers, is mild compared to a conventional long-haul system with six to eight spans and with greater gain ripple per amplifier. As the number of cascaded amplifiers increases, the required preemphasis needs to be much stronger; the OSNR before pre-emphasis of the weakest channel will be much lower than the average. The OSNR of the preemphasized channels will then represent a much more dramatic improvement in overall system performance. Due to the large number of cascaded amplifiers present in ultra-long-haul systems, the accumulation of gain ripple generally will be so great that it cannot be adequately managed with pre-emphasis. It then becomes necessary to reset the channel powers to desired levels at periodic sites along the link, as illustrated in Fig. 5.2. This can be done by demultiplexing the channels and adjusting the power of each individually and then multiplexing them again to continue on their way. Alternatively,the wavelengthscould be divided in bands, and the powers of the various bands could be balanced. This approach would be less expensive and more compact, but for high-capacity systems with close channel spacing, it will be necessaryto sacrifice some wavelengthchannels, and the systemcapacity will be correspondinglyreduced because filtering the bands with adequate cross-talk rejection in the demultiplexing and remultiplexing filters requires guard bands between the signal bands. Furthermore, if the bands are too wide, then the gain ripple within a band may exceed the range that can be corrected by transmitter pre-emphasis, and system performance would suffer. Alternatively, if the bands are too narrow, much of the available bandwidth would be eaten up by the guard bands, resulting in significantly reduced system capacity. An ideal device for maintaining the power balance among channels in ultra-long-haul systems would be a reconfigurablegain flatteningfilter (GFF). A reconfigurable GFF can be adjusted to compensate for the accumulated gain nonuniformity from the previous spans. Several different technologies

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are currently being investigated and developed for implementing reconfigurable GFFs, including silica waveguide arrays (Doerr et al. 1999), MEMs (Ford et al. 1998), liquid crystal spatial light modulators and acousto-optic tunable filters (Kim et al. 1998). Ultimately, simple and low-cost reconfigurable GFFs may find a place in every optical amplifier. This would ensure optimum amplifier gain flatness and assist the manufacturer in eliminating the wide range of fixed GFFs that become necessary for producing different amplifier designs. While the cost and size of the first devices preclude their use in every amplifier, they are attractive for periodic use in ultra-long-haul systems. For DWDM systems with high channel counts and broad optical bandwidth, Stimulated Raman Scattering (SRS), an optical nonlinear interaction among the signal channels, transfers power from short-wavelength channels to long-wavelength channels, thereby inducing a tilt in the power spectrum. Additional tilt is induced in each span, and the tilt grows cumulatively with the number of spans. The magnitude of the tilt induced in each span is proportional to the number of channels, to their launched power and to the optical bandwidth that they occupy (Forghieri et QZ. 1999). As with other nonlinearities, the effects of SRS are reduced if the fiber’s effective area is larger and if the launched signal channel powers are lower. The effects of SRS tilt may be managed along with other sources of power ripple and power tilt by the use of pre-emphasis and periodic filtering. But for high-capacity systems with large total power and wide optical bandwidth, it may be necessary to combat the accumulation of SRS tilt by filtering at each amplifier site. In considering how such systems will actually be deployed in the field, it is important to develop automated procedures to ensure quick and accurate balancing of the channels of the DWDM channels, i.e., to adjust the powers of the individual transmitters and the spectral characteristics of the optical amplifiers and the power equalization sites. Otherwise, turning up the system or adding additional waves to an already operational system will be very time consuming and will also be susceptibleto errors that would degrade the performance of the system. As a 1 dB additional penalty will shorten the reach of a 2500-h,noise-limited system by 500 km,accurate and efficient pre-emphasis and power balancing are essential.

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111. Transmission Impairments In order to realize the reach and the capacity made possible through the OSNR enhancementsmentioned in this chapter, distortions arising from transmission impairments must be limited so that the associated penalties are modest. These penalties are typically accounted for during the system design phase by budgeting an allowance for the associated penalties when the target OSNR is set, and the smaller these penalties are, the further the system reach and/or the

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higher its capacity. One of the objects in the design of high-capacity, ultralong-haul systems is to minimize the impact of these penalties on the target OSNR and to ensure that the penalties for these impairments do not exceed their allocated penalties.

A. CHROMATICDISPERSION AND OPTICAL NONLINEARITIES

Chromatic dispersion results from the dependence of the optical fiber’s index of refraction on optical wavelength and is the most important source of distortion of high-speed signals. As a result of chromatic dispersion, different frequencies of light travel at different speeds. For on-off keyed data transmission, where data 1s and Os are represented by the presence and absence of light, respectively, the pulses representing 1s contain a range of frequencies, and chromaticdispersion causes the pulses to spread as they propagate. Signal pulses correspondingto 1swill spread into the time slots for adjacent bits leading to the generation of bit errors when the distorted data trains are detected after transmission. The dispersion length LD, corresponding to the distance after which a pulse has broadened by one bit interval, is: 1

whereB is the bit rate, D is the dispersion, and AA is the spectralwidth of a pulse (Gnauck 1997).This length, which provides an estimate of the limit chromatic dispersion imposes on the length signals can be transmitted, is shorter when the bit rate is higher, when the dispersion is greater, or when the spectral width of the signal is greater. For high bit-rate long-haul transmission, external modulation of continuous wave diode lasers is used in preference to direct modulation of diode lasers because of the narrower spectrum that results. For signals produced by external modulation, the spectral width approximatesthe bit rate, B. The dispersion limit is then:

zyxwv zyxwvu zyxwvu 105 LD X D*B2’

(5.5)

where LD is in km,D is in ps/nm. km,and B is Gb/s. The precise limit depends on the details of the modulation format and the design of the receiver circuitry, but Eq. 5.5 provides a reasonable approximation. The dispersion limit for externally modulated signals is inversely proportional to the square of the bit rate; for lO-Gb/s OC-192 signals on standard single mode fiber (SMF) with a dispersion of 17ps/nm km,it is about 60 km, corresponding to a residual dispersion of about 1000ps/nm, and for 4O-Gb/s OC-768 signals, it is less than 4 km, correspondingto about 60 pdnm. These lengths are a great deal shorter than the link lengths permitted by noise accumulation, and techniques to compensate and manage the dispersion are essential for high-capacity, ultralong-haul transmission.

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Two complementaryapproaches are used to manage the fiber chromaticdispersion: design of transmission fiber to reduce dispersion in the signal bands in the 1500-1600nm spectral region, and the use of dispersion compensation to provide negative dispersion to compensate the accumulated positive dispersion of transmission fiber. In a system with no nonlinear effects, transmission fibers designed to have no chromatic dispersion at about 1550nm (so-called dispersion shifted fiber, or DSF) could be used, and the small residual dispersion for channels whose wavelengths do not coincide with the zero dispersion wavelength could be compensated at any point in the link, as long as the final residual dispersion at the receiver is less than the dispersion limit. However, in typical high-capacity, ultra-long-haul-systems, it is desirable to launch the highest signal powers possible in order to maximize the OSNR (see Eq. 5.5), but as the launched power increases the impairments resulting from optical nonlinearities become more severe. The optimum launched signal power is therefore determined by the tradeoff between maximizing the launched power to maximize the OSNR and reducing the launch power to mitigate nonlinearities. At the optimal launch power, nonlinearities are sigdicant but not unduly severe, and the BER at the end of the system as a function of launch power is a minimum. In order to design the system with optimized launch power and thus the best system performance, it is not suEcient merely to control the residual dispersion at the end of the system. The local dispersion and the accumulated dispersion at each point along the length of the system are also important. Where dispersion compensation is used, both the amount of dispersion compensation and its placement are also important; if the dispersion map is not properly designed, impairments from nonlinearities will be severe, resulting in stricter limits on the launched channel power. Forghieri et al. (1997) have provided a comprehensivereview of optical nonlinearities and dispersion management. In this chapter we shall focus on some of the aspects that are of particular importance for high-capacity, ultra-longhaul systems. The effects of cross-phasemodulation and self-phasemodulation can be converted into amplitude modulation by chromatic dispersion if the accumulated dispersion is allowed to grow too large before compensation. The dispersion map must be designed so that either the dispersion of the transmission fiber is very low or its dispersion is compensated with sufficient frequency along the route to keep the accumulated dispersion sufficiently low at all points along the link. Against this need for keeping the accumulated dispersion low is the need for local dispersion to be suf€iciently large in order to minimize nonlinear interactions among the channels. Four-wave mixing and cross-phase modulation are especially severe when the local dispersion is low. Only fibers with substantial local dispersion are suitable for most DWDM applications. DSF with zero dispersion near 1550nm is not suitable. Standard single mode fiber (SSMF), which has zero dispersion at 1310nm and a dispersion of 17ps/nm .km at 1550nm (sometimes also called nondispersion shifted fiber,

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or NDSF), is well-suited to DWDM transmission in both the C- and L-bands but residual dispersion accumulates very quickly. Nonzero dispersion shifted fibers (NZDSF) have been designed to support transmission of high-data-rate DWDM channels. The dispersion of NZDSF in the signal band is designed to be large enough to avoid significant impairments from four-wave mixing for practical systems with channel spacing of 50 GHz (about 0.4 nm) or greater (typically about 4 ps/nm .km)but small enough that dispersion accumulates much more slowly with propagation distance than for NDSF. However, even for NZDSF, the dispersion limit is only about 240 km for lO-Gb/s signals at the center of the C-band and about 16km for 40-Gbh signals. In fact, because the dispersion increases with wavelength, for transmission fibers the limit is even lower at the red end of the C-band and in the L-band. Thus, both NDSF and NZDSF require dispersion compensation for both 10-Gb/s and for 4O-Gb/s signal channels, but for NDSF much more is needed. For transmission over more than a few spans in systems where the channels cover a broad spectral range, careful attention must be given to matching the dispersion slope, defined as the derivative of dispersion D with respect to the wavelength, so that an acceptable dispersion map can be provided for all channels across the channel band. This requires matching the relative dispersion slope (i.e., RDS, the ratio of the dispersion slope to the dispersion) of the transmission fiber and the dispersion compensation. A mismatch in the relative dispersion slope between the transmission fiber and dispersion compensationwill cause a walk-off in the accumulated dispersion that varies across the channel band and increaseswith distance. Consequently, a small group of channels may have good transmission, whereas channels in the remainder of the band perform poorly. Dispersion compensating fiber (DCF) is single mode fiber designed to have a large dispersion opposite in sign to that of the transmission fiber to be compensated, and is the technology most widely used to compensatedispersion. It is generallylocated between the stages of optical amplifiers, which are designed with two amplifyingstagesand accessto the mid-stageregion to accommodate the dispersion compensation and optical add/drop filters. DCF typically has a far lower RDS than transmission fibers This disparity is especially severe for the NZDSF fibers, which have been widely deployed for high-speed DWDM applications. NZDSF fiber designs tend to have a large RDS because of their low absolute dispersion. In recent years there has been a drive to address this problem by reducing the dispersion slope of transmission fibers and increasing it for DCF. The walk-off in accumulated dispersion across the C-band with transmission distance for two different fiber and DCF combinations is illustrated in Fig. 5.8. In these figures the accumulated dispersion is plotted for three wavelengths across the C-band (1530, 1546, and 1562nm) for a system comprising twenty 100-km fiber spans with equal amount of dispersion compensation applied at the end of every span. Figure 5 . 8 ~ shows the accumulated dispersion for TrueWave Classic fiber, an early NZDSF, that has a

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Fig. 5.8 Dispersion maps illustrating the walk-off in accumulated dispersion across the band due to residual dispersion slope. The walk-off is large in case of (a) older TW-classic fiber that had a large slope, but is substantially smaller when using (b) TrueWave Reduced Slope fiber in conjunction with newer DCFs with greater slope. The far smaller walk-off allows the eyes to be recovered across the band.

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high RDS (where D = 2.7 ps/nm/km at 1550nm and S = 0.07 ps/nm2/km) compensated by an older DCF with negligible dispersion slope. The walk-off in accumulated dispersion across the band over 2000 km is 4000 pshm. It is tempting to try and use dispersion management at the end of the link on each channel independently to bring its accumulated dispersion to the optimum. Unfortunately,this works only for channels near the center of the band. This is illustratedby the simulatedeye diagrams for the two channels at the edges of the band that, in addition to the common dispersion compensation at each optical amplifier, have been passed through a dispersion compensating fiber located before the receiver, the length of which is adjusted for optimum performance of that individual channel. The eyes cannot be recovered because the impact from fiber nonlinearity on the signals while they are substantially dispersed

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cannot be undone using dispersion compensation at the end. This result is expected as the effects of dispersion and nonlinearity are not commutative. Figure 5.8b plots the accumulated dispersion for a similar system with TrueWave RS fiber that has a much lower dispersion slope (where D = 4.4ps/nm/km at 1550nm and S = 0.045ps/nm2/km) compensated by a newer DCF having RDS S / D = 0.0067 ps/nm. Here the walk-off in accumulated dispersion has been reduced to around 1100ps/nm. In this case, by using appropriate per-channel dispersionadjustment of the channels at the end of the link, the eyes can be recovered across the band. With further improvements in slope-matched dispersion compensation, the need for end-of-the-system, per-channel dispersion adjustment can be minimized or even avoided. The design of single mode DCF with sufficiently high dispersion slope to match that of NZDSFs is the object of intense work and is progressing rapidly. Single mode DCFs have been reported for two of the most widely deployed NZDSF fiber designs (Srikant 2001; Quang Le et al. 2001). However, the design and manufacturing of single mode DCFs with sufficientlyhigh relative dispersion slope to match the NZDSFs with the highest relative dispersion is quite challenging and, at this writing, commercial single mode DCF solutions are not yet generally available for some of the widely deployed varieties of NZDSF with high dispersion slope. Because of the importance of slope-matched dispersion compensation for ultra-long-haul systems at 10 Gb/s, and even more so at 40 Gb/s, other technologies to provide slope-matched dispersion compensation for NZDSF have been proposed. One possible alternative technology that can provide high negative dispersion slopes is higher-order mode dispersion compensation, first proposed in 1993 (Poole et al.) and presently the subject of revived interest to meet the need for slope-matched dispersion compensation for NZDSF (Gnauck et al. 2000; Ramachandran 2000). These are wideband devices that work across the C- or L-band. Signalsare passed through amode converter and transformed into a higher mode that propagates through a length of specially designed higher-order mode fiber that has negative dispersion and high RDS for this transmitted mode. A second converter at the output end transforms the signals back to single mode to continue down the link. In addition to the possibility of higher relative dispersion slope, higher-order mode dispersion compensation also offers the possibility of lower losses and, because of the larger effective area of the higher-order mode fiber, reduced nonlinear impairments compared to single mode DCFs. The Virtually Imaged Phased Array (VIPA), another potential technology for slope-matched dispersion compensation for NZDSFs with high relative dispersion slope, is a resonant device. It works for a prescribed comb of wavelengths, and is thus more limited for use in wide optical bandwidth applications than single mode DCF or higher-order mode dispersion compensators (Ishikawa and Ooi 1998; Shirasaki and Cao 2001). Because it is based on bulk optics, the VIPA will avoid the nonlinear effects that are produced in single mode DCFs.

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Without dispersion compensating modules that adequately match the dispersion slope of transmission fiber, or to the extent that slope matching is imperfect, it may be necessary to perform dispersion slope equalization at periodic sites along the link (Zyskind et al. 2000), as shown in Fig. 5.2. This can be done either on a per-channel basis, which is expensive, bulky, and difficult to manage, or it can be done on groups of channels or bands (Haxell et al. 2000). As with power balancing by bands, the use of bands is less attractive than broadband slope-matched dispersion compensation because elaborate filtering arrangements are required for compensation by band. Such band filtering entails a reduction in system capacity because of the necessity for dead bands in which no channels can be supported and because, compared to use of broadband slope-matched dispersion compensation, it is more expensive, complex, and bulky. Nondispersion shifted single mode fiber has larger dispersion than NZDSF, and thus requires longer lengths of dispersion compensating fiber, which have higher loss. But the RDS of NDSF is smaller than that of NZDSF, and NDSF is the transmission fiber for which commercially available DCFs provide the best slope compensation. NDSF also has the largest effective area, which permits higher launched signal powers and the largest local dispersion, which tends to minimize interchannel nonlinear effects, particularly four-wave mixing. For 40-Gbls transmission where residual dispersion must be much smaller than for 10-Gbls, additional trimming will be required to compensate for imperfect dispersion slope compensation and for variations of dispersion arising from temperature variations experienced by transmissionfiber over the link (Kato 2000). Tunable dispersion compensation on a per-channel basis will be able to provide the required slope trimming, as well as adjust for temporal variations. Tunable dispersion compensationmay also be required for dynamically reconfigurable networks to compensate for differences in cumulative dispersion a wavelength channel will experience when its path through the network is changed. Component suppliers are now working on developing such devices (see Eggleton 2001 for a review of work on tunable dispersion compensation) using a variety of approaches. Tunable dispersion compensation has been reported for dispersion compensating chirped-fiber Bragg gratings controlled by temperature or strain tuning (Eggleton 1999; Eggleton 2000; Willner 1999; Fells 2000); integrated all-pass filters (Madsen 1999; Horst 2000), which are planar deviGes based on ring resonators; and the virtually imaged phased array devices (Shirasaki 2000), which as described previously, are bulk optic devices based on resonant multipath reflections. The ideal fiber span would have high local dispersion to mitigate nonlinearities, but would have accumulated dispersion that is small and equal to the value for optimal transmission performance (depending on the modulation format). It has been proposed to create such spans by combining fibers having large positive dispersion with fibers having large negative dispersion (Reverse

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Dispersion Fibers, RDF) in the same span. The positive dispersion fibers typically have a large effective area-wbich reduces optical nonlinearities-and small RDS, so as to facilitate matching of dispersion slope of the positive dispersion and reverse dispersion fibers. Such fiber spans would obviate the need for additional dispersion compensation at the amplifier sites In addition to the direct cost savings of dispensing with dispersion compensation, such fiber spans would be more suitable than currently deployed fiber networks for all Raman systems in which only distributed Raman amplifiers are used. Without the need to compensate the loss of dispersion compensation at amplifier sites, it would be more practical to compensate the fiber span loss with distributed Raman amplification, which would improve OSNR performance, reduce costs, as well as reduce the power transients that accompany changes in channel loading in EDFAs. Such fiber spans would also be well adapted to support dispersion-managedsoliton transmission. Such dispersion-managed spans are currently used for undersea systems where the fiber spans and the system equipment are designed together, and each fiber span is the same length. For terrestrial systems with nonuniform spacings between-amplifierhuts, it would be necessary to tailor the lengths of the two fiber types for each individual span to the total length required for that span. Before such networks are deployed it will be necessary to meet these practical engineering challenges in the deployment of such fiber networks. B. POLARIZATION EFFECTS

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Polarization effects arise from three phenomena: polarization-mode dispersion; polarization-dependent loss and polarization-dependent gain; or polarization hole-burning. Polarization-dependent losses and polarization hole-burningare effectsthat become important in systems where signals propagate over long distances through many optical amplifiers and other components. Polarization-mode dispersion (PMD) becomes increasingly important for higher data rates and the effectgrows with the squareroot of the link length. Polarization-dependent loss (PDL) arises from the fact that the optical components (such as isolators, filters, optical amplifiers,etc.) through which the signals pass have insertion loss that depends on the incident polarization. When the light impinges on a component in a polarization state with relatively less loss, the input power to subsequent optical amplifiers is raised and the OSNR improves. Conversely, when the light impinges on a component with a polarization state with relatively greater loss, the input power to subsequent optical amplifier is lowered and the OSNR is degraded. PDL manifests itself as a statistical impairment because of the random and variable evolution of the polarization state as light propagates over long distances in fiber; the PDL arising from each of many components is a random variable that varies with time. PDL is controlled in long systems by requiring that the PDL is small for

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all components in the signal path. Components with sufficientlylow PDL for terrestrial ultra-long-haul applications are commercially available. Polarization-dependentgain (PDG) or polarization hole-burning(PHB) in the optical amplifiers arises from inhomogeneity in the saturation characteristics of the gain. Polarization hole-burning arises from the greater saturation experienced by erbium ions oriented so as to be preferentially saturated by light with the polarization of the signal. The result in a system with a long chain of optical amplifiers is that a strong saturating signal experiences more severe gain saturation than ASE with the orthogonal polarization because the signal always interacts most strongly with precisely those ions that will not be as deeply saturated for the polarization state that is orthogonal to that of the signal. This effect, unlike PDL, is deterministic, and the orthogonal ASE steals power from the signal at each optical amplifier as the signals propagate down the amplifier chain. But PHB is very weak, therefore it is only a problem for very long chains of amplifiers, such as are used in submarine systems. In addition, for DWDM systems with multiple channels, the polarization states of the differentwavelengthchannels are independent and their PHB contributions cancel each other. PDG also arises from the relative orientation of the pump light and the signal light. The system behavior of pump-induced PDG is similar to PDL, but, like PHB, it is very weak and in multistage EDFAs with multiple pumps the PDG tends to get washed out. Polarization-mode dispersion (PMD) is the most important polarization effect for high-capacity, ultra-long-haul systems with high bit-rate channels. PMD arises from the birefringence in the fiber that gives rise to differential group delay between the two principal states of polarization. PMD is manifest as a time varying and statistical pulse broadening and pulse distortion because the perturbations to the fiber symmetry that give rise to the birefringence vary randomly in orientation along the fiber and are also dependent on environmental variations, particularly temperature. For lengths of fiber longer than the correlation length for the birefringence, which is generally the case for a fiber span, PMD is characterized in terms of the differential group delay (DGD) between the two principal states of polarization after a given length of fiber. Because of the statistical nature of PMD, the differential group delay increases with the square root of the length of the fiber and is expressed in units of p s / G . The PMD of a fiber span is typically specified in terms of a mean PMD, which is the average over time of its net DGD. The statistical distribution of DGD about this mean is determined by the physics of PMD and follows a Maxwellian distribution. Because of its statistical nature, the possibility of errors arising from PMD can never be totally eliminated, but the probability of an outage, defined as the probability of a penalty greater than the OSNR margin assigned to PMD, can be calculated from the mean PMD and its statistical distribution. In practice, a given amount of margin is allocated to PMD impairments, and the probability of an outage is defined as the probability that the instantaneous

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DGD will exceed that value that induces a penalty equal to this margin allocation. When the DGD exceeds this value, the possibility of PMD-induced bit errors at the end of the system cannot be excluded. For modest DGD, the penalty due to PMD goes up quadratically with both the bit rate and with the DGD (Poole and Nagel 1997). This means that the acceptable mean PMD is inversely related to the bit rate, but that as the instantaneous PMD increases above the acceptable level, the penalty increases rapidly. It follows that the acceptable mean differential group delay is proportional to the bit period and is generally of the order of 10-15% of a bit period depending on the modulation format and other detailsof the systemdesign and the permitted outage probability (Poole and Nagel 1997). In addition to DGD, or first-order PMD, second-order PMD must be considered when the PMD varies over the bandwidth of the source. Components of higher-order PMD tends to increase as first-order PMD increases (Shtengel et al. 2001), therefore higher-order PMD becomes relatively more important when the PMD is larger, and in fact becomes dominant for 10Gb/s per second above about 20 ps of mean PMD (Taga et al. 1998). For recently manufacturedfiber with a mean PMD of 0.125 ps/& or less (Noutsias and Poirier 2001), PMD is not an obstacle to ultra-long-haultransmission at 10Gb/s. However, for older fiber where PMD can be significantly larger or for 4O-Gb/s ultra-long-haultransmission,PMD can limit the reach of a system. For IO-Gb/s ultra-long-haul transmission on older vintage fiber and for 40-Gb/s ultra-long-haul transmission over a wide range of fibers, PMD compensation will be necessary. Because of the importance of higher-order PMD for larger PMD where compensation is needed, it is likely compensation of second-order PMD, in addition to fist-order PMD, will be necessary in a useful compensator. The development of optical and electrical components to counteract the PMD is an area of active research and commercial development. See Penninckx and Lanne (2001) for a recent review.

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C. MODULATIONFOR2MAT The modulation format is also an important consideration in the design of ultra-long-haul systems. The most commonly used format in long haul optical communications is Nonreturn to Zero (NRZ) modulation, in which 1s are represented as rectangular pulses occupying the full bit period and Os by the absence of a pulse. N R Z pulses are normally formed either by directly modulating a semiconductor laser (for DWDM transmission generally a single longitudinal mode Distributed Feedback Laser) to turn its power on for a data “1” and off for a “0,” or by using a continuous wave semiconductor laser followed by an external modulator (or sometimes by an integrated modulator on the same semiconductor chip with the diode laser) passing the laser’s optical power for a “1” and blocking it for a “0.”

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In high bit rate (2.5 Gb/s per channel or greater), long-haul transmission, it is necessary to use external modulation. Direct modulation of semiconductor lasers induces chirping, and the associated spectral broadening entails unacceptable dispersion penalties, as can be seen by reference to Eq. 5.4. External modulators for IO-Gb/s applications are commercially available and widely deployed. The two most widespread technologies are electro-optically controlled Mach-Zehnder interferometers fabricated in LiNbO3 and electroabsorption modulators fabricated in semiconductor-based devices. In fact, a modest amount of chirp of the proper sign (a chup parameter of approximately -0.7) results in improvement in performance because dispersion initially acts to narrow the c h q e d pulse (Agrawal 1992). LiNb03-based Mach-Zehnder modulators are commercially available that can provide properly prechirped NRZpulses. Return to Zero (RZ) modulation uses pulses that are substantially narrower than a bit period to represent “ls,” so even for consecutive “1s” the power level returns to zero between successive pulses. For practical receiver designs, RZ modulation results in receiver performance superior to that for NRZ modulation by 1 to 2 dB (Boivin and Pendock 1999). With RZ modulation, systems can also be designed to be more robust against impairments such as self-phase modulation and polarization mode dispersion (Taga et al. 1998; Sunnerud et al. 2001). In fact, if the dispersion map and signal powers are appropriately managed and the input pulse is properly shaped to produce solitons (Mollenauer 1997) or dispersion managed solitons (Suzuki et al. 1995; Smith et al. 1997; Cao and Yu 2001) the effects of dispersion and self-phase modulation can be held in balance. In this case, pulse spreading induced by dispersion is balanced by pulse narrowing induced by self-phase modulation so that, in the case of classical solitons, the pulse shape is maintained for transmission over arbitrary distance, or so that, in the case of dispersion managed solitons, it returns to the same shape at the end of each span for an arbitrary number of spans. Carrier-suppressed RZ (Miyamoto et al. 1999; 2001) and chirped RZ (Bergano et al. 1997) modulation have also been proposed as modulation formats to further mitigate nonlinear interactions. Although RZ modulation offers improved performance, transmitters for RZ modulation are more complex and expensive than those for NRZ modulation. Generally, two modulation stages are required, one to form the pulses and a second to modulate the pulses to imprint the data on the signals. For example, whereas NRZ modulation can be implemented with a single LiNbO3 Mach-Zehnder modulator, RZ modulation requires either two separatemodulators or a two-stagemodulator. For dispersion-managedsoliton transmission, the dispersion map must generally be controlled more tightly than for NRZ transmission, which can pose a practical challenge for commercial systems deployed on carriers’ actual fiber networks with highly variable amplifier-hut separations.

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IV. Optical Networking

A. CHANGING NETWORK NEEDS

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The 1990s marked tremendous advances in optical networking. In particular, the 1990s saw the widespread deployment of SONET systems. SONET, or Synchronous Optical Networking, was a tremendous step forward for the public telecommunications network infrastructure over the preceding plesiosynchronoussystem, enabling networks to be built that provided switching granularity (down to a voice call), scalability (up to 40 Gb/s or beyond), and high availability though the use of automatic protection switching (APS) and ring-based restoration. In addition, the 1990ssaw the widespread deployment of point-to-point DWDM systems used for fiber multiplication. By the end of the 199Os, most major public telecommunicationsnetworks were primarily built by stacking SONET rings on top of one another through the use of DWDM. The 1990s also saw an explosion in data traffic driven by both corporate and public demands. IP, driven by the Internet, corporate requirements, and the World Wide Web, became the dominant data networking technology by the end of the 1990s. The dominatingtrend of IP is continuing, with most technologists agreeing that IP will within the next 10 years become the technology of choice to carry all traffic, including voice. As IP traffic grew, IP routers grew in size, speed, and complexity, which drove fundamental changes in the way backbone IP and optical networks were constructed. At first, data growth helped spur the deployment of WDM as more and more SONET rings were stacked. However, as the speed of the backbone router ports increased, the core network evolved from a highly layered one (e.g., IP over Frame Relay over ATM over SONET over DWDM) to a flat IP-over-wavelength architecture. The latter architecture, also known as an IP-over-glass architecture,was motivated, enabled, and in a large sense required when IP router ports started to run at the speed of a wavelength (first OC-48c, now OC-l92c, and moving to OC-768c). So dramatic was the failure of SONET rings to respond to the high-speed service requirements on IP, that many backbone networks had bifurcated by early 2000, with the SONET network providing voice and lower-speed services, and the WDM network providing wavelengths to the IP layer, SONET layer, ATM layer, and for sale to external customers as “transparentunprotectedwavelength services.”These customers in turn used these wavelengths to construct their IP, SONET, and ATM networks. In summary, the core of the public network infrastructure is changing for three fundamental reasons. First, the service requirements are changing from voice to data, electrical to optical, and static to dynamic. Second, the existing SONET-over-WDMinfrastructure is insdlicient to meet those changing requirements. Third, new technologies and architecturesare available to meet the new requirements in a far more economical and scalable fashion. For these

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reasons, the first decade of the new millennium will see the maturation of the second phase of optical networking, the intelligent optical network, beginning with IP over wavelengths as the first step. The rest of this section will discuss the use of ULH transmission as a key enabler of this new architecture.

B. THE VALUE OF ULTRA-LONG-E4UL TRANSMISSION

Data networks are not the same as voice networks. There are many fundamental differences, including the use of packet switching, statistical multiplexing, and the use of both connectionless data transfer and logical connectionoriented data transfer in data networks versus the use of circuit switching, time division multiplexing, and physical-connection-oriented bit transfers in voice networks. There are also fundamentally different traffic and service requirements with data traffic being characteristically distance insensitive, dynamic, and unpredictable, and voice tr&c being characterized as more local, steady, and predictable. For these and other reasons, the SONET ring networks optimized for the voice network are no longer optimal, or even adequate, to continue to build the public data infrastructure. Because of the different traffic requirements, the different underlying technologies, and the different historical evolution of the two technologies (data being an unregulated and relatively new technology), data networks are not planned, engineered, or constructed the same way as voice networks. Two key attributes of an IP backbone are: (1) that it is typically an irregular mesh topology, often evolving in an organic and hard-to-predict fashion; and (2) the trunks of the mesh run at wavelength speeds (OC-48c/OC-192c/OC-768~). The design and optimization of an IP network is a complicated process, but ideally the trunks should be determined from the traffic requirements and not the physical layout of the fiber backbone. In fact, this is currently done with wavelength services criss-crossingthe country interconnectingdistant routers. This enables the construction of flatter IP networks whose topologies are better optimized to the traffic. Such a design has the benefits of using fewer IP router ports (which reduces costs and keeps the routers smaller) and reducing latency. In fact, the construction of long trunks is absolutely critical in the construction of a scalable optical Internet in that the IP layer traffic is essentially off-loaded to the more scalable optical layer. Today, these trunks are constructed with the concatenation of shorterreach WDM systems. For instance, a 5000-km, cross-continental trunk, for example, from New York to Los Angeles, might be required to cross 8-10 or more DWDM systems with a corresponding number of costly optical-toelectrical-to-optical (OEO) conversions along the way. It is the reduction of these intermediate OEO conversions by using optical bypass that saves money, space, and power and leads to a far more economical and manageable network. Optical bypass and long trunks are not only useful in constructing IP networks. In fact, one of the driving forces behind ULH transmission is the move away from an interconnected SONET ring-based architecture to an optical

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mesh network. Similar to an IP network, the optical mesh network topology is optimized by considering the traffic demands, not the physical fiber topology. Whether for express wavelengths for an IP-over-glass architecture, the construction of an optical mesh network, or for more narrow applications, ultra-long-haul transmission can greatly reduce costs by reducing the amount of required OEO conversions in the network. In general, the higher the bandwidth-distance requirements on the traffic, the more motivation there is for optical bypass and ULH transmission.

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C. ALL-OPTICAL NETWORKS'

With the advent of ultra-long-haul transmission, it is now possible to construct IP and optical mesh networks with long express trunks with little or no intermediate OEO conversion. Such a technology has significant architectural implications on building the network, as has already been alluded to. One of these implicationsis the ability to construct all-optical networks. An all-optical network is one in which the signal remains in the optical domain from the source to destination without any conversion to electronics within the network. The primary motivation for an all-optical network is that optics, and not electronics, is the most cost effective way to tap the multi-Tb/s capacity of the optical fiber, i.e., through the use of optical bypass and optical switching nodes. Another motivation is that fiber transparency provides an element of future proofing the network against advances in technology. Two other architectural implications were already discussed: that long express wavelengths enable the construction of flatter IP and optical mesh networks optimized to meet the traffic demands rather than on the physical layout of the fiber. With automation in the all-optical layer, these express trunks can be quickly brought into service and/or reconfigured to meet changing tr&c demands. All-optical networks have been commercialfor some time now, albeit in very limited form; linear and ring systems with intermediate wavelength-selective adddrop are widely deployed in long-haul as well as metropolitan networks. By slotting in a transponder card of the appropriate wavelength, the carrier can route the signal from the source node to the destination node without any conversion to electronics. The technologies that have enabled these static wavelength routing networks are well known and include DFB lasers, LiNbOs modulators, thin filmfilters, fiber Bragg gratings, etc. Tunablelasers and reconfigurable adddrop technologies promise to enable configurable versions of these systems. ULH transmission enables the construction of larger networks, to the point that now linear or ring network topologies are insufficient to realize the full benefit of the transmission capabilities, i.e., the reach exceeds the normal distance between the major backbone junction nodes (a node with

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a fiber-route degree greater than 2; typically 3 4 in a continental U.S. network, or sometimes even higher). Thus, having surpassed the unregenerated reach required to connect junction nodes without intermediate regeneration, carriers can now further reduce OEO conversion cost by building a ULH mesh network optically interconnecting many or all of these junction nodes. These junction nodes may be manually patch-paneled or may contain alloptical switches. The choice of a manual versus automatically configurable node depends on the trade-off between the cost of the optical switches and the benefits of wavelength configuration. In fact, there are more detailed cost trade-offs involving levels of network configuration/automation dependent on such things as the tuning range of the transmitters, and in some cases the tunability of the dispersion compensation. Such trade-offs are complicated and time and business sensitive depending upon such considerations as the dynamic nature of the IP trunks, OXC trunks, or wavelength services, the predictability of such traffic, the potential lost opportunity costs, as well as the operational cost savings of the automatic node over the manual node, to name more than a few.

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ULH and all-optical mesh networks can greatly reduce the OEO conversion cost in the network. However, these cost savingsdo not come without potential drawbacks. First, because of the lack of standards for optical midspan meet, the larger the mesh, the larger the portion of the network built from one vendor. Unlike the o/e/o intelligent optical networking interoperability standards that have been demonstrated several times and that are continuing to be addressed at various industry fora (IETF GMPLS, OIF UNI, ITU G.ASON,ODSI UNI), there is no current or expected activity to standardize the interfaces necessary to support an optical midspan meet. Thus, for the foreseeablefuture, all-optical networks will have to be interconnected through OEO. Second, for a given technology at a certain point in time, the capacity (per lit fiber) of the optical mesh will decrease as the reach of the wavelengths is increased. If the supported capacity is sufficient, then the reduced OEO cost will result in reduced network cost. However, if more capacity is required, extra fibers will have to be lit, increasing the amplifier costs. Thus, infinitely extending reach (toward the goal of one optical hop across the core backbone) at the expense of capacity may or may not be the most cost effective way to build the network. Third, although optical switching is maturing, the level of configuration/ automation in an all-optical junction node is less than in its OEO counterpart. For example, the OEO nodes typically support STS-1 grooming, fully automatic circuit setup, various protection and restoration mechanisms, logical dissociation between the client-side interfaces and the network-side interface/wavelength, client-side APS, rate adaptation (e.g., 10G to 40G),

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conversion of transmission formats such as from NRZ to RZ or from FEC to SuperFEC, wavelength changing, etc. Thus, there is a balance to be made in the core backbone architecture between functionality and cost, and a carrier may choose to make some nodes all OEO, others all or mostly OEO, and others hybrid. For these and other reasons, larger backbone networks will continue to be built from an interconnectionof all-opticalnetworks, or islands. These islands are surrounded by OEO performing regeneration, wavelength changing, rate adaptation, format conversions, etc. These islands not only encompass the traditional static linear point-to-point systems, the emerging ULH meshes, but also newer, short fat-pipe OC-768 systems and future islands using as yet undeveloped technologies. Over time these islands will become larger, support more capacity, and become more sophisticated in their functionality. Future islandswill likely support optical regeneration as well as wavelength changing. Because of the OEO around the islands, multivendor and multitechnology networks are easily constructed. It also allows the use of different technologies in different parts of the network, for example, high-capacity, short fat-pipe systems in shorter distance, high density areas and longer skinnier ultralong-haul pipes in more widely spaced, sparse parts of the network. The use of OEO switches ties this bandwidth together into a complete multivendor multitechnology mesh network.

V. Conclusions Some of the most exciting technological advances in optical communications have made possible dramatically increased reach for high-capacity DWDM systems. The ability to extend high-capacity optical paths to thousands of kilometers between regenerators makes possible dramatic reductions in network cost as well as scalable network architectures, based on increased optical functionality, to support the rapid growth of data-based servies.

Acknowledgments The authors would like to acknowledge useful conversations and fruitful collaborations with our colleagues at Sycamore Networks.

References 0. Ait Sab, “FEC Techniques in Submarine Transmission Systems,” Paper TuF1, Proceedings OFC 2001, OSA, Anaheim, California, 2001. 0. Ait Sab and V. Lemaire, “Block turbo code performances for long-haul DWDM optical transmission systems,” Proceedings of OFC 2000, Baltimore, MD, paper ThS5, pp. 280-282,2000.

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N. Bergano, “Undersea Lightwave Systems Design,” in Optical Fiber Communications IIIA, I. P. Kaminow and T. L. Koch, eds., pp. 302- 335, Academic Press, 1997. N. Bergano, et al., Proceedings OFC 1997, Paper PD16, 1997. L. Boivin and G. Pendock, “Receiver Sensitivity for Optically Amplified R Z Signals with Arbitrary Duty Cycle,” in OpticalAmpliJers and TheirApplications, 1999, Nara, Japan: Paper ThB4, pp. 106-109 (Optical Society of America). X. Cao and Y . Yu, “Ultra Long-Haul DWDM Transmission via Nonlinearity Management,” Optical Amplifiers and Their Applications, OSA Trends in Optics and Photonics, vol. 44, A. Mecozzi, M. Shimizu, and J. L. Zyskind eds., Optical Society of America, Washington DC, 2001, pp. 203-210. A. R. Chraplyvy, J. A. Nagel, and R. W. Tkach, “Equalization in Amplified WDM Lightwave Transmission Systems,” IEEE Photon. Technol. Lett., vol. 4, p. 920, 1992. V. Dominic, A. Mathur, and M. Ziari, “Second-order Distributed Raman Amplification with a High-Power 1370-nm Laser Diode,” in O p t i d Amplijiers and Their Applications, 2001, Stresa, Italy, OMC6 (Optical Society of America). V. Dominc, E. Mao, J. Zhang, B. Fidric, S. Sanders, and D. Mehuys, “Distributed Raman Amplification with Co-PropagatingPump Light,” in O p t i d AmpliJers and Their Applications, 2001, Stresa, Italy, OMC5 (Optical Society of America). C. R. Doerr, et al., “DynamicWavelength Equalizer in Silica Using the Single-FilteredArm Interferometer,”IEEE Photon. Technol.Lett., vol. 11, pp. 581-583, 1999. B. J. Eggleton, J. A. Rogers, P. B. Westbrook, and T. A. Strasser, “Electrically Tunable Power Efficient Dispersion Compensating Fiber Bragg Grating,” IEEE Photon. Technol. Lett., vol. 11, pp. 854-856, 1999. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated Per-ChannelDispersion Compensating Bragg Gratings,” Journal of Lightwave Technology, v01. 18,2000. B. J. Eggleton, “Dynamic Dispersion Compensation Devices for High-speed Transmission Systems,” Paper WH1, OFC 2001, Anaheim, California (Optical Society of America). J. A. J. Fells, et al., “Twin Fiber Grating Adjustable Dispersion Compensator for 40 Gbith,” ECOC 2000, Munich, Germany, Postdeadlinepaper 2.4,2000. Y . Emori and S. Namiki, “100-nm Bandwidth Flat Gain Raman Amplifiers Pumped and Gain-Equalized by 12-wavelength-channelWDM High-Power Laser Diodes,” OFC 1999, San Diego, CA, Postdeadline paper PD19. J. E. Ford and J. A. Walker, “DynamicSpectralPower EqualizationUsing Micro-OptoMechanics,” IEEE Photon. Technol. Lett., vol. 10, pp. 1440-1442, 1998. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Fiber Nonlinearities and Their Impact on Transmission Systems,” in Opical Fiber Communications IIIA, Ivan P. Kaminow and Thomas L. Koch, eds, pp. 196264, AcademicPress, San Diego, 1997. L. D. Garrett, et al., “Demonstration of VIPA Device for Tunable Dispersion Compensation in 16 x 10-Gb/s WDM Transmission over 480 km Standard Fiber,” OFC 2000, Baltimore, Maryland (Optical Society of America). A. H. Gnauck and R. M. Jopson, “Dispersion Compensation for Optical Fiber Systems,” in Opical Fiber Communications IIIA, Ivan P.=now and Thomas L. Koch, eds., pp. 162-195, Academic Press, San Diego, 1997.

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A. H. Gnauck, L. D. Garrett, Y. Danziger, U. Levy, and M. Shur, “Dispersion and Dispersion Slope Compensation of NZ-DSF for 40 Gbps Operation over the Entire C-band,” Technical Digest of OFC 2000, San Diego, CA, PD-8,2000. P. B. Hansen, et al., “Capacity Upgrades of Transmission Systems by Raman Amplification,” IEEE Photon. Technol. Lett., vol. 9, pp. 262-264, 1997. I. Haxell, et al., “2410 km All-Optical Network Field Trial with 10 Gb/s DWDM Transmission,” OFC 2000, Postdeadline paper PD41. I. Haxell, M. Ding, A. Akhtar, H. Wang, and P. Farmgia, “52 x 12.3 Gbit/s DWDM Transmission over 3600 km of True Wave Fiber with 100km Amplifier Spans,” Optical Amplifiers and Their Applications, OSA Trends in Optics and Photonics, vol. 44, A. Mecozzi, M. Shimizu, and J. L. Zyskind, eds., Optical Society of America, Washington, DC, 2001, pp. 217-219. F. Horst, “Tunable Ring Resonator Dispersion Compensators Realized in HighRefractive-IndexContrast SiON Technology,” ECOC, Munich, Germany, Postdeadline paper PD2.2,2000. G. Ishikawa and H. Ooi, “Demonstration of Automatic Dispersion Equalization in 40 Gbps OTDM Transmission,” ECOC 1998, WdC-6, pp. 519-520,1998. ITU-T G.975, November 1999, “Forward Error Correction for Submarine Applications.” T. Kato, Y. Koyano, and M. Nishimura, “Temperature Dependence of Chromatic Dispersion in Various Types of Optical Fiber,” Optics Letters, vol. 25, pp. 115 6 1 158, 2000. S. Keeton, S. Sridharan, and M. Jarchit, “EnablingNext Generation Optical Networks with Forward Error Correction,” NFOEC 2001 Proceedings, pp. 54-59, Baltimore, Maryland, 2001. H. Kidorf, et al., “PerformanceImprovement in High-Capacity, Ultra-Long-Distance, WDM Systems Using Forward Error Correction Codes,” OFC 2000, San Diego, CA, THS3, pp. 274-276. H. S. Kim, et al., “Actively Gain Flattened Erbium-Doped Amplifier over 35 nm by Using All-Fiber Acousto-OpticTunable Filters,” IEEE Photon. Technol.Lett., vol. 10, pp. 790-702,1998. C. K. Madsen, et al., “Integrated All-Pass Filters for Tunable Dispersion and Dispersion Slope Compensation,” IEEE Photon. Technol. Lett., vol. 11, pp. 1623-1625, 1999. Y. Miyamoto, et ab, Electronics Letters, vol. 35, no. 23, pp. 2041-2042, 1999. Y. Miyamoto, S. Kuwahara, A. Hirano, Y. Tada, Y. Yamane, and H. Miyazawa, “Reduction of nonlinear crosstalk of carrier-suppressed RZ format for 100GHzspaced Nx43-Gbith WDM in non-zero shifted band,” Proceedings of ECOC 2001, Paper Th.B.3,2001. R. E. Neuhauser, P. M. Krummn’ch, H. Bock, and C. Glingener, “Impact of Nonlinear Pump Interactions on Broadband Distributed Raman Amplification,” Paper MA4-1, OFC 2001, OSA, Anaheim, California, 2001. C. D. Poole, et al., “Elliptical-CoreDual Mode Fiber Dispersion Compensator,” IEEE Photon. Technol. Lett., vol. 5 , pp. 194-197, 1993.

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P. Noutsios and S. Poirier, “PMD Assessment of Installed Fiber Plant for 40 Gb/s Transmission,” NFOEC 2001 Proceedings, pp. 1342-1 347, Baltimore, Maryland, 2001. D. Penninckx and S. Lanne, “Reducing PMD Impairments,” Paper TuP1, OFC 2001, OSA, Anaheim, California, 2001. A. Puc, E Kerfoot, A. Simons, and D. Wilson, OFC 1999, ThQ6, pp. 255-258. N. T. Quang Le, T. Vng, and L. Gruner-Nielsen, “New Dispersion Compensating Module for Compensation of Dispersion and Dispersion Slope of Non-Zero Dispersion Fibres in the C-band,” Paper TuH5, OFC 2001, OSA, Anaheim, California, 2001. S. Ramachandran, B. Mikkelsen, L. C. Cowsar, M. F. Yan, G. Raybon, L. Boivin, M. Fishteyn, W. A. Reed, P. Wisk, and D. Brownlow, “All-fiber, Grating-Based, Higher-Order-Mode Dispersion Compensator for Broadband Compensation and 1000-km Transmission at 40 Gbps,” ECOC 2000, PD-2.5,2000. K. Rottwitt, A. Stentz, T. Nielsen, P. Hansen, K. Feder, and K. Walker, “Transparent 80-km Bidirectionally Pumped Distributed Raman Amplifier with Second-Order Pumping,” in European Conference on Optical Communications 2000, Nice, France, 11-14. M. Shirasaki, et al., “Variable Dispersion Compensator Using the Virtually Imaged Phase Array (VIPA) for 40-Gbh WDM Transmission Systems,” ECOC 2000, Munich, Germany, Postdeadline paper 2.3,2000. M. Shirasaki and S. Cao, “Compensation of Chromatic Dispersion and Dispersion Slope Using a Virtually Imaged Phased Array,” Paper TuS1, OFC 2001, OSA, Anaheim, California, 2001. G. Shtengel, E. Ibragimov, M. Rivera, and S. Suh, “Statistical Dependence Between First and Second-Order PMD,” Paper MO-3, OFC 2001, OSA, Anaheim, California, 2001. N. J. Smith, N. J. Doran, W Forysiak, and E M. Knox, “Soliton Transmission Using Periodic Dispersion Compensation,” Journal ofLightwave Technology,vol. 15, p. 1808, 1997. V. Srikant, “Broadband Dispersion and Dispersion Slope Compensation in High Bit Rate and Ultra Long Haul Systems,” Paper TuHl, OFC 2001, OSA, Anaheim, California, 2001. H. Sunnerud: M. Karlsson, and P. A. Andrekson, “A Comparison Between NRZ and RZ Data Formats with Respect to PMD-induced System Degradation,” Paper WT3, OFC 2001, OSA, Anaheim, California, 2001. M. Suzuki: I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electronics Letters, vol. 31, p. 2027, 1995. H. Taga, et al., “Polarization Mode Dispersion Tolerance of 10-Gbitls NRZ and RZ Optical Signals,” Electronics Letters, vol. 34, pp. 2098-2100, 1998. J. L. Zyskind, J. Nagel, and H. D. Kidorf, “Erbium-Doped Fiber Amplifiers for Optical Communications: in Optical Fiber Communications IIIB, I. P. Kaminow and T. L. Koch, eds., pp. 13-68, Academic Press, San Diego, 1997. J. L. Zyskind, G. J. Pendock, M. J. L. Cahill, G. D. Bartolini, J. K. Ranka, and S. Y. Park, “High Capacity, Ultra-Long-Haul Transmission,”Pmc. of NFOEC 2000, Denver, CO, 2000.

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Chapter 6

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Pseudo-Linear Transmission of High-speed TDM Signals: 40 and 160 Gb/s

Renk-Jean Essiambre, Gregory Raybon, and Benny Mikkelsen* Bell Laboratories, Lucent Technologies. Holmdel, New Jersey

1. Introduction High-capacity fiber-optic communication systems transport bits of information (optical pulses) by having them first time-division multiplexed (TDM) to form a channel centered at a given wavelength. Many channels at different wavelengths are then wavelength-division multiplexed (WDM) together and launched in an optical fiber for transport. A given capacity can be implemented through a large number of low-speed TDM channels or a reduced number of high-speed TDM channels. By July 2001, the highest bit rate per channel in state-of-the-art installed commercial WDM systems is 10 Gb/s. The next anticipated higher standard bit rates for the synchronous optical network (SONET) and synchronous digital hierarchy (SDH) standards are 40Gb/s and 160 Gb/s. The deployment of transmission systems based on 40 Gb/s per channel and above (from here referred to as high-speed TDM systems) can be advantageous in many ways. Benefits include a reduced number of opto-electronic components used for transport such as lasers, modulators, and receivers. The size of optical networking components used for routing and switching, such as optical add-drops and cross-connect, is also reduced dramatically for low channel count. Such reductions in component count, complexity, and size generally lead to a decrease in overall system size, cost, electrical power consumption, and channel sparing. Besides the advantages in hardware mentioned above, provisioning, operation, administration, and maintenance (POAM) are also simplified by the deployment of high-speed transport as the number of paths to monitor and restore in case of hardware failure or malfunction is reduced. Also, it is cheaper to spare a single high-speed transponder than several lowspeed WDM transponders. Furthermore, as networks predominantly carry Internet protocol (IP) traffic, it is important to take into account that a few high-data-rate links perform better than many low-data-rate links in a packetswitched network. While offering many advantages, high-speed systems have not been deployed because they faced numerous challenges.

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* Author’s present address: Mintera Corporation,Lowell, Massachusetts.

232 OPTICAL FIBER TELECOMMUNICATIONS, VOLUME IVB

Copyright 0 2002, Elsevier Science (USA). All rights of reproduction in any form reserved. ISBN 0-12-395173-9

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A first challenge is related to the development of commercial-grade broadband high-speed electronics for high-speed transmitters and receivers (see chapters found elsewhere in this book). Depending on the availability of such components, it may become necessary to introduce optical multiplexing and/or demultiplexingtechniques, especially if speeds higher than 40 Gb/s are considered. Transmission of high-speed signals over optical fibers by itself brings an important set of challenges. Higher-speed signals become increasingly demanding in dispersion accuracy. For instance, in the absence of fiber nonlinearity and dispersion slope, a 40-Gbls-based WDM system has 16 times less dispersion margin than a 10-Gb/s-based WDM system for a given modulation format. Such high-speed systems may exhibit sensitivity to dispersion variations induced by temperature variations in the transmission fiber [l, 21, whereas 10-Gb/s-basedsystems are less critically affectedby these environmental changes. The effects of polarization-mode dispersion (PMD) also become an important factor for high-speed systems as the PMD values of commercial transmission fibers and other optical components in the transmission path may start producing distortions for medium-haul (300 to 1000km), long-haul (1000 to 3000 km),and ultra-long-haul (>3000 km) high-speed TDM systems. Metropolitan systems (e300km) are fairly immune to intrinsic PMD ifstateof-the-art low-PMD transmission fibers and optical components are used. Schemes and devices for PMD compensation (PMDC) are being developed (see chapters found elsewhere in this book) to reduce the impact of PMD on transmission and detection. Despite important technical challenges, the dispersion accuracy and PMD characteristics of transmission fibers and optical components have steadily improved over time. On the other hand, improvement of the nonlinear characteristics of transmission fibers have only been minimal (nonlinear coefficient has been reduced by -1 dB). These minimal improvements in nonlinearity characteristicsexacerbate the problem of transmitting high-speed signals, because the higher density of bits in high-speed signalsrequires proportionally higher power per channel to preserve the energy per bit. Until recently, it was believed that the distortions induced by fiber nonlinearity in high-speed transmission were too large to allow the energy per bit of high-speed TDM signals to become comparable to the energy per bit of low-speed signals for comparable signal distortion. However, with the uncovering of pseudo-linear transmission [3-91, there has been a renewed interest in high-speed TDM transmission as it opens the possibility of having efficient transmission of information with high-speed TDM signals. Pseudo-lineartransmissionis a regime for transmission of high-speedTDM signals where fast variations of each channel waveform with cumulative dispersion (see Fig. 6.1) allow important averaging of the intrachannel effects of fiber nonlinearity. As a result of the redistribution over many bits of the effects of fiber nonlinearity, pulse distortions are minimized. Additionally, a partial cancellation of some intrachannel effects can be achieved through appropriate dispersion mapping. Nonlinear interactions between WDM channels

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Fig. 6.1 The fast waveform evolution of rapidly dispersing pulses provide a redistribution of the effects of fiber nonlinearity that is the basis for pseudo-linear transmission. The upper part of the figure shows the location of a 40-ps t h e window in the pulse train made of 5-ps pulses. The average power of the full train is 8 a.u. The lower part shows the waveform evolution in that time window after the pulses have been dispersed by 100 to 120p s / m of cumulative dispersion by step of 5 pdnm. After such dispersion, pulses strongly overlap and any trace of the intensity proiile of individual pulses is lost. Note that each step of 5 pslnm corresponds to the cumulative dispersion of about 300 m of STD unshifted fiber.

(interchannel interactions) are generally much weaker than intrachannel nonlinear interactions for pseudo-linear transmission. The evolution of the signal during propagation is generally characterized by important pulse overlap. In this regime, the optimum transmissionis obtained when the net residual dispersion at the end of the system is nearly zero, a characteristiccommon with transmission when fiber nonlinearity is negligible, i.e., when transmission is linear. The origin of the term “pseudo-linear” transmission (pseudo means false, spurious, etc.) can be understood as follows The ultimate performance of a transport system is measured as the energy per bit it can transport at fixed signal distortion from fiber nonlinearity for a given spectral efficiency S (bits/s/Hz). It can be shown that the maximum energy per bit of a highspeed TDM signal transmitted in the pseudo-linear regime is on the order of the energy per bit of systems using lower bit rates (lOGb/s per channel and below) for high but practical spectral efficienciesof intensity-modulatedsignals (S = 0.2 to 0.4 bits/s/Hz). It follows that the transmission in the pseudo-linear regime is highly nonlinear since the energy per bit in this regime does not

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wavelengths are multiplexed together to form a WDM signal that is transmitted and demultiplexed before being detected by receivers. A number of spans made of transmission fibers are linked with discrete amplifiersthat are used to periodically amplify the signal. In some instances, the transmissionfiber can be Raman pumped to reduce the generation of amplified spontaneous emission (ASE) noise in the system. Typically dispersion compensation is applied at the amplification sites and is included within two stages of a multistage amplifier. This positioning inside an amplifier reduces the impact on ASE noise generation associated with the introduction of a lossy element in the transmission line. Amplifiers linking two spans are referred to as in-line amplifiers, and dispersion compensation at these amplifier sites is referred to as in-line compensation. The amplifier following the transmitter is called a postamplifier (the prefix “post” is relative to the transmitter as the amplification is generally considered as an extension of the transmitter). The dispersion compensation at this amplification site is referred to as precompensation (the prefix “pre” is relative to the transmission line as the choice of dispersion compensation is dictated mainly by the transmission line ahead). Similarly, the amplifier just before the receiver is the preamplifier, and the associated dispersion compensation for this amplifier is the postcompensation. One should note that additional lossy elements might be present in the in-line amplifiers to perform other functions such as gain equalization, channel adddrop, channel crossconnect, performance monitoring, optical regeneration, polarization-mode dispersion (PMD) compensation, etc. Additional amplification stages may be inserted in the amplifiers to accommodate these additional elements. A typical cumulative dispersion map is displayed in Fig. 6.3. It is generally desirable to have identical spans so as to minimize system complexity and cost. For such systems, the three parameters, pre-, in-line, and postcompensation, uniquely define the map. When convenient, in-line compensation is sometimes replaced by the residual dispersion per span and postcompensation by the net residual dispersion at the end of the link. Points of zero cumulative dispersion are labeled ZO. In the absence of nonlinear effects and residual dispersion slope, the pulses at these points are identical to the pulses at the output of the transmitter. For pseudo-linear transmission, the pulses at zo are nearly transform-limited like those in linear transmission. Positions corresponding to launch points to the transmission fibers are labeled zin.

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NOISE ACCUMULATION AND OPTICAL SIGNAL-TO-NOISE RATIO REQUIREMENTS

In optically amplified systems, the main source of noise is the accumulation of ASE of the optical amplifiers. The noise accumulation can easily be calculated for passive transmission fibers. The ASE noise generated in both polarization statesby an individualamplifier (composed of multiple stages or not) measured

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in a bandwidth A u at its output is given by [lo]:

where nsp is the spontaneous emission factor of the amplifier, G its gain, u the optical frequency, hu the energy of a photon of frequency, and Au the optical bandwidth considered. The value of nspis generallygiven through the amplifier noise figure N F = 2 nsp(l - 1/G) 1/G knowing the amplifier gain. In a chain of amplifiers, the total noise generated is the sum of the noise generated by each amplifier. It is useful to calculatethe optical signal-to-noiseratio (OSNR) of a channel after propagation over a chain of Nap identical amplifiers. The OSNR (in dB) is given by [lo, 111:

+

where P i n is the launch averaged power per channel (at the input of the transmission fiber) in dBm; N F is the noise figure of the amplifiers and Lsp is the span loss, both in dB. The reference bandwidth, Au, for the OSNR calculation is 0.1 nm (12.5 GHz at 1550nm). Note that Eq. 6.2 shows that, assuming similar signal distortion from fiber nonlinearity at the end of the transmission line, each dB gained in permissible launch power, P i n , is translated into a 1 dB gain in OSNR. Figure 6.4 displays the OSNR evolution with an increase in the number of amplifiers, Namp, in a link. The launch power, P i n , is OdBm, and the noise figure of each amplifier, NF, is 5 dB. The transmission fiber loss varies from 13 to 28 dB in steps of 5 dB from the upper to the lower curve.

238

Renk-Jean Essiambre et al. I

"

"

I

"

zyxwv zyxwv zyxw z zyxw zyxw zyxw "

l

~

"

"

'

" ' 13 dg SpanLoss

....... 18 dB span Loss

--.-.-.

23 dB Span Loss 28 dB Span Loss

.................. ..................

---------_

__

-.-.-.-.-._._._._,_.

0

10

20

30

40

50

Number of Amplifiers

Fig. 6.4 OSNR evolution as a function of the number of amplifiersNmp. The launch power per channel is Pi, = 0 dBm and the noise figure of each amplifier is NF = 5 dB. At 40 Gbk, a typical OSNR requirement for bit-error-rate is 23 dB.

The required OSNR to achieve a given bit-error-rate (BER) depends in general on the nature of noise limiting detection, the type and distortions of the waveform being detected, and the receiver design. One can, however, derive an approximateexpression for the required OSNR, assumingthat the main source of noise results from the beating between the signal and the ASE noise and for large duty cycle intensity-modulated formats. Under these approximations, one can express the required OSNR, OSNRR,as [12],

zyxwvuts Q2Be l + r OSNRR = Bo ( 1 - a 2 '

where Bo is the optical reference bandwidth of 12.5GHz and Be is the electrical Nter's bandwidth of the receiver. The transmitter extinction ratio, I, is defined as r = Izems/Iones, where Io, (Izems) is the instantaneous current at the sampling instant for a "1" ("0")bit. The parameter Q is given by [13]: Iones

- Izems

Q = aones + azeros where cones (azems) is the standard deviation of Iones (Izems). At the optimum decision threshold, the parameter Q is related to the BER through the relation [131, ~ X (-Q2/2) P BER=-er$c Q2/2;7 '

($)%

where erfc(x) = 2/fiLm exp (-u2)du is the complementary error function. A BER of corresponds to a value of Q = 6. The parameter Q is often quoted in dB by using 10 loge', giving 15.6dB for Q = 6. According to Eq. 6.3, the corresponding required OSNR is 19.4dB for an electrical filter bandwidth of Be = 30 GHz and an infinite extinction ratio (r = 0).

zyx zy zyxwvu

zyxwv

6. Pseudo-Linear Transmission of High-speed TDM Signals

239

Alternatively, one can estimate the OSNR requirement if the receiver sensitivity Prec is known using: OSNRR = 58 + P m

- NF,

(6.6)

where NF is the noise figure of the optically preamplified receiver. For such receivers the best (quantum-noise-limited) receiver sensitivity for an intensity-modulated format and direct detection corresponds to 38 photons per bit (NF = 3 dB), which gives an ideal OSNR requirement of 17.8 dB at 40Gb/s (infinite extinction ratio and ideal electrical filtering). This ideal OSNR requirement is 1.6dB lower than the value given by the approximate expression of Eq. 6.3. For realistic transmitters and receivers with nonideal responses, the required OSNR is generally higher by more than 3 dB from the quantum limit. A direct measurement of receiver sensitivitycan determine the required OSNR for a given transmitter-receiver pair by using Eq. 6.6. One should also mention that 40-Gb/s systems using Reed-Solomon (239,255) forward-error correction (FEC) operate at a higher bit rate of 42.68 Gb/s and have a slightly higher OSNR requirement than systems operating without FEC (see chapters found elsewhere in this book). One can estimate the impact on the noise figure of an in-line amplifier from the presence of an additional amplikation stage required to compensate for the loss of a dispersion-compensatingfiber (DCF). Assuming the same noise figure NF for all amplification stages, the noise figure NFDCof an amplifier that includes a dispersion compensation module (DCM) of loss r] is approximately given by

zyxw zyxwvut zyx

where Pk is the average power at the input of the amplifier and PDCFis the averagepower at the input of the DCM (see Fig. 6.2). Let’s consider an example where the presence of a DCM significantly impacts the amplifier’snoise figure. For a 12-dBDCM loss ( r ] = 12dB), a PDCF of -2 dBm to avoid nonlinearities in the DCF, and a Pk of -16 dBm (launch power Pi,= 4 dBm and 20 dB span loss), the excess noise figure contribution is 2.1 dB. The impact of the presence of dispersion compensation can be minimized by using dispersion compensation devices that have higher-power thresholds for nonlinearities or lower loss such as the higher-order mode (HOM) DCF described in Section 3.1.1.

2.2 INTENSITTY-MODULATEDFORMATS AND SPECTRAL EFFICIENCY

Intensity-modulated direct-detection (IMDD) formats are the most commonly used transmission formats in high-capacity fiber-opticcommunication systems (for alternative formats see chapters found elsewhere in this book).

240

RedJean Essiambre et al.

zyxwv zy zy

These formats generally lead to the simplest designs for transmitters and receivers. Such simplicityis desirablesince the fabricationof commercial-grade high-speed receivers and transmitters is a challenge by itself. The IMDD formats are defined by the duty cycle and the pulse shape. The duty cycle d is defined as: d = - T,P (6.8) TB

where Tp is the pulse full-width at half maximum (FWHM) and TB the bit period. The IMDD formats consideredhere are the non-return-to-zero(NRZ) format and the return-to-zero(RZ) format with Gaussianpulse shapes. Besides simplicityin transmitter and receiver designs, there are two important properties determining the choice of optimum format for WDM transmission. The first is related to the spectral efficiency S defined as: B S=-, Vch

(6.9)

where B is the bit rate and Vch is the channel spacing. The spectral efficiency correspondsto the spectraldensity of information and is expressedin bits/s/Hz. The spectra of various modulation formats differ in their bandwidths and shapes. Moreover, the intersymbol interference created by narrow optical or electrical filtering varies widely according to the modulation format. As a result, the ability to achieve high spectral efficiency by closely spacing WDM channels generally depends on the modulation format. Figure 6.5 shows an exampleof the differencesbetween formats for demultiplexinga 40-Gbls signal from a WDM field with 100-GHzspacing. The fist two columns are the speo tra of an isolated channel and the WDM field, respectively. Third and fourth columns are the eye diagrams after demultiplexingfor an isolated channel and from an arbitrary channel from the WDM field, respectively. For both cases, optical demultiplexingis performed using a 80-GHz FWHM Gaussian optical filter and a 28-GHz, 3-dB electrical Bessel filter included in the receiver. The upper row is the NRZ format, whereas from second to fourth row, the format is RZ (Gaussianpulses) with duty cycles of 50,33, and 20%, respectively. Singlechannel eye diagrams clearly show minimal distortions, whereas eye diagrams of the demultiplexed WDM channel are distorted from coherent cross-talk. Coherent cross-talk originates from the overlap of the spectra of neighboring channels with the demultiplexed channel. The coherent cross-talk increases as the duty cycle decreases because the broader spectra of short pulses lead to greater spectral overlap. As a result, one should expect low-duty-cycleformats to be limited to lower spectral efficienciesthan formats with larger duty cycles. Nonetheless, it is noticeable that for duty cycles as low as 20%, the eye diagrams still show significant opening for the spectral efficiency of 0.4 bits/s/Hz of Fig. 6.5.

zyx zyx zyxwvutsr

6. Pseudo-Linear Transmission of High-speed TDM Signals Isolated Channel

WDM spectrum

speceum

241

DemultiplexedIsolated DemultiplexedWDM Channel Eye Diagram ChannelEye Diagram 2

1.5

1 0.5

zyxwvuts

0 2

z

-1 v

zyxwvutsrq zyxwvuts

go

!.I22 1.5

I 0.5

0

3

-30

40 do

0 50 100 -100 do 0 50 loo Frequency (GHz) Frequency (GHz)

-100 -50

0

10

5

15

20

Time (ps)

250

5

10

15

20

25

Time (ps)

Fig. 6.5 Coherent cross-talk and eye diagrams in dense WDM systems. From fmt to fourth column: single-channel spectra, WDM spectra, single-channeleye diagrams, and eye diagrams of center channel. For both single channel and WDM cases, eye diagrams are obtained using an optical demultiplexer consisting of a Gaussian filter of bandwidth 80 GHz and an electrical Bessel filter of 28 GHz. The relative time delay between channels is a random number of bits, including fractional bit delays. The bit rate is 40 Gbls and channel spacing 100 GHz (0.4 bitslslHz spectral efficiency). The displayedoptical spectra were generated by passing the signal through a 0.02-nmoptical filter. Degradation of the eye diagrams as the duty cycle decreases comes from spectral overlap between channels causing coherent cross-talk.

zyxwvuts zyxwv

2.3 DISPERSION

The equation of evolution of a field A(z,t) representing a modulated signal propagating in a lossy/amplifyinglinear dispersive medium is given by, aA

aZ

zyxw

i a2A a(z) + -/32(z)+ -A2 2 at2

= 0,

(6.10)

where BZ(Z) is the group velocity dispersion (GVD) representing the dispersion of group velocity with angular frequency. This is obtained from the propagation constant B(w) using /32 = [d2B/d~2]0=00, where wo is the angular frequency. The fiber loss/gainis accountedfor through a(z),which describes the signal power evolution, for passive transmission fiber a(z), equal to the fiber loss coefficienta0 over the length of the fiber. Solving Eq. 6.10 for a pulse labeled n (n = 1,2, . ..) with the initial condition of an unchirped Gaussian

242

RenLTean Essiambre et al.

zyxwv

pulse at location zo (where the cumulative dispersion is zero), gives,

(6.11)

zyxwv zyxw

where the characteristicpulse width T, is given by:

the chirp C,(z) by:

CGVD(Z) C,(Z) = -, To2 the cumulative GVD, CGVD(Z), from point zo to z by:

(6.13)

(6.14) and finally the complex amplitude b,(z) is given by:

zyxw zyxwvu zyx (6.15)

where the cumulativelosdgain factor Z(z) is given by: Z(Z) =

Jc,l

.(z’)h’.

(6.16)

zyxwv zyxw zyx

The pulse position t,(z), frequency w,(z), and phase &(z) are not affected by linear dispersive propagation and keep their initial values to, WO, and 00, respectively. The parameter TOis the characteristic pulse width and is related to the pulse full width at half maximum Tp at the transform-limited points zo by Tp 3 TP(zo) = 2 m TO.A0 is the initial pulse amplitude at z = ZO. The pulse bandwidth does not change with dispersive propagation. Note that the pulse characteristicbandwidth is given by (2nTo)-l, whereas the pulse full bandwidth at half maximum Av, is given by:

(6.17)

and the root-mean-square (RMS) bandwidth is given by ( 2 n a To)-’. One can associate to the pulse temporal broadening induced by dispersion a characteristic length referred to as dispersion length LD defined as: ‘F2

LD=

-.1 0

1821

(6.18)

zyx zyx zyx zyxw zyx zy zyxwvuts zyxw 6. Pseudo-Linear Transmission of High-speed TDM Signals

243

This length is indicative of when dispersive effects start to impact a pulse and corresponds to the broadening of a Gaussian pulse by a factor of &. It is often useful to express the evolution of the pulse width Tp(z)in more commonly used quantities as

(6.19)

where c is the speed of light in vacuum and cumulative dispersion C&) from to z,

20

(6.20)

and dispersion D,

2RC D(z) = -- B ~ ( z ) .

(6.21)

h2

Figure 6.6 shows the pulse width evolution with cumulative dispersion of initially transform-limitedGaussian pulses. Significantpulse overlap in a pulse train occurs when the pulse width approaches the bit period TB. At 40 Gb/s, TB = 25 ps, and pulses of width Tp = 2.5,5,8.3, and 1 2 . 5 ~broaden s to 25 ps after 18, 35, 56, and 77ps/nm of cumulative dispersion (see Fig. 6.6), respectively. The shorter the pulse the faster it broadens and the faster neighboring pulses in a train overlap. This range of cumulative dispersion corresponds, for instance, to the cumulative dispersion of 1 to 4.5 km of standard (STD) unshifted fiber [D = 17ps/(kmnm)]. Such small tolerance on cumulative dispersion makes it impossible to prevent pulse overlap during propagation within one span (50-100 km) made of either nonzero dispersion-shifted fibers [NZDSFs, 4ps/(kmnm) < ID1 < 8ps/(kmnm)] [14] or STD unshifted fibers.

0

20

40

zyxwvu 60

80

100

Cumulative Dispersion (pdnm)

Fig. 6.6 Pulse broadening with cumulative dispersion for Gaussian pulses. Short pulses reach the boundary of the bit slot (25 ps at 40 Gb/s) faster than long pulses.

244

zyxwvutsr zyxwvu zyxwvu zyxw zyx RenC-Jean Essiambre et al.

However, the use of dispersion-shifted fibers [DSFs, 101 < Zps/(kmnm)] makes it possible to prevent pulse broadening for long pulses (Tp > lops). Alternatively, dispersion compensation on a short scale (a few kilometers) using segments of NZDSF or STD unshifted fibers can prevent the a m mulation of dispersion. The impact of nonlinearity on high-speed TDM transmission using these low cumulative dispersion maps can be quite different from the impact of nonlinearity in the pseudo-linear regime and will not be covered in this chapter (even though a glimpse of the effects of nonlinearity on dispersion-shifted fibers (DSFs) for high-speed TDM signals can be seen in the upper part of Fig. 6.24). Accumulating dispersion not only leads to pulse broadening, but also to pulse chirping. This can be understood by considering that dispersion leads to a spread in delays between the different frequency components of a pulse. As a result, in a medium having normal dispersion(negativeD,positive &), the leading edge of a dispersed pulse becomes composed of the lowest-frequency components (“red”) of the pulse, whereas the trailing edge contains the highestfrequency components (“blue”). The opposite situation occurs for a medium having anomalous dispersion (positive D,negative 82). Because the phase of these frequency components evolve at different speeds, a chirp is created across the pulse. The waveform evolution of a 40-Gbh pulse train made of 5-ps Gaussian pulses is shown in Fig. 6.7. As dispersion accumulates, the initially transformlimited pulses (Fig. 6.7a) broaden (Fig. 6.7b) until significant pulse overlap

zyx

001001001 10110101 101 60

60

40

40

20

20 n

n

zyxw zyxwvuts (d) 30pdnm

40 20

0

0

100

200

300

Time (ps)

400

500

0

100

200

300

Time (ps)

zy 400

500

Fig. 6.7 Waveform evolution of a 5-ps Gaussian-pulse train at 40 Gb/s with cumulative dispersion. The transform-limited pulses in (a) gradually broaden in (b) until there is significant overlap between nearest neighbors in (c)-(f). At large values of cumulative dispersion (100 ps/nm and above) a large number of pulses overlap in time and individual pulses are no longer identifiable.

6. Pseudo-Linear Transmission of High-speed TDM Signals

245

zy

10

0

5

10

15

Time (ps)

20

2t

zyxw zyx zyxwvu 5

10

15

20

25

Time (ps)

Fig. 6.8 Electrical eye diagrams for the waveforms of Fig. 6.7. A 28-GHz Bessel electrical filter is used in the receiver.

occurs between neighboring pulses (Figs. 6.7c-e). The oscillations between pulses seen in Figs. 6.7c-e are the result of the beating between the dispersed pulses, “blue” and “red” frequency components. For large cumulative dispersion (Fig. 6.7f), the large number of pulses interfering at a given location in time and the wide distribution of phases that originates from pulse chirping creates the appearance of a “random field” (but with the limited bandwidth content of individual pulse spectra). Because the waveform is determined by interference of fields (the chirped pulses) as opposed to addition of powers (if the pulses were chirp-free), the waveform evolves very rapidly in a dispersive medium as any small change in phase due to dispersion affects greatly the interference between the dispersed pulses. This rapid waveform evolution leads to a generally beneficial redistribution of nonlinear phase distortions among pulses and is one of the bases of the pseudo-linear regime. The eye diagrams for the dispersing pulses of Fig. 6.7 are presented in Fig. 6.8. There is no optical demultiplexer and a 28-GHz electrical Bessel filter is included in the receiver. One notices that the fast oscillations observed between pulses in Figs. 6.7c-e that result from the beating of the high-frequency components of the pulses are reduced as a result of electrical filtering.

zy

2.3.1

Eye Closure Penalty

To compare the transmission performance of various modulation formats it is important to be able to isolate the deterministic effects of distortion (dispersion, nonlinearity, and coherent cross-talk)in the eye diagrams from stochastic effects(such as the effectof amplifier noise). To be able to do a meaningful comparison between various transmission formats (without having to do extensive simulation to achieve statistical averaging), we excluded the effect of optical amplifier noise in the simulations presented in this chapter. Under such conditions, the shape of an eye diagram becomes a reliable indicator of the effect

zyxw zyxwvutsr

RenC-Jean Essiambre et al.

246

40 35

-+

m

30

25 20

(u

15 10

5 n

0

zyxwvuts zyxw 5

10

20

15

25

30

35

Time (ps)

zy zyxwv

Fig. 6.9 Example of the determination of the eye diagram closure using a box of width 20% of the bit duration.

of transmission. One measure of distortions of an eye diagram is given by the eye closure penalty. It is calculated by first determining the height PR of the highest rectangle that can be fitted inside the eye opening. The rectangle width is 20% of the bit period TB.This width is chosen to include the effect of clock jitter on the decision sampling instant. The eye closure penalty (expressed in dB) is then given by: Ceye= -1Olog

~

(2ppXe)’

(6.22)

where Paveis the signal average power. Note that twice the average power is equivalent to the height of the rectangle for an unfiltered NRZ sequence having the same number of “zeros” and “ones.” A negative eye closure Ceyerepresents an eye more opened than the reference (the unfiltered NRZ signal), whereas a positive Ceyerepresents an eye more closed than the reference. Figure 6.9 shows a typical example of the positioning of the box for determining PR used in the eye closure calculation of Eq. 6.22. Note that the relation between eye closure penalty and receiver sensitivity penalty or BER penalty is not straightforward, as it depends on the nature of the noise and the type of waveform distortion.

2.3.2 Dispersion Margin and Modulation Formats High-speed TDM systems based on intensity-modulated formats use closelyspaced short pulses that rapidly broaden and overlap (as seen in Fig. 6.7), causing intersymbol interference (ISI) [15]. This leads to much tighter requirements on dispersion margins for high-speed TDM systems than for lowerspeed systems. Dispersion margins are dependent on the modulation format. Figure 6.10 shows the eye closure as a function of the cumulative dispersion applied to transform-limited RZ and NRZ formats. One first notices that RZ formats have negative eye closure at the transform-limited point (0 pshm) that represents the fact that the eye opening is larger for RZ than unfiltered NRZ,

zyx zy zyxwv zyx zyxw

6. Pseudo-Linear Transmission of High-speed TDM Signals I. ' ' '

'

I

' ' ' '

' ." '

I

I'

y ' ' ' '

I..'

' ' '

I

'y '

247

1

1 ....... 12.5 ps

zyx zyxw I-NRZ

0

20

60 80 Dispersion (ps/nm)

40

100

120

Fig. 6.10 Eye closure penalties at 40 Gb/s for the RZ format with duty cycles of 0.2, 0.33, and 0.5 and the NRZ format. Low duty cycles have reduced dispersion margins. The eyes diagram are obtained after electrical filtering with a 28-GHz Bessel filter. No optical filtering is applied.

the reference. However, as cumulative dispersion CD increases, the larger eye opening for RZ decreases faster than NRZ. This is because the broader spectrum of RZ as compared to NRZ makes the shorter pulses broaden faster (see Fig. 6.6). The lower the duty cycle (shorter pulses) the faster the eye closes with cumulative dispersion. Consequently, in systems with negligible fiber nonlinearity, the lower the duty cycle the more sensitive the transmission becomes to offsets of dispersion. 2.4 FIBER NONLINEARITY 2.4.1

Introduction

The evolution of the optical field A(z, t ) experiencing Ken- nonlinearity in optical fibers has been derived in Ref [16]. Assuming that the slowly varying envelope approximation (SVEA) holds, the equation of evolution for the field A(z, t ) can be written as:

zyxwvu zyx

The coefficient83 accounts for the change of the GVD ( 8 2 ) with angular frequency Cg3 [dp2/dw],=,) and is referred to as the third-order dispersion (TOD) parameter. When fiber losdgain and TOD are neglected and 82(z)is a constant independent of z, Eq. 6.23 is known as the nonlinear Schrodinger equation (NSE), which has soliton solutions when dispersion is anomalous (negative /32 or positive 0)(see Ref [17] and Chapter 11 of Ref [18]). When &(z) is a periodic function with suf€iciently low path-averaged value, Eq. 6.23 can have an approximate solution called dispersion-compensated (DC) or dispersion-managed soliton (see chapters found elsewherein this book). When

248

zyxwvutsr zyxwvu zyxwvuts zyxw zyx zyxwvu zyxwvu RenC-Jean Essiambre et al.

any additional terms are included, Eq. 6.23 is referred to as a generalized nonlinear Schrodinger equation (GNSE). The coefficient 83 of Eq. 6.23 is related to the more straightforwardly measurable quantity dispersion slope S through the following relation,

dD

4nc

S(2) = - = -p dh h3

zy zyxwvu (6.24)

The coefficient y in Eq. 6.23 represents the effect of the Kerr nonlinearity and is defined as: y = - n 2 wo (6.25) cAeff ’ where 122 is the nonlinear refractive index coefficient and A& is the effective mode area. Typical fiber parameter values for some common fibers are given in Table 6.1. One can associate different length scales that are specific to nonlinear transmission. A first length scale is related to power only and is defined as:

1 LNL=-, YPP

(6.26)

where LNL is the fiber length required to produce nonlinear phase rotation of one radian at a power Pp. When Pp is interpreted as a pulse peak power, LNLis related to the effect of self-phase modulation (SPM, see Section 2.4.3). A second length scale is related to the power evolution in fibers; for a passive fiber this is known as the effective length L,ff and is given by: Leff =

1 - exp (-a0 L) Y

(6.27)

a0

where L is the length of the fiber segment considered. The effective length L,ff gives the length over which the power decreases by a factor of e in passive fibers. This length is related to most nonlinear effects but is perhaps most critical for SPM and cross-phase modulation (XPM) (see Chapter 8 of Ref. [18] and chapters found elsewhere in this book). A third length scale is the walk-off length and is defined as: L w = - TD DAV ’

(6.28)

where Av is the spacing between the two spectral components of interest and TO is a time delay. In WDM systems experiencing XPM (see Fig. 6.1 l), the relevant delay corresponds to 2 Tp (see Chapter 8 of Ref [18]), the delay necessary for two pulses from channels separated by Av to fully walk through each other. The time delay TD may have different values depending of the nonlinear interaction of interest. Note that the dispersion length LD defined in

zyxwvutsrqp zyxwvu zyxw zyxwvutsrqpo zyxwvuts zyxwvutsrq zyxwvutsr

Table 6.1 Some Nominal Values of Fiber Parameters at 1550 nm of Different Commercial Fiber Brands. The Ratio Dispersion to Slope (RDS) Is Defined as S/D D

Fiber

TrueWaveTMRS LEAFW TeralightTMUltra STD unshifted fiber Submarine DeeplightTM TeralightTM Metro DCF WB-DCF HS-DCF

N

A W

Manufacturer

Lucent Corning Alcatel Lucent, Coming, Furukawa Lucent Pire11i Alcatel Lucent Lucent Lucent

ps/(km nm) 4.5 4.2 8 16.9

-3.1 -2.2 8

-100 -95

-100

S ps/(ltm nm2)

0.045 0.09 0.052

0.055

RDS

nm-’

0.01

0.021 0.0065 0.0033

0.05

-0.016

t0.12 0.058

>-0.055 0.0073

-0.22 -0.33 -0.67

0.0022 0.0035 0.0067

PMD

(110

Aefi

dBhm

pm2

0.22 0.22 t0.22 0.23

55

t o .1

12 63 87

tO.l

0.215 t0.23 t0.25

50 70 63

t o .1 to. 1

0.5

20 19 15

t0.25 t0.25 t0.25

0.5 0.68

ps/&

(0.04 t o .1

t0.08

250

zyxwv zy zyxwvuts zyxwvu RenkJean Essiambre et al.

z

Eq. 6.18 can be interpreted as a walk-off length within a pulse where the delay To = TO,the characteristic pulse width, and the spectral separation Au = -sgnm(B$t2/(ncTo). The various length scales defined in Eq. 6.18 and Eqs. 6.26-6.28 characterize different length scalesfor the effects of nonlinearity. In general, these length scales depend on channel bit rate, channel spacing, modulation format, fiber types, input powers, power evolution, dispersion mapping, amplifier spacings, system length, etc. It is difficult to determine a general rule that would determine which scale is the most important for a given set of system parameters. Nonetheless, it is still instructive to define these length scales and, whenever possible, we will point out the scale relevant to nonlinear interactions specific to pseudo-linear transmission. Equation 6.23 describes the evolution of the full field (which may include many WDM channels) with distance. In general, nonlinear interactions for the WDM field can be decomposed into more basic nonlinear interactions (see Fig. 6.1 1). These interactions are single-channel self-phase modulation, multiple-channelcross-phase modulation (XPM), and multiple-channel fourwave mixing (FWM). Cross-phase modulation and four-wave mixing are interchannel interactions that are the strongest for moderate- (-10 Gb/s) and low-speed (c10Gb/s) signals. Cross-phasemodulation and four-wave mixing

---Basic Nonlinear Interactions

Single Channel

Multiple Channels (WDM)

zyxwvu

SingleChannel Modulation Self-Phase Modulation Instability (MI) - \

Self-Phase Nonlinear Modulation (SPM) Intersymbol (Soli:ons, etc.) Intefierence Pulse Distortion

Four-Wave Cross-Phase Mixing {FWM) Modulation JXPM)

v Coherent Cross-talk

v Timing Jitter and Pulse Distortion

/\

Intrachannel Intrachannel Cross-Phase Four-Wave Modulation Mixing U m a I I F W M )

v Timing Jitter Amplitude Jirrer

10 Gbls and Above

...

10 Gb/s and Below

Fig. 6.11 Distribution of inter- and intrachannel nonlinear impairment in a WDM system for different bit rates per channel. For high-speed TDM systems, the dominant nonlinear interactions are self-phase modulation (SPM), intrachannel cross-phase modulation (IXPM), and intrachannel four-wave mixing (IFWM).

zyx zyx zyxwv

6. Pseudo-Linear Transmission of High-speed TDM Signals

251

have been extensively studied (see Ref [ 161and references therein and chapters found elsewherein this book). For high-speed systems operating in the pseudolinear regime of transmission, XPM and FWM are usually much weaker than the nonlinear interactions within each channel (intrachannel interactions). This can be evidenced by numerical simulations or system experiments where single-channel transmission is compared to WDM transmission. For pseudo-linear transmission, one observes that when adding WDM channels, in the worst case, only a moderate increase in waveform distortions compared to single-channel transmission is observed. Moreover, assuming small spectral overlap between channels, adding WDM channels has rather small impact (if any) on the choice of the optimum schemes of transmission, such as dispersion mapping for instance. In a way similar to the decomposition of nonlinear interactions among channels in WDM systems, it is possible, when operating in the pseudo-linear regime, to separate the various nonlinear interactions among bits of the same channel. These intrachannel interactions are single-pulse self-phase modulation or simply self-phase modulation (SPM), cross-phase modulation among pulses or intrachannel cross-phase modulation (IXPM), and four-wave mixing among pulses or intrachannel four-wave mixing (IFWM). The field of a single channel can be represented as a sum of the fields of individual pulses, A = A , where A , is the field representing the mth of M pulses centered at tm.By replacing this sum in Eq. 6.23 we obtain,

zt=,

zy zyxw zyxw zyxw zy M

A,A;A~.

=i y

m= I

m,n,p=l

(6.29)

The nonlinear terms on the right-hand side (RHS) of Eq. 6.29 can be identified as follows: when m = n = p we have SPM, when m = n # p or m # n = p it is IXPM, and when m # n # p or m = p # n it is IFWM. This separation between nonlinear interactions is meaningful only if all Am’s fields in Eq. 6.29 can be separated in time, Le., that the pulse width (at the transform-limited point) Tp is smaller than the bit period TB (d < 1). This condition is similar to the condition of separability between nonlinear interactions in the analysis of WDM transmission where the channels are assumed to be separated in frequency by more than their bandwidth. In the pseudolinear regime of transmission where pulses disperse rapidly and extensively (Lo*N ( z , t)}vanish. As a result, no energy exchange among pulses results from these two nonlinear interactions. On the other hand, the IFWM terms generally lead to a nonvanishing %{A,(z, t)* N(z, t)},resulting in pulse energy variations and exchange of energy between bit slots. Using this property, it was possible to identify that the formation of shadow pulses in pseudo-linear transmission originated from IFWM [6].

+

2.4.3 Self-Phase Modulation The effect of nonlinearity on the propagation of an isolated pulse is referred to as self-phase modulation (SPM) and can take many forms. One form, thoroughly studied, is the optical fiber soliton (see Ref. [16], Chapter 12 in Ref. [18], Ref [19], and chapters found elsewhere in this book). The soliton in fibers is characterized by a strict balance between the effect of fiber nonlinearity and the dispersive effects for isolated pulse propagation. It requires a medium having an anomalous dispersion (positive D),which happens to be the sign of dispersion of fused silica at wavelengths longer than -1300nm. Thus, the most straightforwardlymanufacturable fibers have positive D in the third communication window (-1 550 nm) where fiber loss is minimum. The requirement of an exact balance between dispersion and nonlinearity for solitons is not always necessary to achieve acceptable isolated pulse transmission. In many instances, an average compensation of dispersion by nonlinearity leads to adequate isolated pulse transmission. An example of intricate pulse evolution that still produces low distortion is given by chirpedRZ transmission [20, 211. Another one is related to transmission of NRZ signals where some compensation of dispersion by nonlinearity can occur despite the fact that the NRZ pulse shape is quite dif€erent from a soliton (see optimum dispersion for NRZ in Fig. 6.24 for instance). For high-speed TDM systems, two forms of solitons are of particular interest. In its first form, SPM can compensatecontinuously for the local dispersion, and the corresponding pulses are referred to as local solitons, adiabatic solitons, or simply solitons. In a second form, SPM compensates for the residual dispersion in a periodically dispersion-compensated system according to a precise prescription of the dispersion map, and the corresponding pulses are referred to as dispersion-compensated(DC) or dispersion-managed solitons. It is difficult to use local solitons in high-speed systems with constantdispersion fibers (fibers with constant dispersion along its length). This is due

zyx zyx

254

zyxwvutsrq zyxwvu zyxwvu Red-Jean Essiambre et al.

to the large range of signal power experiencedduring propagation in the transmission fiber. This range is approximately 10to 25 dB for passive transmission fibers. Self-phase modulation (SPM), the nonlinear effect that compensates the effects of dispersion also experiences the same range as the power evolution. To preserve the local soliton, the width of each local soliton would also experience the same range as the power evolution, and consequently, the spectral bandwidth of the local soliton would vary by 10 to 25dB [22-251. Such large variations in spectral bandwidth prevent efficient use of WDM techniques. It is possible, however, to preserve the balance of nonlinearity and dispersion required by local solitons without the spectral broadening by tailoring the fiber dispersion along its length. For passive fibers, the dispersion should decrease exponentially along the length, and such fibers are referred to as dispersion-decreasing fibers (DDFs) [26-281. Even though interesting and manufacturable from a single fiber draw [29-331, DDFs impose some important constraints on system designs by forcing fixed values of powers (the local soliton power) for the signal evolution, as well as unidirectionality for individual fibers. Moreover, the wide dispersion range necessary to accommodate the span loss (>20 dB) for large amplifier spacings (100 km) requires large values of dispersion at the input end of the fiber. Such a high dispersion value increases significantly the path-averaged dispersion and can lead to large timing jitter [34-371. The other possibility for using the soliton effect in high-speed TDM systems is to use DC solitons. The design of DC soliton links allows some pulse broadening but limited to the bit slot duration to prevent pulse overlap during transmission. As shown in Fig. 6.7, at 40 Gb/s the pulse overlap becomes significant when the cumulative dispersion reaches approximately f10ps/nm. For large amplifier spacings (-100 km), this requirement restricts the dispersion of the transmission fiber to a range of ID1 c 2 ps/(km nm), assuming a precompensation of half the span cumulative dispersion. Dispersion-shifted fibers (DSFs) meet the requirement of low-dispersion values (over a limited bandwidth of -60nm however) and can support DC solitons [38-44]. Such low, local dispersion, however, makes WDM difficult due to four-wave mixing (FWM) [45] and limits the use of DSFs in high-capacity transport. An alternative to DSFs is to use dispersion compensation on a short length scale (on the order of a few kilometers) [46-48]. Such short-scale dispersion compensation allows one to use fiber segments with relatively high dispersion and still have a low value of average dispersion and a low excursion of cumulative dispersion. As for the fabrication of DDFs, one can fabricate continuously dispersion compensating fibers (CDCFs) from a single fiber draw [49]. However, the scale of dispersion compensation cannot be arbitrarily small because for too frequent dispersion compensation, the fiber starts to behave like a constant-dispersion fiber with a low average value of dispersion. As for DSF, such CDCF would suffer from FWM in WDM transmission [46]. As a result, an optimum scale of dispersion compensation may exist that will correspond

zyxw

zy zyxw

6. Pseudo-Linear Transmissionof High-speed TDM Signals

zyx zyx 255

zyx zyxwv zyxwv zy zyxwvu

to a tradeoff between the effects of pulse broadening and FWM. One should note that the design of such a CDCF is a priori bit rate and modulation format specific. Since the use of DSFs is likely to be limited by FWM, it suggests that the effectiveuse of DC solitons in high-speed systems may require deployment of special transmission fibers. In pseudo-linear transmission, the propagation of short pulses (Tp 10ps) over dispersive fibers [ID1> 2 ps/(km nm)] is dominated by dispersion (LD LNL.Fortunately, this is also compatible for combating multichannel nonlinearities, as will be described in the following sections.

zyx

zyxwvu zyxw zyx zyx zyxwv zyx zyxwv

3. Four-Wave Mixing

In multichannel transmission the beating between light at different frequencies leads to the phase modulation of the channels and hence generation of modulation sidebands at new frequencies, termed four-wavemixing [8,18-24]. If three components copropagate at frequenciesJ,A and fk, a new wave is generated at frequencyJyk,where, (13.7)

f. y k -f - I

This causes penalties if the frequency J j k is equal or close to the frequency of an existing WDM channel, so that the resulting interferometric noise falls within the bandwidth of the receiver. To predict the effect of FWM, an expression predicting the efficiency, 9,of the FWM process has been derived (see e.g., [SI). The power of the generated new signal is given by [9], Pijk

= (dFyL)2PiPjPke-ffLT),

(13.8)

where the degeneracy factor dF = 1 when i =j , dF = 2 when i # j . The FWM efficiency is given by,

'=I

+

1 - exp( - [a A/3]L) (a+iA/3)L

(13.9)

assuming the original channels are copolarized. The quantity Aj3 in Eq. 13.9 is the difference in the propagation constant between the channels due to the

618

zyxwv zyxwvut zyxwv zy zyx

Polina Bayvel and Robert KiJley

fiber dispersion

AS = pi

+

pj

-pk

- &k

= bZ(wi - wk)(aj - ak),

(13.10)

where D is the dispersion at the signal wavelength A andA,J, andfk are the optical frequencies of channels i , j , and k. Equation 13.9 predicts that the FWM efficiency is largest when AB is low and the phase matching between the channels is high, for example in systems with close channel spacing and dispersion-shiftedfiber at wavelengths close to the zero dispersion wavelength, LO.The FWM efficiency as a function of channel spacing with two values of fiber dispersion is plotted in Fig. 13.2, showingthe increasedefficiencywith low dispersion. In WDM systems based on low-dispersionfiber, an effective technique to minimize crosstalk due to FWM is to use unequal channel spacing [25], so that the FWM components are not generated at frequencies corresponding to the channel frequencies. In practical WDM systems, installed over existing fiber, the implementation of this would be to use a subset of the transmitter wavelengths, even though the standard transmitter wavelengths (current systems are equipped with as many as 160 wavelength channels) have a constant wavelength/frequency spacing. However, the most effective technique to avoid FWM crosstalk is the use of transmission fiber with high local dispersion, so that the phase matching between WDM channels is minimized. Periodic dispersion compensation can be used to maintain a low accumulated dispersion-all part of optimizing the dispersion-managementof the link. Although the use of high local dispersion is effective at suppressinginterchannel FWM in WDM transmission systems, its detrimental impact in limiting transmission distances of very high channel

0

zy zy

zyxwv

50 100 150 Channel spacing Af (GHz)

200

Fig. 13.2 Plot of the four-wave mixing efficiency r] (normalized to the efficiency with perfectly phase matched channels), calculated for standard single-mode and dispersion-shifted fiber links of length 100lan and loss a! = 0.21 dB/km.

zy zyxwvu

13. Nonlinear Optical Effects in WDM Transmission

619

bit rates within the high local dispersion region due to the nonlinearinteraction of pulses within the same channel, has recently become apparent. This effect is described in Section 5.

4. Cross-Phase Modulation

zyxwv zyxwv zy

As was shown, FWM in densely spaced WDM can be suppressed effectively using high local fiber dispersion and dispersion management. However, another effect of the nonlinear refraction, cross-phasemodulation (XPM), has emerged as the dominant impairment limiting the achievable capacity in long haul transmission systems [26]. In fact, it affects all WDM transmission, independent of signal format (RZ, soliton, or NRZ), and thus deserves detailed treatment. In XPM, the phase of the signal in one channelis modulatedby the intensity fluctuations of the other channels (see early references, e.g., [27,28]). For a signal with amplitude us, copolarized with a second signal with amplitude up, propagating through the fiber at a different wavelength, Eq. 13.2 can be written as follows: aus

az

+ 2i

zyxwvu

-B2-

a2us at2

+ -us = iy(lus12+ 21~,1~)u,, 2 (11

(13.11)

assuming the channels are linearly polarized. The phase shift induced on channel s by channelp due to XPM as they propagate over distance Az is A h M = 2YP,Az,

(13.12)

where Pp is the power of the interfering channel p. The factor of two results from the number of terms in the expansion of the nonlinear polarization that contribute to the XPM [7], and deviation from the copolarized states results in a reduction in the phase shift [29]. Parallel linear polarization leads to the worst-case distortion, and XPM between waves in orthogonal linear polarization states, reduces this factor to two-thirds Comparison of Eqs. 13.2 and 13.11 would seem to indicate that XPM is a far more damaging effect than SPM, first because of the factor of two, and second due to the large number of WDM channels contributing to the distortion. Fortunately, as for FWM, the effect of chromatic dispersion is to reduce the impact of XPM due to the velocity mismatch between the channels. However, unlike FWM, the effect of XPM is not so effectivelyreduced by avoidingphase matching between the channels, and cannot be eliminated by unequal channel spacing. At best, judicious choice of dispersion management can minimize it and XPM remains one of the most significant sources of penalty in long-haul dense WDM systems. Indeed, its significance had not been fully appreciated until recently, mainly due to the difficulties in its characterization and separation from other nonlinearities. Recently, much work has been carried out

zyxwv zyxwvut

Polina Bayvel and Robert KiUey

620

to understand and minimize its effects using techniques described in the next sections.

4.1 CRARACTERLZING THE IMPACT OF XPM USING PUMP-PROBE TECHNIQUES

As with self-phase modulation, the main impact of XPM in direct-detection systems results from the conversion of the phase modulation to intensity distortion by the fiber dispersion. To understand, characterize, and quantify this effect and its impact on transmission system penalty, it is vital to separate it from other nonlinearities A technique which has been developed to quantify the level of this intensity distortion is the pump-probe characterization, in which an intensity-modulatedpump channel distorts a continuous wave (cw) probe channel spaced AA away, as shown in Fig. 13.3 and the distortion on the cw channel can be used both to understand the physics of the effect as well as to accurately predict the likely penalty due to this effect in a more complex multiple channel system. This system has recently been analyzed in [30-361. Analytical description of cross-phase modulation allows a more rapid estimation of the resultant distortion than numerical methods based on the split-step Fourier algorithm to solve the nonlinear Schrodinger equation. In addition it gives an insight into the physical mechanism of the interaction of XPM and dispersion. The simplest method is to calculate the distortion in the frequency domain; the discrete Fourier transform of the pump waveform at the input, Pp(z = 0, o),is calculated and the contribution to the XPM intensity distortion at the receiver

7

1

Probechannel

zs Transmission

0

Q

zy zyx zyx zy zyxw zyxw

Time

5

2

Pump channel Time

zyxw

2 Time

Fig. 13.3 Schematic of pump-probe experiment to quantify cross-phase modulation distortion in a fiber link. The intensity modulatedpump signalat wavelengthAP distorts the cw probe at As. The amplitude of the induced distortion or its standard deviation gives the measures of XPM. Pulse distortion on the pump channel due to SPM can also be seen.

zyxwv zyxw zyx zyxwv zyxwvu zyxwvu zyxwvu zyxwvu 13. Nonlinear Optical EffeeQ in WDM Transmission

621

is obtained for each sinusoidal frequency component. These contributions are combined to give the resulting probe spectrum, and the inverse Fourier transform of the probe signal is then calculated to obtain the total probe distortion in thetime domain in the followingway. Key to the characterizationofXPM is the concept of the walk-off between channels, delined as the distan-dependent relative temporal position of the channels, in units of ps/km, which arises as a result of the different group velocities us and up of the probe and pump,

zyx (13.1 3)

The walk-off parameter, d results in the phase shift of the pump modulation componentPp(z,o)= IupI relative to the probe as they co-propagatethrough the fiber:

T

h ( z r 0 = 2Y

i=

lup(0, t

+ dspd)[2e4&.

(13.14)

The walk-off between the channels reduces the magnitude of the total phase modulation of the probe f37. In the analysis of the intensity distortion due to XPM,the phase modulation of the probe over inhitesimal lengths, L, of the transmission fiber is calculated and the resulting sinusoidal intensity modulation, dPs(o), at the receiver due to the dispersion of the following fiber is estimated, using the equation describing the phase-to-intensity conversion [38]: (13.15) where dPs(z,o) is the power modulation, normalized to the average probe power, and /?z(re~)is the residual accumulateddispersion, (13.16) between the position of the nonlinear phase distortion at distance z and the d v e r at distance L. It can be seen that reducing the value of #3qm)results in lower intensity distortion because of a less efficient phaeto-amplitude conversion. This can be achieved throughinline dispersioncompensationand is one of the techniques for nonlinearity-suppressingdispersionmanagement. Integrating Eq. 13.15 over the full length of the link, the total distortion due to XPM is given by [38]:

622

zyxwvutsr zyxwv zyxwvuts zyxw Polina Bayvel and Robert Killey

zyxw zyx

where AP, is the probe modulation depth at the output, normalized to the average probe power at frequency w , and Hsp(w)is the XPM transfer fmction.

[

Hsp(w)= 2yi exp (i4)

- exp (- i4)

+

1 - exp (-a ibi) a-ibl 1 - exp (-a + ib2)

(

a!

- ib2

where

4 = i&,,p2, bi = (dspw- B2w2/2) L and b2 = (dspw+ &w2/2) L. (13.19-13.21)

The probe waveform in the time domain is given by the inverse Fourier transform of AP,. For multispan systems, the total distortion is the sum of the distortion components generated from each span. From Eq. 13.18, it can be seen that the XPM-distorted probe waveform at the output resembles a high-pass filtered version of the pump input waveform, with the filter transfer function given by Hsp, so that the distortion of the cw probe is significant only at high frequencies. By way of an example, the calculated transfer functions, IHspI,of dispersion-compensated60-km spans are shown in Fig. 13.4 for channel spacing of Ah = 0.4nm, comparing the XPM distortion in SMF and non-zero dispersion-shifted fiber (NZ-DSF, D = 4ps/(nm/km)). In both links, the dispersion was compensated at the receiver, and a fiber nonlinear coefficient of y = 1.2W-lkm-' was assumed. Despite the large difference in dispersion between the links, the magnitude of the transfer functions are similar. The phase modulation in the NZDSF

zyxw

0.0°3

O0.002

.

O

0.000 L d L 0

1

o

3

2 3 4 Frequency (GHz)

V

zyxwvut

r----

5 Frequency (GHz)

Fig. 13.4 XPM transfer function, Hsp, of 6 0 h fiber spans, with channel spacing of AA = 0.4ps, in SMF (D= 17ps/(nm/km)) (left) and non-zero dispersion-shifted fiber (NZ-DSF, D = 4ps/(nm/km)) (right), both with dispersion compensation at the receiver. Values calculatedfrom Eq. (13.17)(lines) and by split-stepFourier simulations (markers). See ref [45].

zyx zy zyxwvuts zyxwvuts 13. Nonlinear Optical Effects in WDM Transmission

623

is greater; however, the conversion of this phase modulation to intensity distortion is lower due to the lower fiber dispersion. This trend was confirmed in experimental pump-probe measurements comparing XPM in the two fiber types, each with a span length of 80km [39]. The XPM-induced intensity distortion was found to be approximately two times larger in the dispersionshifted fiber, due to the smaller effective area of 55 ,urn2 compared with the 80 ,urn* of the standard fiber. Equation 13.18predicts areduction in intensity distortion as the wavelength spacing is increased due to the increase in the walk-off between the chanA ~ , appears in the denominator terms of the transfer nels, dsp = D ~ M F which function, Hsp.Pump-probe experiments have been carried out by a number of groups confirming the inverse relationship between channel spacing and XPM distortion. Figure 13.5 shows the experimentalresult of pump-probe measurements [40] over a two-span, dispersion-compensated standard fiber link, also shown in Fig. 13.5. The standard deviation of the detected probe level, C T X ~ M , is plotted as a function of wavelength spacing, Ah, exhibiting the reduction with increasing spacing predicted by Eq. 13.18,.withC T X ~ M= 0.1 (normalized to the average detected probe power) with 0.4-nm spacing, reducing to < 0.02 for 2 nm and above. An experimentallymeasured probe waveformat the output of this two-span, standard single-mode fiber (DSMF= 17ps/(nm/km)) is shown in the inset of Fig. 13.5. The XPM high-pass filtering effect can be observed as the peaks in the distortion arising from the pulse edges in the PRBS pump waveform. In a practical system this would have the effect of causing additional noise on the “lyy-railand, hence, increase the bit-error rate. This is further addressed in the next section.

zyxwvu zyxwvutsr Pattern generator 10 GbiW

Probe

zyxwvutsrqp DCF1

E

b

0

0.5

1

1.5

2

Wavelength spacing (nrn)

Fig. 13.5 Left: Pump-probe experiment, over a two span link with standard singlemode fiber (D = 17ps/(nm/km)) and pre- and post-dispersion compensation. Channel launch powers: 13 dBm in the first span, 9 dBm in the second. Right: Standarddeviation of the probe distortion with a PRBS modulated pump signal, as a function of channel spacing, experimentalvalues (markers) and simulations, with parallel and orthogonal polarization states (lines). Inset: Measured distorted probe waveform. See ref [40].

624

zyxwvutsr -zyxwvut

zy zyxwvuts

Polina Bayvel and Robert Killey Repeated section

Transmitters

60 krn 12km SSMF DCF

ODOCn.

20 krn SSMF

Demux

Receiver

Fig. 13.6 Multi-span transmission system, used for pump-probe and Q-factor measurements to characterize XPM distortion.

zy zyx

As already mentioned, the appropriate positioning of the dispersion compensation element can partially suppress XPM intensity distortion. One effective dispersion management technique is to place the compensators so that the residual dispersion between the position of XPM generation and the receiver is minimized. This keeps the value of &res) in Eq. 13.15 low, hence reducing the phase-to-intensity conversion. To investigate this, multispan, distance-dependent pump-probe experiments have been done using a recirculating fiber loop [33], simulating a typical setup shown in Fig. 13.6. The positioning of the DCF at the end of each span achieves the desired reduction of the XPM-induced intensity distortion, resulting in a measured normalized value of ~ Q M< 0.12 after 7 spans (see Fig. 13.7). The effects of XPM and fiber dispersion can result both in vertical eye closure and jitter, depending on the modulation format, and are described in the next two sections. However, with increasing spectral efficiencies in WDM systems, that is the ratio of bit rate to channel spacing, spectral overlap between adjacent channels causes additional penalties. This is exacerbated by XPM-induced spectral broadening, and leads to eye closure due to the interferometriccrosstalk between the signal and the sidebands of the adjacent channels, as has been shown in [41,42]. 4.2 PM-INDUCED AMPLITUDE DISTORTION PENALTY IN NRZ TRANSMISSION

The XPM-induced penalties in systems using NRZ signal formats result mainly from vertical eye closure. In fact, it has been shown that the intensity noise on the “1” level is of a similar amplitude to that of the distortion of a cw probe channel [43,44]. Hence, Eq. 13.18 can be used to directly estimate the XPM-induced penalty. With a PRBS in the interfering channel, the waveform of the cw probe intensity at the output of the link is detected and electrically filtered by the receiver. The additional standard deviation caused by XPM, q p ~ of, the resulting received voltage can then be included in the calculation of the Q-factor. If there are contributions to the distortion from many channels and over a number of spans, the XPM distortion approachesa

zyx zyx zyxwvu

13. Nonlinear Optical Effects in WDM Transmission

625

normal distribution from the Central Limit Theorem, and the BER is given by, 1 BER = -e$c 2

(-$) ,

(13.22)

zyxwvu zyxw zyxwvu zyxwvu

where the Q-factor can be given by,

(13.23)

where and po are the “1” and “0” levels, a1 and a0 are the standard deviations of the levels due to electrical and ASE noise and a x p is ~ measured or calculatedusing Eq. 13.17 [45]. In fact, the accuracyof Eq. 13.23improveswith increasing number of interfering channels, but it has been shown to provide a sufficientlyaccurate estimate even for two channels. For the transmission over multiple amplified spans [44,45], the distortion increases with distance, but critically depends on the dispersion map used, which determines the shape of the pulses in the interferingchannels. For example, for links with exactly postcompensated amplified spans, the distortion increases approximatelylinearly but with a reducing slope over distance due to SPM-inducedpulse broadening in the interfering channel. In this case, in Eq. 13.17, rather than assuming an undistorted pump waveform Pp(O,w ) at the input to each span, the accuracy of the calculation can be improved by modifyingPp(O,w ) to account for SPM and dispersion, as shown in Fig. 13.7. The graphs in this figure also show the measured values of the Q-factor as a function of channel spacing in an experimental 6-span system with launch power of 8 dB per channel into each span. The XPM-induced degradation of the Q-factor by 2.5 dB with 0.4-nm channel spacing is predicted by Eqs. 13.17 and 13.23, and the Q-factor increases with channel spacing, confirming that a x p ~ is inversely proportional to walk-off as expected, since dsp appears in the denominator of Eq. 13.18. 4.3

COLLISION-INDUCED DISTORTION PENALTIES DUE TO XPM IN RZ TRQNSMISSION

For potential applicationin long-haullandline and transoceanicsystemsspanning several thousand kilometers, the return-to-zero signal is typically used due to its robustness to self-phasemodulation in systemswhere the dispersion length LD > LNL.Unlike NRZ signals, each pulse has the same shape, and the systemdispersion map and initial pulse chirp can be optimizedto achieve longdistance, stable propagation. This has been demonstrated by many groups through the use of variously termed RZ, chirped RZ pulses, and dispersion managed (DM) solitons [46-501. The RZ pulses, in general, are more resistant to SPM and chromatic dispersion as all pulses are distorted in the same way, unlike NRZ, leading to lower patterning, Le., distortion that is dependent on the bit sequence. Chirped RZ (CRZ), in which the instantaneous frequency

626

zyxwvutsr Polina Bayvel and Robert Killey

10

9 0.15

zyxwv zyxwvuts 7

0.05

zyxwvuts zyxwvuts 6

0 0

1

2

3 4 5 Number of spans

6

7

0.5

1

1.5 2 ~ i f(nm-') i

2.5

3

Fig. 13.7 Lej?: Standard deviation of probe channel XPM distortion in a 10Gbit/s/channel transmission experiment over multi-span system with 8 dBm pump power and channel spacing of 0.4 nm. Experimental values (markers), calculated values (line).Ref [45].Right: Q-factor vs channel spacing in the same multi-span systems after transmission over 6 spans with 8 dBm per channel. Values predicted from pump-probe

calculation (line) and directly measured values (markers). varies linearly across the pulse at the transmitter, using either a phase modulator or dispersivefiber, are used to overcome the effects of SPM and nonoptimal accumulated link dispersion. This could occur in wideband WDM systems where the dispersion slope (or third-order dispersion) is not fully compensated over the wavelength comb. Potentially the longest transmission instances can be achieved with dispersion-managedsolitons. To generate these, a high local dispersion (relative to the path-average value) is used with periodic compensation to achieve a low value of anomalous path-average dispersion. The SPM and path-average dispersion balance each other, as in conventional soliton transmission, although the pulse width varies periodically along the transmission length, (also termed pulse-breathing), with the period of the dispersion map. The initial pulse width and peak power have to be carefully selected to achieve output pulse width and spectrum that are the same as the input values, and depend on both the path-average and the local dispersion values. The advantages of DM solitons over conventional solitons that use low, uniform fiber dispersion include their increased signal energy for a given path-average dispersion, which improvesthe achievable signal-to-noise ratio and reduces the Gordon-Haus jitter. Compared to conventional solitons based on dispersionshifted fiber, all these dispersion-managed RZ formats are compatible with WDM transmission; however, although the dispersion management of these RZ systems effectivelyreduces interchannel distortion in WDM transmission, timing jitter and amplitude distortion due to XPM still occur, and techniques to understand and evaluate their impact have recently been explored by a number of groups.

13. Nonlinear Optical Effects in WDM Transmission

627

With multichannel transmission, the pulses in different channels propagate at different velocities due to the high local dispersion of the fiber, and consequently, collisions between pulses (i.e., two or more pulses at different wavelengths, spatially overlapping and walking through each other) occur during transmission, leading to nonlinear crosstalk. To minimize the nonlinear crosstalk, extremely low channel powers are required [50], limiting the transmission distance to a maximum (to date) of 4500 km for 32 WDM channels at 40 Gbit/s [51]. The effect of XPM during the collisions is not only to distort the pulse amplitude as in NRZ systems, but also to vary the arrival times of the pulses at the receiver. This contributes to the total timing jitter defined as the standard deviation of the timing shifts of all the pulses. Both of these impairments are described in Fig. 13.8. Much work has focused on characterizing the XPM-induced timing jitter in dispersion-managed RZ systems, and optimizing the dispersion map to minimize this effect. The timing shift of a probe pulse arises from the shift of its carrier frequency, Aws, due to a collision with a pump pulse. Applying the soliton perturbation method to the nonlinear Schrodinger equation [52], the XPM-induced frequency shift of the probe pulse, Ams, and timing separation of the peaks of the pump and probe pulses, AT,, are given by,

zy

zyx zyxwv zyxwv zy 100ps%-dt’

d(Aw,) -2y(z) dz - EO

O0

aP,

(13.24) (13.25)

AmmM=

IA. zyxwvuts I$ zyx loL*&

=

L

0

dP -2yLdz dt

Velocity change, giving timing jitter:

Power at 4

Power at

“=AmXPMN&es)

Chirp-induced amplitude distortion

Fiber

time

AwXPMata,

.dispersion

N-number of spans following XPM &,,-residual dispersion per span

Fig. 13.8 Schematic of the process of pulse collisions and the effect of interchannel cross-phase modulation, explaining the mechanism for the resultant pulse amplitude distortion and timing jitter.

628

zyxwv zyxwvuts zyxwvu zyxw Polina Bayvel and Robert Killey

where EO is the probe pulse energy and P, and Pp are the pump and probe powers at distance z. A consequence of the XPM-induced frequency shift, Ams, in the ith amplifier span is a timing shift, At,, of the received pulse due to the residual dispersion of the following N - i + 1 spans: ATs = Aws(N - i

+ 1)BZ(reS),

(13.26)

where is the residual accumulated dispersion of each span. A major contribution to the net frequency shift arises from incomplete collisions, for example those resulting from pulses initially overlapping at the input [53], or the collision of pulses at a line amplifier, in which a large change in the signal power occurs midway through the collision. In this case, the frequency shift caused by one pulse edge is not compensated by a shift in the oppositedirection due to a followingedge, as is the case for the less damaging complete collisions, in which pulses f d y pass through each other. For Gaussian-shaped pulses with powers P = POexp (- t2/T;)that overlapwith their peaks separatedby ATspat the input to a span, the XPM-induced frequency is given by the approximate solution of Eq. 13.24,

zyx zy zyxw (13.27)

derived by using the approximation of Eq. 13.24 d(Aw,)/dz FZ -2y(dFp/dt), where dPp/dtis the time derivative of the pump pulse at the center of the probe pulse at distance z. The calculated value of Aw, can then be used in Eq. 13.26 to obtain the collision-induced timing shift At,. A number of groups [5&56] have pointed out the benefit of increasing the local dispersion of the transmission fiber in long distance dispersion-managed WDM transmission, due to the reduced walk-off length (TFWHMIDAh) between pulses and hence lower XPM timing jitter. The values plotted in Fig. 13.9 illustrate the dependence of the XPM-induced timing shift on the local dispersion. The timing shift, AT, of a 35-ps FWHM probe pulse resulting from a single overlapping pump pulse, calculated by Eq. 13.27, is plotted for a 20-span soliton system with transmission fiber dispersion D ~ M= F 8 ps/(nm.km), dispersion compensation at every line amplifier with spacing 60 km, and launched pulse peak power PO = 20 mW. With a channel spacing of Ah = 0.4 nm, the timing shift is 20 ps, or 20% of the 10Gbit/s bit period. The benefit of using a high local dispersion in reducing XPM jitter becomes apparent when the calculation is repeated with the local dispersion increased to DSMF= 17ps/(nm.km). In this case, the walk-off length of the pulses is halved, and at a channel spacing of 0.4 nm, the timing shift induced by the pulse collision is reduced to 10ps. Figure 13.9 also shows the results of copolarized pump-probe measurements of the XPM-induced timing jitter, in a recirculating loop transmission experimentfor 10 Gbit/s dispersion-managedsoliton transmission with 8 dBm

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an interfering pulse with 0.4nm separation and spatially overlapping at the input. Gaussian pulses with To = 35 ps and peak power Ppk = 20 mW. Markers: Simulations. Lines: From approximate solution of Eqs. (13.24-1 3.26). Transmission fiber dispersion: 8 ps/(nm.km) (squares) and 17 ps/(nm.km) (circles), with inline undercompensation of 5%. Right: Copolarized pump-probe measurements of the XPM-induced timing jitter in 10 Gbit/s dispersion-managed soliton transmission, eight dBm channels, channel spacing 0.4 nm. Transmission fiber: SSMF with 17 ps/(nm.km). Inset: Eye diagrams after transmission over 1800km with 100 GHz (Zeft) and 1500km with 50GHz (right) channel spacing, respectively, showing severe eye distortion due to XPM with narrow channel spacing. See ref. [56].

power per channel, carrying decorrelated pseudorandom bit sequences, and spaced by 0.4 nm. Transmissionfiber with 17 ps/(nm.km) dispersion was used and the span length, including DCF, was 74 km. The standard deviation of the timing shift as a function of distance with at = 7.1 ps reached after 20 spans. It is interesting to compare these results with the calculations described previously, where the collision of only two pulses was considered. Despite the increased number of pulses within the PRBS sequence, the magnitude of the timing jitter is comparable to the timing shift arising from the collision of only two pulses overlapping at the input. This can be explained as follows. In dispersion-managed systems with in-line dispersion compensation within each span, so that the residual accumulated dispersion, D,,, of each span is low and the dispersion-map period is equal to the amplifier span length, the net pulse walk-off between adjacent line amplifiers is only a fraction of the bit period rbit (DresAh.> T, the effect becomes small, as the pulse power is low due to the large broadening. It would appear that allowing the pulses to broaden out during transmission, and only using dispersion compensation at the receiver, so that t >> T during transmission, would be an effectivetechnique to minimize intrachannel XPM. This technique, termed “quasi-linear”propagation has been successfullydemonstrated with 160-320Gbit/s transmission experiments [58,59]. However, for pulse widths in the range t / T =- 1, a second intrachannel nonlinear effect occurs [60],namely four-wave mixing between the frequency components of adjacent, now overlapping pulses, within the same wavelength channel, which results in the depletion of the pulse energies and power transfer into the “zero” bit slots, schematically shown in Fig. 13.12. The result is an increase in the noise on the “zero” and “one” rails, 00 and cq in Eq. 13.23, as can be seen in Fig. 13.13, and a corresponding reduction in the Q-factor. Intrachannel FWM has been experimentally observed [61] in NZDSF and

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standard single-mode fiber at 40 Gbit/s in an 80-km span with up to 20 dBm channel power, and theoretically analyzed in [62]. One technique to simultaneously minimize both of these effects is to appropriately precompensate part of the fiber dispersion [63,64] to minimize the pulse overlap during transmission, without significantly increasing interchanne1 XPM. Figure 13.14 shows the calculated values of intrachannel XPM jitter at the receiver of a 12-span system (DSMF= 17ps/(nm.km)) as a function of precompensation for different channel powers. It is striking that the distortion is minimized for the same value of precompensation (compensating approx. 10km of transmission fiber) which minimizes the path-average pulse width during transmission. In general, reducing the transmission fiber dispersion reduces pulse broadening and hence intrachannel FWM, so that for >40-Gbit/s systems, the use of non-zero-dispersion-shiftedfiber is attractive. This provides an optimum value of dispersion where both intra- and interchannel distortion are reduced, and for wideband WDM systems, a low dispersion slope is important to maintain the optimum dispersionvalue across the wavelength range of the signals.

6. Suppressing Nonlinear Impairments The analysis of SPM, FWM, and XPM in the previous section highlights the requirement for careful dispersion-managementin long-distance WDM links. To avoid intersymbol interference due to the linear group velocity dispersion, it is necessary to minimize the accumulated dispersion of the link. At high powers and bit rates, and over long distances when the effect of SPM becomes

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zyxwv zyxwvutsr zyxwvut Polina Bayvel and Robert Killey

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significant, a small anomalous path-average dispersion is desirable to avoid the pulse broadening that occurs when the SPM chirping is followed by normal dispersion, D < 0 ps/(nm.km). Hence, for high-speed single-channel transmission, independent of format, fiber with a low, uniform value of dispersion is sufficient for good performance, such as dispersion-shifted fiber (DSF), with dispersion, 0 < DDSF < lps/(nm.km) at the operating wavelength, h = 1.55pm. However, in dense WDM transmission, more complex dispersion management is needed to minimize inter and intrachannel effects simultaneously. Non-zero dispersion fiber, Le., with sufliciently high values to suppress interchannel FWM and XPM, must be used, and the fiber dispersion is compensated, either using spans of transmission fiber with alternating sign of dispersion (sometimes called reverse-dispersion compensation) or by using periodic lumped compensators, such as dispersion compensatingfiber (DCF), DDCF M -100 ps/(nm.km) or dispersion-compensating fiber gratings, as shown in Fig. 13.15, and the positioning of these dispersion compensators afTects the performance of the system.

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50

100

150

200

250

Distance (km)

F'ig. 13.15 Accumulated dispersion of two typical dispersion managed system maps. Top: Spans of standard single-mode fiber, with dispersion compensation at the amplifiers: local dispersionis kept high to minimize interchannelnonlinearities,whilst the low overall anomalous path-averaged dispersion minimizes SPM-induced pulse broadening. Bottom: Spans of alternating positive and negative dispersion NZDSF optimized to maintain the pulse shape in ultra-high channel bit-rate systems.

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A number of components and techniques have been developed to further suppress the distortion caused by fiber nonlinearities. The most direct is the use of large effective area fiber. By optimizing the fiber index profile, values of A,ff as high as 100-170 p,m2 have been achieved with a range of dispersion values ranging from several ps/(nm.km) up to >20ps/(nm.km) [lo]. From Eq. 13.3, it can be seen that the nonlinear phase shift is inversely proportional to the effective area, and thus assuming the dispersion map is optimized, long-distance transmission with narrow channel spacing can be achieved. A second technique is the use of Raman amplification employing counterpropagating pump light from the end of the span, and using the transmission fiber itself as the gain medium. This allows the signal launch power to be reduced while maintaining an adequate signal-to-noise ratio at the receiver, thus reducing nonlinear distortion at the start of the span. This technique is used to reduce the launch power by typically 10dB, or alternatively, increase the interamplifier span length by approximately50 km.AlternativelyDCF can be used simultaneouslyas a gain medium and for dispersion compensation. The use of orthogonal polarization states of adjacent WDM channels is effective at reducing the distortion due to XPM and FWM. From Eqs. 13.12 and 13.13, it can be seen that the XPM is reduced by two-thirds, and the fourwave mixing becomes negligible. The effectivenessof this technique is reduced by the polarization-mode dispersion of the fiber (described in Chapter 15, OFT IVB), which is wavelength dependent and leads to a change in the relative alignment of the channels. In addition, nonlinear polarization rotation caused by cross-phase modulation further reduces its benefits. However, from the discussion in Section 3.3, a large component of XPM distortion in long-haul systems arises from the incomplete collisions of the pulses at the input, and at this point in the system, the polarization states of the signals have not been affected by the transmission. In optical time-divisionmultiplexed systems operating at 40 Gbit/s and above, intrachannel distortion limits the system performance, and in this case, the use of alternatingpolarizationstatesbetween pulses in the same channel is effective at suppressing intrachannel XPM and FWM, see for example [65]. Further development of optimized dispersion maps is expected to allow increased system performance. New “continuous dispersion-managed” fiber, alternating normal and anomalous dispersion with periods of as short as 1km,will improve single-channeltransmission while simultaneouslyminimizing interchannel four-wave mixing, as described in the previous section. This will be combined with low dispersion slope over the wavelength range of the broadband signals, allowing the optimum dispersion profile to be obtained for all the WDM channels. Work is underway on optimizing the signal format, with promising modulation formats, including the more spectrally efficient carrier-suppressedRZ. Much work has been devotedto answeringthe question of which fiber has the optimum dispersion to minimize all the nonlinearities. Figure 13.16 shows the choice facing the designer; for a given channel bit

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rate and signal format, an optimum choice of fiber dispersion exists that can minimize all nonlinearities for all channel powers and distances. Thus, one of the open questions for the future is what fiber properties, in addition to the large effective area, are required to reach the fundamental limits to fiber capacity, and what tolerances in the management of the chromatic dispersion and dispersion slope are necessary to achieve these limits. Although there are different metrics to quantify the transmission limits (total number of channels, channel spacing, bit rate per channel, achieved transmission distance), a convenient measure for comparison is the bit rate x distance product for any given experiment. As this chapter goes to press, the highest reported aggregate transmission capacity is 29 petabits/s/km-using 365 x 11.6Gbit/s NRZ-modulated channels over 6850 km in standard singlemode fiber compensated by reverse-dispersion fiber [3]. By comparison, at 40 Gbit/s, this is approximately 6 petabits/s/km, achieved with RZ modulation (4500 km with 32 channels over carefully dispersion-managed spans of standard and reverse-dispersion fibers) and filtered-NRZ (125 channels over 1200km of non-zero dispersion-shifted fiber compensated by DCF) [5 1,661. The decreased bit rate x distance product is a result of the combination of the increased noise accumulation dominated by amplified spontaneous emission, but mainly due to the increase in the nonlinearities at this increased bit rate. The highest reported single channel experiment at 1.28 Tbit/s, the achieved transmission distance, was only 70 km, limited by the difficulty of propagating

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such short pulses [67J The future research in this area will attempt to identify what is practically achievable at bit rates higher than 40 Gbit/s (80-320 Gbit/s per channel), the optimal modulation formats as well as in optimizingthe fiber properties and increasing the dispersion tolerances. The future research aims to continue to investigateand combat the nonlinearitiesin order to propagate and route the largest possible capacities over long distances, and the understanding of the fundamentallimits to fiber transmission are likely to drive the developmentof this exciting, rapidly changing and competitivefield of optical networking in the Coming years. It should be noted that throughout this chapter, residual or residual accumuZated dispersion Ips/nm] is &fined as the fiber chromatic dispersion integrated over distance between two specified positions along the link. Path-average dispersion [ps/(nm.km)] is used for dispersion-managed links with repeating sections of positive and negative dispersion with period L. Dehed as the residual accumulated dispersion over N periods of the dispersion map, divided by NL, where N is an integer.

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Acknowledgments

The authors would like to thank their colleagues Hans Jorg Thiele, Vitaly Mikhailov, and other members of the Optical Networks Group (UCL) for their contributions to the modelling, experiments, and discussions that have been included in this paper, as well as for critical reading of this paper. Alan Robinson of Nortel Networks (Harlow, UK) and Chris Park of Agilent Technologies (Ipswich, UK) are also thanked for their comments. Support from the Engineering & Physical Sciences Research Council and the Royal Society is gratefully acknowledged.

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[56] V. Mikhailov, H. J. Thiele, R. I. Killey, P. Bayvel, “Experimental investigation of collision-induced timing jitter and pulse distortion in WDM return-to-zero dispersion-managed systems,” Proc. OFC 2001, vol. 2, pp. TuN4.1-TuN4.3, Anaheim, CAYMarch 2001 [57] S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, K. Mori, “3Tbit/s (160Gbit/s x 19 channel) optical TDM and WDM transmission experiment,” Electron Lett. 35,826 (1999) [58] G. Raybon, B. Mikkelsen, R.-J. Essiambre, A. J. Stentz, T. N. Nielsen, D. W. Pekham, L. Hsu, L. Gruner-Nielsen, K. Dreyer, J. E. Johnson, “320 Gbit/s singlechannel, pseudo-linear transmission over 200 km of nonzero-dispersion fiber,” Photon. Tech. Lett. 12, 1400 (2000) [59] R. Ludwig, U. Feiste, S. Diez, C. Schubert, C. Schmidt, H. J. Ehrke, H. G. Weber, “Unrepeatered 160Gbit/s RZ singlechannel transmission over 160km of standard fiber at 1.55 bm with hybrid MZI optical demultiplexer,” Electron. Lett. 36, 1405 (2000) [60] P.V.Mamyshev, N. A. Mamysheva, “Pulse-overlappeddispersion-manageddata transmission and intrachannel four-wavemixing,” Optics Lett. 24,21, 1454-1456, 1999 [61] R.-J. Essiambre, B. Mikkelsen, G. Raybon, “Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems,” Ekctmn. Lett. 35, 18, 1999 [62] A. Mecozzi, C. B. Clausen, M. Shtaif, “Analysis of intrachannelnonlinear effects in highly dispersed optical pulse transmission,”Photon. Tech. Lett. 12,4,392-394, 2000 [63] P. Harper, S. B. Alleston, I. Bennion, N. J. Doran, “40 Gbit/s dispersion managed soliton transmission over 116Okm in standard fiber with 75km span length,” Electmn. Lett. 35,24, 1999 [64]R. I. Killey, H. J. Thiele, V. Mikhailov, P. Bayvel, “Reduction of intrachannel distortion in 4O-Gb/s-based WDM transmission over standard fiber,” Photon. Tech. Lett. 12, 12, 1624-1626,2000 [65] E Matera, et al., “Field demonstration of 40Gb/s soliton transmission with alternate polarizations,” J. Lightwave Tech. 17,2225 (1999) [66] S. Bigo, et al., “Transmission of 125 WDM channels at 42.7Gbit/s (5Tbit/s capacity over 12 x 100km of Teralight Ultra fibre,” Proc 27th European Conference on Optical Communications,ECOC2001, October 2001, Amsterdam, paper PD.M.1.1 [67l M. Nakazawa, T. Yamamoto, K. R. Tamura, “1.28 Tbit/s-70km OTDM transmission using third- and fourth-order simultaneousdispersion compensationwith a phase modulator,” Electron. Lett. 36,2027 (2000)

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Chapter 14 Fixed and Tunable Management of Fiber Chromatic Dispersion Alan E. Willner

University of Southern California,Los Angeles, California and Phaethon Communications, Inc.. Fwmont, California

Bogdan Hoanca Phaethon Communications, Inc., Fwmont, California

I. Introduction In 1993, Linn Mollenauer of Bell Laboratories mentioned to us a simple thought that we think puts this chapter into perspective. He said, “One can transmit infinite bandwidth over zero distance.” Unless the fiber issues of chromatic dispersion and nonlinearities are managed in a transmission link, propagation of high-speed signals over nontrivial distances may be impractical. As recently as 1998, a debate was raging as to whether 10-Gbids systems were needed given the simplicity of deploying more 2.5-Gbith wavelengthdivision-multiplexed(WDM) channels. At 2.5 Gbids, the optics and electronics were fairly straightforward to implement. In what seemed like the blink of an eye, the debate ended in 1999 when Nortel was able to successfully sell -$6 billion of lO-Gbit/s equipment. Although 2.5-Gbids equipment still accounts for a sizable fraction of the optical communications market, we are now squarely in the lO-Gbit/s phase of deployment. The new debate now raging concerns the timing of 40-Gbids systems deployment. When progressing from 2.5- to 10-Gbidssystems, most technical challenges are less than four times as complicated and the cost of components is usually much less than four times as expensive. One critical exception to this “rule” is the deleterious time-spreading effect that optical-fiber-induced chromatic dispersion has on the transmission of a data bit stream; chromatic dispersion can be illustrativelythought of as the effect that each photon within a single bit exists at a slightly different frequency and travels down the fiber at a slightly different speed. When increasing the bit rate by a factor of 4, the effect of chromatic dispersion increases by a staggering factor of 16! Furthermore, chromatic dispersion effects increase linearly with transmission distance. To put this transmission problem in perspective, we can compare the longest distance that a data channel can be transmitted over conventionalsingle-mode fiber. Whereas dispersion limits a 2.5-Gbit/s channel to roughly 900 km (1 dB power penalty), a 10-and 40-Gbids channel would be limited to approximately 642 OITICAL FIBER TELECOMMUNICATIONS, VOLUME IVB

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Copyright 0 2002, Elscviu Science (USA). All rights of reproductionin any form r e ~ e ~ e d . ISBN 0-12395173-9

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60 and 4 km, respectively. Some method of dispersion compensation must be employed for a system to operate beyond these distance limits. Although this was not much of an issue for 2.5-Gbit/s systems, it is crucial for transmitting more than 10Gbit/s. Chromatic dispersion is one of the most basic characteristics of fiber. Although it is possible to manufacture fiber that induces zero chromatic dispersion, it should be emphasized that such fiber is incompatible with the deployment of WDM systems since harmful nonlinear effects would be generated. As long as WDM is dominant in the marketplace, chromatic dispersion must exist, and therefore must be compensated. In theory, compensation of chromatic dispersion for high-speed or longdistance systems can be fixed in value if each link’s dispersion value is known. However, there are several important aspects of optical systems and networks that make tunable dispersion compensation solutions attractive, including: (1) it significantly reduces the inventory of different required types of compensation modules, (2) it tunes to adapt to routing path changes in a reconfigurable network, (3) it tracks dynamic changes in dispersion due to environment, and (4)it achieves a high degree of accuracy necessary for 4O-Gbit/s channels. Dispersion compensation enables robust optical systems that can accommodate longer distances, higher speeds, and/or network reconfigurability. This chapter will address the issues surrounding the compensation of chromatic dispersion in high-performance optical systems. We will describe the effects of dispersion, various k e d compensation techniques, the need for tunable compensation and its potential solutions, and also techniques for monitoring accumulated dispersion.

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11. Chromatic Dispersion and Its Effects on Optical Fiber Systems ILa. FUNDMENTM CONCEPTS

In any medium other than a vacuum and in any waveguide structure, different electromagnetic frequencies propagate at different speeds. This is the essence of chromatic dispersion. Chromatic dispersion in optical fibers is due to the frequency-dependent nature of the propagation characteristics for both the material (the refractive index of glass) and the waveguide structure [l].Using a Taylor-series expansion of the value of the refractive index n as a function of the wavelength h, the speed v of a particular wavelength will be:

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where co is the speed of light in vacuum, ho is a reference wavelength, and the terms in a n p i and a2n/ah2are associated with the chromatic dispersion

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and the dispersion slope (Le., the variation of the chromatic dispersion with wavelength), respectively. (Note that frequency and wavelength can, to some extent, be used interchangeably and are related by the relationship c = f . A). This speed is constant for a single, monochromatic frequency. However, any type of modulated data has a nonzero spectral width and has an inherent information bandwidth that spans a range of frequencies that is roughly the same order of magnitude as the bit rate itself. These different spectral components of modulated data travel at different speeds down the fiber. In particular, for digital data intensity modulated on an optical carrier, chromatic dispersion leads to pulse broadening, which in turn limits the maximum data rate that can be transmitted through optical fiber (see Fig. 14.1). One can think of an optical “Iy7bit pulse as being composed of many different frequency components, with each frequency component propagating along the fiber at a slightly different speed. The pulse temporally broadens, causing a penalty of the “1 ” bit and significant intersymbol interference. Depending on the diameter of the fiber, either one or more spatial modes can propagate through the fiber. In multimode fiber (that typically has a core diameter greater than or equal to 50 microns), modal dispersion (different spatial modes traveling at different speeds) is very large, perhaps 100 times larger than chromatic dispersion. This is why multimode fiber cannot be used for high-speed or long-distance propagation. Single-mode fiber (SMF) is fabricated such that only one mode can propagate through the fiber and its

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14. Fixed and Tunable Management

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core is typically 8-12 microns in diameter. But even for single-mode fiber, the spectral broadening due to the data modulation itself makes chromatic dispersion a very important signal degrading effect for 2 10-Gbit/s data rates. This chapter deals with the management of chromatic dispersion in single-mode fiber only. The effect of chromatic dispersion is cumulative and increases linearly with transmission distance. More importantly, it increases quadratically with the data rate. The quadratic dependence of dispersion with the data rate is a result of two effects, each with a linear contribution. First, a doubling of the data rate will double the Fourier-transformed frequency spectrum of the signal, thereby doubling the effect of dispersion. Second, the same doubling of the data rate makes the data pulses only half as long in time and therefore twice as sensitive to temporal spreading due to dispersion. The combination of a wider spectrum and shorter pulse width leads to the overall quadratic impact. Dispersion are usually measured in picoseconds of delay per nanometer of signal spectral width per kilometer of transmission Lps/(nm . km)]. Conventional single-mode fiber has positive dispersion at 1550 nm in which longer wavelengths experience longer propagation delays. Note that there are three signal-wavelength regions for standard fiber: positive dispersion, negative dispersion, and zero dispersion at 1310nm in which all optical frequencies travel at the same speed. The conventional wisdom for the maximum distance over which data can be transmitted is to consider a broadening of the pulse equal to the bit time period. For a bit period Bya dispersion value D and a spectral width Ah, the dispersion-limited distance is given by LD

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(see Fig. 14.2). For example, in standard single-mode fiber for which D = 17ps/(nm. km) at a signal wavelength of 1550nm, the maximum transmission distance before significant penalty occurs for 10-Gbit/s data is LD = 52 km. In fact, a more exact calculation shows that for 60 km, the dispersion-induced power penalty is less than 1dB (see Fig. 14.3). The power penalty for uncompensated dispersion increasesexponentiallywith distance, and dispersion must be compensated to maintain good signal quality. 1I.h HISTORICXL PERSPECTIVE

Historically, the two signal wavelengths of greatest interest in standard singlemode fiber were 1310 and 1550nm, the wavelengths for which, respectively, the fiber causes zero chromatic dispersion and the fiber has a power loss minimum. Initially, the greater concern was chromatic dispersion, and fiberoptic communications started in the 1310-nm window. At the time, optical communications was achieved using a single channel from a single greater

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than nm-wide multifrequency-mode Fabry-Perot laser transmitter, which was placed at the zero-dispersion wavelength of the fiber. The need for more capacity over longer distances was satisfied first with the adoption of single-frequency-modedistributed feedback (DFB) [2] lasers

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and later with the advent of erbium-doped fiber amplifiers (EDFA) [3]. The EDFA enabled several independent wavelength channels to be transmitted over a single fiber and amplified economically in a single device, thereby opening the low-loss 1550-nm window to WDM. Unfortunately, SMF has a fairly large chromatic dispersion value of 17ps/(nm . km) for this wavelength range (Fig. 14.4). The first WDM systems were not terribly concerned with chromatic dispersion since the data rates used were OC-48 (2.5 Gbids) and lower, accommodating over 600 km of transmission before dispersion compensation was required. It is important to emphasize that early 2.5-GbWs system integrators needed to address the issue of optical modulation. A DFB laser may lase in a single frequency, but its spectrum is “chirped” and spread across a much wider bandwidth when the optical power is modulated by directly turning the laser’s current ON and OFF. This additional chirping of the signal can be as large as 10 GHz, and will increase the deleterious effects of dispersion. In order to avoid this additional problem, external optical modulators were used. These modulators, such as lithium niobate Mach-Zehnder [4] and on-chip semiconductor electroabsorption [5] types, tend to not introduce a chirping of the signal. External modulators are used in many 2.5-Gbids systems and in almost all 10-Gbit/s systems. With the deployment of the first OC-192 systems, it became apparent that dispersion would become a severe limitation. At OC-192, dispersion-limited distances in SMF are as short as 60km. An instructive simulated view of signal degradation is shown in Fig. 14.5 in which a lO-Gbit/s signal is severely distorted after being transmitted over 100km of standard fiber, whereas a 2.5 Gbit/s signal is not affected at all by dispersion over the same distance. Over the course of the 1980s,another parallel track was taking place. Fiber manufacturers saw value in fabricating an optical fiber whose zero dispersion wavelength point coincided with the loss minimum of the fiber. The reasoning

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for pursuing dispersion-shifted fiber (DSF) was simplein terms of reducing the two main limitations imposed by the fiber itself. The feat of shifting the D = 0 point to 1550nm was achieved through a clever balancing of the material and the waveguide dispersion in which the shape of the fiber waveguiding core was modified [6]. The two parallel tracks for increasing performance of WDM and DSF met in the late 1980s and early 1990s with problematic results. Although it was always thought that chromatic dispersion is bad, it is, in fact, a necessary evil for the deployment of WDM systems. When the fiber dispersion is near zero in a WDM system, different channels travel at almost the same speed. Any nonlinear mixing effects that require phase matching between the different wavelength channels will accumulate at a higher rate than if the channels travel at widely different speeds (the case of higher-dispersion fiber). The deleterious nonlinear effects that tend to destroy the signal integrity are self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) [7]. A brief explanation of these effects are as follows: 0

S P M a n d P M . The index of refraction of glass is not only dependent on the frequency of light, but also on the intensity. A million photons “see” a different glass than does a single photon, and a photon traveling along with many other photons will slow down. SPM occurs because an optical pulse on a single WDM channel has an intensity profile, thereby causing an index profile and a speed differential causing temporal broadening. When considering many channels copropagating in a fiber, the scenario becomes much more complex. The photons from channels 2 through N can distort the index profile that is experienced by

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zyxwvutsrqp channel 1, potentially causing a very serious problem in implementing WDM. This effect is called cross-phase modulation [I]. FWM. As mentioned previously, the index of refraction of glass is dependent on the optical intensity. The optical intensity propagating through the fiber is the electric field squared. In a WDM system, the electric field is the sum of all the individual channel’s electric fields. When squaring the sum of different items, product terms emerge. Since the electric fields are cosines, these product terms are beat terms that are produced at various sum and difference frequencies of the original signals. If one of the WDM channels exists at one of the FWM beat-term frequencies, then the beat term will interfere coherently with this other WDM channel and potentially destroy the data [l].

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Both FWM and XPM are strengthened by interactions between wavelengths over long propagation distances. A dispersion value as small as a few ps/(nm . km) is sufficient to make XPM and FWM negligible (see Fig. 14.6) since the different wavelength channels are not phase matched and “walkoff” from each other quickly, thus ensuring that they interact with each other only over relatively short distances. Alternatively, FWM can be reduced by increasing the channel spacing (see Fig. 14.7), but this would greatly decrease the bandwidth capabilities of existing systems. Most systems are currently designed with channels on the ITU grid, spaced either 50, 100, or (less frequently) 200 GHz apart. The channel spacing is expected to decrease to 25 and (a)

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perhaps even 12.5 GHz, depending on the bit rate. This means that nonlinear effects can only be reduced by introducing nonzero dispersion, and that zero dispersion is simply not acceptable in WDM systems. To mitigate the effects of nonlinearities, the next generation of fibers introduced relatively modest amounts of chromatic dispersion. The intent was to avoid distorting the signal with too much dispersion, but still introduce enough dispersion to counteract the nonlinear effects. Two of the best-known nonzero dispersion-shifted fiber (NZDSF) types introduced in the mid-1990s are Corning’s large effective area fiber (LEAF) [8] and Lucent’s TrueWaveTMfiber. The dispersion of NZDSF is roughly 4-6 ps/(nm. km), low enough to allow transmission over longer distances than SMF but with a dispersion value large enough to reduce FWM and XPM that occurred in DSF. A historic irony occurred in Japan, where DSF was deployed extensively in the late 1980s and early 1990s [9]. At that time, WDM was still several years away from commercial acceptance and the best strategy was to attempt the best design for single-channel transmission. The nonlinearities of the DSF now make it difficult to deploy WDM in the so-called “C-band” conventional EDFA wavelength window of 1530-1570nmYwhere DSF has zero dispersion. Instead, Japan has been leading the efforts to utilize the wavelengths in the L-band at 1570-1610nmYwhere dispersion-shifted fiber has a dispersion of 2 4 ps/(nm km), nearly equivalent to using NZDSF in the C-band, and sufficiently high to allow WDM transmission with low impairments from nonlinearities. More recently, the trend seems to have become even murkier. Recent studies show that for very dense, high-channel-count, high-speed WDM systems,

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even the dispersion of NZDSF may be too low [lo]. Fiber manufacturers are returning to fibers with larger dispersion (see Fig. 14.4). For example, Alcatel has introduced a higher dispersion fiber VeraLight, 8ps/(nm km)].

I . c . CHROMATIC DISPERSION MANAGEMENT

The key to dealing with chromatic dispersion is that it must be managed rather than eliminated. To review, zero dispersion is not practical for WDM transmission and an accumulation of dispersion will eventually limit the system performance. A simple yet elegant solution is to create a dispersion "map," in which the designer of a transmission link alternates elements that produce positive and then negative dispersion (see Fig. 14.8). This is a very powerful concept: At each point along the fiber the dispersion has some nonzero value, effectively eliminating FWM and XPM, but the total accumulated dispersion at the end of the fiber link is zero, so that minimal pulse broadening is induced. In general, 10-Gbit/s systems over distances exceeding 100 km will use some form of dispersion management. The specific system design as to the periodicity of management depends on several variables, but a typical number for SMF as the embedded base is compensation every 80 km in a 10-Gbit/s system. Introducing negative dispersion along a link having positive dispersion can be referred to as either dispersion compensation or as dispersion management. There are many kinds of dispersion maps that are possible. A transmission system can be designed such that positive dispersion accumulates first or negative dispersion accumulates first. The specific technique may depend on the type of embedded fiber used and the type of traffic being transmitted. For example, SMF has positive dispersion, but some of the new varieties of NZDSF can have either positive or negative dispersion at 1550nm. Even reverse-dispersionfiber

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Dispersion Values (in ps/(nm.km)): SMF: +17, DCF -85, DSP: 40-Gbit/s channels. A key element of a dynamic dispersion compensator is a chromatic dispersion monitor in the feedback loop that can measure the required compensation while the data is being transmitted through the optical link. This is quite different from the more traditional chromatic dispersion measurement techniques in which dark fiber is usually measured off-line. Chromatic dispersion monitoring can be performed at the receiving end, where the Q-factor, eye diagram, or bit-error rate of the received data would be monitored to assess the accumulated dispersion. As data rates increase or if inline monitoring is needed, it may be highly desirable to monitor dispersion

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without necessitating the recovery of the data bits using expensive timing circuitry. Several schemes have been reported that can monitor dispersion online, fast, and at relatively low costs. We will first briefly describe two methods, and then we will describe two techniques in more detail in the following sections. One method is to monitor the conversion of a phase-modulated signal into an amplitude-modulated signal due to chromatic dispersion [77]. This requires adding a phase modulation onto the WDM channel at the transmitter and a phase modulation-toamplitude modulation measurementcircuit at the receiver. A simplified system was used to demonstrate fully automatic tuning ina lO-Gbit/s 1000-kmsystem. Another method is to use a variable threshold receiver and build a linkdispersion map as a function of the receiver threshold [124]. Based on this map, the optimum operating point in terms of both dispersion and receiver threshold can be used for system operation. Unfortunately, this method is limited to off-line monitoring.

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VILa. DISPERSION MONITORING USING RF POWER FADING

One of the simplest means of monitoring dispersion is based on dispersioninduced changes to the RF power spectrum of the signal [125]. Due to chromatic dispersion, the high-frequency components in the RF spectrum of the signal will be attenuated. Intuitively, this happens because of a fading effect. Chromatic dispersion induces a time delay between the sidebands corresponding to a certain frequency component. As the phase difference corresponding to this time delay increases, the sidebands become out of phase, to the point where the sidebands start canceling each other and the amplitude of the RF components becomes very small. Because of the nonlinear mixing of a continuum of frequencies in the signal spectrum, the phenomenon is rather complex, and does not result in the complete extinction of any frequency in a broadband signal, but can nonetheless reduce the amplitude. Moreover, the fading is periodic, such that the power of a given frequency will start increasing beyond a certain transmission distance. This limits the maximum useful range of the technique to the distance over which the amplitude change is monotonically decreasing (or increasing). In practice, an equalizer can be built with several banks of tunable filters that monitor different frequency passbands of the received signal. A weighted sum of the amplitudes of these spectral components can be used as the measure of dispersion-inducedsignal distortion.

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VILb. DISPERSION MONITORING USING NRZ CLOCK REGENERATIONAND RZ CLOCKFADING

Another powerful monitoring technique is also related to the power fading effect noted previously. In this method, the power variations of the signal’s

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40 km SMF

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clock frequency component is monitored [126]. It is well known that the power spectrum of an NRZ signal does not contain any power at the clock frequency (i.e., a 10-Gbit/sdata rate stream will not contain any power at 10 GHz where there is a null in the Fourier spectrum). The effect of dispersion is to regenerate the clock and to induce an increase in the power at the clock frequency (see Fig. 14.62). Within a range of values of signal dispersion, the clock power is proportional to the amount of accumulated dispersion. Beyond this distance, the clock power fades, but will continue to increase and decrease periodically with transmission distance (see Fig. 14.63). A chromatic dispersion monitor can be built, albeit limited to the first range of monotonic behavior. A similar approach was used to automatically compensate for dispersion in a 40-Gbit/s system over 200 km [78]. For RZ data, the technique can be used with a similar monitoring approach, but with the opposite phenomenon. The clock component in RZ data is relatively strong, but it fades and decreases under the effect of dispersion. Dispersion is inversely proportional to the power spectral density at the clock frequency over some finite range of dispersion values. Similar techniques can be used for optically time-division-multiplexed data [1271. By combining the two monitoring techniques presented above, the R F power monitoring and the clock power monitoring, the maximum distance can be substantially extended beyond the limits of using either of the two methods alone.

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VILc. DISPERSION MONITORING USING PEAK POWER

Considering the time-domain representation of the signal, it is possible to measure the chromatic-dispersion-induced distortion using a peak detector [125]. The concept is that chromatic dispersion will round the edges of the signal and will reduce the amplitide peaks of pulses. Hence, the output of a peak detector circuit is strongly correlated with the amount of chromatic dispersion affecting the signal.

VII.d. DISPERSION MONITORING USING DUTY CYCLE Another time-domain monitoring technique is based on measuring the duty cycle of a signal and is most suitable for RZ pulses [125]. Chromatic dispersion will tend to broaden the pulses, hence increasing the duty cycle of the signal. By using a threshold element, it is possible to measure the signal duty cycle, which is then indicative of the amount of chromatic dispersion on the signal.

VILe. DISPERSION MONITORING USING A PHASE SHIFT BETWEEN TWO WDM CHANNELS A final monitoring technique is to calculate the dispersion based on the relative delay between two WDM channels [128]. One channel is modulated only with the data, while another channel carries both its own data and a clock modulation in sync with the data of the first channel. By monitoring the phase delay between the data of the first channel and the reference clock modulated on the second channel, the change of dispersion can readily be calculated by a microprocessor. This technique was used to monitor and adjust the temperature-dependent dispersion for 40-Gbith transmission over 400 km

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14. Fired and ’Ihnable Management

707

of SMF.The change in the zero-dispersion wavelength was measured to be 30 pm/”C, and the dispersion slope changed by 27 ps/nm2. The dispersiontuning mechanism consisted of tuning the wavelength of the transmission lasers to track the changes in the zero-dispersionwavelength of the fiber. Temperature variations between 0°C and 40°C induced large power penalties for the uncompensatedcase, but no observable power penalty was observed when the monitoring and compensation loop was operating. The importance of monitoring techniques continues to rise, just as tunable dispersion solutions become more mature. When both technologies develop suiliciently, the natural symbiosis of online monitoring and fast tunable chromatic dispersion devices will lead to adaptive compensation modules.

VIII. Summary Chromatic dispersion is a phenomenon with profound implicationsfor optical fiber communicationssystems. It has negative pulse-broadeningeffects, but it also helps reduce the effects of fiber nonlinearhies For this reason, managing dispersion, rather than trying to eliminate it altogether, is the key. Several fixed compensation solutions exist, and several tunable solutions have also emerged. Tunable dispersion components may be needed to fully optimize a system, and such tunable modules should have low loss, low nonkearity, and be cost effective. Although several technologies have emerged that meet some or most of the above requirements, no technology is a clear Winner at present. There is a trend away from the static, passive fiber devices towards tunable devices that will allow system designers to cope with the shrinking system margins and with the rapidly emerging reconfigurable optical networks. For a long time, tunable dispersion compensation has been an interesting research topic. With the rapid deployment of 10-Gbit/s systems and the potential for future reconfigurable networks, tunable compensation is ready for commercial deployment. In fact, the future emergence of 40-Gbit/s signals will depend on an understanding and development of robust solutions for tunable chromatic dispersion compensation.

IX. Acknowledgments The authors wish to acknowledge the kind help and insight of the following individuals, listed in alphabetical order: Anna Babayan, Dr. Pat Chou, Dr. Kaiming Feng, Dr. Steve Havstad, Dr. Reza Khosramni, Dr. Tingye Li, Dr. Yao Li, John McGeehan, Zhongqi Pan, Yong-Won Song, Lianshan Yan,and Dr. Qian Yu. Special appreciation goes to Lara Garrett of Celion for her gracious assistance and advice.

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Appendix A

The following tables describe various solutions for chromatic dispersion compensation. ~

Compensator Type

Technology

Fixed dispersion compensators

DCF Higher-order-modeDCF Chirped FBGs Spectral inversion

Tunable compensator+ in fiber

Linearly chirped FBGs stretched nonuniformly

~~

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Dispersion Range Insertion Loss OC-768 Ready

Piezoelectricstack Rigid beam

Nonlinearly chirped FBGs stretched uniformly

Nonuniform section medium Piezoelectric stretcher Mechanical stretcher

FBGs with tunable chirp from thermal tuning FBGs with grating induced by MEMS feelers

Up to 150pslnmkm Up to 800 pslnmlkm 500-2000 pslnm Automatic

0.2-0.5dBh 1dBkm 2-4dB 10dB

Automatic Automatic With low ripple Auto

Hard to build low dispersion Hard to build low dispersion Hard to build low dispersion Hard to build low dispersion Hard to build low dispcrsion Hard to build low dispersion Hard to build low dispersion

2-4 dB

Unlikely

2 4 dB

Diilicult

2 4 dB

Difficult

2 4 dB

With low ripple

2-4 dB

With low ripple

2-4 dB

Unlikcly

2 4 dB

Difficult

Compensator Type Tunable compensatorsnonfiber

Technology Free space

Virtual phased army

zyx z zyxwvu zy Dispersion Range

Insertion Loss

0 6 7 6 8 Ready

+/- tuning, hard to

2-1 0 dB

Unlikely

build high dispersion

Waveguide based

Diffraction grating Arrayed waveguide with thermal tuning Mach-Zehnder interferometer with thermo-optic tuning Electro-optical grating

-

2-1 0 dB

-

4 lOdB

Unlikely Automatic

+/- tuning, hard to

4 1 0 dB

Automatic

4-1OdB

With low ripple

build high dispersion -.

-~

Compensator Type

Technology

Fixed dispersion compensators

DCF Higher-order-mode DCF Chirped FBGs Spectral inversion

Tunable compensatorsin fiber

Linearly chirped FB.Gs stretched nonuniformly

Nonlinearly chirped FBGs stretched uniformly FBGs with tunable chirp from thermal tuning FBGs with grating induced by MEMS feelers Tunable compensatorsnodiber

zy

zyxw

Free space

Piezoelectric stack Rigid beam Nonuniform section medium Piezoelectric stretcher Mechanical stretcher

Virtual phase array Diffraction grating

Waveguide based

Arrayed waveguide with thermal tuning Mach-Zehnder interferometer with thermo-optic tuning Electro-optical grating

Channel Spacing

Nonlinear Effects

Ease of Manufacture

Any Any Fixed h Y

High Lower Low

Difficult Difficult Rclatively easy Extremely difficult

Fixed Fixed Fixed

Low Low Low

Very difficult Difficult Difficult

Fixed Fixed Fixed

Low Low Low

Relatively easy Relatively easy Relatively difficult

Fixed

Low

Difficult

zyxwv

Fixed, FP periodicity Fixed, grating periodicity Fixed, AWG periodicity Fixed

Low

Difficult

Low

Difficult

Low

Relatively easy

Low

Relatively easy

Fixed, electrode positioning

Low

Difficult

Compensator Type Fixed dispersion compensators

Technohgy DCF Higher-order-mode DCF Chirped FBGs Spectral inversion

Tunable compensatorsin fiber

Linearly chirped FBGs stretched nonuniformly

Piezoelectric stack Rigid beam Nonuniform section medium Piezoelectricstretcher

Nonlinearly chirped FBGs stretched Mechanical stretcher uniformly FBGs with tunable chirp from thermal tuning FBGs with grating induced by MEMS feelers Tunable compensator+ nodiber

Packaging Complexity

Slope Matching

Avoid PMD, bending loss Avoid bending loss

Can be done

Thermal stabilization Extreme

Can be done

Stack control Adhesive uniformity Adhesivc uniformity Low Low Low

Can be done

Automatic

zy zyx Tuning Speed

Not tunablc

Not tunable Not tunable Not tunable

Very difficult May not be done

1ms lOOms

May not be done

100ms

Can be done

1ms

Can be done May not be done

1ms 100ms

Can be done

10 ms

Free space

Virtual phase array Diffraction grating

Complex Complex

May be done May be done

lOms Not tunable

Waveguide based

Arrayed waveguide with thermal tuning Mach-Zehnder interferometer with thermo-optic tuning Electro-optical grating

Low

Can be done

100ms

Low

Can be done

100ms

Low

Can be done

Compensator Type Fixed dispersion compensators

Tunable compensatorsin fiber

Technology

Patent or Paper Reference

zy zyxw

Most Diflcult Challenge

DCF

US5361319

Fabrication

Higher-order-mode DCF Chirped FBGs Spectral inversion

Lasercomm NFOEC 99 3M PTL 11(2), 275

Mode conversion

US5694501, OFC'97 WJ3 US5694501

Packaging and control

Linearly chirped FBGs stretched nonuniformly

Piezoelectricstack Rigid beam

Nonuniform section medium Nonlinearly chirped FBGs stretched uniformly FBGs with tunable chirp from thermal tuning FBGs with grating induced by MEMS feelers

Grating attachment

Grating attachment

Already mailable commercially, quite expensive High bend sensitivity, PMD; has not been sold yet Requires thermal stabilization Not proven, based on nonlinear optics Good flexibility, may tailor the shape of the passband Good performance requires uniform bond along grating length Good performance requires uniform bond along grating length Simple stretcher, one moving part Simple stretcher, one moving Pad No moving parts, but slow; must be heated to 200°C

zyxwv zyxw

Piezoelectricstretcher US05982963 Mechanical stretcher

Low ripple, athermal Phase conjugation

Notes, Comments

US05982963

Grating design, piezo stabilization Grating design

PTL 11(7), 854

Electrode deposition

Alexis?

MEMS feeler design

-

Compensator Type Tunable compensators nonfiber

Technology Free space

Waveguide based

Patent or Paper Reference

Most DlSCUit Challenge

Virtual phased array

US5969865

Coating, alignment

Diffraction grating

US05497260

Alignment

Arrayed waveguide JP1123 1156A2 Packaging and control with thermal tuning Mach-Zehnder JLT 14(9), 2003 Packaging and control interferometerwith thcrmo-optic tuning Electro-optical Electrode deposition grating

Notes, Comments

zy

Easy to make multiple identical channels Easy to make multiple identical channels Easy to make multiple identical channels Easy to make multiple identical channels

May be the fastest solution, but one of the most difficult and most expensive

714

zyxwvuts zyxwv zyxwvut zyxwvut Alan E. Willner and Bogdan Hoanca

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[81] T. Imai, T. Komukai, and M. Nakazawa, “Dispersion tuning of a linearly chirped fiber B r a g grating without a center wavelength shift by applying a strain gradient,” IEEE Photon. Tech. Letters, vol. 10, no. 6, p. 845, June 1998. [82] B. J. Eggleton, J. A. Rogers, P. S. Westbrook, and T. A. Strasser, “Electrically tunable power efficient dispersion compensating fiber Bragg grating,”IEEE Photon. Tech. Letters, vol. 11, no. 7, pp. 854-856, July 1999. [83] B. J. Eggleton, B. Mikkelsen, G. Raybon, A. Ahuja, J. A. Rogers, P.S. Westbrook, T. N. Nielsen, S. Stulz, and K. Dreyer, “Tunable dispersion compensation in a 160-Gbitls TDM system by a voltage controlled chirped fiber Bragg grating,” IEEE Photon. Tech. Letters, vol. 12, no. 8, pp. 1022-1024, August 2000. [84] K.-M. Feng, J.-X. Cai, V. Grubsky, D. S. Starodubov, M. I. Hayee, S. Lee, X.Jiang, A. E. Willner, and J. Feinberg, “Dynamic dispersion compensation in a 10-Gbit.h optical system using a novel voltage tuned nonlinearly chirped fiber Bragg grating,” IEEE Photon. Tech. Letters, vol. 11, no. 3, pp. 373-375, March 1999. [85] J.-X. Cai, K.-M. Feng, A. E. Willner, V. Grubsky, D. S. Starodubov, and J. Feinberg, “Simultaneous tunable dispersion compensation of many WDM channels using a sampled nonlinearly chirped fiber Bragg grating,” IEEEPhoton. Tech. Letters, vol. 11, no. 11, pp. 1455-1457, November 1999. [8s] J. A. J. Fells, S. E. Kanellopoulos, P. J. Bennett, V. Baker, H. E M. Priddle, W. S. Lee, A. J. Collar, C. B. Rogers, D. P. Goodchild, R. Feced, B. J. Pugh, S. J. Clements, and A. Hadjifotiou, ‘‘Twin fibre grating adjustable dispersion compensator for 40 Gbitls,” European Conf on Optical Communication 2000, Paper PD 2.4,2000. [87] J. A. J. Fells, P. J. Bennett, R. Feced, P. Ayliffe, J. Wakefield, H. F. M. Priddle, V. Baker, S. E. Kanellopoulos, C. Boylan, S. Sahil, W. S. Lee, S. J. Clements, and A. Hadjifotiou, “Widely tunable twin fiber grating dispersion compensator for 80Gbit/s,” Optical Fiber Communication Conf 2001, vol. 4, pp. PD11-1PDll-3,2001. [88] M. Shirasaki, “Chromatic dispersion compensator using virtually imaged phased array,” IEEE Photon. Tech. Letters, vol. 9, no. 12, pp. 1598-1600, December 1997. [89] M. Shirasaki, A. N. Akhter, and C. Lin, “Virtually imaged phased array with graded reflectivity,” IEEE Photon. Tech. Letters, vol. 11, no. 11, pp. 1443-1445, November 1999. [go] A. Corchia, C. Antonini, A. D’Ottavi, A. Mecozzi, F. Martelli, P. Spano, G. Guekos, and R. Dall’Ara, “Midspan spectral inversion without frequency shift for fiber dispersion compensation: a system demonstration,” IEEE Photon. Tech. Letters, vol. 11, no. 2, pp. 275-277, February 1999. [91] C. K. Madsen and G. Lenz, “A multichannel dispersion slope compensating optical all-pass filter,” Optical Fiber Communication Conf 2000, Paper WF5, 2000.

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[92] E Horst, C. Berendsen, R. Beyeler, G.-L. Bona, R. Germann, H. W. M. Salemink, and D. Wiesmann, “Tunable Ring Resonator Dispersion Compensators Realized in High Refractive Index Contrast SiON Technology”European Conf on Optical Communication 2000, Paper PD2.2,2000. [93] H. Takenouchi, T. Goh, and T. Ishii, “2 x 40-channel dispersion slope compensator for 40 Gbit/s WDM transmission systems covering entire C- and L-bands,” Optical Fiber Communication Conf2001, Paper TuS2,2001. [94] K. Takiguchi, S. Kawanishi, H. Takara, A. Himeno, andK. Hattori, “Dispersion slope equalizer for dispersion shifted fiber using a lattice-form programmable optical filter on aplanar lightwave circuit,” IEEEJournal OfLightwave Technology, vol. 16, no. 9, pp. 1647-1656, September 1998. [95] V. Polo, J. Marti, E Ramos, and D. Moodie, “Mitigation of chromatic dispersion effects employing electroabsorption modulator-based transmitters,” IEEE Photon. Tech. Letters, vol. 11, no. 7, pp. 883-885, July 1999. [96] K. E. Anderson and K. H Wagner, “Chromaticand polarizationmode dispersion compensation using spectral holography,” Optical Fiber Communication Con$ 2001, Paper TuH2,2001. [97l C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applicationsfor dispersion compensation,” IEEE Photon. Tech. Letters, vol. 10, no. 7, pp. 994-996, July 1998. [98] C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Tech. Letters, vol. 11, no. 12, pp. 1623-1625, December 1999. [99] C. K. Madsen, S. Chandrasekar, E. J. Laskowsky, K. Bogart, M. A. Cappuzzo, A. Paunescu, L. W. Schultz, and L. T. Gomez, “Compact integrated tunable chromatic dispersion compensator with a 4000 ps/nm tuning range,” Optical Fiber Communication Conf2001, Paper PD9: 2001. [loo] C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Tech. Letters, vol. 12, no. 6, pp. 651-653, June 2000. [loll H. Tsuda, T. Kurokawa, K. Okamoto, T. Ishii, K. Naganuma, Y. Inoue, and H. Takenouchi, “Second- and third-order dispersion compensation using a high resolutionarrayed waveguide grating,” European Conf on Optical Communication 1998, vol. 1, pp. 533-534, 1998. [lo21 T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “New possibilitieswith holey fibers,” Optical Fiber Communication Conf2000, pp. 1 0 6 108,2000. [lo31 D. J. Richardson, T. M. Monro, and N. G. R. Broderick, “Holey fibres - a review of recent developments in theory, fabrication and experiment,” European Con$ on Optical Communication 2000, Paper 10.2.2,2000. [lo41 B. Srinivasan and R. K. Jain, “First demonstration of thermally poled electrooptically tunable fiber Bragg gratings,” IEEE Photon. Tech. Letters, vol. 12, no. 2, pp. 170-172, February 2000.

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[lo51 L. Griiner-Nielsen, S. N. Knudsen, B. Edvold, P. Kristensen, T. Veng, and D. Magnussen, “Dispersion compensating fibres and perspectives for future developments,” European ConJ on Optical Communication 2000, Paper 2.4.1, 2000. [I061 L. Griiner-Nielsen, S. N. Knudsen, T. Veng, B. Edvold, and C. C. Larsen, “Design and manufacture of dispersion compensating fibre for simultaneous compensation of dispersion and dispersion slope,” Optical Fiber Communication Con$ 1999 and International Con$ on Integrated Optics and Optical Fiber Communication, OFC/IOOC ’99, Technical Digest, vol. 2, pp. 232-234, 1999. [lo71 L. Griiner-Nielsen,T. Veng, S. N. Knudsen, C. C. Larsen, and B. Edvold, “New dispersion compensating fibres for simultaneous compensation of dispersion and dispersion slope of non-zero dispersion shifted fibres in the C or L band,” Optical Fiber Communication ConJ2000, vol. 1, pp. 101-103,2000. [lo81 G. E. Berkey and M. R. Sozanki, “Negative slope dispersion compensating fibers,” Optical Fiber Communication Con$ 1999 and International Con$ on Integrated Optics and Optical Fiber Communication, OFC/IOOC ’99, Technical Digest, vol. 2, pp. 235-237, 1999. [lo91 K. Mukasa, R. Sugizaki, T. Yagi, Y Suzuki, and K. Kokura, “Wide-band dispersion management transmission line with medial dispersion fiber (MDF),” European Con$ on Optical Communication 2000, Paper 2.4.2,2000. [110] M. Hirano, T. Kato, K. Fukuda, K. Tamano, M. Onishi, Y Makio, and M. Nishimura, “Novel dispersion flattenedlink consisting of new nz-dsf and dispersion compensating fiber module,” European Con$ on Optical Communication 2000, Paper 2.4.4,2000. [ l l l ] M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, and R. I. Lamming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” European Conf on Optical Communication 1997, pp. 49-52, 1997. [I 121 M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuouslywritten fibre Bragg gratings for combined second- and third-order dispersion compensation,” IEEE Electronics Letters, vol. 33, no. 22, pp. 1891-1893, 1997. [113] J. E Brennan 111, E. Hernandez, J. A. Valenti, P. G. Sinha, M. R. Matthews, D. E. Elder, G. A. Beauchesne, and C. H. Byrd, “Dispersion and dispersionslope correction with a fiber Bragg grating over the full C-band,” Optical Fiber Communication Con$2001, Paper PD12,2001. [114] S.-C. Lin, S. Chi, and J.-C. Dung, “WDM soliton transmission system using dispersion slope compensators,” IEEE Photon. Tech. Letters, vol. 11, no. 1, pp. 99-101, January 1999. [115] H. Takenouchi, H. Tsuda, T. Goh, A. Hirano, K. Yonenaga, T. Ishii, and K. Okamoto, “16-channel dispersion-slopecompensator for 4O-Gbit/s WDM transmission systems using an AWG and a spatial phase filter,” European Con$ on Optical Communication 2000, Paper 3.2.3,2000.

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[116] T. Inui, T. Komukai, and M. Nakazawa, “A wavelength-tunable dispersion equalizer using a nonlinearly chirped fiber Bragg grating pair mounted on multilayer piezoelectric transducers,” IEEE Photon. Tech. Letters, vol. 12, no. 12, pp. 1668-1 670, December 2000. [117] Y. Xie, S. Lee, Z. Pan, J.-X. Cai, A. E. Willner, V. Grubsky, D. S. Starodubov, E. Salik, and J. Feinberg, “Tunable compensation of the dispersion slope mismatch in dispersion-managed systems using a sampled nonlinearly chirped FBG,” IEEE Photon. Tech. Letters, vol. 12, no. 10, pp. 1417-1419, October 2000. [118] H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” IEEE Electronics Letters, vol. 31, no. 21, pp. 1848-1849,1995. [119] J. Marti, J. M. Fuster, and R. I. Laming, “Experimental reduction of chromatic dispersion effects in lightwave microwave/millimeter-wavetransmissions using tapered linearly chirped fiber gratings,” ZEEE Electronics Letters, vol. 33, pp. 1170-1171,1997. [120] H. Sun, M. Cardakli, J. X. Cai, K. M. Feng, H. Long, M. I. Hayee, and A. E. Willner, “Tunablecompensationof dispersion-inducedR F power degradationin multiple-channel SCM transmission by nonlinearly-chirped FBGs,” ZEEE Conf on Lasers and Elecho-Optics 1999, Paper CWK2, 1999. [121] S. A. Havstad, A. B. Sahin, 0. H. Adamczyk, Y. Xie, and A. E. Willner, “Distance-independentmicrowave and millimeter-wave power fading compensation using a phase diversity configuration,”IEEEPhoton. Tech. Letters, vol. 12, no. 8, pp. 1052-1054, August 2000. [122] G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators,” IEEE Microwave Theory and Techniques,vol. 45, no. 8, pp. 1410-1415, 1997. [123] C. Lim, D. Novak, and G. H. Smith, “Implementation of an upstream path in a millimeter-wave fiber-wireless system,” Optical Fiber Communication Conf1998; Paper TuC3, pp. 1617,1998. [ 1241 K. Yonenaga, A. Sano, M. Yoneyama, S. Kuwahara, Y. Miyamoto, and H. Toba, “Automaticdispersion equalizationusing bit-error-ratemonitoring in a 4O-gbit/s transmission system,” European Conf on Optical Communication 2000, Paper 3.2.5,2000. [l25] T. Ihara, and Y. Oikawa, US patent 5,999,289, Detection oJ;and compensation fol; waveform change due to chromatic dispersion assigned to Fujitsu, Ltd., Dec 7,1999. [126] G. Ishikawa, H. Ooi, and N. Kuwatya, US patent 6,081,360, Method and apparatus for optimizing dispersion in an optical fiber transmission line in accordance with an optical sigrralpower level assigned to Fujitsu, Ltd., June 27,2000. [127] G. Ishikawa and H. Ooi, “Demonstration of automatic dispersion equalization in 40 GbitJs OTDM transmission,” European Conf on Optical Communication 1998, V O ~ .1, pp. 519-520, 1998.

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[128] A. Sano, Y Miyamoto, S. Kuwahara, and H. Toba, “Adaptivedispersion equalization by monitoring relative phase shift between spacing-fixed WDM signals,” IEEE Journal of Lightwave Technology,vol. 19, no. 3, pp. 336-344, March 2001. [129] B. Bakhsbi, M. Vaa, E. A. Golovehenko, W. W. Patterson, R. L. Maybach, and N. S. Bergano, “Comparison of CRZ, RZ and NRZ modulation formats in a 64 x 12.3Gb/s WDM transmission experiment over 9000 km,” Optical Fiber Communication Con$, vol. 3, pp. WF4-1-WF4-3,2001. [130] R. Kashyap, Fiber Bragg Gratings, New York: Academic (1999). [131] R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, andR. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol. 13, no. 5, pp. 841-849, 1995. [132] h t t p : / / w w w . l a s e r c o m m - i n c . c o m / m e d i a l W P _ F u - 2 8 - 2 0 0 0 .pdf [133] T. A. Birks, D. Mogilevtsev, J. C. Knight, and P. St. J. Russell, “Dispersion compensation using single-materialfibers,” IEEE Photon. Technol. Lett., vol. 11, no. 6, pp. 674676, 1999. [134] Z. Pan, Q. Yu, Y Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, and J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” Optical Fiber Communication Conf, vol. 3. pp. wh5-1-wh5-3,2000.

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Chapter 15 Polarization-Mode Dispersion

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Herwig Kogelnik and Robert M. Jopson

Crawford Hill hboratory, Bell Laboratories, Lucent Technologies,Holmdel, New Jersey

Lynn E. Nelson

OFS Fitel, Holmdel, New Jersey

1. Introduction As the bit rate and distance of optical fiber transmission systems continue to increase, the understanding of polarization-mode dispersion (PMD) and its system impairments and mitigation are becoming ever more important. In an ideal circularly symmetric fiber, the two orthogonally polarized modes have the same group delay. In reality, fibers have some amount of birefringence due to imperfections in the manufacturing process and/or mechanical stress on the fiber after manufacture. PMD has its origins in this optical birefringence and the random variation of the birefringent axes orientation along the fiber length. PMD causes different delays for different polarizations, and when the difference in the delays approaches a significant fraction of the bit period, pulse distortion and systempenalties occur. Environmentalchanges, including temperature and stress, cause the fiber PMD to vary stochastically in time, making PMD particularly difficult to manage. In addition, although amplifiers or other components such as add-drop multiplexers in an optical system may have constant birefringence,variable polarization rotations between them due

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Fig. 0 Flip movie of changes in the DGD spectrum of a 110-km test span having a mean DGD of 41 ps (Nagel et al. 2000). The signal passed through a 55-km span, was amplified, and returned over a second fiber in the same cable. This cable was buried for much of its length but passed over a river on an automobile bridge at one point and traveled near railroad tracks at another point. The horizontal axis represents a 0.20 nm range of wavelength, centered at 155Onm, while the vertical axis displays the DGD and ranges from 0 ps at the bottom to 80 ps at the top. Successive measurements were made at approximately9.3-minute intervals. The number in each frame indicates time in units of 9.3 minutes; hence, the movie spans about 21 hours. J. A. Nagel, currently of Terraworx, P. D. Magill and Misha Brodsky of AT&T Labs Research provided the movie, which appears courtesy of AT&T Labs.

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OPTICAL mBER TELECOMMUNICATIONS, VOLUME IVB Copyright 0 2002, Elsevier Science (USA). All rights of reproduction in any form reserved.

ISBN 0-12-395173-9

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to the environment cause these components to randomly add to the PMD of the total system. PMD therefore differs from group-velocity dispersion (GVD). While GVD also causes pulse broadening, GVD is basically constant over time (or at least predictable if the temperature changes significantly or the received signal’s route changes due to add-drop), and compensation can be set once and forgotten. This chapter is modeled after the classic review of Poole and Nagel (1997) and attempts to update and complement their work. It is written for the practicing researcher and engineer designing transmission systems. For a detailed discussion of the theoretical background of PMD, we refer the reader to Gordon and Kogelnik (2000), which can be accessed at www.pnas.org. We adopt their notation throughout this chapter, with the exception of minor changes listed in Appendix A summarizing our notation. We refer the interestedreader to Poole and Nagel (1997) for historicalinformation on PMD. Proposals for deployment of commercial systems at 40 Gb/s and 80 Gb/s over installed fiber have fueled a resurgence of interest in PMD phenomena over the last three years. In 1997, the Poole and Nagel review listed about 90 publications relevant to PMD, of which about 25 had appeared by the end of 1986, the year marking the concept of the Principal States Model. An indication of the rapidly growing interest in the field over the past three years is the fact that this chapter’s reference list contains over 401) publications, and this list is incomplete. With the growth of interest in the field, this could be the last comprehensive book chapter on PMD. Subsequent reviews will have to divide the material and specialize on particular aspects of PMD or present the material in a book-length manuscript. In Section 2 we focus on fundamental concepts of PMD. Measurement techniques are discussed in Section 3, with most attention devoted to recently developed techniques far PMD vector measurement and single-ended PMD measurements. Section 4 contains an outline of PMD statistics, including higher-order PMD. Simulation and emulation of PMD are addressed in Section 5, followed by Section 6 on PMD systems impairments, with some focus on higher-order PMD. Finally, in Section 7 we review PMD mitigation strategies, both optical and electrical, and include a discussion of PMD monitoring. Four appendices summarize notation, key rotation matrices, and acronyms.

2. Fundamental Concepts This section focuses on basic concepts of PMD, beginning with birefringence and polarization-mode coupling, the short- and long-length regimes of

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PMD, and the Principal States Model. More advanced concepts include the PMD vector, second-order PMD, and the bandwidth of the principal states. The concatenation rules of Section 2.7 are usefully applied in PMD simulation, statistics, and compensation, as discussed in later sections.

2.1 BIREFMNGENCE

PMD has its origins in optical birefringence. Although telecommunications fibers are often called “single mode,” even in an ideal circularly symmetric fiber, there are two orthogonally polarized HE11 modes. In a perfect fiber, these modes have the same group delay. However, in reality, fibers have some amount of asymmetry due to imperfections in the manufacturing process andor mechanical stress on the fiber after manufacture. The asymmetry breaks the degeneracy of the orthogonally polarized HE11 modes, resulting in birefringence-a difference in the phase and group velocities of the two modes. Even very small amounts of birefringence can cause evolution of the polarization state as light propagates through fiber. Optical fiber birefringence is caused by both intrinsic and extrinsic perturbations. Imperfections in the manufacturing process set up permanent, intrinsic perturbations in the fiber. Form (geometric) birefringence arises due to a noncircular waveguide, whereas stress birefringence is due to forces set up by a noncircular core. Since less than 1% core ellipticity and the associated stress can result in significant birefringence, much work in fiber manufacturing has focused on reducing deviations in the circularity of the fiber preform. When fiber is spooled, cabled, or embedded in the ground, birefringence can be induced from a number of extrinsic perturbations, including lateral stress, bending, or twisting. These perturbations will change as the fiber’s external environment changes. In a short section of fiber, the birefringencecan be considered uniform. The difference between the propagation constants of the slow and fast modes can be expressed as:

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where w is the angular optical frequency, c is the speed of light, and An = n, -nf is the differential effective refractive index between the slow (s) and fast (0 modes. Except for fiber twist, which creates circular birefringence (Ulrich and Simon 1979), the perturbations discussed in the previous paragraph generally create linear birefringence where there are two linearly polarized waveguide modes whose electric field vectors are aligned with the symmetry axes of the fiber.

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When an input wave that is linearly polarized at 45" to the birefringent axes is launched into a short fiber, the state of polarization evolves in a cyclic fashion as the light propagates down the fiber, i.e., from linear to elliptical to circular and back through elliptical to a linear state orthogonal to the launch state. Analogously, for a fixed-input polarization state, if the light frequency is varied, the output polarization state from a short length of birefringent fiber will cycle in the same way through the various states. This frequency-domain picture of PMD is illustrated in Fig. 2.1 for a launch state near the birefringent axis. The output polarization traces out a circle on the surface of the PoincarC sphere (see for example, Derickson 1998; Huard 1997), a three-dimensional mapping of every polarization state. Several PMD measurement techniques, including Jones Matrix Eigenanalysis and the Muller Matrix Method, use this frequency-domain picture (see Section 3.3). The differential index, together with the optical wavelength A, allows us to define a beat length, Lb = A,/An, as the propagation distance for which a 2n phase difference accumulates between the two modes or, equivalently, the polarization rotates through a full cycle. Standard telecommunicationstype fibers can have beat lengths of -10m (Galtarossa et al. 2000b), giving An lop7,which is much smaller than the -lop3 index difference between core and cladding. On the other hand, polarization-maintaining fibers (PMF) are intentionally manufactured to have large An and beat lengths of -3 mm. In the time-domain picture, for a short section of fiber, the differential group delay (DGD), AT, is defined as the group-delay difference between the slow

-

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Fig. 2.1 Illustration of the frequency-domain behavior of PMD in a short birefringent fiber showing how for a fixed input polarization, the output polarization 2 traces out a circle on the surface of the PoincarC sphere as the frequency is varied. The fiber's birefringent axis ? is aligned with the SI axis.

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Fiber axes

v4

n

Y

Fig. 2.2 Illustration of the time-domain effect of PMD in a short fiber, where a pulse

launched with equal power on the two birefringent axes, x and y , becomes two pulses at the output, separated by the DGD, AT.

and fast modes. This AT can be found from the frequency derivative of the difference in propagation constants (Eq. 2.1): L

dw

(2.2)

This “short-length” or “intrinsic” PMD, AT/L, is often expressed in units of picoseconds per kilometer of fiber length. The linear length dependence of DGD applies when the birefringence can be considered uniform, as in a short fiber. In the following sections, we will discuss the “long-length”PMD regime, where DGD has a square root of length dependence. Figure 2.2 is an illustration of the time-domain effect of PMD in a short fiber, where a pulse launched with equal power on the two birefringent axes results in two pulses at the output, separated by the DGD, A t . From Eq. 2.2 and ignoring the dispersion of An, we can then see that the DGD for a single beat length, Lb, is equal to an optical cycle:

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which is 5.2 fs at 1550nm. The polarization-dependentsignal delay method for measuring PMD, described in Section 3.2, relies on the time-domain picture of PMD.

2.2 POLARIZATION-MODE COUPLING

While DGD in the short-length regime is deterministic because the birefringence is inherently additive, fiber lengths in today’s terrestrial and submarine transmission systems are 100’s or 1000’s of km, and the birefringence is no longer additive. There are random variations in the axes of the birefringence along the fiber length, causing polarization-mode coupling wherein the fast

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and slow polarization modes from one segment each decompose into both the fast and slow modes of the next segment. Polarization-mode coupling results from localized stress during spooling/cabling/deployment, from splices and components, from variations in the fiber drawing process, and from intentional fiber “spinning” during drawing, which induces mode coupling at “meter” lengths (Judy 1994). Long fibers are often modeled as a concatenation of birefringent sectionswhose birefringence axes (and magnitudes) change randomly along the fiber, as shown in Fig. 2.3. Due to mode coupling, the birefringence of each section may either add to or subtract from the total birefringence, and therefore the DGD does not accumulate linearly with fiber length. In fact, it has been shown that in long fiber spans, the DGD accumulates as a three-dimensional random-walk, and on average increases with the square root of distance (Poole 1988a; Poole and Nagel 1997). Although mode coupling helps to reduce the DGD of a fiber span, because the mode coupling is determined by the fiber’s environment, variations in, for example, external stresses will change the mode coupling and thus the fiber’s DGD. Therefore, a statistical approach for PMD must be adopted, as discussed in Section 4. The categorization of a fiber in the short- or long-length regime is determined by a parameter called the correlation length L,, also referred to as the coupling length (Kaminow 1981). This parameter describes weak random coupling between two waveguides or the equivalent random coupling between the two polarization modes of a fiber with mostly uniform birefringence subject to random perturbations. One considers the evolution of the polarizations as a function of length in an ensemble of fibers with statistically equivalent perturbations. While the input polarization is fixed, it is equally probable to observe any polarization state at large lengths. The evolution is characterized by the difference (p,) - (p,,) of the ensemble averages of the power in the x and y polarizations. Assuming (p,) = 1 and (p,,) = 0 at the input, this difference evolves from a value of 1 at the input to a value of zero at large lengths. L, is defined as that length where the power difference has decayed

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Fig. 2.3 Model of a long fiber as a concatenation of birefringent sections with birefringence axes (and magnitudes) that change randomly along the fiber length.

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to (p,) - by)= l/e2 (for further detail see Poole and Nagel 1997). Correlation lengths can be less than 1m when fiber is spooled (due to large amounts of polarization-mode coupling); conversely, L, can be -1 km when fiber is cabled. The actual fiber behavior can be affected by fiber “spinning” during draw, temperature, spool diameter and tension, cable design, installation conditions, and fiber relaxation. The correlation length then defines the two different PMD regimes. When the fiber transmission distanceL satisfiesL > L,, the - fiber is considered to be in the long-length regime and the mean DGD, A T , increases with the square root of distance. Transmission systems are generally in the long-length regime, so fiber PMD is often specified using a PMD coefficient having units of ps/(km)’/2. While fibers manufactured today can have mean PMD coefficients less than 0.1 ps/(km)’l2, “legacy” fibers installed in the 1980s may exhibit PMD coefficients higher than 0.8 ps/(km)ll2 (Peters et ~ l1997). . The statistical theory of PMD (Foschini and Poole 1991;Wai and Menyuk 1996) has provided an elegant expression linking the mean square DGD of the fiber to Lb and L,, valid for both regimes and also the transition region between them:

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For L > L,, Atms = ( A t b / L b ) m , reflecting the length dependence discussed earlier. In Section 3.6 we will discuss how single-ended backscattering measurement techniques can determine birefringence (Lb) and the mean square DGD. Then the correlation length (L,) can be inferred from the fundamental Eq. 2.4 relating the three quantities. 2.3 PRlNCIPAL STATES MODEL

The propagation of a pulse through a long length of fiber is very complicated due to random mode coupling and pulse splitting at every change in the local birefringence axes. But a (perhaps) surprising aspect of PMD is that even for long fibers, one can still find two special orthogonal polarization states at the fiber input that result in an output pulse that is undistorted to first order. An example is shown in Fig. 2.4, where a lO-Gb/s, 50% duty-cycle return-to-zero signal was launched with various polarizations through a 48-km fiber with large PMD. The figure shows an output pulse for each of two polarization

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zyxwvu

H. Kogelnik et al.

Input Polarization Setting: BER minimized BER minimized BER maximized

-

3

-

P

E

9

s. ?I

-8= a

,'-\

I

'\

/-\

zyxwvutsrq 0

-100

0 Time (ps)

100

Fig. 2.4 Output pulse shapes for three polarization launches of a 10-Gbh, 50% duty-cycle return-to-zero signal through a 48-km fiber with -60 ps DGD. The dashed and dot-dashed pulses result from the two polarization launches that minimize the BER. The solid pulse results from the polarization launch that maximizes the BER at the output.

zyxwv

launches that minimize the bit-error rate (BER) at the fiber output. Note the difference in arrival times, the DGD. Also shown is the output pulse shape for a polarization launch that maximizes the BER at the output. It is apparent that the two launches minimizing the BER result in fairly undistorted pulses, while the pulse from the third launch is signzcantly broadened. The two undistorted pulses are the fastest and the slowest pulses of all the polarizations launched. In this experiment, the bandwidth of the pulses must be small, with a pulse length greater than the PMD-induced DGDs. This is because PMD is intrinsicallyan interferencephenomenon. It is caused by the coherent addition of the complex amplitudes of the multiplicity of pulses created by the repeated pulse splitting. For large bandwidths, this interference usually causes a splitting of the pulse into several irregularly shaped pulses. The Principal States Model, originally developed by Poole and Wagner (1986), was the first to describe this phenomenon and is still in common use today for the characterization of PMD. The model provides both a time domain and a frequency domain characterization of PMD. Figure 2.4 illustrates the time-domain picture. The frequency-domain picture allows a very simple definition. It states that, for a length of fiber, there exists for every

zyxwvu zy

15. Polarization-ModeDispersion

733

frequency a special pair of polarization states, called the Principal States of Polarization (PSPs). A PSP is defined as that input polarization for which the output state of polarization is independentof frequencyto first order, i.e., over a small frequency range. In the absence of polarization-dependentloss, the PSPs are orthogonal. For each pair of input PSPs, there is a correspondingpair of orthogonal PSPs at the fiber output. The input and output PSPs are related by the fiber's transmission matrix, just as any input polarization is related to a polarization at the fiber output. Using the common Stokes vector description of polarization (for more detail see Appendix A), any output polarization, 3, is related to its input polarization, 5, by the 3 x 3 Muller rotation matrix, R, via ? = %. The unit Stokes vectors,j, of the input PSP a n d j of the output PSP, are similarly related, i.e.,j = Rj,.

zyxwv zyxwvu zyxwvu zyxwvutsr

2.4 PMD VECTOR

Using the Principal States Model, PMD can be characterized by the PMD vector: ? = AT$, (2.5)

a vector in three-dimensional Stokes space, where the magnitude, AT, is the DGD. The unit vector, j,points in the direction of the slower PSP, whereas the vector -j indicates the orthogonal faster PSP. The latter is 180" from? in Stokes space. Note that the definition used here is in right-circular Stokes space (Yith S3 denoting right-circular polarization),whereas the originalPMD vector $2of Poole et al. (1988b) was defined in left-circular Stokes space. See Appendix B for further explanation of the relation between the two. The PMD vector at the fiber input ?, is related to the output PMD vector ? by 3 = R?,. One can then show that the frequency derivative of? = % leads directly to the law of infinitesimal rotation: d? t --=txt, dw

where ? x =R,RT and RT is the transpose ofR. Here, the PMD vector describes how, for a fixed input polarization, the output polarization ? will precess around ? as the frequency is changed. The direction o f ? relative to ? determines the angle of precession, whereas the magnitude, AT,determines the rate at which ? precesses around ?. For example, if 3 is launched with equal power along the PSPs, ? x will have its largest value, and the largest change in the output polarization will occur for a frequency change Aw. The precession has

zyxwv zyxwv zyxwvu zyxwvu

734

zyxwvu z

H. Kogelnik et al.

magnitude 4 = A t A o , where 4 is the rotation angle on the PoincarC sphere. If 2 is aligned with &?, then there is no precession and no change of the output polarization with frequency. This is, of course, the postulate for a PSP. The rotation law, Eq. 2.6, thus provides a precise mathematical definition of the PSP and of its length, A t , the DGD. The law also says that there are only two PSPs corresponding to the two possible alignments, 1 aligned with &?. A length of polarization-maintaining fiber (PMF) has a constant PMD vector whose length, the DGD, and directionj do not change with frequency. For this simple case, the output vector 2 will trace out a circle on the Poincare sphere as the frequency is varied. This is illustrated in Fig 2.1. In real fibers, however, both the magnitude and the direction of 2 change with frequency, as shown in Fig. 2.5. The rotation law still applies locally in this case, describing l ( w ) as a circular arc for a small range of frequencies. In this range, characterized by first-order PMD, the behavior of the real fiber resembles that of the PMF. The DGD at an instant in time for such a range is often called the “instantaneous DGD” to distinguish it from a mean DGD obtained by averaging over time or frequency. The longer-range motion of ?(w)around ?(w) is more complicated, reflecting higher-order PMD. This is illustrated in Fig. 2.6. Now return to the time-domain picture of Fig. 2.4. Whereas the frequency domain provides a continuous wave, single-frequency view of PMD, the time

0 1540

1545 1550 1555 Wavelength (nm)

1560

--

zyxwvu zyxwv 0.1 nm

Fig. 2.5 Measurement of the PMD vector 7 for a 14.7-ps mean DGD fiber. (a) Magnitude of T’ (the DGD, AT) plotted as a function of wavelength. (b) Direction of T’ (the slow PSP, j)plotted on the PoincarC sphere as a function of wavelength. The markers indicate 0.1-nm intervals. 133

15. Polarization-Mode Dispersion

735

z

zyxwvuts zy 0.1 nm

Fig. 2.6 Trajectory of the output polarization state ? as a function of wavelength (for a fixed input polarization) for the same 14.7-ps mean DGD fiber as in Fig. 2.5. The markers indicate 0.1-nm intervals.

zyxw zyxwv zy

domain involves pulses. This allows an alternative physical interpretation of the DGD parameter, A t , to the speed of precession identified previously. The time-domain view uses laboratory coordinates, Jones vectors to characterize polarization, and a 2 x 2 unitary complex transmission matrix T to relate the input and output Jones vectors, Is) and It), by It) = TIS).For more detail and the relation of T to the Jones matrix U , see Appendix A. In this framework, the PSPs are characterized by the unit Jones vectors, lp) and lp-), corresponding to the Stokes vectors, j-j and -j,discussed previously. Using the PSPs as an orthogonal basis set, any input or output polarization can be expressed as the vector sum of two components, each aligned with a PSP. Within the realm of first-order PMD, the output electric field from a fiber with PMD has the form: Eout(t) = alp)Ei,(t - to - At/2)

+ blp-)Ein(t - to + At/2)

(2.7)

where Ein(t) is the input electric field, a and b are the complex weighting coefficients indicating the field amplitude launched along the slow and fast PSPs, lp) and Ip-), and to is the polarization-independent transmission delay. In this formulation, A t is identified as the difference in arrival times between the two principal states, explaining its designation as the DGD. It is usually stated in picoseconds (ps). It is apparent from Eq. 2.7 that PMD can cause pulse broadening due to the DGD, and that there is no pulse broadening when

I

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zyxwvuts zyxwvu zyxwvuts zyxw zyxw zyxwvu H. Kogelnik et aL

the input is aligned with a PSP, Le., when a or b is zero. Note that the simple PMD Stokes vector, ?, does not have a vector analog in the laboratory frame where Eq. 2.7 separates the DGD from the PSP polarizations. Section3 gives themathematicalbackground for a precise definition of PSPs and DGD in the time domain. It is based on the polarization-dependentsignal delay, defined by the first moments of the transmitted pulses. This time-domain definition identifies the PSPs as those input polarizations that maximize or minimize the signal delay. This definition turns out to be equivalent to the earlier frequency-domain definition. The traditional Jones Matrix Eigenanalysis (JME) approach (discussed in Section 3) provides yet another equivalent definition bridging the time and frequency domain. Haus (1999) observes that the Hermitian appearing in the JME is connected to the energy of the light stored in the fiber. The light in the slow PSP spends more time in the fiber and maximizes the stored energy, whereas transmission along the fast PSP minimizes the stored energy. The evolution of the PMD vector with fiber length is described by the dynamical equation for PMD (Poole et al. 1991b),

zyxwv zyxwv

d?- -

dz

do

zyxwvu

relating the PMDvector to the microscopic birefringence. Herez is the position along the fiber. #3 is the three-dimensional, local birefringence vector of the fiber (Eickhoff et al. 1981) pointing in the direction of the birefringence axis with a magnitude A#3 proportional to An (see Gordon and Kogelnik 2000). This equation is the basis for the statisticaltheory of PMD (Foschini and Poole 1991). 2.5 SECOND-ORDERPMD

Because the fiber PMD vector varies with optical angular frequency, a,a Taylor-series expansion of ?(w) with Am about the carrier frequency 00 is typically used for larger signal bandwidths (Foschini and Poole 1991; Gleeson et al. 1997; Biilow 1998b),

So-called second-order PMD is then described by the derivative, (2.10)

zyxwvu zyx zyxwvu zyxwvu zyxwv zyx 15. Polarization-ModeDispersion

737

where the subscript w indicates differentiation. Second-order PMD thus has two terms. Since j,, which is not a unit vector, is perpendicular to j @e.,j .j, = 0), the first term on the right-hand side of Eq. 2.10 is 51,1, the component of 2, that is parallel to 5, whereas the second term, ?,l, is the component of 2, that is perpendicular to 5. Figure 2.7 shows a vector diagram of the principal parameters and their interrelationships. The magnitude of the first term, At,, i s the change of the DGD with wavelength and causes polarization-dependentchromatic dispersion (PCD) (Poole and Giles 1988c; Foschini et al. 1999), resulting in polarization-dependent pulse compression and broadening. It can be viewed as a polarizationdependent change in the chromatic dispersion, DL, of the fiber, described by an effective dispersion,

zyxwvut zyxw

In accordance with the customary dispersion measure, DL, the PCD is defmed as, 1d A t ti = -(nc/h2)At - -(2.12) "-2 d c

zyxwv

Fig. 2.7 Schematic diagram of the PMD vector ?(a)and the second-order PMD components showing the change of ?(w) with frequency. Note thatj- is perpendicular to 5. The angular rotation rate, d4/dw, of the PMD vector ?(w) with w is described bY @ w l -

738

zyxwvu zyxwvu zyxwvu zyxw H. Kogelnik et al.

zyxw zy zy zyxwv

where c is the velocity of light, h is the wavelength, and ti is usually expressed in ps/nm. The PCD is proportional to the wavelength derivative of the DGD spectrum. The plus and minus signs in Eq. 2.11 correspond to alignment with the two PSPs. Note that the magnitudes of ?,I, and At, are equal and At, = zll, has a sign that is negative when ?I, points in the direction opposite t o j . Figure 2.8 shows the PCD of the fiber from Fig. 2.5. The DGD data were numerically differentiated to obtain the PCD. It is apparent that PCD causes the effective dispersion to fluctuate rapidly with wavelength. The second term, AT&,, describes PSP depolarization, a rotation of the PSPs with frequency. As shown in Fig. 2.7, the angular rate of rotation, dcp/dw = & I, of the PMD vector ?(w) is measured by the magnitude E, I, which we express in ps. Note that d @ / d v[mradGHz] = 2nE,l[ps], where v is the optical carrier frequency and w = 27cv. We have already seen in Fig. 2.5 the rapid motion of j for the 14.7-ps mean DGD fiber. Figure 2.9 is a plot of Eml for this same fiber and wavelength range. As discussed in Section 6, pulse distortions caused by depolarization include overshoots and generation of satellite pulses. PSP depolarization can also have a detrimental effect on ht-order PMD compensators.

zyxwvuts

50 -

PCD = -( n c / l i ? ) A ~[pdnm] ~

-50 1540

1545

1550

1555

1560

Wavelength (nrn)

Fig. 2.8 Plot of the polarization-dependent chromatic dispersion (PCD) for the 14.7-ps mean DGD fiber from Fig. 2.5. To obtain the PCD, the DGD data in Fig. 2.5 were numerically differentiated.

zyxwvu zy

15. Polarization-ModeDispersion

739

zyxwvuts zyxwv zy zyxw zyxw 0 1540

1545

1550

1555

1560

Wavelength (nm)

Fig. 2.9 Plot of the PSP depolarization,&,I and wavelength range of Fig. 2.5.

for the same 14.7-ps mean DGD fiber

zu,

Note that the input and output second-order PMD vectors and respectively) transform the same way as the first-order PMD vector, so that

?* = R&

(2.13)

where R is the Muller rotation matrix (Gordon and Kogelnik 2000). For the third-order PMD vectors, one can show that

zyxwvuts ?mm

= R?-

+ t x tu. +

+

(2.14)

The statistical theory of second-order PMD (Foschini and Poole 1991; Foschini et al. 1999) has provided probability density functions for the various second-order components that have been experimentally confirmed (Foschini ct il. 2000; Jopson et al. 2001), as has their scaling with mean DGD (Nelson t, 1.1999b). These results will be outlined in Section 4. Higher-order PMD has ais0 been described using other formulations (Bruyere 1996; Shieh 1999; Eyal et al. 1999), rather than the Taylor-series expansion described above. These formulations attempt to better describe how the PMD vector changes with optical frequency. However, the statistics have not been completely derived yet for these formulations.

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zyxw zyxw zyxw zyxwvu

2.6 THE BAND WIDTH OF THE PRINCIPAL STATES

The bandwidth of the principal state is an important concept providing guidance on the change of the PMD vector ?(o)of the fiber with frequency (or wavelength). It is the bandwidth, Awpsp = kAupsp, or the corresponding wavelength range, AApsp, over which the PMD vector is reasonably constant. Examples of the utility of this concept include the frequency-domain measurement of PMD vectors (covered in Section 3) and the measurement of PMD statistics. Consider, for example, the determination of the PMD vector at the different wavelengths, A I , h2, and A3, as sketched in Fig. 2.10. As will be explained in Section 3, for each of these determinations, measurements of polarization rotations at two or more frequencies are required. These frequencies have to be confined to the range AApsp as indicated in order to reduce inaccuracy caused by higher-order PMD. In statistical PMD measurements, on the other hand, measured samples of ?(A) are deemed to be statistically independent if their wavelengths are at least 6Ahpsp apart. This is indicated in Fig. 2.10, where ?(LO)and ?(h6)are considered statistically independent. Thus, measurements over a spectral range from Amin to A, will yield a number of statistically independent samples, Nsamples, given by

While varying constants are reported in the literature (Betti et al. 1991; Bruyere 1996), studies of the accuracy of measurements of PMD provide a

I

I

zyx

Fig. 2.10 Diagram showing the important wavelength (or frequency) intervals for measurements of the PMD. For PMD vector measurements, the wavelength interval should be smaller than Akpsp to avoid inaccuracy from higher-order PMD. For PMD statistics, in order to consider the measured samples statistically independent, the wavelength interval should be at least 6 A k . p ~ .

zyxwvu zyx zyxw

15. Polarization-Mode Dispersion

741

zyxwvuts zyxwvuts zyxwvu

good practical estimate for Aopsp given by the relation (Jopson et al. 1999a):

where S is the mean DGD of the fiber. This implies a frequency band Aupsp = 1/(8=), or Avpsp = 125GHz/S,

(2.17)

when is expressed in ps. For wavelengths near 1550nm, the corresponding wavelength range Ah = Au x A2/c can be written in the simple form AApsp = 1n m / z . As an illustration, inspect the data of Fig. 2.11for a fiber with a mean DGD = 40ps shown over the range of 2nm with 0.1-nm markers. Here, the measured values of AT appear reasonably constant over the calculated AApsp of 0.025 nm. Clearly, the Awpsp concept must be consistent with the concept of secondorder PMD, describing the change of the PMD vector, ?(@), with

1535

1536

1537

Wavelength (nrn)

Fig. 2.11 Measurement of DGD as a function of wavelength for a fiber with mean DGD, %, of 40 p s Markers indicate 0.1-nm intervals. Note that the measured values of ATappear reasonably constant over the calculated bandwidth of the principal states, AA-psp, of O.O25nm, i.e., one quarter of the marked intervals.

742

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H. Kogelnik et al.

frequency. At ~0 f Awpsp the PMD vector is ?(wg

1 2

f AupspI2) = ?(mo) f -AOPSP . Zm.

(2.18)

zy zyxw

Using the above expression for Aupsp and the known relation (Foschini and Poole 1991) I?m:wlrms = . (nE2/8), one finds that the root-mean-square (rms) magnitude ofthe change (?(q+Aopsp/2)-?(wo)) equals 0.267dz. This relatively large value may seem to imply that the Awpsp values are somewhat too large. However, on average, the vector 2w is perpendicular to ? (Foschini et al. 1999) as discussed in Section 4.In this case, there is only a small (3%) change in the magnitude of? accompanied by a rotation of the PSP by about 15" in Stokes space (Le., 7.5" in the laboratory for linear polarization). The correlation function of the PMD vectors ?(mg) and ?(* + Am) recently reported by Karlsson and Brentel (1999) and Shtaif et al. (2000b) (and discussed further in Section 4) provides an elegant confirmation and interpretation of the Awpsp concept and its practical implications. Figure 2.12 shows a (normalized) plot of this correlation as a function of the frequency = 1.25 ps. For this value, separation, Av = Aw/2n, for a mean DGD of the bandwidth of the PSP is Avpsp = 1OOGHz. At this frequency spacing the correlation is seen to drop from 1 to 0.89, supporting the idea that ? is essentially constant over the 100-GHz width. At 6Aupsp = 600 GHz, the correlation drops to 0.1 1,indicating that PMD vectors at that frequency spacing are essentially uncorrelated.

zyxw

2.7 CONCATENATIONOF PMD VECTORS

The total PMD vector of a series of two or more elements with known PMD vectors can be determined using the simple, but powerful concatenation rules (Curti et al. 1990; Poole et al. 1991b; Foshini and Poole 1991; Gisin and Pellaux 1992; Mollenauer and Gordon 1994; Gordon and Kogelnik 2000). The concatenation rules have been used in the analysis of how the PMD vector grows with fiber length (Curti et al. 1990) and for statistical PMD modeling (Foschini and Poole 1991). They are also useful for PMD simulation and in the design of multisection PMD compensators. Although the concatenation rules have appeared in sum, differential, and integral formulations for both first- and second-order PMD vectors, this section will concentrate on the sum rules See Gordon and Kogelnik (2000) for the other formulations. The concatenation rule for first-order PMD is similar to that for transmission-line impedances: To obtain the PMD vector of an assembly, transform the PMD vectors of each individual section to a common reference

zyx zyx zyxwv zyx zyxwvuts 15. Polarization-Mode Dispersion

3

0

I

743

AVlAVPSP

9

zyxwvuts

0;

300

0

600

900

Av (GHz)

+

Fig. 2.12 Plot of the (normalized)correlation function, (?(uo) x ?(UO Av))/(At2), as a function of the frequency separation, Au, for a mean DGD of = 1.25ps and bandwidth of the PSP, Aupsp = 100 GHz. The top x-axis shows the normalized frequency separation, Au/Al)p~p,allowing general use of the plot. Note that the correlation drops from 1 to 0.89 at Au = 100GHz (Au/Aupsp = l), showing that ? is essentially constant over Aupsp. At Au = 600GHz (Au/Aup~p = 6), the correlation drops to 0.11, indicating that P M D vectors at that frequency spacing are essentially uncorrelated.

point and take the vector sum (in three-dimensional Stokes space). This vector can then be transformed to any other location in the system using the known rotation matrices of the different sections. For example, for the two sections shown in Fig. 2.13, the PMD vector at the midpoint, -

tm

+

+

= tl

+ 2s2 =

+R:&,

(2.19)

where all ?i and Ri are functions of frequency. To iind the total PMD vector at the output, 2, we must then transform it by R2, so that

? = Rztl

+ 22,

(2.20)

since R2RT?2 = 22. The corresponding PMD vector diagram is shown in Fig. 2.13. It provides a simple geometrical interpretation of the concatenation. Equation 2.20 is the basic concatenation rule. We can use it to similarly

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zyxwvutsr zyxwvut zyxwvutsr zyxwvut zyxwvu zyxwv H. Kogelnik et al.

Fig. 2.13 Diagram of the concatenation of PMD vectors for two sections. To find the total PMD vector ? at the output, add the PMD vectors of the two individual sections at the output after transforming ?I by R2 : ? = R z ? ~+ 6 . The corresponding PMD vector diagram shows the geometrical interpretation of the concatenation.

Fig. 2.14 Concatenation of m sections of PMD, each with known rotation matrix R,, and output PMD vector ?,. The sum rules of the assembly for first- and second-order PMD are given in Eqs 2.23 and 2.24.

find the total PMD vector at the input, ?, by the transformation

zs= RT?,,,= RT(?i + Rz?2).

(2.21)

The rule can be generalized to multiple sections as well as to differentiallysmall sections. Second-order PMD can also be concatenated. By differentiating Eq. 2.20 and making the proper substitutions, one can show that

?,,, = ?2 x i + R&

+ ?h.

(2.22)

The first- and second-order PMD vectors for many sections can be determined by repeated application of the two-section rules in Eqs 2.20 and 2.22. For the fiber in Fig. 2.14 consisting of m sections, each with known rotation matrix R, and output PMD vector in,the sum rules of the assembly are for first-order PMD ,.

...

?= n= 1

R(m,n + l)?,,

(2.23)

zy zyxwv

15. Polarization-ModeDispersion

and for second-order PMD

745

(2.24)

+

where we define the rotation matrix of the last m - n 1 sections as R(m, n) = R,,,R,-l. . R,, where R(m, m) = R, and R(m, m 1) is the identity matrix. The differential concatenation rule for PMD shows how ?(z) changes due to the differential addition of length Az (Gordon and Kogelnik 2000) and is equivalent to Eq. 2.8, the dynamical PMD equation.

+

3. Measurement Techniques A considerable number of techniques for the measurement of PMD have been proposed. Several have been extensively tested and standardized. Some of these measure the (scalar) instantaneous DGD, others determine the mean DGD, and a few allow measurement of the instantaneous PMD vectors as a function of frequency. Some methods operate in the time domain by sensing pulse delays, whereas others employ frequency-domain concepts detecting changes of polarization with frequency. Measurement capabilities of various instruments range from around 1 fs to about 100 ps of DGD. The smaller ranges are needed for the measurement of the (instantaneous) DGD of optical components or short pieces of fiber, whereas the larger ranges are used to characterize long communication spans. Our discussion will cover five techniques: interferometrictechniques allowing rapid determination of the DGD, optical time-domain reflectometry (OTDR) methods convenient for in-field measurements where only one end of an installed fiber line is accessed, and three methods permitting the characterization of PMD vectors, the polarization-dependent signal delay (PSD) method, and the closely related Jones Matrix Eigenanalysis (JME) and Miiller Matrix Methods (MMM). For broader reviews the reader is referred to Poole and Nagel (1997) and Hernday in Derickson (1998). These reviews also cover the PoincarC sphere method (Andrescianiet al. 1987; Bergano et al. 1987),the fixed analyzer method (Poole 1989; Poole and Favin 1994) and the modulation phase-shift method used for the measurement of dispersion and scalar DGD (Costa et al. 1982;Williams et al. 1998; Williams 1999b).

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746

3.1 INTERFEROMETRIC TECHNIQUES

A variety of interferometric techniques for PMD measurement (Mochizuki et al. 1981; Thevenaz et al. 1989; Gisin et al. 1991b; Namihira et al. 1993a,b) have been developed into compact field instruments that can make a DGD measurement in as little as 30s. With modifications, these instruments can measure the instantaneous DGD of optical components or short fibers to an accuracy better than 1 fs (Oberson et al. 1997; Simova et al. 2000). A schematic of a typical interferometric system is shown in Fig. 3.1. The method usually employs a Michelson interferometer, as shown in the figure, or a Mach-Zehnder interferometer. Often the interferometer is implemented using a fiber-directional coupler constructed with PM fiber. The interferometer has a ked-mirror arm and an arm with a scanning mirror. The maximum scanning range of the latter determines the maximum DGD that can be measured. In some variations on this method additional components are inserted. Examples are the use of bias birefringent plates following the fiber under test or the insertion of a quarter-wave plate in the fixed-mirror arm.

zyxwvut Fixed mirror

LED

Polarization Control

Fiber under test

Scanning mirror

zy 4 A2

Polarizer 8

zyxw

Detector

Fig. 3.1 Typical interferometric measurement system. The example of a Michelson interferometer is shown using a fixed and a scanning mirror arm. The system uses a broadband light-emittingdiode (LED), polarization control, and a polarizer analyzer. The scan range is Az.

zyxwvu zyx

15. Polarization-ModeDispersion

747

The conventional implementation for low-coherence interferometry employs an unpolarized broadband source of light, such as an LED, providing a spectral width of about 100nm. The coherence length of this source determines the smallest PMD that can be measured for optical components. For long fibers, the method provides the mean DGD averaged over the spectral width of the source. The light from the source is sent through the fiber and split into two parts in the interferometer. The two parts are delayed relative to each other by a time delay, AT, proportional to the scan distance, Az, from interferometer balance, AT = ~ A z / c , (3.1)

zyxwvuts zyxwvu zyxwv zyx

where c is the speed of light. The delayed parts are recombined for interference at the detector. Scanning of the mirror distance creates a fringe pattern at the detector from which DGD information is extracted. As an example, consider first the fringe pattern generated by a narrowband pulse with polarizations properly adjusted. The fiber under test splits the pulse into two parts, delayed by the DGD, A t . When the interferometeris balanced, there is a central interference peak. As the mirror is scanned away from balance, the fringe pattern shows two side peaks when AT = &At, providing DGD information. For broadband light there are complex fringe patterns and correlation peaks that have been modeled and analyzed. A typical fringe pattern is shown in Fig. 3.2. The mean DGD is extracted from this fringe pattern by such methods as determining the second moment, a,, of the fringe distribution (Gisin 1994a; Perny et al. 1996)or the Gaussian fit shown. The mean square DGD is approximately equal to this moment, i.e., (At’) % a,. The polarization controller and polarizer shown in Fig. 3.1 are, in some designs, used to ensure that the desired interference takes place, as orthogonal polarizations at the detector will not interfere.

3.2 THE POLARIZATION-DEPENDENTSIGNAL DELAY METHOD The polarization-dependent signal delay (PSD) method (Jopson et al. 1999b; Nelson et al. 2000a,c) is a time-domain technique for the measurement of PMD vectors. The method uses conventional phase-detection instruments, such as network analyzers, that have been perfected to measure the phase delay of periodic signals with great accuracy. These instruments, also used in the modulation phase-shiftmethod mentioned at the beginning of this section, can, for example, determine the delay of a sinusoidal 100-MHz signal to an accuracy of 1ps. The PSD method exploits the polarization dependence of the propagation delay of light passing through a fiber possessing PMD.

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-0.8

zyxwvut

zyxwv zyxwv zyxw zyxw -0.4

0.0

0.4

0.8

Displacement (ps)

Fig. 3.2 Example of a typical fringe pattern obtainedwith the interferometricmethod. Information about the mean DGD is extracted from this pattern by signal processing. The example shows the interferogram for a fiber with a mean DGD of 0.17 ps (courtesy of Alan McCurdy).

Consider a fiber with a DGD, A T , and an input PMD vector, ?. The two principal states are described by the Jones vectors lp) and lp-), and the corresponding Stokes vectors j and $- = -$. The light carrying the signal has an input polarization with Jones vector Is) and Stokes vector 3. We know that signals launched at the PSPs, i = ztj, will experience group delays tg of

where TO is the polarization-independent delay of the fiber (whose wavelength dependence leads to chromatic dispersion). For arbitrary polarization 3, the input light couples to both PSPs resulting in the superposition:

where a = ( p I s) and b = ( p - I s) are the amplitudes in the two states as in Eq. 2.7. The fractional powers in the two PSPs are aa* and bb* obeying aa* + bb* = 1, assuming a total power of unity. Using the dot-product rule (Gordon and Kogelnik 2000), these functions can be expressed in terms of the

zy zyxwvu zyxwvut zyxwv zyxwv zyxw zyx 15. Polarization-Mode Dispersion

Stokes vectors as

uu* = ( p I s)(s Ip) = ;(l

+j

749

m i ) ,

(3.4)

bb* = ( p - I s)(s Ip-) = ;(l -j .i).

An instrument detecting total power will sense a power-weighted mean signal delay of tg = uu*(ro At/2) bb*(to - At/2), (3.5)

+

+

which, with the help of Eq. 3.4 becomes

This equation is the basis for the PSD technique. It was originally derived and further substantiated by analysis based on moments (Mollenauer and Gordon 1994; Karlsson 1998; Shieh 1999; Gordon and Kogelnik 2000). A schematic of a PSD measurement system is shown in Fig. 3.3. It consists of a tunable laser for selection of the wavelength of interest, a wavemeter to monitor that wavelength, a modulator, insertable polarizers to control the polarization at the fiber input, and a network analyzer for measuring signal delay, rg.

Tunable Laser

I

Wavemeter

PC

MOD IGHz

I

Circular Polarizer

\

1

Network Analyzer

Rx

Fiber span

808 Polarizers

Fig. 3.3 Schematicof a polarization-dependent signal delay (PSD) measurement system. The transmitter uses a wavelength tunable laser and a sinusoidal modulator. A network analyzer is used for the precise measurement of signal delay for four different launch polarizations.

750

zyxwvutsr zyxwvu zyxwvutsrq zyxwvu zyxwv H. Kogelnik et al.

zyxwvu

At any chosen wavelength, Eq. 3.6 contains four unknown scalar quantities of interest, to and the components of 2 = (tl,t2,q).Their determination requires four independent delay measurements, tgi,for four different input polarizations, i i . The quantities, to and ?, are then extracted using linear matrix algebra (Nelson et al. 2000~). Care must be taken during the measurement process to correct for any significant changes of the delay, to, due to temperature changes. As to is quite large (about 500 ~.l.s for a 100-kmfiber), such changes could mask the accurate measurement of the much smaller components o f ? (which can be less than lops). Figure 3.4 depicts in open circles the results of wavelength-dependent measurements of the relative signal delay t&) - t o ( h 0 ) for light launched with vertical linear polarization, = i l . The central solid curve shows the relative polarization-independentdelay, TOR = to(h)- to(ho),where the reference wavelength was ho = 1542nm. The fiber under test had a length of 62 km, a mean DGD of 35 ps, and a dispersion of 124pshm. Note also the curves indicating the boundaries of delay, occurring when light is launched at the PSPs, j and -j,for each wavelength. Their vertical spacing is At,which varies with

zyx

100 r

I

50

-50

-1 00

1541.5

1542.0 Wavelength (nm)

1542.5

zyxwv

Fig. 3.4 Signal delay as a function of wavelength measured with the PSD method with 31 used as launch polarization (open circles). Also shown is the measured relative polarization-independent delay, toR,and the maxima and minima of the delays, measured when light is launched at the PSPs at each wavelength. The mean DGD of the . fiber was 35 ps. From Nelson et ~ l(2000~).

zyx zyxw zyxwvu zyx zyxwv zyxwvu 15. Polarization-ModeDispersion

751

wavelength. The delay measured for the SI launch fluctuates between these boundaries as ? changes with wavelength. Similar fluctuations are obtained for other launch polarizations. Given certain inaccuracies in the measurement of tg,one finds that the results obtained for TO and 2 become more accurate for particular choices of the four input Stokes vectors ? (Nelson et al. 2000a). Accuracy improves with increasing the volume, V , of the tetrahedron defined by the endpoints of the four vectors &.The maximum V attainable is V, = 8/9& = .513. A good practical choice with V = 0.433 are the four Stokes vectors, including ?3 (rightcircular polarization), and the linear polarizations at 0" (&), 60°, and 120". PMD results measured with these input polarizations are shown in Fig. 3.5 (Nelson et al. 2000~).This figure also shows the good agreement between the PSD method and the MMM method to be described in the following section. In the strict sense, Eq. 3.6 applies to well-isolated single signal pulses of arbitrary shape. However, the PSD method is easily modified for other modulation formats, particularly for sinusoidal modulation (Nelson et al. 2000~). In the latter case, one has to examine the relation between the DGD delay, AT, and the period l/vm of the modulation, where v, = wm/2nis the modulation frequency. The situation is sketched in Fig. 3.6 showing the sinusoidal

zy

154.5

1542.0

1542.5

Wavelength (nm)

Fig. 3.5 Measured DGD and PMD vector components as a function of wavelength. Symbols represent PSD measurements, solid lines represent MMM results. The polarization-independentrelative delay, tOR, was obtained with the PSD only. From Nelson et al. (2000~).

I"

14

1

752

H. Kogelnik et al.

t

zyxwvu

zyxwvuts zyxwv zy

Fig. 3.6 Sketch of the sinusoidal signals in the two PSPs after differential delay by the fiber PMD. Note the ambiguity arising in phase detection when the delay, Ar, exceeds one half of the signal period, 1/2vm.

zyxw zyxw

signals in the two PSPs after delay by the fiber. As the sum of the two signals is detected, there are ambiguities that can arise in phase detection when the delay At exceeds one half of the signal period, 1/2vm.At a modulation frequency of 1 GHz, this folding limit occurs at At = 500ps. Equation 3.6 can be used as long as At 3.1 ps occur where the histogram bins contain either one or zero counts. To scale to different mean DGDs, the label on the abscissa can be viewed as being At/=.

zyxwv zyxwv

Fig. 4.1 Probability densities of first- and second-order PMD quantities for a mean DGD of 1ps (Foschini and Poole 1991; Foschini et al. 1999; Foschini et al. 2000; Nelson et al. 1999b; Jopson et al. 2001). The smooth solid lines show analytic predictions from Table 4.1. The staircase curve depicts experimental results obtained from a fiber having a mean DGD of 14.7 ps. The measured densities have been normalized to a mean DGD of 1ps. The markers show results obtained from simulation. Some simulation points have been removed from the plots to enhance the visibility of the curves. Note the logarithmic scale of the vertical axis. Densities are shown for (a) the DGD, Ar; (b) a component of the PMD vector, ?; (c) the magnitude of the second-order PMD vector; (d) a component of the second-orderPMD vector; (e) the parallel component of ?m; (f) the magnitude of the perpendicular component o f t ; and (g) the PSP depolarization.

770

zyxwvutsr zyxwvu zyxw zyxw

z

H. Kogelnik et al.

an.

obtained for one to densities for another For first-order -- densities, multiply the density P by and the outcome x , by At2/Atl. --The scaling of second-order densities is performed similarly except ( A t 1 / A t 2 ) ~is used -instead of Aq/At2 and correspondingly for the outcome. Note that as jjw is the ratio of a second-order quantity and a first-order quantity, it scales as first-order PMD. The scaling rules for the means and the mean squares of PMD quantities follow from the scaling of the densities. The mean square of first-order PMD quantities increases quadratically with mean DGD, as does the mean of second-order PMD quantities. The mean square of second-order PMD quantities increases as the fourth power of mean DGD. Some of these scaling predictions have been compared to results obtained by experiment and simulation. One measurement used a selection of 11 different fibers with mean DGD values between 1.3 and 3 6 . 0 and ~ ~ a~ wavelength range of 1460 to 1580nm for most of the fibers. This provided 30 to 300 independent samples (depending on the fiber mean DGD) for the rms values of Ifiwl, l?wll and Atw (Nelson 1999b; Jopson etal. 2001). The same quantities were evaluated by a simulation using 600 delay elements that obtained 29,000 independent realizations for each of 13 mean DGDs. The results are shown in Fig. 4.3. The lines are predictions from Table 4.1 that contain no free parameters whereas the markers show results from experiment and simulation. It can

zyxwvuts zy 1000

1

1

2

5 10 Mean DGD (ps)

20

50

Scalingof therms values of l&.,l, Aq,, (denoted Q2,11, and I?2,toll,for fibers with different mean DGD. The lines are theoretical predictions and the markers represent results obtained by experiment and simulation.

Fig. 4.3

zy zyxwv zyxw zy zyxwvuts zyxw 15. Polarization-Mode Dispersion

771

be seen, as expected, that the rms of l?lw and the rms liwll scale quadratically with mean DGD whereas the rms I scales linearly with mean DGD. Examination of the expressions in Table 4.1 reveals many interesting relationships. For instance, the densities of the first-order components, ti,are equal, showing that no axis is favored. As mentioned earlier, all of the delay in the analyticmodel used to derive the densities lies along the first component of Stokes space. The symmetry in the first-order densities shows that this bias is removed by the frequency-independent rotation term. The rms of the secondorder magnitude, I?wl, is l/& the value of the mean square of the first-order magnitude, A t , and it is split quite unevenly between the PCD or parallel component and the perpendicular components. Indeed, the mean square of I?wl I accounts for 8/9 of the total mean square second-order whereas the mean square of the parallel component consumes the remaining 1/9. Summarizing: = 3(?:)

= 27{At:).

(4.3)

Thus, as stated in Section 2, changes in ? are much more likely to take the form of a change in a direction than a change in length, information important to the designers of second-order compensators. One very useful scaling relationship that has not received much explicit experimental attention links bit rate and mean DGD: The allowable in a system scales inversely with bit rate. This scaling is not constrained to systems with purely first-order PMD, but it does assume that other sources of impairment are either absent or scaled appropriately. Its usefulness is that it allows results from PMD experiments performed at low bit rates to be applied to higher bit rates where experiments might be more difficult to control. This scaling follows from the model of Eq. 5.6 as illustrated in Fig. 2.3, which predicts that if the element delays, At,,, and the bit rate are changed in a manner that preserves their product, any particular output waveform will also scale with the bit rate.

4.4 CORRELATIONFUNCTIONS An alternate, powerful description of PMD statistics is provided by autocorrelation functions, which contain the effects of all PMD orders in simple, compact form. They provide information about the means or expectation values of products of PMD vectors or states of polarization (SOPS) corresponding to different frequencies or different times. An example is the spectral autocorrelation of the PMD vectors recently derived by Karlsson and Brentel(1999a) and Shtaif et al. (2000b). It applies to the PMD vectors

772

zyxwvu zyxwvu zyxwvuts zyxwv zyxwv zyxwvut

H. Kogelnik et al.

at the frequencies m1 and w;! = m1+ A m and has the form:

This correlation function has been used in Section 2 for the characterization of the bandwidth of the PSP; it impacts the inherent uncertainty in measuring the mean DGD, an issue discussed in Section 3.7. The spectral correlation between output SOPS, (f(w1) - $(w;!)), is given in Eq. 6.24. It is used in Section 6.6 to analyze the effect of PMD on the FWM efficiency in the fiber and in Section 6.7 to determine the PMD effect on polarization-dependent gain in fiber Raman amplifiers. The corresponding temporal correlation functions both for the SOPSand the PMD vectors are given in Eqs. 7.1 and 7.2 where they are used to discuss the time response required for PMD mitigation.

zyxwvutsr

4.5 FURTHER READING

For additional information on the evolution of PMD with distance, see Poole (1988a), Pooleetal. (1988b), Bettietal. (1991), FoschiniandPoole(1991), and Karlsson (200la). Information on joint probability densities can be found in Penninckx and Bruyere (1998), Shtengel etal. (2001), and Jopson et al. (2001).

5. Emulation and Simulation 5.1 PURPOSE

Although lightwave systems are typically specified to have outage probabilities of less than testing system robustness to PMD-induced outage to these levels is rarely practical in the field. A three-pronged attack employing analysis, numerical simulation, and experimental emulation can be used instead. Analytic derivation of probability densities, described in Section 4, provides the best information about asymptotic behavior, but these derivations are not easily undertaken and require assumptions about the nature of birefringence in fiber. As described in Section 4, analytic solutions to first- and second-order PMD quantities have been obtained for the Taylor-series expansion model of PMD. Simulation of PMD can be used to verify statistical predictions derived analytically, to make statistical predictions that have not been derived analytically, to test assumptions made about the behavior of fiber birefringence, and to incorporate PMD into a system simulation. Laboratory emulation is used to corroborate results obtained through analysis or simulation, to study system impairment caused by PMD, and to test compensators of PMD impairment.

zyxwvu zyx zy

15. Polarization-Mode Dispersion

773

Emulators are of crucial importance in the latter role since numerical simulation cannot be trusted to mimic all the vagaries of physical components. In addition, emulation can be faster than numerical simulation. Since thousands or millions of PMD realizations may be needed to obtain usable statistics on system performance, emulation may offer the only practical way to obtain this information. However, one must ensure that the model used to construct an emulator or simulator mimics the system properties of interest.

zyx zyxwvutsrq zyxwv

5.2 COMPARISON OF MODELS

The total PMD of a system contains contributions from fiber and from discrete components. The PMD arising from a random combination of small amounts of birefringence from a large number of sources is well understood. This includes the PMD of most fiber spans and also includes the PMD of systems wherein the birefringence of each component is much smaller than the total system PMD. The most common model used in numerical simulations is a concatenation of linear birefringent elements oriented at random angles (illustrated in Fig. 2.3) that are chosen randomly over the range 0 to n (Poole and Nagel 1997). Other models use linearly birefringent elements, but restrict the orientation of the elements in various ways that reduce the average change in orientation between successive elements. The statistics of the simulated firstand second-order PMD do not appear to depend on the details of the model so long as a sufficient number of birefringent elements are used in the simulation. However, the number of such elements required for a desired statistical accuracy will depend on the details of the model (Prola et al. 1997; Dal Forno et al. 2000; Lima et al. 2000; Khosravani et al. 200 1a). The densitiesplotted in Fig. 4.1 show remarkableagreementbetween experiment, theory, and simulation even though the underlying models used to generate the curves differ significantly.As will be discussed in detail below, the simulation used a large number of small sections of linear birefringence that were longer than a birefringent beat length. These sections provided polarization rotation about the Stokes SI axis. They were rotated relative to each other by a random angle between 0 and IT radians. First- and second-order PMD were determined at a single frequency by calculating the transmission matrix in Jones space for several closely-spaced frequencies and taking derivatives. In contrast, the theory combines infinitesimally small sections of linear birefringence with infinitesimallysmall, random rotations about the Stokes space. The PMD was evaluated at a single frequency using Stokes space differential concatenation rules for ? and zm.For both simulation and theory, the statistical variation was determined by changing the random rotations between the

zyxwvu

774

zyxwvutsr zyxwvu H. Kogelnik et al.

sections. The birefringence of the fiber used in the experiments was probably similar to that of the theoretical model except that the sections of linear birefringence and the rotations were not infinitesimally small. In addition, there was random variation in the birefringence of the linear sections. The experimentally derived densities were obtained by averaging over frequency rather than orientation of fiber birefringence, thus for the experimental densities, the orientations of the birefringent axes were frozen. The randomness was probably introduced by the frequency dependence of the s1 rotation in the linear sections. These three different models appear to lead to similar statistics. This can be understood for 2 from the concatenation rule, Eq. 2.23. The statistics of ? arise from the vector sum at the end of the fiber of the transformed random birefringences. Any model that creates this vector sum should generate similar statistics. The DGD density obtained from most emulator models does deviate at high DGD values from most theoretically derived densities. This is a consequence of the finite number of sections available in practical emulators. Consider a fiber with an rms DGD of Y. This fiber can be modeled using N randomly oriented birefringent sections, each having a birefringence T/&. The maximum PMD in the model, obtained by perfect alignment of the birefringence in each section, is N times the section birefringence or T a .Thus theories employing an infinite number of sections include the possibility of arbitrarily large PMD (with small probability), whereas the DGD density obtained from emulation or simulationwill truncate at a DGD value determined by the number of birefringent sections used in the model. Similar deviations between theory and simulation are also seen in the densities of other first- and secondorder PMD components. While schemes may be devised to bypass this limit, they are unlikely to provide a better model of fiber PMD. Real fiber PMD itself arises from a finite number of birefringent elements; hence, the densities of some PMD quantities for real fibers are expected to be truncated.

zyxwvu zyx zyx

5.3 EMULATION OF FIRST-ORDER PMD First-order PMD emulation is important, not only for testing system performance, but also as a key component of several of the PMD compensation techniques in Section 7. The most easily implemented emulator of first-order PMD is a length of polarization-maintaining fiber. One obtains about 2 ps/m of delay from most commercially available PMFs. The usefulness of PMF as a hst-order emulator is limited to applications for which the delay need not be adjustable. For these applications, PMF is the lowest cost, most stable method for providing first-order PMD.

I

15. Polarization-Mode Dispersion

zyx zyx 775

Figure 5.1 shows a method commonly used in commercial instruments to provide adjustable first-order PMD. This bulk-optics design uses a polarization beam splitter to separate an input signal into two orthogonally polarized beams. A variable optical delay is applied to one of the polarized beams prior to the recombination of the beams in a second polarization beam splitter. The design, like a length of PMF, provides pure first-order PMD without higher-order PMD. However, the output polarization depends on the optical phase difference between the two orthogonally polarized beams at the point of recombination. Since the variable and fixed delays in the emulator rarely are interferometrically stable, the polarization of the output beam fluctuates. This polarization fluctuation usually occurs with a time scale of 10’s to 1000’s of milliseconds and limits the placement of bulk-optic emulators to locations downstream of all polarization-dependent components in a system. Note that a length of PMF also requires interferometricstability in the two signal paths if polarization fluctuation is to be avoided at the output. However, since the two signal paths are in the same fiber, the necessary stability can be easily achieved by temperature control and isolation from external mechanical stress. Taping a jacketed fiber to a table in the open air usually provides sufficient stability to increase the time scale of polarization fluctuations to minutes or hours. The second design, shown in Fig. 5.2, uses the concatenation rule, Eq. 2.20. Two lengths of PMF are connected through a polarization controller. The PMD at the midpoint (input to the second length of PMF) will be the vector sum in Stokes space of the second section’s PMD and the first section’s PMD as rotated by the polarization controller. (For simplicity, we neglect the PMD of the polarization controller, which is always less than 6 fs for 4 quarter-wave retarders at 1550nm.) The polarization controller adjusts the angle, 8, between

zyx

PBS

PBS

OUT

Fig. 5.1 Bulk-optics method of providing adjustable first-order PMD. PBS refers to polarization beam splitters.

776

zyxwvuts zyxwvu H. Kogelnik et al. PMF

PMF

zyxwvutsr

zyxwvutsr I

IN

I

Polarization Controller

OUT

Fig. 5.2 Fiber implementation of adjustable first-order PMD. PMF refers to polarization-maintainingfiber.

the two PMD vectors. The magnitude of the vector sum is given by

where At1 and At2 are the DGDs of the lengths of PMF. The DGD of the emulator can range from l A q - At21 to At1 At2. The PMD vector at the output or input of the emulator can then be obtained by rotating the PMD vector at the input to the second fiber by R2 or R;', respectively. RZ is the rotation matrix of the second fiber, whereas R,' is the inverse of the rotation matrix of the first fiber combined with the polarization controller. Note that these rotations change the orientation of the total PMD vector, but not its magnitude, which is set by the polarization controller in the center. The twosection emulator provides a means for implementing rapidly adjustable, firstorder PMD when used with electrically controllable polarization controllers, such as those implemented using liquid crystals with millisecond response times or ones using lithium niobate structureswith nanosecond response times (see Section 7.7, Heismann and Wayland 1991). When implemented with two lengths of PMF, each having a delay of At1 ,the emulator can provide DGDs ranging from 0 to 2 A q . One feature of the two-section emulator, often a disadvantage, is that it unavoidably provides second-order PMD along with the desired first-order PMD. This second-order PMD is a consequence of frequency dependence in the rotation that translates the vector sum to the input or output of the emulator. From the second-order concatenation rule, Eq. 2.22, it can be seen that the magnitude of the emulator input or output second-order PMD is AtlAt2 sin (e), since for PMF, ?lo and ?h are both zero. Despite the presence of second-order PMD, the two-stage emulator is an important component of PMD compensators.

+

zyxwv zy

zyx zyxwv zyxwvu

15. Polarization-Mode Dispersion

5.4 EMULATION OF FIBER PMD

777

A full understanding of PMD can be gained only by emulating all orders of PMD. A useful PMD emulator should be able to reach all combinations of first- and higher-order PMD present in the optical fiber being emulated; it should mimic the PMD spectrum of an optical fiber; it should be stable over measurements lasting hours to days; and it should be possible to both predict the emulator PMD for a given instrument setting and to predict the instrument setting required to obtain a desired PMD. It would also be useful if the emulator could easily mimic the complex statistics of fiber PMD. One approach that can be viewed as laboratory emulation of fiber PMD is to use a short fiber with high PMD (Jopson et al. 1999~).This approach can provide PMD with statistics similar to those encountered in the field; however, the PMD is not adjustable and the fiber may add additional impairments such as loss, dispersion, or nonlinearity. A multiplate emulator can be used to obtain adjustable PMD (Damask 2000; Williams 1999a). Light passing through a multiplate emulator transits a series of birefringent elements sandwiched between random interelement polarization coupling. The birefringent elements are often crystalline waveplates, but PMF is also common. Orienting the axes of successive birefringent elements at random angles can provide the random polarization coupling. An alternativeis to use polarization controllers. Adjustment of the emulator PMD can be obtained by changing the polarization coupling between elements, by changing the amount of birefringence in each element, or by changing both. The former course is usually chosen. Since the emulator PMD is sensitive to small changes in the birefringence of its components, it is difficult to adjust a multiplate emulator to a desired state of PMD and it is difficult to predict the PMD obtained from a known setting. However, a group of random settings of the emulator will provide a sample of PMDs that match the statisticalvariation of fiber PMD. The statisticalmatch is not perfect. While a fiber may effectively consist of hundreds or thousands of birefringent sections (Galterossa et al. 2000b), multiplate emulators generally have less than 20 sections or elements. As mentioned previously, the peak DGD is roughly the root-mean-square DGD times the square root of the number of elements. Thus, for a given mean DGD, the peak DGD achievable by an emulator is considerably less than that possible in a fiber. This limitation causes a truncation of the emulator’s probability density for DGD and other PMD values. Figure 5.3 shows the deviation from theoretical predictions of the densities expected from a 12-plateemulator for the magnitude and one Stokes component of both first- and second-order PMD, as well as the parallel and perpendicular components of second-order

zyx

zyxwvuts zyxwvu lozyxwvutsrqp 4I €3. Kogelnik et al.

10 4

zyxwvutsrqp zyxw zyxwvutsrq

109 104

104

First-Order Components

104

I0-7 -XI0

h

x

Emulator

,

-50

0

50

100

0

40

20

60

,

x,

8 0 '

zyxwvutsrq 109

I

.22

d

.B

2 e n

104 104

106

ond-Order Componen x

Emulalor

I0-7

1000

-1 000

xxxx

-1000

400

0 ATm ( P d

500

1OW

50

100

18,l

150

X%

200

(PSI

Fig. 5.3 PMD densities expected from a 12-plate emulator having a mean DGD of 3 1.9 ps. The average delay of each element was 9.2 ps.

PMD. The probability densities expected from the emulator were obtained by a simulation of 12 birefringent plates that could be rotated in the plane of the birefringent axes A quarter-million set of random orientations were used. The birefringent plates had slightly different thicknesses, but these differences did not change during the simulation. This mimics a real-world emulator for which the plates can be rotated rapidly but have slightly different retasdances that change slowly. It can be seen that 12 plates provide first-order densities accurate to 30% or better for DGD or first-order component values of about

zyx

zy zyxwv

15. Polarization-Mode Dispersion

779

3 times their rms value. However, the second-order densities obtained from the 12-plate emulator are inaccurate.

5.5 NUMERICAL SIMULATION OF PMD

When simulating PMD numerically, one usually follows the approach used for PMD emulation: A series of birefringent elements are sandwiched between polarization adjustment. Simulations usually use more sections than emulators and can use more sophisticated polarization adjustment than emulators. Emulators most commonly adjust polarization by physically rotating the birefringent elementsas described previously.The polarization adjustment options in simulators include, in addition, three-axis polarization controllers and random orientation over all of Stokes space for the birefringence in the delay elements. Simulation can be used to explore the behavior of system performance in the presence of PMD (see Section 6), to understand the behavior of PMD monitors or compensators (see Section 7), and to provide insight into the statistics of PMD (see Section 4).The flexibility inherent in numerical calculation allows randomness to be achieved more easily than in emulators. For instance, adjustments to the retardation of birefringent elements are difficult in an emulator and trivial in a simulator. Although simulation is usually performed in Jones space (see Section 2), it is also done in Stokes space. The PMD concatenation rules (see Section 2, Gordon and Kogelnik 2000) can be applied sequentially for each birefringent element in the simulation. Figure 2.13 shows two birefringent elements with first-order PMD 21 and 22 together with rotation matrices R1 and Rz, respectively. The rotation matrices contain, in addition to the rotation matrix of the element, the intraelement polarization adjustment preceding it. As discussed in Section 2, the PMD at the output of the two sections is given by: ? = 22 R2t;. (5.2)

zyxwv zyxwv zyxwv zyxwv +

As birefringent elementsR3, R4,and so on are added as illustrated in Fig. 2.14,

this rule can be cascaded. The result is a sum of the PMD of each of the birefringent elements in the simulation, each rotated by the product of the rotation matrices of the birefringent elements following it:

This becomes a sum of PMD vectors having magnitudes corresponding to the PMD of the birefringent elements but with a nearly random orientation. A deviation from randomness occurs for the last few birefringent elements: The vector corresponding to the final element is not rotated by any

I

.

.

.

.

.

.

.

.

.

I

780

zyxwvutsr zyxwvu zyxwvuts H. Kogelnik et aL

succeeding elements; hence, it retains its orientation. The angle between that vector and the vector correspondingto the penultimate element will retain its original value. For a good statistical sample of first-orderPMD, one can use a sum of randomly oriented PMD vectors and dispense with the rotation matrices in Eq. 5.3. However, the rotation matrices are needed if the wavelength dependence of the PMD is of interest. Second-order PMD can be obtained (see Section 2, Gordon and Kogelnik 2000) by cascading the expression for the second-order PMD of the two sections shown in Fig. 2.13:

Second-order components as well as higher-order components can also be obtained by using Eq. 5.2 for closely spaced wavelengths and calculating the PMD using one of the methods described in Section 3. Simulations are often performed in Jones space, perhaps because they are usually done by experimentalistswho appreciatethe intuitive correspondence between Jones matrices and real-world components and angles. One simple approach, similar to many PMD emulators, is to cascade linear retarders with the birefringent axes oriented at random angles This is illustrated in Fig. 2.3. In the simulation, each plate becomes a linear retardation matrix sandwiched between two rotation matrices. The rotation matrices, which effectively orient the retarder at a random angle, correspond to a rotation of first -8 and then 8, where 8 is chosen randomly. Thus, a two-element simulation would have a transmission matrix given by:

zyxwvu zyxwvu zyx zyxwv zyxw

and the V(8,) are matrices for rotation about the z axis They wherej = rotate the orientation of linear polarization states through an angle of 8, in the laboratory, and are given as U3 in Table C1 of Appendix C, with p/2 = 8,. Notice that these rotationsare independentof w,the angular opticalfrequency. Birefringent element n has a delay of tn.Immediately after the rotation operation 81 we rotate by -6% in Eq. 5.5. Since both of these angles are chosen randomly, the two rotations can be replaced by a single rotation through a randomly chosen angle, &. The two-element simulation now becomes:

15. Polarization-ModeDispersion

781

where we have added the rotation through 03 to decrease the correlation between the simulated output PMD and the orientation of the final birefringent element. From the transmission matrix, one can determinethe PMD that it represents. One of the disadvantages of working in Jones space is the need to convert transmission matrices in Jones space to PMD vectors in Stokes space. This can be accomplished by simulating one of the measurement techniques that are described in Section 3. If the DGD is all that is needed, it can be obtained from the determinant of the frequency derivative of the transmission matrix (Gordon and Kogelnik 2000):

zy

zyxwvuts zyxwv zyxwvuts zyxwv zy zyxwv

where T, = [T(m+ Am) - T(w)]/ A m for a small frequency step, Am. The tnshould have different values if realistic PMD spectra are desired. The lowest curve in Fig. 5.4 shows the spectrum of the DGD obtained from a 100-elementsimulation when the tnall have the same value. It can be seen that the spectrum is periodic, with a period of l/tn.This is the frequency interval over which the arguments of the exponentials in the delay matrix change by n.The lowest curve in Fig. 5.4 was obtained using one-tenth of the rms DGD for the tn:109 fs. Thus, the repetition period is 9.2THz. In addition to the periodicity, there are also mirror symmetries visible in Fig. 5.4, and a plot of the spectra of the first-order components will reveal an inversion symmetry in addition to those present in the DGD. Repetition can be avoided in any desired spectral range by making the delay elements sufficiently small such that the repetition period exceeds the spectral range of interest. However, the spectral range may still include symmetry points for injudicious choices of tn. A common approach to reducing the problems presented by periodicity is to add some randomness to the t,,. One should avoid large scatter in the values of the tn,lest the distribution chosen to implement this scattering color the probability densities obtained from the simulation. A common choice is to add variation to the values of the tnwith a Gaussian distribution having a width of 20% the mean value (Prola et ul. 1997). The upper curves in Fig. 5.4 show the effect of adding randomness to the delays used in the simulation for the lowest curve. The U(0,) remained unchanged for all curves in Fig. 5.4. As the amount of scatter in the tnincreases, the periodicity and symmetries decrease. The curves for a scatter of 0.1 optical cycles are quite similar to the lowest curve. Although 0.5 cycles of scatter modify the spectrum significantly, the periodicity is readily apparent. The curves obtained using a scatter of five optical cycles show greatly diminished periodicity. A scatter of 5 optical cycles means that the 109fs nominal delay for each element has been spread over 26 fs,

782

zyx

zyxwvutsr zyxwvut zyx H. Kogelnik et al.

15

Retardation Dither (cycles)-

-

5.0

Y

10

2.0

-

1 .o

zyxwvutsrq 190

200

Frequency (THz)

Fig. 5.4 Spectrum for 1 ps of mean PMD obtained from simulations using 100 ele-

ments with linear birefringence oriented at random angles. The same set of random orientations was used for all nine curves. For the lowest curve, the 100 elements had equal delays. The remaining curves used elements having a delay that varied randomly with a uniform distributioncentered on the delay used for the lowest curve. The amplitude of the distributionis shown to the right of each curve in units of the optical period, 5.2 fs. The successive curves are shifted upwards in units of 2 ps for clarity. The dashed lines show a second instantiation of the random delay values for the curves labeled 0.1 and 5.0.

zy zyxwvutsr

so it is not surprising that the DGD spectrum shows little periodicity. Even with the randomization of delay elements, many delay sections are required to obtain realistic probability densities by frequency scanning (Khosravani et al. 2001a). The use of randomness in the delay elements is not as important when densities are obtained by changing the polarization coupling rather than changing the frequency. However, it has been observed that the use of nonidentical delay elements can reduce the number of such elements required to provide a desired level of accuracy in the densities (Khosravani et al. 2001a). Once again, although simulation techniques tend to be judged on the basis of how closely they mimic purely random PMD, actual fiber PMD and system PMD will deviate from this analytically tractable “ideal.”

zyxwvutsrq zyxwvutsr zyxwvutsrqp zyxwvutsr zyxwv 15. Polarization-ModeDispersion

k

(a)

"

"

"

"

"

"

"

"

783

'

1

4 delays

'2 x

.2.

0.1

m

c

0" .2. -

0.01

a m

n g 0.001

a

0.0001

11

,

,

,

,

,

,

I

,

,

,

1

0

3

2

AT

zyxwvutsrqpo 1

N -

'2

v

X

0 .m C

0.1

: 0 0.01 .-

a m n

;0.001 0.0001

0

1

zyxwv zyxw 2

IrmlI (

3

a'

Fig. 5.5 Effect of number of delay elements on PMD densities obtained by simulation for 1ps mean DGD for (a) the DGD and (b) the magnitude of second-order PMD. The average delay of each element is J W G ,where N is the number of delay elements, and is the mean DGD obtained for large N . The plots are normalized by this "asymptotic" mean DGD.

784

zyxwvutsr zyxwvu zyxwvu zyxwv zyxwv H. Kogelnik et al.

Much effort has been devoted to determining the influence of both the number of delay elements used in a simulation and the method used to couple between them (Prola et aI. 1997; Dal Forno et al. 2000; Lima et al. 2000; Khosravani et al. 2001a). Figure 5.5 illustrates the changes in several PMD probability densities as the number of delay elements used in the simulation is increased. These simulations used the algorithm based on Eq. 5.6. It can be seen that agreement with theory becomes better as the number of delay elements increases; the value at which the densities truncate increases as the number of delay elements increases; and, accuracy in second-order densities require more delay elements than the same degree of accuracy in first-order densities. The number of delay elements required for a particular application depends on the degree of accuracy required. 5.6 FURTHER READING

zyxw

The importance of importance sampling in PMD simulation is demonstrated by Menyuk et al. (2001) and Lima et al. (2001), particularly for the densities of finite element models near the truncation. Karlsson (2001a) provides exact probability densities for 3-D PMD models with finite number of delay elements.

6. System Impairments Due to PMD

zyxwv

Fiber PMD causes a variety of impairments in optical fiber transmission systems. First of all there is the intersymbol interference (ISI) impairment of a single digital transmission channel. The IS1 impairment is caused by the differential group delay, A t , between the two pulses propagating in the fiber when the input polarization, & of the signal does not match the PSP of the fiber, j. In this first-order PMD effect the fractional powers launched into t h e P S P s a r e y = {s I p ) ( p I s ) = ; ( l + j . E ) a n d ( l - y ) = i ( 1 - j . ? ) . Systems impairments due to second- and higher-order PMD occur for larger signal bandwidths, particularly when these PMD components combine with chromatic fiber dispersion or signal chirp. PMD impairments due to interchannel effects occur in polarizationmultiplexed transmission systems. Examples are WDM systems where adjacent wavelength channels are launched with orthogonal polarizations in order to suppress nonlinear impairments such as cross-phase modulation (XPM) or four-wave mixing (FWM). PMD destroys the orthogonality of these polarizations. A related PMD effect is the decorrelation between the polarizations of

zy zyxw zyxw zyxwv zyxwvut zyx zyxw zyxwv 15. Polarization-ModeDispersion

785

pump and probe in Raman fiber amplifiers reducing polarization-dependent gain. Another example is a system wherein polarization multiplexing is used for close packing of WDM channels in order to achieve high bandwidth efficiency. Here, PMD induces coherent cross-talk between multiplexed channels leading to system impairments. The above impairments of digital systems are described in the succeeding sections. For reviews of the impact of PMD on analog systems, the reader is referred to Poole and Nagel (1997) and to Ciprut et al. (1998). Literature discussing system impairments because of polarization-dependentloss (PDL) is listed in Section 6.8; the following sections assume absence of PDL.

6.1 POWER PENALTIES DUE TO FIRSTORDER PMD

In the first-order picture, PMD splits the input signal entering the fiber into two orthogonally polarized components that are delayed by A t relative to each other during transmission. The impairment caused by this effect can be expressed as a power penalty E of the form (Poole et al. 1991) &(dB)= (A/T2)At2y(l - y ) = A(At/2T)* sin’ 8,

(6.1)

where the penalty, expressed in dB, is assumed to be small. Here, T is the bit interval, 0 5 y 5 1 is the power-splitting ratio, and 8 is the angle between the input polarization, ?, and the input PSP, h. The y(1 - y ) dependence shown in this expression has been verified by experiment in Kim et al. (2001a). The dimensionlessA-parameter depends on pulse shape, modulation format, and specific receiver characteristics such as the detailed response of the electrical filter and whether optical or thermal noise predominates. For pin receivers the reported values for A range from 10 to 40 for NRZ and from 20 to 40 for RZ, whereas the A ranges for optically preamplified receivers are 10 to 70 for NRZ and 10 to 40 for RZ. report the penalty measurements, emulations, and simJopson et al. (1999~) ulations for optical preamplifiers shown in Fig. 6.1. For these specific receiver types, the data for NRZ transmission show a good fit to the penalty formula (6.1) for an A-parameter of about 60 to 70. For RZ transmission the measured A parameters range from about 15 to 25. Sunnerud et al. (2001a) used a different approach, reporting simulations for PMD-induced RZ and NRZ system degradation. The DGD value, At, appearing in Eq. 6.1 is the “instantaneousyy DGD value, assumed to be constant during the penalty measurement. For polarization-maintaining fibers (PMFs), often used as PMD emulators, this constancy is assured. However, in communication fibers, the DGD and the

786

zyxwvu

H. Kogelnik et al.

NRZ simulator NRZ emulator fit: RZ fiber RZ emulator RZ simulator RZ emUlatOr fit:

zyxwvu zyxwvu zyxwvut zyxw E

[de] = A ( A T I ~ ~ A ' , = 70

E

[dB] = A (Ad2n2, A = 30

zyx zyxwvuts 2

0

10

20

30

40

50

60

70

DGD (psec)

Fig. 6.1 RZ and NRZ penalty measurements, simulations,and emulations for optical preamplifier receivers as a function of instantaneous DGD. Worst-case polarization launch is assumed. From Jopson et al. (1999~).

zyxwv

direction of the PSP changes as a function of time, temperature, stress, wavelength, etc. While some of these changes occur on a time scale of days or hours, changes of the order of milliseconds have been reported (Biilow 1999~). These times are in contrast to bit intervals, T , that are fractions of a nanosecond, and to measurement intervals that require many bit intervals. The penalty formula (Eq. 6.1) should be regarded as a semiempirical rule at this time. The receiver parameter, A , in particular, needs to be determined by simulation and experiment. However, the general nature of the formula, particularly the dependence of the penalty on the DGD and the direction of the PSP, are in good agreement with analysis of the moments of the received signal (Karlsson 1998; Shieh 1999; Gordon and Kogelnik 2000). As reflected in Eq. 6.1, the power penalty, E , changes with the DGD and with the launch penalty factor, g , where g = sin2 e = [I - (j.i)7 = (jx i)2

(6.2)

depends on the alignment between the Stokes vector, i, of the input polarization and the instantaneous PSP, j.We have g = 0 for perfect alignment, where there is no power penalty, and a maximum of g = 1 when the Stokes

zyxwvu zy zyxwvut zyxwvu

zyxwvutsrq zyxwv zyxwv zyxwvut zyxwvut 15. Polarization-Mode Dispersion

787

vectors ;and j are perpendicular (i.e., when equal powers are launched on the PSPs). The latter is the worst-case launch resulting in the maximum power penalty, and is often used in receiver penalty experiments such as those shown in Fig. 6.1.

6.2 LAUNCH PENALTY STATISTICS

Consider the launch penalties g(8) = sin28 that occur for given input polarization, ;, as the Stokes vector, fi, of the PSP of the fiber changes. Assume that the PSPs occur with a uniform distribution over the Poincart sphere, and that P is aligned with the north pole of the sphere as shown in Fig. 6.2. The probability density of PSPs being in the range d8 about an angle 8 relative to ;is proportional to the differential area 2n sin 8.d8 sketched in the figure. As there is northhouth symmetry in the penalty and differential area, we combine the (0 to n/2) and (n/2to n)ranges of 8, double the differential area, and obtain the combined probability density ps(8) = sin 8

(6.3)

for the effective range (0 to n/2)describingthe occurrence of PSPs with angle 8 (and 7t -8)relative to hi.Here, we use subscripts such as 8 and g to distinguish the various density functions. The mean launch penalty is

Fig. 6.2 Sketch of differential area on Poincart sphere as a function of elevation angle 0.

788

zyxwvu zyxwvut zyxwvuts zyx zyx

H. Kogelnik et al.

This mean value is relatively large compared to the maximum of g = 1 as there is more area for PSPs near the equator than there is near the pole. The probability density for the occurrence of a launch penalty g is P ~ W=Pe(eW * dQ/dg =

;/G-

(6.5)

Integrating this density one finds the cumulative probability of a penalty g exceeding the value G as

zyxw zyx

Inserting G = 0.75, we find that for 50% of the possible PSPs, the launch penalty exceeds 75% of the maximum penalty of 1. This means that for onehalf of the PSPs occurring in a fiber as time changes, the launch penalties are almost as large as those obtained in worst-case tests. 6.3 SYSTEM OUTAGE DUE TO PMD

Outage specifications for optical fiber transmission systems depend on the application. Usually one requires the power penalty contributions of PMD to be less than 1dB for all but a specified cumulative probability. This specification ranges between outage probabilities of and Disregarding the potentially large PMD correlation times (see the 19 hours mentioned in Section 7), this is commonly translated to average cumulative outages ranging from fractions of a second to 60 minutes per year. To specify this limit one requires knowledge of the probability density, P,(E), for the occurrence of a power penalty E.The penalty formula (6.1) shows that E is proportional to the product of the launch penalty g and a DGD term, At2. The probability density of g for uniform distribution over the Poincart sphere is given in Eq. 6.5. The density of A t is Maxwellian (see Table 4.1) from which the density of the DGD term can be derived. From the densities for g and the DGD term, one can deducep,(s) using standard probability theory for the density of a product (Poole and Nagel 1997). However, we follow another, more direct, approach shedding further light on the mechanisms of PMD penalty statistics. In view of A t 2 ( j x i)2= (2 x i)2= (21 x i)2= At: we can rewrite the first-order penalty formula as E

= (A/4T2)Ati,

(6.7)

where 21 is the component of 2 perpendicular to i, and A t 1 is its magnitude. The penalty E is caused only by the components of the PMD vector 2 that are perpendicularto i. The statisticsof the two componentsof 21 are described by

zyx zyxwv zy zyxwvutsrqponm zyxwv

zyxwvuts 15. Polarization-Mode Dispersion

789

two independent Gaussians. The magnitude A t l , therefore, follows a Rayleigh distribution, with the probability density

where

and

is the mean DGD. The mean penalty parameter is, therefore,

E=

Jd

oc

dx. E ( X )

.PA~~(= X )Aa2/2T2= (nA/16T2)-2A t

.

(6.10)

One can now transform the Rayleigh density for AT^ to the density for E and obtain the known exponential (Boltzmann) distribution: ~ E ( E ) - = P A ~ - ( A T. dArl/dE ~ ( E ) ) = (l/E) .e-'/'.

(6.11)

Figure 6.3 shows a test of the exponential density predicted by Eq. 6.11 using computer simulation (Poole and Nagel 1997). Here, the frequency of occurrence for penalties was calculated far 10,000 fibers, each modeled as a concatenation of 1000 birefringent fiber sections with random orientation. Good agreement was found between the simulated data and the predictions. From Eq. 6.11 follows the outage probability, Pout,i.e., the probability for the penalty to exceed N dB, (6.12) where the penalty limit, N , is usually specified as 1 or 2 dB. The mean penalty associated with the specification of an outage probability, Pout,is

E =N/ln(l/Pout).

(6.13)

Inserting Eq. 6.10 we can formulate this condition as a requirement for the mean DGD of the fiber: A~/= T 4 . &/Jn

A . In (l/Pout),

(6.14)

where A is the receiver parameter discussed earlier. Figure 6.4 shows a plot of this requirement for three values of the parameter AIN covering the mentioned range of values encountered in NRZ and RZ systems. Note that for

790

zyxwvu zyxwv

H. Kogelnik et al.

zyxwvuts

0

Simulation Results

- Exponential Fit with A = 25

zyxwvuts zyxwvutsrqpo -1

h

C VI

B C =

6 CI)

3

-2

-3

zyxwvu zyxwvuts zyxwvu -4

0.0

0.5

1 .o

0.5

2.0

Power Penalty E in (dB)

Fig. 6.3 Test of the exponential distributionof the power penalty,p,(s), by computer simulation.From Poole and Nagel (1997).

an outage probability of (3 seconds/year), a typical RZ system (A = 30, N = 1) requires a At/T ratio of 10% whereas the corresponding typical NRZ system (A = 70, N = 1) requires At/T to be less than 7% (assuming receivers with optical preamplifers). We should reemphasize that A values are strongly dependent on pulse shape and receiver chracteristics and must be determined for each specific system. Some workers find it convenient to express this requirement in terms of the DGD value, A ~ Lthat , characterizes a worst-case-launch PMD penalty measurement in the laboratory, such as that shown in Fig. 6.1. Here, ATLis the 1-dB intercept, i.e., the instantaneous DGD value causing a 1-dB PMD penalty. The intercept ATLfollows from Eq. 6.1 by setting E = 1 and y = 1/2. The requirement for the mean fiber DGD becomes

-

A t / a t ~= 2.&/,/n-ln(l/POut)

(6.15)

Figure 6.5 shows a graph of this requirement for two outage criteria (N = 1dB and N = 2dB). For an outage probability of loe5 and N = 1, the required

zyxwvu zy zyxwvuts zyxwv zyxwvu 15. Polarization-ModeDispersion

791

0.25

---

.r

. m .0 0.20 -

& a

.c m

\

\

--

..... .---_--

RZ (A=30), 2-dB Penalty RZ ( A = 3 0 ) , 1-dB Penalty NRZ (A=70), I-dB Penalty

- - - - - - -- - -

.

---_.

----0.05

-

zyxwvutsr zyxwvutsrq

At/Aq 113, implies that the mean DGD must remain below one-third of the instantaneous DGD value causing 1 dB penalty.

6.4 IMPAIRMENTS DUE TO SECOND-ORDER PMD

The concept and definition of second- (and higher-) order PMD, discussed in Section 2, suggest that its effects on system performance increase with the frequency separation, Aw, from the carrier (w = wo). No significant secondorder effects are expected as long as the bandwidth of the signal, Au, is smaller than the bandwidth of the PSP, Aupsp (see Section 2). Compare this statement with the PMD outage criteria discussed earlier. They specify the allowed ratio of mean DGD to bit interval as approximately Z / T 5 0.1. As the signal bandwidth is roughly equal to 1/T, and at is related to Aupsp via Eq. 2.17, the outage criterion is roughly equivalent to

zyxw

AU5 A~psp.

(6.16)

Together, the PSP-bandwidth statement and the outage specification imply that second-order penalties are negligible as long as the first-order outage

792

zyxwvutsr zyxwvu zyxwvu zyxwv

zyxwvu zyxwvut H. Kogelnik et al.

t

1

---

2-dB Penalty

- 1-dB Penalty

\

. n

x

0.3

10 9

1o4

I 0-5 10 4 Outage Probability

10-7

zyx 10-8

Fig. 6.5 Outage requirement: plot of the allowed ratio ofmean DGDI ArL, where ArL is the instantaneous DGD giving a measured 1dB penalty for the worst-case launch

polarizations.

specification is met. This important observation has been confirmed repeatedly by experiments and simulations (Gleeson et al. 1997; Biilow 1998a,b). Restated in plain language this means there is no need to worry about secondorder PMD as long as there is no need for first-order PMD compensation. However, when the outage specification for is not met, there is a need for PMD compensation as well as a need for concern about second-order PMD impairments. The variety of electrical and optical techniques used for PMD mitigation will be discussed in Section 7. The second-order PMD impairment of the overall compensated system will, of course, depend on the specifics of the mitigation technique. A good illustrative example is the case of a common optical mitigation technique where the fiber’sPMD, ?(w), is canceled at w = q by a compensator section with a PMD vector of 2comp= -?(wg). Using Eq. 2.9, the resulting overall PMD of the fiberkompensator combination is seen to be Zo-l1(~o

+ Am)

Am *

2,

+

*

.. ,

(6.17)

leading to impairments dominated by the second- and higher-order PMD components of the fiber-compensator combination.

zyxwvu zyxwvuts zyxwvuts zyxwv

zyxw zyxw zy

15. Polarization-Mode Dispersion

793

A second relevant issue is the occurrence of spikes of the second-order PMD depolarization in parts of the spectrum as numerically simulated by Gleeson et al. (1997) and measured by Nelson et al. (1999b). Figure 6.6 shows the measured data for the DGD and depolarization, pwl,for a fiber with a mean DGD of 35 ps. The figure shows several instantaneous DGD peaks of 70 ps and above, leading to excessive first-order penalties (see Eq. 6.1). This fiber clearly violates the at specificationand requires PMD compensation for 10-Gb/s transmission. However, in the spectral regions near 1545.4, 1545.7, and 1545.85nm7the instantaneous DGD drops to 20ps and below. WDM channels in these regions do not require first-order PMD compensation at 10-Gb/srates (at that instant in time). The $J values, on the other hand, are seen to spike to very high values in these regions, warning of potential secondorder PMD impairments. Although three spikes are shown in the figure, an average of 24 such depolarization spikes were observed over a 10-nm spectral range. The occurrence of these spikes is in good agreement with the data of the scatterplot of Fig 3.10 showing the correlation between low DGD and high $wl values. Whereas first-order PMD deals with two pulses delayed relative to each other, pulse distortions due to second-order PMD can be visualized in terms of the interplay of six different pulse replicas (Bruyere 1996; Francia et al.

1000

-1 000

Wavelength (nm)

Fig. 6.6 Measured instantaneous DGD, PSP depolarization, and PCD as a function of wavelength for a fiber with a mean DGD of 35 ps.

794

zyxwvuts zyxwv zyxwvu zyxwvu H.Kogelnik et al.

1998). These mechanisms result in pulse overshoots and the generation of satellite pulses. For higher PMD orders, Leppla and Weiershausen (2000) suggest distortion mechanisms involving a number of pulses proportional to

zyx zyx zyxwv zyxw

AV/A*SP.

The simplest second-order impairment mechanism is polarizationdependent chromatic dispersion (PCD) first pointed out by Poole and Giles (1988c,d). As explained in Section 2, PCD is caused by the ; ,component parallel to the PSI? It is described by the PCD measure TA defined in Eq. 2.12. Given a fiber chromatic dispersion, DL, the PCD impairment is equivalent to that of an effective chromatic dispersion of the transmission system,

(DL)eff= DL fTA,

(6.18)

that is different for the two PSPs as the plus/minus signs indicate. While PCD is a simple mechanism, it is a relatively minor component of the second-order PMD vector since 2, has a statistical tendency to point away from the PSP (see Section 4). The dominant impairment mechanism is due to the depolarization component perpendicular to the PSP that is proportional to PmI. Statistical analyses and numerical simulations of system impairments indicate a strong interaction between chromatic dispersion in the fiber and the second-order PMD in general (Bruykre 1996; Penninckx and Bruybre 1998). Similarly, it has been found that chirp in the transmitted signal has a significant impact on second-order PMD impairments (Biilow 1998b). Recent PMD vector measurements have enabled the correlation of system penalties to measured instantaneous first- and second-order PMD vectors (Nelson et al. 2000b). In these experiments, signal launch polarizations were known and controlled relative to the PSP and the second-order PMD vector. Impairments were found to be dependent on chirp and chromatic dispersion, and to be highly dependent on launch polarization. Measurements of the impairment of IO-Gb/s NRZ signals were made near the depolarization spike at 1545.45 nm of the fiber with 35 ps mean DGD (Fig. 6.6). Care was taken to ensure a dispersion-free system, however, signal chirp was known to be present and is thought to be responsible for the large penalties that were observed. As an illustration, Fig. 6.7 shows the output bit patterns and eye diagrams for the three launch polarizations with the largest impairments. These launches were perpendicular in Stokes space, with +pa, indicating a polarization aligned with j,, -p indicating alignment with the fast PSP and -pp designating a launch perpendicular to these two. Pulse overshootsin the output bit patterns are evident. Large optical-receiver penalties were measured for these three launches reaching as high as 4 dB for thep, alignment. Launch polarizations

zyxwvuts I

15. Polarization-Mode Dispersion

795

zyxwvuts zyxwvu

Fig. 6.7 lO-Gb/s NRZ output bit patterns and eye diagrams showing the effect of second-order PMD. Results are for the three launch polarizations with the largest impairment. From Nelson et al. (2000b).

zyx zy

aligned with -pw, +p, and +pp exhibited minor system impairments. Penalty differences between orthogonal launches such as =tjare a characteristic of second-order PMD.

6.5 PMD IMPAIRMENTS IN POLARIZATION MULTIPLEXING

Polarization multiplexing of WDM channels has been proposed and investigated for WDM transmission system architectures that may allow an increase in spectral efficiency to, for example, 0.8 bit/s/Hz at the bit rate of 40 Gb/s per channel (It0 etal. 2000; Nelson and Kogelnik 2000d). In one such architecture, polarization-division multiplexing (PDM), each wavelength carries two channels on two orthogonal polarizations (e.g., 40 Gb/s per channel with 100-GHz wavelength spacing). In another architecture, polarization interleaving, adjacent WDM channels have orthogonal polarizations (e.g., 50 GHz spacing of 40-Gb/s channnels). A schematic of a polarization multiplexing architecture is shown in Fig. 6.8, where, at the fiber input, the channels labeled A are launched orthogonally to the channels labeled B. Polarization beam splitters (PBS) are used to combine the A and B channels at the input and to separate them again at the fiber output. PMD causes system impairments in these architectures because it destroys the orthogonality of spectral signal components that differ in frequency. Other impairments faced by polarization multiplexing architectures are those caused by fiber nonlinearities such as cross-phase modulation (Mollenauer et al. 1995; Collings and Boivin 2000a,b).

zyxwvuts

zyxwvutsr zyxwvu zyxwvut zyxwvutsrq -, , zyxwvutsr H. Kogelnik et al.

796

Fiber

A/P ;/+ ,

Polarization Control

Filter

WGR

e

D

?J

‘

+Ao”t

1

t

B

BO,

Fig. 6.8 Schematic of a polarization multiplexing system using polarization beam splitters (PBS) at the transmitter and receiver ends.

To discuss the physical process causing PMD impairments in somewhat more detail refer to Fig. 6.8 and consider a polarization-interleaved system with channel spacing of 50 GHz and a bit rate of 40 Gb/s. Because of the close packing of the WDM channels, the a t e r of the waveguide router (WGR) will not perfectly separate the neighboring B channels from a given A channel. Some leakage will occur, but this will be eliminated by the output PBS, at least when no PMD is present in the fiber. When PMD is present, it causes the polarization at the fiber output to be a function of frequency. To first order, this change of polarization with frequency is described by the law of inkitesimal rotation, &/dw = ? x i(wg), (6.19) discussed in Section 2, where i(w0) is the output polarization at the carrier frequency of A (w = wg). As the output PBS is aligned with the polarization, i(wg), of the A carrier, polarizations at other frequencies, w # wg, will move away from alignment because of PMD. This causes each neighboringB channel to leak into the A channel and also causes some depletion of the A signal. Ideally, the PBS is adjusted for maximum reduction of the B to A leakage. The spectral components of the depleted A channel and the leakage from the neighboring B channels add in amplitude at the A,,, port,

zyxw zyxwvu zyx AOUtb)

= a(w)A(w) +jP(w)

my

(6.20)

where A and 8 are the spectral ampljtudes and a and are frequencydependent depletion and coupling coefficients. The amplitude addition leads to coherent cross-talk at the A receiver, resulting in system impairments. The optical phase between the A and B amplitudes is an important parameter in the interference effects producing coherent cross-talk. A detailed discussion of the associated mechanisms is given in Nelson and Kogelnik (2000d). There it is shown that, for PDM, cross-talk is largely due to pulse edge effects causing

J

zy zyxwvu 15. Polarization-ModeDispersion

797

impairments proportional to A t / A T , where AT is the pulse rise time after the filter. For systems employing interleaving, impairment is dominated by beating between channels. The filter characteristics have, of course, an important effect on the magnitude of the impairments in both multiplexing architectures. Nelson et al. (2001) have measured worst-case coherent crosstalk impairments using filters of 50-GHz FWHM (about as narrow as tolerable for 4O-Gb/s NRZ), first-order PMD emulation, and worst-case launch polarizations, i.e., Stokes vectors perpendicular to the PSP. The observed penalties for 4O-Gb/s NRZ transmission are shown in Fig. 6.9 as a function of the instantaneous DGD of the polarization-maintaining-fiberemulator. Penalties induced by PMD are shown for both the interleaving and PMD cases. The corresponding singlechannel penalties are shown for comparison (and can be compared to Fig. 6.1). For small DGD, the latter are proportional to A t 2 conforming with Eq. 6.1 and a receiver parameter of about A = 70. The instantaneous DGD inducing a 1-dB single-channel penalty is approximately ATL = 7 . 5 in ~ good ~ ~ agreement with the scaled lO-Gb/s data from Fig. 6.1. For the single 4O-Gb/s

z

zyxwvu

zyxwv zyxwv

-

PolarizationInterleaved

v-

3 2

0

2

4

-+ Single Channel 6

Differential Group Delay (ps)

8

10

Fig. 6.9 Observed PMD penalties for 4O-Gb/s NRZ transmission as a function of instantaneous DGD for worst-case launch polarizations.Data are shown for polarization interleaving, polarization-divisionmultiplexing, and for a single channel. From Nelson et al. (2001).

798

zyxwvutsrq zyxwvu zyxwvu zyxw H. Kogelnik et al.

zyx

channel, the penalty statistics of Section 6.3 translates this ATLvalue into an = 2.5ps for a 1 dB-penalty outage of allowable mean fiber DGD of (see Eq. 6.15). We note in the figure that the penalties for the two polarization multiplexing cases are about equal and that they are also nearly proportional to A t 2 . However, here the instantaneous DGD for a 1-dB penalty is A ~ = L 1.5 ps, a factor of 5 less than in the single-channel case. For the interleaving case this value agrees with the measurements of Ito et al. (2000). This suggests that the polarization-multiplexedsystems with high spectral efficiency considered here are about a factor of five more sensitive to PMD impairments than a single-transmission channel. While detailed outage statistics for polarizationmultiplexed systems have yet to be developed, we note some close similarities between the single-channel case (whose statistics are described in Section 6.3) and the case of polarization multiplexing: In both cases the penalties depend quadratically on A t , and in both cases the underlying mechanisms seem to depend on the perpendicular component ATL only (see, e.g., Eq. 6.19). One would, therefore, expect that the allowable mean fiber DGD for the mentioned polarization-multiplexed 40-Gbh systems is about 0.5 ps for a 1 dB-outage of 1O-5.

6.6 PMD EFFECT ON THE REDUCTIONOF F W A N D X P M B Y POLARIZATION INTERLEAVING Four-wave mixing (FWM) and cross-phase modulation (XPM) are two effects caused by fiber nonlinearities that result in considerable system impairments in WDM long-haul and ultra-long-haul transmission (Forghieri et al. 1997). System designs attempt to minimize these impairments by maximizing the WDM wavelength spacing and by judicious management of local power levels and local fiber dispersion, the technique called dispersion management. As the FWM and XPM effects are strongly dependent on the relative polarization between the relevant WDM channels, the technique of polarization interleaving has been proposed and explored for the reduction of these effects (Hill et al. 1978; Mahon 1990; Inoue 1991;Evangelideset al. 1992).The system layout for this technique is similar to the one sketched in Fig. 6.8, with two notable differences: (1) the optical filters of the WDM channels are chosen narrow enough compared to the wavelength separation so that no coherent crosstalk occurs (as opposed to Section 6.5), (2) the output PBS is usually not present (for an exception note Mahon et al. 1996). Polarization interleaving can reduce the power level of some of the important FWM components generated in the fiber by a factor of four and eliminate other important FWM components (Inoue

I

799

15. Polarization-ModeDispersion

w o

zy

zyxw zyxw

ch 8 pol interleav, 3.5 dBm/ch ch 8 aligned pol, 0 dBrn/ch ch 8 pol interleav, 6.5 dBrn/ch -

zyxwvuts zy zyxwvutsr -48

-46

-44

-42 -40 -38 -36 Received Power (dBm)

-34

-32

Fig. 6.10 Measured BER sensitivity of a 16-channel WDM system at 2.5 Gb/s per channel showing the effect of reduced four-wave mixing (FWM) due to polarization

interleaving.

1992). XPM penalties induced by neighboring channels are reduced by interleaving to one half the value induced by parallel polarizations (Mollenauer et al. 1995). The illustration of Fig. 6.10 shows the measured BER of a 16channel WDM system operating at the bit rate of 2.5 Gb/s per channel over a distance of 600 km of fiber. The channel spacing was 50 GHz, the amplifier spacing was 100 km, and the fiber dispersion was about 2 ps/nm-km. At a power level of 3.5 dBm per channel one notes that polarization interleaving in this system results in a receiver sensitivity advantage of at least 6 dB compared to transmission with parallel polarized channels. This power advantage is attributed to reduced FWM. The presence of PMD in the fiber will reduce the orthogonality of the polarizations of interleaved channels as well as the alignment of channels that were initially aligned. PMD will, thus, tend to negate the power advantagegained by interleaving. To obtain an estimate for the effect of PMD on FWM, consider partially degenerate FWM between two WDM channels of carrier frequency u1 = uo and v2 = uo + AWDM having Stokes vectors &(z) and i2(z), respectively. The channels are launched at z = 0 with orthogonal polarizations, i.e., 51 (0) = -52(0). The polarization-dependent FWM efficiency, qpol(Aq),

zyxwv l""""'l

38

800

zyxwvu zyxwvu zy zy zyxwvut zyx zyx zyxwvu H. Kogelnik et al.

depends on the Stokes angle, Ap(z), of the misalignment of iz(z) relative to the ideal orthogonal alignment, -&(z). (Note that, with this notation, the two polarizations become parallel when the misalignment reaches Ap = n.) This alignment changes with the frequency spacing, AWM, and the propagation distance, z, in the fiber. The efficiency is qpol(0) = 0 for orthogonal polarizations and qpol(n) = 1 for parallel polarizations. For reasonably small misalignments we have, using the results of Inoue (1992), q p 0 d A d = ;AVO2.

(6.21)

PMD causes the misalignment, Ap(z), to change randomly with position, z, in the fiber. Within the bandwidth of the PSP, Aupsp = 1/(8=), the misalignment is determined by the law of infinitesimal rotation of the output Stokes vectors (Eq.2.6)as Ap = 2 n . A t . s i n I 3 . A ~whereAt(z)isthelocalDGD, ~~~ and e(z) is the angle between i 2 and the local PSF? In our above experiment, for example, where the mean DGD was = 2.4 ps and Aupsp = 50 GHz, angular shifts as large as A&) = 30" were measured at the fiber output (z = L). The overall FWM efficiency (qpol) of the system represents a weighted average over the local efficiencies qpol(z)throughout the length, L, of the transmission system. Assuming a uniform distribution of the relative PSP angles I3 over the Poincark sphere, we have, according to Eq. 6.4, that (sin28) = 2/3. The model further assumes that the local instantaneous DGDs, At(z), fluctuate around the mean DGD. The mean square DGD, (At2(z)),grows linearly with z, leading to a distance-averaged DGD term of (1/2)(At2(L)) = (3n/16)z2.Thus, we obtain an overall FWM efficiency of (6.22) Since random polarizations will lead to an FWM efficiency of qpol = 1/2, we judge interleaving to be effective as long as the FWM efficiencies are below about 1/4. This happens as long as AWDM 5 1/(4G) = 2Avpsp.

(6.23)

Note that this rule of thumb depends on the mean DGD of the transmission line only. It should, therefore, be the same for all WDM channels, regardless of instantaneous DGD fluctuationswith frequency. Now compare the rule of thumb for the effkctiveness of interleaving with the single-channeloutage criterion as stated in Eq. 6.16 in terms of the signal bandwidth Au. Recall that for closely packed WDM we have, approximately,

I

zyxwvu zyx zyxwvuts 15. Polarization-Mode Dispersion

801

zyxwv zyxwvu zyxw zyx zyxwv zy

AWDM = 2Au. For this case it follows that interleaving should be effective in suppressing FWM in closely packed WDM systems as long as the single channels do not require first-order PMD compensation. While rule (6.23) requires further testing, it is consistent with our exper~ wasMsuf€iciently small to prevent imental results of Fig. 6.10 where A PMD effects, and those of Hansryd et al. (2000), as well as the results of Kovsh et al. (2001), who have found the same rule by numerical simulation of a transoceanic system. Hansryd et al. (2000) also discuss the correlation function, (& .52), derived by Karlsson et al. (2000a), providing a compact description of the scrambling of polarizations occurring when the frequency spacings, Aw = ~ ~ A V W D M , exceed the bandwidth of the PSP. The correlation function is (& - & ) = ?,"

exp(-Ad(At2)/3),

(6.24)

for the dot product of the output Stokesvectors, 51 (9)and &(w+Aw), at two different frequencies for given input Stokes vectors, Sp. Equation 6.24 tells us that polarizations get totally scrambled for large frequency spacings and large distances, leading to their uniform distribution over the Poincark sphere. The or A W D M = ~ 0.21, correlation drops to one half for A w G = ,/defining the correlation length used in Section 6.7. At large spacings the expected angle between the Stokes vectors of two frequencies is n/2 (i.e., ( i 1 . i 2 ) = 0). Both initially parallel alignments (i'p= i:) and initially orthogonal polarizations (5: = -i?) will diffuse to this n/2 value. At this point FWM and XPM become the same for both parallel and orthogonal polarization launches. We find that the application of the correlation function also leads to rule (6.23). Finally, we should mention that PMD is not the only effect that can destroy the initial alignment of signal polarizations carried by two (or more) different frequencies in a fiber. There is another effect, sometimes called "powerdependent PMD," which is a second aspect of XPM. This nonlinear process causes the two Stokes vectors i l ( w 0 ) and iz(w0 + Aw) to precess around one another (Mollenauer et al. 1995). Due to the nonlinearity, the infinitesimal rotation law for the change of a Stokesvector after traversal of a short section, dz,of fiber assumes the generalized form (6.25) governing the above precession, where p~ = 2nn2P2/hteff is the normalized power level of channel 2, A,ff is the effective area of the fiber, n2 is the

802

zyxwvutsr zyxwvu zyxw zyxwv

zyxwv zyxwvut zyx

H. Kogelnik et al.

polarization-averaged nonlinear index, and P2 is the power in channel 2 (the differential rotation for & is obtained by interchanging indices). The birefringence vector appears also in the dynamical PMD equation (Eq. 2.8), whose relation to the linear rotation law (for p2 = 0) is detailed in Gordon and Kogelnik (2000). The power-dependent PMD effect associated with Eq. 6.25 can acceleratethe scrambling or depolarizationof the WDM channels beyond the rate caused by PMD alone. Collings and Boivin (2000a) have reported quantitative results of this depolarization in an interleaved WDM transmission systemmeasuring impairmentsfor power levels ranging from 0 to 10 dBm per channel. Further, they have shown that the depolarizationcan change from bit to bit, making compensation of associated impairments in interleaved systems very difficult. Even without interleaving, WDM channels can interact to induce power-dependent PMD and depolarization in each individual channel. This effect creates an obstacle to optical PMD mitigation as discussed by Moller et al. (~OOOC),Moller et al. (2001) and Khosravani et al. (2001b). Section 7 also discusses the PMD resistance of solitons, another manifestation of the interaction of fiber nonlinearities and PMD.

3

6.7 PMD EFFECTS ON POLARIZATION-DEPENDENT GAIN IN RAMAN AMPLIFIERS The gain in fiber Raman amplifiers is known to depend on the relative alignment between the pump and signal polarizations. When the two polarizations are aligned, the gain can be as much as 10 times larger than the gain for orthogonal polarizations. This effect is a relative of PDL and is called polarization-dependent gain (PDG). There is no PDG when a depolarized pump is used (Zhang et al. 2000). The presence of PMD in the fiber will scramble the relative alignment of the polarizations to various degrees and reduce PDG. When the pump is counterpropagating,the scramblingis so strong that PDG is minimized. PDG is strongest when a polarized copropagatingpump is used, and the following discussion addresses this case. Consider a Raman pump spaced Au from the optical carrier frequency and an effective Raman interaction length, L, in the fiber. The correlation between the pump and signal polarizations in the presence of PMD is described by Eq. 6.24 discussed in Section 6.6. As the mean DGD in the fiber grows with the square root of the distance, =(z) = =(L) one can determine the correlation length, L,,, for the two polarizations from the condition A u E m r r = 0.21 mentioned in Section 6.6. Thus we can visualize the Raman interaction as N statistically independentinteractions in N sections of fiber of constant relative

zyxwvu m,

zyx zyx zyxwvu 15. Polarization-Mode Dispersion

803

zyxwvutsrq zyxwvutsr

polarizations between pump and signal. The number of these sections is N = L/L,,,,

A -

%

22Au2z2,

(6.26)

where nt = At(L) is the mean DGD of the interaction length. For large N , the relative polarizations in the sections can be assumed to be uniformly distributed over the Poincart: sphere. Their mean determines the mean gain. The PDG is related to the standard deviation, which scales like l / a , predicting a PDG inversely proportional to the mean DGD of the interaction length. An illustrative example is a typical pump frequency spacing of 100nm, i.e., Au = 12.5THzYand a mean DGD of 0.1 ps. For this case one gets N = 35 independent interactions. For more detail refer to Mahgerefteh et al. (1997) who report experimental investigations of the PDG of Raman amplifiers as a function of PMD. Ebrahimi et al. (2001) study the statistics of PDG in fiber Raman amplifiers due to PMD by simulation and experiment. Their results show that a mean DGD of 0.66 ps is enough to reduce the mean PDG to 10% of the average gain. 6.8 FURTHER READING

More information on PMD system impairments can be found in Beltrame et al. (2000), Cameron et al. (2000), Chowdhury et al. (2000), Lee et al. (2000),

Shieh (2000a), Bruyere and Audouin (1994a), Zhou and O’Mahoney (1994), and Yamamoto et al. (1989). Literature on PDL systemimpairments includes Wang and Menyuk (200 l), Haunstein and Kallert (2001a), Kim et al. (2001b), Yan et al. (2001), Bessa dos Santos et al. (2000), Huttner et al. (2000), Gisin (1995), and Bruyere and Audouin (1994b). Second-order PMD impairments are discussed in Watley et al. (1999b), Ciprut et al. (1998), and Bruyere et al. (1997). More information on polarization multiplexing can be found in Him et al. (2001), Yeniay et al. (2000), Zheng et al. (2000), and Bergano et al. (1998).

7. PMD Mitigation Increased understanding of PMD and its system impairments, together with a quest for higher transmission bandwidths, has motivated considerable recent work on PMD mitigation. One of the primary objectiveshas been to enable system upgrades from 2.5-Gb/s to lO-Gb/s or from lO-Gb/s to 40-Gb/s on older, embedded, high-PMD fibers. PMD compensation techniques must reduce the

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zyxwvutsr zyxwvu H. Kogelnik et al.

impact of first-order PMD and should reduce higher-order PMD effects or at least not increase the higher-order PMD. The techniques should also be able to rapidly track changes in PMD, including changes both in the DGD and the PSPs. Other desired characteristics of PMD mitigation techniques are low cost and small form factor to minimize the impact on existing system architectures. In addition, mitigation techniques should have a small number of control parameters to enable manageable feedback algorithms. In this section we will review various methods of PMD mitigation, from the simple methods, which include deploying low-PMD fiber or using a PMDtolerant modulation format, to more complex optical or electrical PMD compensation techniques that may be implemented at the transmitter or the receiver. As the compensation techniques must follow the temporal variations of PMD, we will also outline several monitoring techniques that provide information for the feedback loops and algorithms controlling the PMD compensators. Note that, as no uniform standard to measure the effectiveness of the various compensation schemes currently exists, we quote the DGD values of the compensated systems as reported in the literature. The reader is advised to consult the cited references for further detail.

zyxw zyxw zyxwv zyxw

7.1 TIME RATE OF CHANGE OF PMD

The required speed of PMD compensators depends on the time rate of change of the PMD in installed fiber links. A number of groups have made longterm PMD measurements, and the consensus is that temperature changes in embedded fibers are slow in general and cause slow PMD variations, Le., on the time scale of hours (Bulow and Veith 1997; Cameron et al. 1998b; Takahashi et al. 1993) to days (Gleeson et al. 1997; Karlsson et al. 1999b, 2000a). In fact, the DGD versus wavelength spectrum for an embedded cable can be quite stable over intervals as long as several weeks (Gleeson et al. 1997). A detailed, long-term study with simultaneous measurements of two fibers in the same embedded cable showed that drift averaged over wavelength was 96% correlated between the two fibers for both the DGD and PSPs (Karlsson et al. 1999b,2000a). Figure 7.1 shows contour plots of the DGD spectra for the two fibers over a 36-day period. A strong correlation between changes in the DGD and PSP was observed, and the study also confirmed that the rate of temporal change of the PMD increased with the cable length and the mean DGD. In another comprehensive study, Nagel et al. (2000) measured the DGD of a 41-ps mean DGD embedded fiber every 5 to 10minutes over a 70-day period. All observed large amplitude, rapid DGD fluctuations were caused by human activity. They found that the measured DGD values at a given wavelength

zy zyxwvuts 15. Polarization-Mode Dispersion

Fiber 1

DGD [PSI

805

Fiber 2

zyxwvut zyxwvuts

1510

1520

1530 1540 1550 Wavelength [nm]

1560

1510

1520

1530 1540 1550 Wavelength [nm]

1560

Fig. 7.1 Contour plots of the simultaneous DGD measurements of two fibers in the same embedded cable over a 36-day period. The mean DGDs averaged over time and wavelength were 2.75 and 2.89 ps for fibers 1 and 2, respectively. Data is courtesy of Magnus Karlsson. See also Plate 7.

did in fact follow a Maxwellian distribution over long times, with average correlation times of 19 hours for DGD and 5 hours for PSPs, indicating that the PSPs are changing more rapidly. From their measurements,they predicted that the DGD would exceed three times the mean DGD at an average rate of once every 3.5 years, for a duration of 13 minutes. An example of the temporal change of DGD in an embedded fiber is shown by the small figures in the lower corner of each page. These measurements are a subset of the data collected for the long-term study described previously (Nagel et al. 2000). The figures are part of the flip movie of Fig. 0 described in greater detail in the Introduction. In addition to slow temperature variations in embedded cable, human operation in huts, mechanical vibrations, or wind for aerial fibers can cause state of polarization (SOP) variations on the Poincart sphere of up to 50 revolutions per second (Bulow et al. 1999~).Bulow et al. (1999~)measured the fastest PMD fluctuations to take place in a timescale of 6 to 13ms on a 52-km, 7.3-ps mean DGD embedded cable, presumedly due to moving of the fiber pigtails in the central office. Measurements of aerial cables have also been reported, where larger strain and temperature changes can occur. In one study where the interferometric technique was used to measure the -9-ps mean DGD (over a 70-nm wavelength range) of a 96-km aerial cable, temperature alone caused mean DGD fluctuations on a time scale of about 5 minutes (Cameron et al. 1998a). Another study measured the upper limit of SOP changes to be

zyxwvut zyxwvuts

806

zyxwvutsr zyxwvu zyxwvu H. Kogelnik et al.

zy zy zyxwvu zyxwvut zyxwv

1.8 seconds (Waddy et al. 2001) on a 12.7-ps mean DGD aerial fiber, seemingly a contradiction to the faster PMD fluctuations measured by Biilow et al. (1999~).Further investigation of these fast perturbations to PMD and SOP is still warranted. Information about the required speed of the different optical compensation methods can be gleaned from the autocorrelation functions for the SOP :(a, t ) and PMD vector ?(w,t) (Karlsson et al. 2000a). The temporal correlation function for two polarization states (SOPS)at the same frequency was shown to be (%tl) ’ i(t2)) = exp(-lAtl/td), (7.1) where IAt( = t l - t2 and td = 2to/(302(At2))is the typical drift time for the polarization states with o the carrier frequency and to a measure of the drift time of the index difference of the birefringent elements of the fiber. td must be measured for each fiber. The temporal correlation function for the PMD vector (at the same frequency) is

From Eqs 7.1 and 7.2, we can see that the PMD vector correlation function has a slower decay. By setting the expectation values equal to 0.5 and solving for the correlation times, fpmd and tsop,one can show that tpmd 2.3 tsop,implying that the PMD vector changes more slowly than the SOP.

7.2 LO W-PMD TRANSMISSIONFIBERS The simplest and potentially least costly way of reducing PMD impairments is to deploy fiber having very low PMD. For example, fiber routes having mean DGD of less than 2% of the current bit rate would have suflicientlylow PMD for current systems, as well as next-generation systems, assuming that bit rates will increase by a factor four. Fiber manufacturers are (painfully) well aware of the burden of producing fibers with the lowest possible PMD, and PMD is routinely measured on every spool of fiber before cabling. Note that there can be large differences in the PMD of spooled versus cabled single-mode fibers (Passy et al. 1991; Gisin et al. 1991d; de Lignie et al. 1994), depending on how the spooling and cabling conditions affect the mode coupling length and birefringence. A more recent study has found that the PMD values of the edge fibers in a high-count ribbon cable on the reel correlate well to the PMD values in the deployed configuration (Jackson et al. 2001). Advances in fiber manufacturing techniques (Norman et al. 1979; Chiang 1985a, 1985b; Barlow et al. 1981; Vengsarkar et al. 1993a)initially led to lower

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807

intrinsic fiber birefringence, and spinning of the fiber during draw (Judy 1994; Li and Nolan 1998;Li et al. 1999)has enabled lower PMD in each new generation of fiber. Spin profiles can be constant or variable, with variable and higher spin rates generally showing lower PMD. Simple theoretical explanations of the benefits of spinning consider birefringent fiber lengths short compared to the correlation length, L,,where the DGD increases linearly with length in the absence of spinning. One conceptual (but impractical) way to reduce PMD in this regime is a periodic abrupt 90" rotation of adjacent fiber sections leading to a periodic change of the fiber DGD with length. Spin profiles treated theroretically include uniform spin, sinusoidal spin, and frequency modulated spin. For the common sinusoidal profile, the fiber designer needs to consider, in addition to the beat length Lb,the maximum spin rate (usually several turns per Lb) and the spin period. It has been reported that a balance between these three parameters can produce phase matching of coupled modes leading to strong reduction of PMD (Li and Nolan 1998). The achievement of periodic DGD variations with distance, recently observed in simultationsby Galtarossa et al. (2001a), requires spin profiles having only odd harmonics and spin rates much faster than Lb. By obtaining periodic DGD for short fiber lengths, the maximum DGD can be reduced both in the absence of random mode coupling as well as in the long-length regime. Today, fibers typically have PMD coefficients less than 0.1 ~s/(km)'/~ on the spool. Fiber manufacturers also use another parameter to specify fiber PMD, the "link design value" (LDV), which defines the maximum value of the PMD coefficient in terms of the probability Q for links with at least N concatenated sections, where typically Q = lop4 and N 2 20 (IEC SC 86A/WGl). The LDV serves as a statistical upper bound for the PMD coefficient of the concatenated fibers comprising an optical cable link. This specificationallows for small variations of the PMD coefficient from section to section. Some manufacturers have recently specified LDVs as low as O.O4p~/(km)'/~. Referring to Fig. 6.4 and allowing a 1-dB penalty for 30 mirdyear, a 4O-Gb/s NRZ (A = 70) signal could be transmitted over 2500 km of fiber with LDV of 0.04 ps/(km)'/2, compared to 400km of fiber with LDV of 0.1 ps/(km)'/2. As the bit rate and system reach continue to increase, fiber manufacturers will continue to search for methods to reduce the PMD of cabled fibers.

zyxwv zyxwvu zyxwv

7.3 A L T E R N A T m MODULATION FORMATS The impact of first-order PMD on unchirped, non-return-to-zero (NRZ) systems has been fairly well characterized (Poole et al. 1991a; Zhou and O'Mahony 1994; Morkel et al. 1994), as discussed in Section 6. However,

808

zyxwvut zyxwv zyxwvuts zyx zyx H.Kogelnik et al.

diflterentmodulation formats may be more or less sensitive to the pulse distortion caused by PMD. Experiments using a PMD emulator (Taga et al. 1998) and high-PMD fiber (Jopson et al. 1999c) have shown return-to-zero (RZ) modulation to be more tolerant to first-order PMD than NRZ in systems with an optically preamplified receiver (see Fig. 6.1). Since the pulse energy is more confined to the center of each bit slot for RZ, even after transmission, power in isolated zeros rises more quickly for NRZ signals than for RZ signals as the PMD is increased. This power, in combination with the change in signal on the ones, leads to a greater penalty for NRZ modulation when using an optically preamplified receiver. Further numerical simulations comparing NRZ and RZ (Sunnerud et al. 200la) have shown that the shorter the pulse width, the more robust to PMD, whereas simulations of other modulation formats have indicated that chirped RZ can be more tolerant to PMD compared to RZ and NRZ (Khosravani and Willner 2000b). Note that the optical and electrical filter bandwidths are important issues when comparing modulation formats. Without PMD, the optimum optical filter bandwidth is approximately two times the bit rate for both formats, whereas electricalbandwidths of approximately 0.6 to 0.7 times the bit rate are optimum for NRZ and already good for RZ (whose sensitivity improves only slightly for higher bandwidths). Filter bandwidths of this magnitude were used in the experiments of Jopson et al. (1999~)as well as in most other models and experiments testing PMD sensitivity. Note also that comparing modulation format sensitivity to PMD using a PIN receiver may yield different results, because PIN receivers are sensitive to eye closure instead of power in the zeros. The PMD tolerance of single-sideband modulation (Woodward et al. 2000) has also been tested and compared to that of NRZ..In an experiment, a 5-Gbls single-sideband modulated signal could be transmitted through a fiber with an instantaneous DGD of 380 ps (mean DGD of 187 ps) by launching on the PSP. Presumably, the narrower optical spectrum of single-sideband modulation reduces pulse impairments from higher-order PMD. In other experiments, phase-shaped binary modulation format in combination with optical PMD compensation has shown an extension of the PMD limit beyond that attainable using NRZ modulation (Lanne et al. 2000a). Note that these more complicated modulation formats can suffer from reduced back-to-back sensitivity when compared to NRZ or RZ due to the stringent requirements on the high-bit-rate electronics. One must therefore evaluate how much advantage in overall receiver sensitivity can be gained in the presence of PMD. The resistance of classical solitons to PMD has been well known for over a decade (Mollenauer et al. 1989; Wai et al. 1991). Just as the fiber nonlinearity interacts with anomalous dispersion to prevent pulse broadening, .in

zy zy zyxwvu

15. Polarization-Mode Dispersion

809

a medium with constant birefringence, the nonlinear attraction between the two polarization components can prevent birefringence-induced breakup of the pulse, sometimes referred to as soliton self-trapping. (Menyuk 1989; Islam et al. 1989).In a fiber with multiple sections of randomly oriented birefringence (Le.¶PMD), the solitons are unstable and emit dispersive-waveradiation into the orthogonal polarization (Wai et al. 1991). Although the power loss could appear to be small, it causes broadening having az1I2dependence (Matsumoto et al. 1997; Xie et al. 2000a; Xie et al. 2000b). Soliton-control methods such as sliding-frequency filters can cancel the growth of this dispersive radiation (Matsumoto et al. 1997),but may not be practical. In an experimental comparison between classical solitons and RZ linear pulses, Bakhishi and coworkers found that solitons were more robust to PMD even without inline soliton control (Bakhishi et al. 1999a). The question of dispersion-managed (DM) solitons’ tolerance to PMD has also been addressed through numerical simulation (Xie et al. 2001a) and experiments(Sunnerud et al. 2000b). Through the same mechanism as classical solitons, DM soliton pulses can hold together in the presence of birefringence. Detailed experiments (Sunnerud et al. 2001b) have quantified the robustness of dispersion-managed solitons to PMD and have shown that dispersionmanaged solitonscan be even more robust to PMD than conventionalsolitons. The robustness is dependent on the average dispersion and dispersion-map strength, S = JB;’Ll - B!&I/t,2, where By, B;’ are the dispersions of fibers with corresponding lengths L1,Lz and rs is the pulse width. DM solitons show enhanced robustness over linear pulses for 0 .e S < 10. For lower average dispersion (e.g., 0.1 pslnm-km vs 1.0pslnm-km), a higher map strength (e.g., S M 6 vs S 2) is required for optimum robustness to PMD (Nishioka et al. 2000; Sunnerud et al. 2001b).

zyxwvu zyxwv zyxwv zyxw

7.4 OPTICAL COMPENSATION TECHNIQUES The goal of compensating PMD in the optical domain is to reduce the total PMD impairment caused by the transmission fiber plus the compensator. Numerous techniques have been proposed and demonstrated in the literature, and Penninckx and Lanne (2001) and Karlsson et al. (2000b) serve as good general reviews. The analytical theory of optical PMD compensation has also been addressed (see Section 7.7). In general, optical compensation consists of an adaptive counter-element, a feedback signal, and a control algorithm, as shown in Fig. 7.2. In this section we will cover the three main types of optical first-order PMD compensation, as well as outline several other techniques.

810

zyxwv zyxwv zyxwvuts H. Kogelnik et al.

Fiber

Transmitter

z

Receiver

Adaptive Counter-Element I

I

I

I

Fig. 7.2 General scheme for optical PMD compensation consisting of an adaptive counter-element,a monitor providing a feedback signal, and a control algorithm.

*- zyxwv I

Transmitter

pc

Fiber

/ /

Receiver

3 I

I

zyxwv zy

d = Bs

Fig. 7.3 Optical PMD compensation by transmitting on a PSP. The polarization controller, PC, at the fiber input is adjusted to match the input state of polarization Q(wO,t ) to the fiber’s input PSPj,(oo, t ) at the carrier frequency WO.

PSP Transmission Transmission on a PSP using polarization control at the fiber input (Ono et al. 1994) was the first optical PMD compensation technique to be demonstrated. A schematic is shown in Fig. 7.3. The simple equation that describes this technique is $

zyxwvu =A,

(7.3)

where 3 is the polarization of the launched signal andli, is the PSP at the fiber input. When the PSPs vary with frequency, this technique can compensate for fist-order PMD only. It also requires special hardware at both the transmitter and receiver, and the compensation speed is limited by the round-trip delay

zyxwvu zy zy zyxwvu zyxwvu 15. Polarization-ModeDispersion

811

through the fiber. Nevertheless, this technique has been successfully demonstrated in a field trial, where a lO-Gb/s signal was transmitted over 450 km of fiber with 60 ps mean DGD (On0 et al. 2000).

PMD Nulling

The second main optical compensation method is to null the PMD vector of the combined system at the fiber output using a PMD compensating element, as shown in Fig. 7.4. The relation that describes this type of compensation is

at the carrier frequency. Note that as dictated by the concatenation rule, we take the vector sum of the fiber PMD and compensator PMD at a common reference point, for example, the fiber outputkompensator input. This scheme requires an adjustablebirefringent element to match the magnitude of the fiber PMD and a polarization controller to adjust the direction of the compensator’s PMD vector. Adjustable birefringence can be difficult to implement practically. Opto-mechanical delay lines (Heismann et al. 1998b), two PM fiber sections with a polarization controller between them (Shieh et al. 2000b), and nonlinearly chirped PM-fiber Bragg gratings (Lee et al. 1999a; Lee et al. 1999b) have all been utilized in these types of compensators. In addition, a discrete first-order variable delay line has been constructed from successively longer lengths of PM fiber spliced together such that a switchable wave plate

Transmitter\ %oq

Fiber

zyx zyxwvuts ‘0“ ?

Receiver

Adjustable T~~ Birefringent Element

zyxwv

Fig. 7.4 Optical PMD compensation by PMD nulling. The length and direction of the compensator’s PMD vector &,mp is adjusted to exactly cancel the fiber’s output PMD vector at the carrier frequency 00.

812

zyxwvutsr zyxwvut zyxwvutsr zyxw H. Kogelnik et al.

operating as either a half- or full-wave plate between each PM fiber pair can add or subtract the various sections of DGD (Sobiski et al. 2001).

Fixed DGD A third optical compensation scheme that has been extensively investigated is shown in Fig. 7.5. This simple and dynamic compensator consists of an adjustable polarization controller and a single element with fixed DGD, often a PM fiber of fixed length (Takahashi et al. 1994; Roy et al. 1999; Francia et al. 1999). There are two possible modes of operation for this compensator. The first mode is to adjust the polarization controller so that the combination of the fiber plus the compensator has a PSP that is aligned with the input

PM fiber Receiver

I

I I

zyxwvu

Fig. 7.5 (a) Optical PMD mitigation using a fixed DGD compensator. (b) The two modes of operation are indicated by PMD vector diagrams, where R-' zc,, is indicated by a dashed vector. For mode 1 there are two possible orientations for R-l&,mp to minimize first-order PMD.

zyx zyxwv zyxwvuts

zyxwvuts zyxwv zyx zyxwvuts 15. Polarization-ModeDispersion

polarization, as described by

5 = &in

+ ~-'?comp),

813

(7.5)

where a is a scalar constant and where the concatentation rule was invoked at the fiber input. As shown in Fig. 7.5, for this mode of to sum ?in and icOmp operation, the compensator's fixed DGD must be sufficiently large such that I?comp I > I?in - sin +I ,where 4 is the angle between the launch state, 5, and the fiber's input PMD vector ?b. Note also that the polarization controller can be adjusted for two possible orientations for R-'?co, to satisfy Eq. 7.5. The second operation mode, applicable when (?camp( < IQ . sin 41, is to adjust the polarization controller to minimize the penalty resulting from the combined PMD vector of the fiber and compensator, min I(?h+ R-' ?camp) . sin el ,

(7.6)

+

where 8 is the angle between the launch state, 5, and the vector ?in R-'?comp. The compensator of Fig. 7.5 is often implemented using degree-of-polarization (DOP) monitoring (discussed in Section 7.6). In maximizing the DOP of the compensated signal, it is irrelevant which operation mode is in use at any particular point in time. This compensator with DOP monitoring was used in several 10-Gb/s field trials with fibers having mean DGDs of more than 30 ps (Chbat et al. 1999; Lanne et al. 2000c; Nagel et al. 2000). Adaptive PMD compensation at 40 Gb/s has also been demonstrated (Lanne et al. 2001). In reality, the PMD nulling compensator (and fixed DGD compensator) may not operate exactly accordingto the above first-order principles, and their detailed operation depends on the monitor and feedback algorithm. Recent studies have shown that these optical compensators may show optimal BER performance (or maximization of the DOP) when the compensator does not completely cancel the first-order PMD vector. In fact, the PMD nulling compensator (as well as the fixed DGD compensator) may be able to mitigate some higher-order PMD (Karlsson et al. 2001b; Lanne et al. 2001;Nagel et al.

zyxwvuts

2000).

2.3 tsop from When applied to PMD compensation, the relation tpmd Section 7.1 provides some information on the required speed of the PSP transmission and fixed DGD compensators. PSP transmission compensators need only operate on the timescale of tpmd, since they track changes of the PSP at the fiber input. Fixed DGD compensators, on the other hand, must operate on the timescale of tsop,since the R-l?comp changes on the timescale of an SOP. Therefore, PSP transmission compensators can operate a factor of 2.3 slower than fixed DGD compensators.

zyxwvutsr zyxwvut zyxwvuts

zy zyxwvut zyxwv zyx

814

H. Kogelnik et al.

Pulse Compression

A PMD compensation scheme that does not fit into the three previous classifications is pulse compression at the receiver end. A compensator consisting of a synchronous phase modulator followed by a dispersive element (Romagnoli et al. 1999a; 1999b) can open the received eye, and has compensated 60 ps of DGD at 10 Gb/s. This technique requires no feedback loop and is independent of the launch state of polarization, $; however, it can only be used with RZ modulation. A criticism mentioned is that, although the average penalty decreases, the probability of obtaining very high penalties remains constant (Penninckx and Lanne 2001). It is also expected that residual and potentially changing chirp from transmission will adversely affect this type of PMD compensation. Higher Order Compensation

Although to date the majority of published reports of optical compensation have addressed only first-order PMD, several techniques for broadband or higher-order optical PMD compensation have been proposed and demonstrated in the laboratory. A number of variations on two-stage compensators have been proposed, as shown in Fig. 7.6. Patscher and Eckhardt (1997) first proposed a method to compensate the DGD and provide a linear PSP variation to mitigate the depolarization component of the second-order PMD.

PM fiber

(b)

PM fiber

zyxwvu

F;'.^H-HXl pi

Adjustable Birefringent Element

zyxwvut h dep.

Pol. Rotation

h dep. Pol.

Rotation

Fig. 7.6 Two-stage optical PMD compensatorsfor compensationof first-order PMD and rotation of the PSPs over a limited bandwidth. (a) Two PM fiber sections connected by a polarization controller, from Patscher and Eckhardt (1997). (b) Proposed compensator consisting of a DGD section between wavelength-dependentpolarization rotators, from Moller and Kogelnik (1999a) and Shtaif et al. (2000~).

15. Polarization-Mode Dispersion

815

zyx

zyxwvut

The compensator consisted of two PM fiber lengths connected by a polarization controller, resulting in a circular sweep of the compensator’s PSP on the PoincarC sphere. The compensator could thus be adjusted to mitigate PSP depolarization over a bandwidth where the fiber’s PSP trajectory can be approximated by a single arc on the Poincark sphere. Moller and Kogelnik (1999a) and Shtaif et QI. (2000~)also have proposed compensators consisting of a DGD section between wavelength-dependentpolarization controllers (Fig. 7.6b) for compensation of first-order PMD and rotation of the PSPs over a limited bandwidth. For this type of device, compensation for first-order PMD is decoupled from the PSP rotation and can be controlled independently. Simulations of a two-stage PMD compensator consisting of the fixed DGD compensator followed by a polarization rotator and a variable differential delay line have indicated that the maximum tolerable mean DGD is 50% higher than when only a fixed DGD compensator is used (Yu et al. 2001). Note that an important issue in all compensation schemes consisting of more than one differentialdelay is that the delays must remain stable on the order of a single wavelength. A subwavelength variation of the differential delay of the first stage rotates the polarization of the signal entering the second stage (Shtaif et al. 2 0 0 0 ~or ) ~equivalently,rotates the input PMD vector of the compensator.

zyxw

Multi-Section Compensators Compensators consistingof multiple birefringent sections (sometimesreferred to as distributed PMD equalizers)that potentially can compensate broadband andlor higher-order PMD have also been proposed and demonstrated in the laboratory. The operation principle is that a large number of short DGD sections separated by polarization transformers can be adjusted so that the PMD vector profile of the compensator follows the profile of the transmission fiber, in reversed order, as shown in Fig. 7.7. Three PM fiber sections with polarization controllers were used to compensate 30 ps of DGD from a PMD emulator (Sandel et al. 1998b). Noe et al. (1998) then proposed a fiber-based distributed equalizer consisting of a long length of PM fiber pulled through the hollow axes of 64 stepper motors to form 16 endless polarization transformers and DGD sections. Compensation of 60ps of emulated DGD for 40-GHz pulses was demonstrated (Sandel et al. 1999). A distributed equalizer was later integrated in X-cut, Y-propagation Ti:LiNbOs (Noe et ~ l 1999a), . and could compensate up to 43 ps of DGD. With fifty lithium niobate sections, this distributed equalizer demonstrated compensation of 20-ps DGD for 6-ps, 40-GHz pulses (Him et al. 1999b). Tests of these distributed compensators are incomplete, since to date all demonstrations have used PMD emulators with

zyxwvu

816

zyxwvut zyxwv zyx H.Kogelnik et al.

(a)

PC

DGD

PC

DGD

PC

DGD

0

zyx zyx zyxwv zyx unused compensator elements

Fig. 7.7 (a) Schematic of compensators consisting of multiple birefringent sections for potential broadband and/or higher-order PMD compensation. (b) PMD proiile of the transmission fiber span (solidarrows) and perfect equalization (dashed arrows) shown in three-dimensional normalized Stokes space, adapted from Noe etal. (1999b).

three or less PM fiber sections A potential problem with these distributed equalizers is that they require a large number of control parameters [e.g., 246 control voltages in Noe etal. (1999a)l. In addition, another critical issue is that the compensation for the various orders is coupled and has to be done simultaneously (Shtaif et al. 2000~).Further details on the theory and operation of these compensators is provided in Noe et al. (1999b).

Multi-Channel Compensators The possibility of simultaneous PMD compensation of multiple channels has been explored also. Khosravani et al. (2000a) demonstrated simultaneous PMD mitigation of four WDM channels by adjusting the single compensating module to optimize overall system performance. The experiment used feedback information about the total degradation of the combined WDM channels, and the PMD compensator was adjusted to minimize the DGD for the worst of the four WDM channels, since that channel dominated the overall system degradation. PMD mitigation using variable equalizing optical

zyx zyxwv zyxwvut 15. Polarization-Mode Dispersion

817

circuits has also been proposed (Ozeki et al. 1994) and extended to broadband compensation (Moller 2000a; 2000b) and multichannel PMD equalization (Yamada et al. 2001). 7.5 ELECTRICAL PMD COMPENSATION TECHNIQUES

Although optical PMD compensation could, in principle, perfectly restore the optical pulse shape because the phase information is not lost, compensating PMD in the electrical domain before the receiver has a number of advantages, including potential low cost, small size, and simultaneous mitigation of intersymbol interference (ISI) from a variety of transmission impairments. The possibility of integrating a PMD mitigator into the receiver electronics is also an advantage, particularly if each channel must be compensated individually. There are three main categories for electrical compensators: linear filters, nonlinear filters, and more complex signal processing techniques. PMD causes linear distortion in the received electrical signal, since the orthogonal signals on the two PSPs add in power at the receiver (Le., in amplitude in the electrical domain). Therefore, a linear filter can be used to equalize PMD as long as the received signal eye is not closed (Winters and Gitlin 1990a). The Transversal Filter (TF), an electrical analog tapped delay line shown in Fig. 7.8a, is the most common linear filter and is also referred to as a Feed-Forward Equalizer. The TF divides the signal, delays the copies by constant delay stages AT, and superimposes the differentially delayed signals at the output port. Note that the delays are often set to be multiples of the bit period T and the tap weights (CoyC1, C2,etc.) are adjusted to maximize the received signal quality. A two-tap, manually adjustable TF of discrete coaxial components was first used for PMD compensation at 1.1Gb/s by Winters and Santoro (1990b). Further work has resulted in demonstrations of PMD and chromatic dispersion compensation at 10Gb/s using a TF of coaxial components (Schlump et al. 1998) or a five-tap discrete prototype TF (Frazer et al. 2000), as well as adaptive PMD mitigation using a voltage tunable, four-tap TF on an SiGe integrated electronic circuit (Biilow et QZ. 1999b). In the demonstration of Bulow et al. (1999b), the tap weights were adjusted using feedback from an eye monitor (to be discussed in Section 7.6), and the TF reduced the penalty by 5-dB for 80-ps of emulated first-order DGD. It was also found that the TF is “blind” to PMD distortions when y = 0.5 and when AT > T, at which point nonlinear equalization is required. The decision feedback equalizer (DFE), shown in Fig. 7.8b, is a nonlinear filter for adaptive nonlinear cancellation of IS1 and was first demonstrated for PMD compensation at 1.7 Gb/s by Winters and Kasturia (1992b). The basic

zyxwv zyxwv zyxw zyxw

818 (a)

z

zyxwvu zyxwvu zyxwvuts zyx 4.3 zyxw FT::FTc7 H. Kogelnik et al. TF

(b)

DFE

B

zyxwvutsr zy zyx

r::i:= sum circuit

delay

Fig. 7.8 ElectricalPMD equalizers. (a) The Transversal Filter (TF) divides the signal, delays the copies by constant delay stages A T , and superimposes the differentially delayed signals at the output port. The tap weights (Co, Cl, Cz, etc.) are adjusted to maximize the received signal quality. (b) The decision-feedback equalizer (DFE) is a nonlinear filter operating on the principle that once a decision has been made whether a bit slot contains a one or a zero, the IS1 that this bit induces on future bits can be subtracted out before the decision is made on these future bits. Similar to the tap weights of the TF, the DFE’s feedback amplitude is adjusted by B. Glthis the threshold voltage and T is a delay equal to the bit interval (after Biilow et al. 2000~).

principle of the DFE is that once a decision has been made whether a bit slot contains a one or a zero, the IS1 that this bit induces on future bits can be subtracted out before the decision is made on these future bits. Similar to the tap weights of the TF, the DFE’s feedback amplitude is adjusted, rather than its delay time. Nonlinear filters can improve the eye opening even when the received signal eye is closed by ISI; however, they require fast signal processing speeds for coupling the decided bit back in time. Simulation shows that DFE’s operating at 10Gb/s require integrated circuit technologies withJ andfmaxof several tens of GHz. The other disadvantageis that DFEs can only compensate for lagging IS1 from PMD (Le., when more power is launched along the slow PSP, y > 0.5), since the leading IS1 will pass through before a decision is made. Using a DFE-integrated circuit design based on AlGaAdGaAs HEMT technology, Moller et al. (1999~)achievedequalizationof 10-Gb/ssignals after up to 120 ps of DGD from a first-order PMD emulator. Buchali et al. (2000) later demonstrated an adaptive, high-speed DFE realized on SiGe-integrated circuits. Using analog signalprocessing and closed loop operation based on the zero-forcing algorithm, mitigation of DGDs up to loops was demonstrated for 10-Gb/s signals. An obvious way to overcome the limitations of the electrical equalizers discussed above is to use a concatenation of the TF and DFE. Biilow et al.

zyxwvutsr

zyxwvu zyx zyxwvu 15. Polarization-ModeDispersion

819

(2000~)compared the measured receiver sensitivity of a TF, DFE, and compound equalizer (TF + DFE) for 10-Gb/ssignals in the presence of first-order PMD. Both the seven-tap TF and DFE having 100-ps delay were realized on SiGe-integrated circuits, with tap weights, feedback weight coefficient, and decision threshold level determined (manually) by external voltages applied to electrodes on the chip. Not surprisingly, the compound equalizer outperforms the TF and DFE alone. The advantage of the TF + DFE was clearest in the high DGD range ( ~ 7 ps), 0 and a penalty of only 3 dB at 80 ps DGD was measured. Experiments at 10Gb/s have also shown that using a compound equalizer in addition to a fixed DGD optical compensator can result in significant reductions in PMD penalties (Bulow et al. 2000d). One of the more complex signal processing techniques for electronic PMD mitigation is phase diversity detection, proposed and demonstrated by Hakki (1997). After propagation through PMD, a received signal can be separated into its two PSPs by maximizing the measured phase difference between the two data streams. By inferring the DGD from the measured phase difference, the two signals can be resynchronized by introducing appropriate delay in their paths before recombining the signals. Experiments at 10Gb/s demonstrated mitigation of up to 42 ps of DGD. Maximum likelihood sequence estimation (MLSE) (Winters and Gitlin 1990a) is another signal processing technique. MLSE is based on the correlation of a complete (undistorted) signal sequence with an estimate of the received sequence over many bits. Selection of the sequence and maximization of the correlation determine the decision for each individual bit. Although not yet experimentally demonstrated for 10-Gb/s PMD compensation, several recent papers have simulated its performance and asserted that it should be superior to the TF, DFE, or compound TF + DFE (Haunstein et al. 2000; Haunstein et al. 2001b; Bulow et al. 2001). At 10 Gb/s, MLSE could be realized as a digital processor using a Viterbi algorithm for correlation after analog-to-digital (AD) conversion. An analog-matched filter placed between the detector and the AD converter can be adapted to the actual signal distortion to improve equalization performance (Bulow et al. 2001). Whereas forward-error correction (FEC) is generally used for extending the reach of transmission systems limited by optical signal-to-noise ratio, FEC has also been considered for PMD compensation. The performance of FEC has been experimentally studied in PMD-limited systems without compensation, and the PMD tolerance was shown to be limited to a mean DGD of -30 ps in lO-Gb/s systems using Reed-Solomon (255/239) FEC code (Ho and Lin 1997; Tomizawa et al. 2000). However, several recent PMD mitigation schemes have utilized FEC in addition to other compensation techniques. Simulations have shown that polarization scrambling along with FEC and a linear equalizer

zyxw zyxwv

820

zyxwvutsr zyxwvut zyxwvut zy H. Kogelnik et al.

at the receiver can enhance PMD tolerance (Wedding and Haslach 2001b). If the polarization is scrambled at a rate sutlicient to make the power ratio y vary between 0 and 1 within one FEC frame, the number of bits affected by PMD per FEC frame is limited, and the FEC can then correct the resulting bit errors. Combining FEC with an optical k e d DGD compensator has been shown to increase the PMD tolerance to a mean DGD of more than 40 ps at 10 Gb/s (Xie et al. 200 1b).

zyxwvut zyxwv

7.6 MONITORING TECHNIQUES

All PMD compensation schemes, whether optical or electrical, rely on some kind of monitoring technique to provide information for the feedback loop and algorithm controlling the compensator. Important characteristics of the monitoring technique are (1) sensitivity to PMD, Le., how much does the signal from the monitor change when the PMD changes; (2) correlation with the BER; and (3) response time (Penninckx and Lanne 2001). If acompensator is expected to react to PMD fluctuations of a certain rate, then the monitor must provide a feedback signal at a faster rate so the algorithm can process the information and adjust the compensator within the allowed time interval. In general, the feedback signal is a compromise between accuracy and response time. This section will review several monitoring techniques proposed and demonstrated in the literature.

RF Spectrum

zyxwv

After propagation through PMD, the strength of the RF signal received by a photodiode is a function of the DGD, launch power ratio y, and R F frequency. It is well known that the pulse broadening induced by PMD results in “spectral hole burning,” i.a, the R F spectrum has a minimum where the DGD is equal to one-half the RF cycle,ffin = 1/(2At), where the two RF components carried by the two PSPs add out of phase. In fact, Bahsoun et al. (1990) proposed a PMD measurement technique based on measuring the strength of the RF signal as a function of the R F frequency and identifyingffi,. The narrowing of the RF spectrum that occurs as a result of the spectral hole can also be used as a monitor for PMD compensators. To assess the electrical spectral width, narrow bandwidth measurements at several frequencies are performed on the detected signal (Takahashi et al. 1994; Ishikawa and Ooi 1998; Sandel et al. 1998b). The bandpass filters often are centered at 0.5/T, 0.25/TYand 0.125/T, where T is the bit period, for example, for 40 Gb/s, the bandpass filters are at 20, 10, and 5 GHz (Sandel et al. 1998b), as shown in Fig. 7.9a. This choice of filters allows unambiguous detection of DGDs above one bit period. The

zy zyxw zyxw zyxwvu 15. Polarization-Mode Dispersion

(4

821

40 Gbls

Rx

PMD Compensator

N

GHz

RF Bandpass Filters

zyxwvu zyxwvutsr 0

25

75

50

(PSI

100

+

zyx zyx

Fig. 7.9 Monitoring using the shape of the RF spectrum. (a) Narrow bandwidth measurements of the detected signal are performed at several RF frequencies. For example, for 40 Gb/s, bandpass filters can be centered at 20, 10, and 5 GHz. (b) Signals from the bandpass filters centered at 20, 10, and 5 GHz as a function of DGD. The receiver can switch between the signals(bold sections of curves) from the three bandpass filters according to whether the signal is above or below certain threshold levels (dashed lines), thus providing unambiguous detection of DGDs above one bit period T , while still retaining good sensitivity for small DGDs (adapted from Sandel et al. 1998b).

feedback algorithm can adjust the PMD compensator t o maximize the signals derived from these narrow bandwidth measurements o r to maximize a suitable linear combination of the three signals. Alternatively, the receiver could switch between the three bandpass filter signals when the signals are above or below certain threshold levels. As shown in Fig. 7.9b, these thresholds can be set t o

822

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H. Kogelnik et al.

detect DGDs up to 4T, while still retaining good sensitivity for small DGDs (Sandel et al. 1998b).

RF Power A monitor signal for PMD compensation can also be extracted from a measurement of the total R F power of the detected signal. Since hole burning due to PMD results in reduction of the R F spectral power, the feedback algorithm can maximize the R F power at the compensator output (Biilow et al. 1999b). The R F power can be measured by a microwave power meter or by automatic gain control to normalize the output voltage from the compensator followed by a signal-squarer integrated circuit. Disadvantages of this method are the difficulty in measuring electrical power over a wide spectrum and its coarse sensitivity (Biilow et al. 1999b).

Eye Monitor Several groups have proposed and demonstrated measurement of the opening in the eye pattern as a useful monitoring technique (Biilow et al. 2000b; Frazer et al. 2000). Estimates of the BER can be achieved by analyzing the eye using error measurements at suboptimal decision thresholds, also called pseudo-error rates. The eye monitor consists of two decision circuits in parallel. The first acts as the simple decision gate in a conventional receiver, and the second functions as a monitor gate with variable threshold to characterize the edges of the eye at variable phase. Choice of the suboptimal decision threshold determines the level of the pseudo-error rate, which again is a tradeoff between response time and sensitivity. (Higher error rates provide faster response times, but have less sensitivity to changes in PMD.) Biilow et al. (2000b) reported an adaptive electrical PMD mitigator containing an eighttap TF and an eye monitor circuit, both integrated on SiGe. Here the eye opening was measured by a monitor decision gate at 3 x BER level, and the tap voltages were tuned consecutively into the direction of an increasingeye opening by a dithering technique. In addition, excellent correlation between and adaptive the BER and eye opening has been shown to BERs < optical PMD compensation using a fast eye monitor has been demonstrated at 10 Gb/s (Buchali et al. 2001).

zyxw zyxw

Other Electrical Monitoring Methods Fast adaptive control of a T F using a continuous-time implementation of the Least Mean Squares algorithm has also been proposed and demonstrated at

zyx zyxwvut 15. Polarization-ModeDispersion

823

10 Gb/s (Wedding et al. 2001a). In this technique, subtracting the regenerated signal at the receiver from the TF output generates an error signal e(t). The adaptive control block then calculates the correlation between the input signal to the TF and e(t) and minimizes the overall error due to distortion and noise. The uncorrected BER before forward-error correction has also been proposed as a monitor for PMD compensation.

Degree of Polarization The concept of the degree of polarization (DOP) characterizes the average polarization state of light over a broad spectral range. For time-dependent signals it is also defined as an average over a specified time period. The definition of DOP is based on the Stokes parameters routinely measured by a polarimeter-based instrument (containing polarhers and four photodiodes) or DOP monitor. A coherent sinusoidal optical carrier (or a narrow spectral component) has a well-defined polarization, described by a unit Stokes vector denoted by a lowercase 5 in the body of this text. The spectrally averaged Stokes parameters, Si, are denoted by capital letters, where SOis the total intensity of the light. The other three parameters are the differences between the measured intensities of pairs of orthogonal polarizations, with 1'5 referring to the verticalhorizontal polarizations, S2 to the f45"polarizations, and S, to right/left circular polarizations. The definition of the DOP is

zyxwvut zyxw zyxw zyxwvu zyxwvu DOP = ,/st

zyxw

+ s,2 + $/so.

(7.7)

A narrow spectral component then has DOP = 1. If the filter of the monitor passes several WDM channels (or spectral components), the measured intensity is the sum of all channel intensities for any given analyzer setting. The monitor, therefore, measures Stokes parameters that are the sum of the Stokes parameters of the individual WDM channels. For the illustrative example of .52)/2 = cos (#J/2), two channels with equal power, one finds DOP = J(1+ where 51 and i 2 are the unit Stokes vectors of the two channels and #J is the Stokes angle between the two channels. If the channels have parallel polarizations, the DOP = 1; for antiparallel polarizations, the DOP = 0. Assume, now, that 51 and Ez are the polarizations at the output of a fiber with a DGD, At, when the two channels (or spectral components) are launched with equal polarizations, and the channel (or spectral) spacing is Am. The fiber PMD rotates 22 relative to &, reducing the measured DOP at the output. The law of inlinitesimal rotation (Eq. 2.6) characterizesthis relative

824

zyxwv zyxw zyxwv zyxwvu zyxwv

H. Kogelnik et al.

rotation and leads to the approximate expression:

DOP = 1 - $(AwAtsin8)2,

(7.8

valid for small A w A t . Here 8 is the angle between the launched Stokes vectoi and the PSP of the fiber. In this simple illustrative case, a monitor algorithn guiding the compensator to DOP = 1 will either lead to a PSP launch wit1 8 = 0 or to a DGD compensated system with A t = 0 (Roy et al. 1999; Francis et al. 1999). This is similar to what happens when the compensator is guided tc minimize the BER. Advantages of the DOP monitor for PMD Compensator: are that it is bit-rate independent (unlike the R F spectrum monitor) and thai it can be high speed, i.e., kHz response time, without requiring electronic: operating at frequencies as high as the bit rate. Kikuchi and Sasaki (1999 have investigated the sensitivity of the DOP monitor and found that the DO€ is independent of the sign of dispersion and modulator chirp, but dependeni on the modulation format and phase modulation characteristics. Recently demonstrated DOP monitors (Fini et al. 2001a; Rosenfeldt et al 2001; Sylla et al. 2001) use polarized broadband sources (such as filtered EDFP noise) or a modulated optical carrier and a scanning polarization controllei varying the fiber input polarization uniformly over the Poincart sphere. Tht output Stokes parameters are measured as a function of the scan time. Tht normalized Stokes parameters define the DOP vector

0.5 0

s3 -0 5 -1

zyxwvu

Fig. 7.10 Three-dimensional plot of DOP vectors, ,; defining an ellipsoid whose major axis is aligned with the (average) PSP of the fiber (courtesy of John Fini).

zyxwvu zyx

15. Polarization-ModeDispersion

825

whose magnitude equals the DOP. A three-dimensionalplot of vectors produced by the scan defines an ellipsoid whose major axis is aligned with the (average) PSP of the fiber. An example is shown in Fig. 7.10. The parameters of the ellipsoid also allow the determination of other PMD information, such as the spectral average of the DGD, when a broadband source is used. This measurement can be performed in fractions of a second with a sufficientlyfast polarization scanner.

zyxwvutsr zyxw

7.7 FURTHER READING

Information on soliton and dispersion-managed soliton resistance to PMD can be found in Matera and Settembre (1995a); Zhang et al. (1998a); Lakoba and Kaup (1997); Chen and Haus (2000); Nishioka et al. (2000); and Lakoba (2000). Literature on theory and comparison of PMD compensators includes Sunnerud et al. (2000a); Karlsson et al. (2000b); Kudou et al. (2000); Madsen (2000); Yu and Willner (2001); Fini and Haus (2001b); and Sunnerud et al. (2001c). Limitations of first-orderPMD compensation are discussed in Mahgerefteh and Menyuk (1999); Bulow (1999a); and Penninckx and Lanne (2000). Polarization controllers for optical PMD compensation are discussed in Heismann and Wayland (1991) and Heismann (1994) (lithium niobate); Shimuzu et al. (1991) and Ono et al. (1993) (fiber squeezing); and Sobiski et al. (2001) (PM fiber as variable phase plates).

Acknowledgments It is a pleasure to thank our colleagues at Bell Labs for extensive discussions on this subject and for their comments on the manuscript, particularly Herbert Haunstein, Art Judy, Heiko Kallert, Kavita Ramanan, Peter Winzer, and Weiguo Yang. We also thank Elsa Thomas for invaluable assistance in the preparation of the manuscript.

Appendix A: Notation We have attempted to keep our notation simple and transparent while linking to the notation already established as much as possible. The following is an abbreviated listing.

I"'."'

51

1

826

zyxwvutsr zyxwvu zyxw zy zyxwvutsrqpo

zyxw

H. Kogelnik et al.

X,Y,Z

Fiber coordinates: z is the direction of propagation;

x , y are the transverse coordinates, i.e., those of Jones

ei(mt-flz)

EYE

space. Continuous wave traveling in the z direction:j is the imaginary unit, 00 is the angular carrier frequency, t is time, and p is the propagation constant. Electric field vectors: &(o)is the Fourier transform of the complex transverse (x, y ) electric-fieldvector E(t) and has a complex amplitude e such that

The vector of the real electric field is Re(Edm'). Deviation from the angular carrier frequency 9 of Am). the light. The optical frequency is (00 2D complex Jones (column) ket vector,

+

( ;)

zyxw zy Is) =

i

The bra (SI indicates the corresponding complex conjugate row vector, i.e., (SI = (sz,s,*). The bra-ket notation is used to distinguish Jones vectors from Stokes vectors. Our Jones vectors are all of unit magnitude, i.e., (sls) = szsx f s;sY = 1, as we assume coherent light (except as noted). 3D Stokes vector of unit length indicating the polarization of the field and correspondingto Is). The components of B are the Stokes parameters: s1 = sxs; - sY s* Y s2

= ss,;

s3 =j(s,s,*

+ s,sy

(A.3)

- s,"sy).

By this definition, SI = 1 for linear polarization aligned with the x axis, s2 = 1 for linear polarization at 45" to this axis, and sg = 1 for right-circular polarized light (sy =js,) conforming with the traditional optics definition. However, left-circular

I T

zy

zyxw zyx zyxwvutsrqp zyxwvuts 15. Polarization-Mode Dispersion

827

definitions are also used in the literature. We always use the same letter symbols for corresponding Jones and Stokes vectors. Note that a common phase shift of both components of Is) does not change 2. 2 x 2 or 3 x 3 identity matrix. The distinction should be clear from the context. 2 x 2 unitary transmission matrix in Jones space. Relates output to input via

We use the symbols s and t when necessary for clarity to designate respective input and output quantities, as illustrated in Fig. Al. 2 x 2 Jones matrix, with det (U)= 1. Related to T by

zyxwv zy zyxw

where $0 is the common phase. 3 x 3 orthogonal rotation matrix in Stokes space isomorphic to U . Relates output to input via

3 = Ri.

(-4.6)

2 x 2 Pauli spin matrices, for our purposes defined as

0 -j

0 -1

(A.7) Pauli spin vector in Stokes space, 2 = (cq, 02~03). 2 x 2 matrix in Jones space, j.2 = Blul B 2 a 2 B 3 a 3 .

+

+

Fig. A.l Block diagram of optical fiber under test.

I

.

.

.

.

.

.

.

.

.

828

zyxwvutsr zyxwvuts zyxwv H. Kogelnik et al.

s ?

At

h, i Subscript w (*)

3D birefringence vector in Stokes space describing local fiber properties. Output PMD vector in Stokes space. Its length, A t , is the differential group delay (DGD), and its direction is that of the Stokes vector of the slow principal state. Mean DGD of the fiber, k (At). Unit Stokes vectors: $ is sometimes used to describe the polarization of the slow principal state, whereas f is used for a rotation axis. Indicates differentiation,i.e., dsldw = s,. Mean or expectation value. Sometimes denoted as E(.).

zyxw zy zyxw zyxwvu

Appendix B: Relation between PMD vectors

and 6

In the main body of this text we have defined the PMD vector 2 to characterize the fiber. To conform with most of the optics literature and the available measurement instrumentation, we are using ccright-circular’y Stokes space, where the Stokes parameter s3 = (s

I 0 3 I s)

(B.1)

is unity and positive fSr right-handed circular polarization. The PMD vector SZ defined and introduced by Poole and Wagner (1986) is widely used in the PMD literature, and this appendix serves to connect 2 and h. The vectors ? and d are different in two respects. The first is that d is dehed in “left-circular” Stokes space, where the s3 Stokes parameter is unity and positive for left-handed circular polarization (and - 1 for right-circular light). The second distinction is that ? is defined to point into the direction of the slow PSP with group delay

zyxwv zyxwvuts tg = to

+ At/2,

(B.2)

whereas 6 is defined to point into the direction of thefast PSP with group delay tg =-to - At/2. (B.3) These two differences combine to ensure that the basic law_of infinitesimal rotation (Eq. 2.6) has the same form and sign for both 2 and SZ. However, the

zyxwvu zyx zyx

15. Polarization-Mode Dispersion

829

Stokes vectors of the two spaces are not the same, and the relation between the PMD vectors is given by

zyxwvu zyxwvu zy zyxwvut zyxwvu zyx

where 2 is in right-circular Stokes space and 6 is in left-circular Stokes space. Our birefringence vector $, defined in Eq. 2.8, and the birefringence vector ,'?I often used in the literature (Ulrich 1997), are related in a similar way as ? and a.We have

with E in right-circular and 6' in left-circular Stokes space.

Appendix C: Rotational Forms of the Jones and Miiller Matrices

For the convenience of the reader, we list here the rotational expressions for both the Jones matrix and the 3 x 3 Muller matrix of a fiber. These expressions explicitlyexhibit the rotation axis f and the rotation angle qo in Stokes space. For derivations and a more detailed discussion we refer to Gordon and Kogelnik (2000). The expressions refer to loss-less fibers in the absence of PDL. C.1 ROTATIONAL FORMS OF THE JONES MATRlx General rotation: U = I cos qo/2 -j f

sin 912,

Exponential form: U = e-j(P/')'''.

(C. 1) (C.2)

The matrix operator F.6 appearing in the exponent is explained in Appendix A.

C.2 ROTATIONAL FORMS FOR THE MULLER MATRlx General rotation: R = cos p .I + (1 - cos qo)ff = ff

+ sin qo f x ,

+ sinqofx - cosqo(Px)(fx),

(C.3)

830

zyxwvuts zyxwvu zyxwvuts zyxwv zyxw zyx zy zy €3. Kogelnik et al.

where the 3D dyadic ii is the projection operator and i x is the cross-product operator:

Exponential form: R = ep('x)m

(C. 5)

C.3 ELEMENTARY ROTATIONS

Elementary rotations in Stokes space are those special cases that rotate the Stokes vectors around the axes El, 22, and E3 of the Poincar6 sphere. The expressions for = 1,2,3 are

The elements of U,and Ri are listed in Table C. 1. Note that U1 and R1 describe the rotation caused by a birefringent phase plate with the slow principal axis aligned with x axis in Jones space. U2 and R2 correspond to a phase plate set at a 45" angle in Jones space. U3 and R3 describe a rotation by p0/2around the z axis. Table C.1 Elementary Rotations Rotation Axis

zyxwvu

Jones Matrix

cos q1/2 i2

-j sin p/2

Stokes Space Rotation

)

R2=(

COSY,

0

01

S i0 nY) ,

-sinp

0

COSY,

zyxwvu zyxwv 15. Polarization-ModeDispersion

Appendix D: Acronyms BER DFE DGD DOP EDFA FEC FWHM FWM GVD IS1 JME MLSE MMM NRZ OTDR PBS PC PCD Pdf PDG PDL PMF PMD PSD PSP RF rms RZ SOP TF XPM

831

zyxw

Bit error rate Decision feedback equalizer Differential group delay, At. Degree of polarization Erbium-doped fiber amplifier Forward-error correction Full width at half maximum Four-wave mixing Group-velocity dispersion, also called fiber chromatic dispersion Intersymbol interference Jones matrix eigenanalysis method Maximum likelihood sequence estimation Miiller matrix method Non-return-to-zeromodulation Optical time-domain reflectometry Polarization beam splitter Polarization controller Polarization-dependent chromatic dispersion Probability density function Polarization-dependent gain Polarization-dependent loss Polarization-maintaining fiber, also called high-birefringence fiber Polarization-mode dispersion Polarization-dependent signal delay method Principal state of polarization, lp), j Radio frequency Root mean square Return-to-zero modulation State of polarization Transversal a t e r Cross-phase modulation

zyxw zyxwv

832

zyxwvut zyxwvu zyxwv zyxwv zyxwvut zyxwvu H.Kogelnik et al.

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at 10 Gbls,” Proc. European Conference on Optical Communication, ECOC’98. 535-536. Schuh, R. E., J. G. Ellison, L. M. Gleeson, E. S. R. Sikora, A. S. Siddiqui, N. G. Walker, and D. H. 0. Bebbington. 1996a. “Theoretical analysis and measurement of the effect of fiber twist on the polarization OTDR of optical fibers,” Proc. Optical Fiber Communication Conference, OFC’96. Technical Digest. 297-298. Schuh, R. E., J. G. Ellison, A. S. Siddiqui, and D. H. 0. Bebington. 1996b. “Polarization OTDR measurements and theoretical analysis on fibres with twist and their implications for estimation of PMD,” Elect. Lett. 32:387-388. Schuh, R. E. and A. S. Siddiqui. 1996c. “Measurement of SOP evolution along a linear birefringent fibre with twist using polarization OTDR,” Symp. Opt. Fiber Measurements, SOFM’96. Technical Digest. 159-162. Schuh, R. E., A. Altuncu, X. Shan, and A. S. Siddiqui. 1997a. “Measurements and theoretical modeling of polarization mode dispersion in distributed erbium doped fibers,” Proc. European Conference on Optical Communication,ECOC’97.3:203-206. Schuh, R. E., X. Shan, A. S. Siddiqui, and E. S. R. Sikora. 1997b. “Measurement and analysis of PMD in spun fibres with different linear birefringence and spinning parameters,” Symp. Opt. Fiber Measurements, SOFM’97. Technical Digest. 122-125. Shieh, W. 1999. “Principal states of polarization for an optical pulse,” IEEE Photon. Technol. Lett. 11:677-679. Shieh, W. 2000a. “Accelerated outage probability testing for PMD induced impairment,” IEEE Photon. Technol. Lett. 12:1364-1366. Shieh, W., H. Haunstein, B. Mckay, D. Fishman, A. Golubchdc, J. Diubaldi, C . Martell, V. Arya, R. Lee, and H. Choudhury. 2000b. “Dynamic polarizationmode-dispersion compensation in WDM systems,” Proc. European Conference on Optical Communication,ECOC 2000.2:41-43. Shieh, W and H. Kogelnik. 2001. “Dynamiceigenstatesof polarization,” IEEEPhoton. Technol.Lett. 13:4&42. Shimizu, H., S. Yamazaki, T. Ono, and K. Emura. 1991. “Highly practical fiber squeezer polarization controller,”IEEE J. Lightwave Technol. 9:1217-1224. Shin, S., I. Yeo, H. Song, J. Park, Y Park, and B. Jo. 2001. “Real-time endless polarization tracking and control system for PMD compensation,” h e . Optical Fiber Communication Conference, OFC’O1. Paper TuP7. Shlyagin, M. G., A. V. Khomenko, and D. Tentori. 1995. “Birefringence dispersion measurement in optical fibers by wavelength scanning,” Opt. Lett. 20:869-871. Shtaif, M. and A. Mecozzi. 2000a. “Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion,” Opt. Lett. 25:707-709. Shtaif, M., A. Mecozzi, and J. Nagel. 2000b. “Mean-square magnitude of all orders of PMD and the relation with the bandwidth of the principal states,” IEEE Photon. Technol. Left. 12:53-55.

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Shtaif, M., A. Mecozzi, M. Tur, and J. A. Nagel. 200012. “A compensator for the effects of high-order polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 12:434-436. Shtengel, G., E. Ibragimov, M. Rivera, and S. Suh. 2001. “Statistical dependence between first and second-order PMD,” Proc. Optical Fiber Communication Conference, OFC’Ol. Paper M03. Simova,E., I. Powell, and C. Grover. 2000. “Measurementof femtosecondpolarization mode dispersion (PMD) using biased n-shifted low-coherence interferometry,” Opt. Express 7:22&236. Sobiski, D., D. Pikula, J. Smith, C. Henning, D. Chowdhury, E. Murphy, E. Kolltveit, and E Annunziata. 2001. “Fast first-order PMD compensation with low insertion loss for 10Gbit/s system,” Elect. Lett. 37:4&48. Song, S. 2001. “The impact of polarization-mode dispersion on four-wave mixing in WDM systems,” Proc. Optical Fiber Communication Conference, OFC’Ol. Paper ThA7. Srivastma, A. K., S. Banerjee, B. R. Eichenbaum, C. Wolf, Y. Sun, J. W. Sulhoff, and A. R. Chraplyvy. 2000. “A polarization multiplexing technique to mitigate WDM crosstalk in SOAs,” IEEE Photon. Technol. Lett. 12:1415-1416. Suetsugu, Y., T. Kato, and M. Nishimura. 1995. “Full characterizationofpolarizationmode dispersion with random-mode coupling in single-mode optical fibers,” ZEEE Photon. Technol. Lett. 7:887-889. Sunnerud: H., B. E. Olson, and F’.A. Andrekson. 1998. “Techniquefor characterization of polarization mode dispersion accumulation along optical fibers,” Electron. Lett. 34: 397-398. Sunnerud, H., B. Olsson, and P. Andrekson. 1999a. “Measurement of polarization mode dispersion accumulation along installed optical fibers,” ZEEE Photon. Technol. Lett. 11:86&862. Sunnerud, H., B. Olsson, M. Karlsson, and P. Andrekson. 1999b. “Techniques for measurement of PMD accumulation along installed optical fibers,” Proc. European Conference on Optical Communication, ECOC’99. 2:6. Sunnerud, H., M. Karlsson, andP. A. Andrekson. 2000a. “Analyticaltheory for PMDcompensation,” IEEE Photon. Technol. Lett. 12:5&52. Sunnerud, H.: J. Li, P. A. Andrekson, and C . Xie. 2000b. “Experimentalquantification of soliton robustness to polarization-mode dispersion,” Proc. European Conference on Optical Communication, ECOC 2000. 3:253-254. Sunnerud, H., M. Karlsson, and P.A. Andrekson. 2001a. ”A comparison between NRZ and RZ data formats with respect to PMD-induced system degradation,” Proc. Optical Fiber Communication Conference, OFC’Ol. Paper WT3. Sunnerud, H., J. Li, P. A. Andrekson, and C . Xie. 2001b. “Experimental quantification of soliton robustness to polarization-mode dispersion in dispersion-managed systems,” IEEE Photon. Technol. Lett. 13:118-120.

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Sunnerud, H., C. Xie, M. Karlsson, R. Samuelsson, and P. A. Andrekson. 2001~.“A comparison between different PMD compensation techniques,” Submitted to ZEEE J. Lightwave Technol.

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and a first-order compensator,” Proc. Optical Fiber Communication Conference, OFC’OI. Paper WAA2. Yamada, K., T. Kudou, and T. Ozeki. 2001. “Simultaneousmulti-channel PMD equalization for WDM systems,”Proc. Optical Fiber Communication Conference, OFC’OI. Paper TuP2. Yamamoto, S., N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi. 1989. “Observation of BER degradation due to fading in long distance optical amplifier system,” Elect. Lett. 29:209-210. Yamashita, S., T. Baba, and Y. Namihira. 2000. “Measurement of polarization mode dispersion (PMD) with a multiwavelengthfiber laser,” Proc. European Conference on Optical Communication,ECOC 2000. 3: 151-1 52. Yan, L.-S., Q. Yu, Y. Xie, and A. E. Willner. 2001. “Statistical measurement of the combined effect of PMD and PDL using a 10-Gbls recirculating loop testbed,” Proc. Optical Fiber Communication Conference, OFC’OI. Paper WT5. Yeniay, A., J.-M. Delavaux, and J. Toulouse. 2000. “Polarization multiplexing technique for SBS suppression,” Proc. European Conference on Optical Communication, ECOC 2000.3:91-92. Yu, Q., L. Yan, S. Lee, Y. Xie, M. Hauer, Z. Pan, and A. E. Willner. 2000. “Enhanced higher-order PMD compensationusing a variable time delay between polarizations,” Proc. European Conference on Optical Communication, ECOC 2000. 2:4748. Yu, Q., and A. E. Willner. 2001. “Comparison of optical PMD compensation using a variable and fixed differential group delays,” Proc. Optical Fiber Communication Conference, OFC’OI. Paper M02. Zhang, J., V. Dominic, M. Misey, S. Sanders, and D. Mehuys. 2000. “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” Proc. Optical AmpliJiersand their Applications, OAA 2000. 13-1 5. Zhang, X., M. Karlsson, P. A. Andrekson, and K. Bertilsson. 1998a. “Soliton stability in optical fibers with polarization mode dispersion,” IEEE Photon. Technol. Lett. 10:376378. Zhang, X., M. Karlsson, P. A. Andrekson, and E. Koltveit. 1998b. “Polarizationdivision multiplexed solitons in optical fibers with polarization-mode dispersion,” IEEE Photon. Technol.Lett. 10:1742-1744. Zheng, X., E Liu, J. Yu, D. Wolfson, A. Koch, and T. Fjelde. 2000. “Simultaneous interferometric crosstalk suppression in WDM channels using polarization multiplexing technique and SOA,” Proc. European Conference on Optical Communication, ECOC2000.3:169-170. Zhou, J. and M. J. O’Mahony. 1994. “Optical transmission system penalties due to fiber polarization mode dispersion,” IEEE Photon. Technol.Lett. 6:1265. Zou, N., M. Yoshida, Y Namihira, and H. Ito. 2001. “Measurement of polarization mode dispersion based on optical frequency domain reflectometry technique,” Proc. Optical Fiber Communication Conference, OFC’OI. Paper ThAl.

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Chapter 16 Bandwidth-Efficient Modulation Formats for Digital Fiber Transmission Systems Jan Conradi

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Corning Incorporated, Corning, New York

1. Introduction As the time-division multiplexed (TDM) bit rates of fiber-optic systems have increased from the early systems operating at DS-3 [l] to modern commercial rates of 9.95328 Gb/s (OC-192/SDH-64) over single-mode fibers, attention has turned to the deleterious effects of chromatic dispersion in nondispersion shifted single-mode fiber (NDSF). For instance, a system operating at 2.48832Gbh (OC-48/SDH-16) using a wavelength in the region of minimum loss (-1550nm) sees a chromatic dispersion coefficient close to 17pdkmnm, which results in a 1dB eye-closure penalty at a distance around 700 km when the signal is transmitted chirp free, such as can be accomplished with a LiNb03 modulator driven in push-pull configuration. Because the chromatiedispersion-limited distance varies approximately inversely as the bit rate squared [2], this distance is reduced by a factor of about 16 at OC-192 compared with OC-48. With a bit of prechirping at the transmitter [3], this distance can be improved to -100 km at 10 Gb/s, a distance that is quite comparable to practical loss-limited distances at this bit rate. However, with the advent of the erbium-doped fiber amplifier (EDFA), dramatic increases in loss-limited transmission distances became possible, with the result that most terrestrial long-haul systems have a degree of dispersion-limited performance, which depends on the type of modem fiber used and the nature of the dispersion compensation technique used to reverse the chromatic dispersion of the fiber [see 4,5]. As the push for higher capacity and longer reach continues, TDM rates and the number of wavelength-division multiplexed (WDM) channels continue to increase, causing WDM channel spacings to decrease, thereby placing added emphasis on the impact of dispersion as well as intra- and interchannel nonlinearities. One technology that could improve system performance is the use of transmission formats that provide better immunity to dispersion and/or nonlinear fiber impairments as well as allowing higher channel density or spectral efficiency. The interplay of these items is often somewhat mutually exclusive in that nonlinear impairments as well as spectral filtering requirements in optical demultiplexersget more difficult to handle as channel separationdecreases.

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OPTICAL FIBER TELECOMMUNICATIONS, VOLUME IVB

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Copyright 0 2002, Elsevier Scienm (USA). All rights ofreproduction in any form rewed. ISBN 0-12-395173-9

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If transmissionformats can be conceived (or adapted from those that have been used in radio or other wireline communications systems) and implemented that produce a transmission spectrum that is narrower than the commonly used non-return-to-zero (NRZ) format, some dispersion benefit should consequently accrue, either by way of not requiring any dispersion compensation at all or requiring less compensation. However, there is another, and perhaps more compelling, reason for exploring alternative transmission formats that have reduced spectral occupancy. This is illustrated in Table 16.1,where we indicate the decreasing channel separations and increasing TDM bit rates at which dense WDM (DWDM) systems have evolved, and through which the total system capacities and spectral efficiencies have been dramatically increased. To a great extent the economics of higher and higher bit rate systems is based on increasing total system capacity within the spectrum available from an EDFA, simply by filling up the EDFA spectrum with signal spectrum. The quantitative measure of this is the system spectral efficiency, which is defined as the ratio of the individual channel bit rate to the DWDM channel separation, and it is this quantity that is becoming the fundamental limiting factor in increasing system capacity. To illustrate this with NRZ transmission in which the individual bits are modeled ideally as rectangular pulses occupying the full time slot of duration T = 1/B whereB is the bit rate, the baseband power spectraldensity (for square NRZ pulses of amplitude A) has a sinc function relationship given by [6]

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and is illustrated in Fig. 16.la. Thus the baseband NRZ signal spectrum can be represented in the frequency domain by a power spectral density that has nulls at +/- NB, where N is an integer, which upon amplitude modulation of an optical carrier at frequencyf, is frequency translated to be situated on either side of the optical carrier frequency, as illustrated in Fig. 16.1b. Thus the transmission bandwidth, if measured between the first nulls on either side of the carrier, is twice the bit rate, and is centered on the optical carrier frequency. Normally, the baseband spectrum above +/- B is filtered Table 16.1 System Capacity Evolution ~~~~

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Bit Rate (Gb/s) Channel Spacing (GHZ) Spectral Eficiency (%) 2.5 10 40

100/50/25 200/100/50 2001100

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Fig. 16.1 (a) Baseband power spectral density for N R Z and (b) power spectral density of an NRZ signal amplitude modulated onto a carrier at& (only positive frequencies shown).

out, which results in practical pulses with nonzero rise and fall times, which also substantially reduces the frequency content of the signal spectrum above the h s t nulls in the spectrum at the bit rate B. This also reduces spectral overlap between adjacent optical channels in a DWDM configuration, which can be placed at frequency intervals of 2B without incurring interchannel interference or cross-talk, and thus the maximum spectral efficiency for NRZ is 50% with this simple approximation. In a practical sense a spectral efficiency of 40% is realistic. Thus for 10 and 40 Gb/s, the channel separations at 40% spectral efficiency are 25 and 100 GHz, respectively, which falls conveniently on the ITU spectral grid. It is worth noting that increasing the bit rate beyond 40 Gb/s cannot increase system capacity in the sense shown by the evolution in spectral efficiency illustrated in Table 16.1. What does result is a coarser channel plan that could have benefit in DWDM networks since a smaller number of wavelengths need to be managed. Additionally, because interchannel nonlinear effects such as four-wavemixing (FWM) and cross-phase modulation (XPM) vary inversely with channel separation, reduced interchannel FWM and XPM penalties do occur as the bit rate is increased while keeping spectral efficiency fixed. Going to closer channel spacings at lower bit rates, while keeping spectral efficiencies in the 40% range, presents difficult challenges from both an optical filtering perspective as well as from the standpoint of fiber nonlinearities and will require further research. Thus, what is required if greater spectral efficiency, and hence system capacity, is to be achieved, are transmission formats that occupy a narrower spectrum while at the same time not causing other system impairments to increase.

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Various formats have been explored over the years, largely driven by the wireless business where spectrum is more at a premium than has hitherto been the case for fiber systems. Many communications engineering texts have extensive chapters devoted to this subject [see 6-91. Those formats that have received some attention for their potential application to optical communications include multilevel signaling or M-ary ASK [lo], various forms of duo-binary signaling [l l-221 (which is a subset of partial response codes), and Optical Single Sideband (OSSB) [23-281. Additionally, much attention has been focused recently on the use of returnto-zero (RZ) signaling [29] because of its demonstrated improved immunity to fiber nonlinearities relative to NRZ. If rectangular pulses were generated with a pulse width of half the bit time, their spectral occupancy would be twice that of NRZ, as the first nulls in the frequency domain would occur at +/- 2B, relative to the optical carrier, and their potential spectral efficiency would be one half that of NRZ signals. With pulse shaping, however, 40% spectral efficiency at 40 Gb/s has been demonstrated [30]. Therefore, it is fruitful to examine whether the nonlinearity improvements associated with F Usignaling can be combined with more bandwidth-efficientformats to achieve still greater system performance. The theme of this chapter, then, is to explore and review some of the work on transmission formats that would permit (or inhibit) increasing spectral efficiency, dispersion immunity, and interchannel nonlinearities. Much of this work has now progressed to the point where some reasonable statements as to future directions can and will be made. The emphasis of this chapter will be on transmission formats that first and foremost have spectral occupancy or a transmission bandwidth on the fiber that is less than that of the true and tried (well loved?) NRZ format. It will be shown that such formats, by and large, are more immune to fiber dispersion, but that other considerations and impairments need close attention. The emphasis will be on the fundamentals of generating and transmitting these signals, with a treatment founded in the theory of linear signals familiar to communications engineers, but possibly less familiar to the optical physics community. It is also worth noting that in this electrical engineering communications context, fiber-optic systems are classified as classical bandpass systems to which well-developed electrical engineering modulation theory applies. The distinguishing differences between optical and radio/microwave systems lies in the carrier frequency (-200 THz vs several GHz) and in the nature of available optical components that can generate or modulate these signals such that a direct comparison with theory can be made. The balance of this chapter is organized as follows. Section 2 develops some basic background in modulation theory that is needed to understand how different modulation formats have different spectral occupancies and how these may be practically developed, as well as how optical modulators shape or

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distort the input signal spectra before they are launched into optical fibers. We also examinehow the commonly used PIN photodiode, which responds to the optical power and hence squares the time-dependent modulated electric field, significantly impacts both the time domain waveform and the spectrum of the square-law-detectedsignal, relative to the modulating signal at the modulator input, and the spectrum of the optical electric field at the detector input, all of which can be different. Section 3 then examines the spectra associated with several bandwidthefficient modulation formats; specifically M-ary ASK and poly-binary signaling with an emphasis on duo-binary and Optical Single Sideband formats where experimental work has been done to permit an assessment of their potential. Present-day understanding of the transmission characteristics of these signals, with an emphasis on the performance of single-channel 10-Gb/s transmission over NDSF, in the 1550-m low-loss spectral region is covered in Section 4, more as an illustration of how formats behave than to claim superiority of a particular format or for a particular optical fiber. Section 5 looks at DWDM experiments that utilize these formats and also examines various formats that combine RZ with various other forms of signal manipulation, in particular some added phase modulation, to achieve improved transmission performance. Section 6 concludes with some suggestions for potential future research. As a general rule, papers listed in the References section contain either the first or particularly illustrative results; other papers of interest are listed in the Bibliography.

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2. Amplitude Modulation and Detection

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2.1 AMPLITUDE-MODULATEDSIGNAL REPRESENTATION1

Fiber-optic transmission systems, where the optical carrier frequency is in the 200-THz region and where the information to be transmitted occupies significantlyless bandwidth than the opticalcarrier frequency, can be classified as bandpass signals. The desired outcome of an amplitude modulation process is to multiply, in the time domain, an information signal a(t) (which may or may not contain a dc component) with a continuous carrier wave represented by cos (2793) to produce a linearly amplitude-modulatedsignal given by s(t) = a(t)cos (2Xf,t),

(16.2)

wheref, is the optical carrier frequency.

Excellent material on the time and fkquency domain representation of modulated signals can be found in [6-lo].

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If we represent a(t) by

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where a0 is a dc component and a&) is the information signal, then the Fourier transforms of these signals give the frequency domain representation of the baseband and modulated signals, respectively, as

and

zyxwv

Therefore, the desired outcome of this linear modulation process is the upshifting of the frequency spectrum of the baseband signal to be centered on the optical carrier frequency, as illustrated in Fig. 16.1. Implicit in this is that the optical carrier can be represented by a pure sinusoid such that it is a delta function in the frequency domain, an approximation to which is that the linewidth of the optical source be much narrower than the bandwidth of the signal to be modulated onto the carrier. It is important to note that it is the optical electn'cjeld spectrum that is represented by an up-shifted version of the baseband signal. It should also be noted that if no dc component is included in the information signal represented by Eq. 16.2, there is no unmodulated carrier present in the final modulated signal, whereas if a dc component is present, so is an unmodulated carrier. This has particular importance when a PIN photodiode detects the signal. Distortion of the signal results from a large number of imperfections in an optical system. The most fundamental of these are: (1) Modulators that, except in various small signal approximations, are rarely linear in the sense of Eq. 16.2. (2) The commonly used PIN semiconductor detector, which responds to the optical power and hence it squares the time representation of the modulated optical electric field. This in turn results in time and frequency representations of the detected signal that are quite different from those of the signal applied to the modulator. (3) Dispersion in optical fibers, which introduces a differential time delay across the various frequency components of the modulated signal, which in turn is equivalent to a frequency-dependentphase shift [31].

These various impairments make it difficult to advantageously implement modulation formats other than the tried-and-true intensity modulated approaches using either NRZ or RZ formats. Progress has nevertheless been

868

zyxwvutsr zyxwvu zyxwv Jan Conradi

made, and in what follows we discuss this progress and outline where necessary, how current implementation capabilities impose limitations on progress and how improvements can be made.

2.2 MODULATOR CHAM CTERISTICS

Of the various approaches to modulating optical signals, really only three have seen significant adoption, namely (1) direct modulation of semiconductor lasers by modulating their drive current [32]; (2) electroabsorption (EA) modulators [33]; (3) Mach-Zehnder (MZ) modulators [34].

The directly modulated semiconductor laser and the electroabsorption modulator result in the opticdpower being modulated in response to an input modulating signal, usually with some accompanying phase modulation that can be either beneficial or detrimental to the transmission of the signal [35]. The MZ modulator, on the other hand, can be a quite flexible device that is capable of performing a variety of modulation functions on the light, and it has been used successfully in creating a variety of modulated signals that are not purely NRZ binary amplitude or intensity modulated signals. Specilically, it has been used to create both duo-binary [13-161 and optical single-sideband signals [25,26,36,37],but invariably with some accompanying distortion in the output signal such that the transmitted signal spectrum is not an undistorted, frequency up-shifted version of the spectrum of the baseband signal. This is, undoubtedly, one of the main reasons why the potential of modulation formats other than NRZ have not fulfilled their potential. Because the modulated output from the semiconductor laser and the EA modulator correspond to intensity modulation (with some added phase modulation), modulation formats requiring electric modulation as described by Eq. 16.2 cannot be used with these devices, and they will not be addressed further. We will examine how the MZ modulator can and has been used to generate modulated signals other than binary amplitude shift keyed (ASK) or intensity modulated (IM) signals Figure 16.2 is a schematic representation of a MZ modulator. The input optical electric field is represented as Ein = lEol eiocr, where in this instance we adopt the exponential representation of the time-varying part of the optical electric field. This unmodulated signal propagates in a waveguide at the modulator input where it is split into two separate waveguides, with a split ratio that ideally is 50%.Electrodes, to which signal voltages v1 ( t )and vz(t) are applied, modulate the propagation constant within each waveguide, resulting in a phase modulation of the signal propagating in each arm. When these two signals are combined at the modulator output, the result is a modulated output

zyxwv zyx

16. Bandwidth-EfficientModulation Formats

869

zyxwvuts zyxwvut zyxw zyxw zyxwvut Fig. 16.2 Schematic representation of a Mach-Zehnder modulator.

electric field given by

(16.6)

The electric field transfer function of the device is

(16.7)

where u, is the modulator extinction voltage, y=-

&-1

&+

1

(16.8)

and S equals the dc extinction ratio of the modulator. To simplify, consider an ideal modulator with infinite extinction ratio such that S+oa or y = l . Then,

zyxwv

To avoid chirp, the time-varying portions of v1 and v2 are often chosen such that vl(t) = -vz(t), and then

870

zyxwvutsr zyxwvu Jan Conradi

and the output optical electric field is

and the output optical power is

zyxwvu zyxwvuts zyxw

This is the usual way in which MZ modulator transfer functions are represented. Figure 16.3 shows both the optical power and electric field transfer functions of the MZ modulator. To look at the effect of a relative bias between the arms retaining chirpless modulation, let vz(t) = vdc - vl(t). Then Eq. 16.9 becomes

\y(vl(t), vdC) = cos

1

(2vl(t) - vdc) ej(nv&12vr)

t

Modulation Term

(16.13)

t

Constant Phase Shift

Fig. 16.3 Normalized optical electric field and power transfer functions of a Mach-Zehnder modulator.

zy zyxwvu zyxwvut zyxwv zyxwvu zyxw 16. Bandwidth-EfficientModulation Formats

871

(a) "Normal" bias Vd, = V,/2

vl(t) = ma(t)V, with a(t) = +/-1 for a digital signal, m = electrical drive amplitude to each arm as a fraction of V,. Then,

zyx (Ignoring the constant phase shift).

(16.14)

zyxwv :>I

To simplify let's invoke the small-signal condition such that nma(t) ) = (2,3(1 + (.5) = ~4 = a7 = 1.

a3 as a6 = a3(1

(17.45)

.3

(17.46)

5.

17.5 Reed-Solomon Codes

zy zyxwvut

With this background in finite fields, we are now in a position to study the Reed-Solomon (RS) code. RS codes are in widespread use, for example in optical fiber communication [17], compact disks (CDs) [29] and deep-space communication [45]. In contrast to the codes discussed thus far, these codes are nonbinary. Parallel to the binary case, a block code C of length n over the finite field F,,q = 2m,m > 1, is said to be linear if whenever c1,5 E C implies that every linear combination

Again as in the binary case, a code C over IF, is said to be cyclic if C is linear and if in addition, whenever (coyc1, . . .,cn-l) is a codeword, so is ( c 5 , c T +..., ~ , cn-l,co,c~,...,cr-~),forO< tsn-I. DeJinition 1

Let q = 2m,m 1 and n be an integer dividing q - 1 and (Y an element in I?, of order n. Then a RS code C having parameters [n, k] over P, can be defined as =f(a') for some polynomial f ( x ) over F, of degree 5 k - 1

ci

1.

(17.48)

RS codes can be shown, using the definition given in Eq. (17.48), to be both linear and cyclic. Minimum Distance As in the binary case, we define the Hamming weight of an n-tuple over IFq to be the number of nonzero symbols in the n-tuple. Similarly, the Hamming distance between the pair of n-tuples a, b E equals the number of symbols in which the two vectors disagree. The Hamming distance d&z,bJ between two n-tuples g , b over F,, once again equals the Hamming weight of their difference, i.e., dH(% bJ = WH(E - b).

(17.49)

zyx zyx zyxw zyxwvutsr zy zyxw zyxwvu zyxwv 17. Error-Control Coding Techniques and Applications

923

It follows that the minimum distance of a linear code C over IFq equals the minimum Hamming weight of a nonzero codeword in C. Since a polynomial of degree Ik - 1 can have at most k - 1 zeros in lF,, the number of zeros in a nonzero codeword of an [n,k] RS code cannot exceed k - 1. On the other hand, the polynomial

n

k-1

(x - ai>

(17.50)

zyxwv

has exactly k - 1 zeros in IF,. It follows that the minimal Hamming weight of a nonzero codeword in an [n,k] Reed-Solomon code equals n - k 1. By our previous observation, this must also be the minimum distance of the code. Thus, Reed-Solomon codes have parameters of the form [n,k,n - k + 11. The Singleton bound states that a block code C of length n over an alphabet of size q having minimum distance dmin has size M upper bounded by

+

Codes achieving the Singleton bound with equality are said to be maximum distance separable (MDS). Thus RS codes are MDS.

Generator Matrix A linear code of length n over IF, is a subspace of F;.The dimension of a linear code is the dimension of this subspace. As with binary codes, the notation [n,k,4 refers to a code of length n, dimension k, and minimum distance d . The notions of generator and parity-check matrices also carry over from the binary case. The generator matrix of any [n,k,dl code over F, is any (k x n) matrix whose rows form a basis for the code. Similarly, the parity-check matrix is any ((n - k) x n) matrix whose nullspace is the [n,k , d ] code. The generator matrix G shown in Eq. (17.52) follows directly from the definition of a RS code

If g ( x ) is a polynomial of degree 5 n - 1 over GF(q) satisfying g(0) = 0, then it can be shown that g(a!') = 0. Setting g(x) = x'f(x), 1 5 i In - k,

924

zyxwvut zyxwvu zyxwvuts P. Vijay Knmar et a].

leads to the following parity-check matrix H of an RS code

zyxwv zyx zyxwv zyxwvuts zyx zyxw

since H has the right rank and Hc = 0 for any codeword c in the RS code.

Probability of Codeword Error

Let us assume that an [n,k,d ] RS code of length n = 2m- 1 is used to transmit information over a BSC having crossover probabilityp. Let d = 2t, 1. To transmit information over the binary channel, each symbol ct E Fp of a codeword is converted into m binary digits. The probability Ps that any such symbol is received in error over the BSC is given by

+

P, = 1 - ( 1 - p y .

(17.54)

Then following the argument used in the case of a general binary code in Section 17.2 to obtain an upper bound on the codeword error probability, we can upper bound the probability Pwe of codeword error in the case of the RS code by Pme 5 1 -

2

&(l

-P y .

(17.55)

i=O

Burst Error Correction RS codes excel in burst error correction. Consider for example an [255,239,17] RS code over GF(256). Prior to transmission, each symbol in GF(256) is converted to a string of eight binary digits, and these are transmitted in sequence. This effectively makes the RS code a binary code of length 8 * 255 = 2,040. Since the RS code can correct up to eight symbol errors, the code will correctly decode even in the presence of a contiguous stream of up to 1 + 7 x 8 = 57 erroneous binary digits, since such a string of errors will cause at most eight symbols over GF(256) to be in error. Of course this burst error correction capability carries over to any nonbinary code with symbols in GF(256).However, in comparison with other nonbinary codes of the same length over GF(256). RS codes offer the largest minimum distance for given dimension.

zyxwvuts zyxwv zyxwvuts

zyxwvutsrq zyxw zy 17. ErroA!ontrol Coding Techniques and Applications

925

Changing the Length of a RS Code

Given an [n,k,d] RS code Cy it is possible to “shorten” the code to an [n - a, k - a, d] code c,h by considering the set A of all the codewords in C whose last a symbols equal zero and then deleting the last a symbols from each codeword to obtain the code Csh. We note that it is possible to define RS codes in a more general setting than what we have done here (see [26]).

Decoding

There are several efficient algorithms, such as the Berlekamp-Massey, WelchBerlekamp, and Euclidean algorithms, for the decoding of RS codes, all with complexity on the order of the square of the length n of the code or less. Details can be foundinmost texts oncoding theory, for examplein [6,26,36,41,44],see also [4b,221. Under certain circumstances, it is possible to decode beyond the minimum distance of the RS code using a procedure known as list decoding, see [14b]. 17.5.1 CONCATENATED CODES Concatenated codes are linear binary codes that are constructed from two component codes called the outer and inner code. In the classical construction of concatenated codes as shown in Fig. 17.4, the outer code is typically a RS code and the inner binary code, a short block code. We illustrate with an example. Example 9

zyxwv

Consider an [255,244,12] RS code over GF(256). Each symbol in this code corresponds to an 8-bit string. Replacing each 8-bit string by the corresponding 12-bit codeword in the [12,8,3] single parity-check code yields a binary code with parameters [12.255,244.8,1 361. In general if the outer and inner codes have parameters [ N ,K , D] and [n,k,d ] , respectively, the concatenated code will have parameter [Nn,Kk, 2 Dd] (Fig. 17.4). Concatenated codes have large length and good minimum distance. The outer and inner codes have properties that complement each other. The RS code by itself, is vulnerable to isolated bit errors since each bit error can potentially cause a different code symbol to be in error. The inner code serves to

K

m

z

zyxwvu

Outer [N,K,D] code oVerGF(zk) N code

Inner [n,k,dl binary code

Nn bEary

926

zyxwvutsrq zyxwvu zyxwvu P. Vijay Kumar et al.

protect the RS code against isolated errors by providing an ability to either detect or correct them. Concatenated codes inherit from RS codes the ability to correct burst errors. Whereas the complexity of decoding a block code of large length is high, concatenated codes are easily decoded using a suboptimal decoding algorithm (in relation to ML codeword decoding) in which the inner binary code is decoded first, followed by the decoding of the outer nonbinary code. Although the outer code is typically a RS code, this is not essential and the RS code can be replaced by any efficient code with symbols lying in GF(29, such as, for example, nonbinary BCH codes [26] or else algebraic-geometric codes [31]. Other means of concatenating two codes also exist, as we shall shortly see.

17.6 BCH Codes

zyxwv zyxw zyxw zyxw

BCH codes are a family of binary cyclic codes that are very flexible in terms of allowing a trade-off to be made between dimension and minimum distance. Also, for code lengths up to a few thousand, these codes are very efficient in terms of the performance trade-off that they offer. Let n be a divisor of 2P - 1 for some integer p 2 3. We assume that p is the smallest integer for which n divides 2* - 1. Let y be a primitive element of GF(2p) and set a! = y(2P-1)/n. Then a has order n. Definition 2 Let n,p, a! be as above. A t-error correcting BCH code C of length n is the set of all binary n-tuples that lie in the null-space of the (t x n) matrix

zyxwvu

Note that if JVdenotes the nullspace of the above matrix over GF(29, then theBCHcodeC = NnF;. Example IO

Consider the singIe and double error correcting BCH codes of length n = 15. Here t E { 1,2},p= 4, n = 15. Let y be a primitive element of GF(16) satisfying

zyxwv zyxwv

zyx zyxwvutsrq zyxwv 17. Error-Control Coding Techniques and Applications

927

+ +

y4 y 1 = 0. Here, since n = 24 - 1, we have a = y. The double-errorcorrecting BCH code is the set of binary 15-tuples that lie in the null-space of the matrix: 1 42 . . . . . . (17.57) H = [ 1 a3 ......

For example, since

zyxwv (17.58)

satisfies a(.) = a(a3)= 0, we have that [100010111000OOO]Tis a codeword in the BCH code. In the case of the single-error-correctingBCH code, the matrix H is given by

1.

zyxwvut H =

[

1 a

......

a2

a14

(17.59)

A more conventional (but less convenient) description of the BCH code can also be obtained. Each element a1in the matrices has a unique representation in terms of the basis { 1,a,a2,a3}for the four-dimensional vector space P16 over Pz.Let the element a1in the H matrix be replaced by its corresponding column vector. If this is done, in the case of the single-error-correcting BCH code, we will obtain the binary matrix

IHbin=

[

0 0 0 1

0 0 1 0

0 1 0 0

1 0 0 0

0 0 1 1

0 1 1 0

1 1 0 0

1 0 1 1

0 1 0 1

1 0 1 0

0 1 1 1

1 1 1 0

1 1 1 1

1 1 0 1

1 0 0 1

I

-(17.60)

zyx zyxwv

The fifth column of this matrix equals fool1ITsince it corresponds to a4 = 0 - a3 + 0 . a2 + 1 a! + 1 . 1. It can be shown that the BCH code can also be described as the set of all binary 15-tuples that belong to the nullspace of this matrix. Since the columns of this (4 x 15) matrix comprise all distinct nonzero 4-tuples, this makes the single-error-correcting BCH code a cyclic Hamming code. This is always the case. For any length n = 2 p - 1, the single-error-correcting BCH code is a cyclic Hamming code. It can be shown that the t-error correcting BCH code, as the name suggests, has minimum distance dfin > 2t + 1. When the channel over which the codeword is transmitted is the BSC, BCH codes can be decoded using techniques very similar to those used to decode RS codes, see [6,26,36,41,44]. Because BCH codes are cyclic, they can be described in terms of a generator polynomial. It turns out that the generator polynomial of the BCH code is the smallest degree polynomial that has zeros a,a3 ..... a21-1

Y

...

Y

a2t-l

(17.61)

928

zyxwvut zyxwvu zyxwvut zyxwvuts zyxwvutsr zyxw P.Vijay Kumar et al.

Example 11

The single-error-correcting BCH code of length n = 15 has generator polynomial

(17.62)

g(x)=x4+x+1,

since this is the smallest-degree polynomial of which the (Y in the example is a zero. The double-error-correcting BCH code of length n = 15 has, for the same reasons, the generator polynomial

zyxwv

~ ( x ) = ( x ~ + x + ~ ) ( x ~ + x ~ + x ~ - ~ x + ~ ) = ~ ~(17.63) + ~ ~ + x ~ + x ~ +

Tables providing the parameters of BCH codes of lengths up to 1023 may be found, for example in [24].

17.6.1 PRODUCT CODES Let C1 and C2 be [ n l , kl, dl] and [nz, kz,d2] systematic codes respectively. The product code C = C1 x C2 is a code having parameters [111n2, klk2, dldz] and may be constructed as follows. Let the k1k2 information symbols be arranged in the form of a (k1 x k2) matrix A. Then construct an (nl x n2) matrix B such that the matrix in the upper-left comer of B is precisely A (see Fig. 17.5). In addition, we require that the first k1 rows of B are codewords in C2 and that the first k2 columns represent codewords in C1. Then let the remaining ((nl - kl) x (n2 - k2)) submatrix in the lower-right corner of B be chosen such that the last (nl - kl) rows of B are also codewords in CZ. (Alternately, the ((nl - k1) x ( n -~ k2)) matrix in the lower-right corner of B could be chosen in such a way that the last (n2 - k2) columns in B are codewords in C1. It can be shown that either method yields the same ((nl - k1) x (n2 - k2)) submatrix.) A straightforward argument shows that the m i n i u m distance d of C satisfies d = dl dz.

I

A

------

Check on rows

iICheck columns

on

'

,I C i e Z on checks

Fig. 17.5 An [nlnz,klk2] product code.

zyx zy zy zyxwvut zyx zy

17. Error-Control Coding Techniques and Applications

929

As with concatenated codes, product codes offer a means of constructing a block code of large length. Again there is a simple suboptimal decoding algorithm for product codes. One first decodes the rows of the code matrix B using a decoding algorithm for code C 2 to obtain the (121 x 122) matrix B1. Next one decodes the columns ofthe matrix B1 using code C1,resulting in the (121 x 122) matrix B 2 . The second decoding step thus attempts to correct errors resulting from incorrect decoding of rows by code C 2 . The ( k ~x k 2 ) matrix in the upper-left comer of B 2 constitutes the decoded information bits. This procedure can be iterated to improve error correcting capability.

17.7 Convolutional Codes Convolutionalcodes [9,19,24,31,36,4244] are examples of tree codes. The distinction between block and tree codes is that in the case of a block code it is possible to partition the input and output of the encoder into finite blocks in such a way that the ith output block is a function only of the ith input block. With tree codes, such a partition is, in general, not possible. Instead, it is possible for a particular output bit to be a function of all previous input bits. Convolutionalcodes are a special class of tree codes in which the input-output relation is given by a convolutionalrelation. We begin with an example.

zyxwvuts zyxwv

Example 12

In the convolutional encoder shown in Fig. 17.6 there is one input stream and two output streams { v ~ ’and } ~ ~ related by

{ut}z0

vjl’ -

+ Ut-1 +

VI“’ = Ut

+ Ut-2,

- Ut

Ut-2,

z0 t z 0. t

(17.64) (17.65)

It is assumed that the convolutional encoder is initialized with U - 1 = 24-2 = 0. The h a 1 output of the encoder is the multiplexed stream {vr’,vf’, vy’, vy’, .. .}.

Fig. 17.6 An example convolutional encoder.

930

zyxwvu zyxwvu zyxwvut zyxw zyxw zyxwvutsrq zyxw P.Vijay Kumar et aL

In the general case, there are k inputs and n outputs related by:

(17.66)

where u is the memory of the convolutional code. Thus our example encoder has memory u = 2. The convolutional code is said to have rate k / n , thus our example convolutional code is of rate 1/2. Consider the case when the inputs {u?} to the convolutional encoder are finite strings of length N u with the last u bits on each string equal to 0. The outputs {vy)} of the convolutional encoder are then finite strings as well. By multiplexing these output strings one obtains a vector (vo(1) )...,vo(n),VI(1) ,...)VI(4,. ..,.. . )v(1)~ - ~ +. .". , v ~ ~ ~ +The , > collection . ofthese vectors may be regarded as codewords in the convolutional code and in this way we may regard the convolutional code as a block code of large block length n(N + u). The minimum distance between codewords as N +. 00 is called the minimumfree distance, dfm, of the convolutional code. Our example code turns out to have df,, = 5. A simplified description of the input-output relationship in a convolutional code can be obtained through the use of power series. Let us define

+

zyxw

Then the convolutional relation in (17.66) is replaced by

c k

vQ(D) =

u q D ) g y D ) , 1 s j 5 n,

(17.68)

i= 1

Example 13

In the case of our example code we have [v(')(D)d2)(D)]= [u(D)] [g'l'(D) g(Z)(D)],

where g(')(D)= 1

(17.69)

+ D + 02 and g(2)(D)= 1 + 02.The matrix g('J)(D) g(',Z)(D) . .. g(1JqD)

G(D) =

(17.70) g(kJ)(D) g(Q)(D)

. ..

g'yD)

17. Error-Control Coding Techniques and Applications

931

zyxwvu zyxwv zyxwv zyxwvu zyx zyxw zyxw

Fig. 17.7 State diagram of example code.

is called thepoZynomiuZgenerutormatrix (PGM) of the code. In the case of the example code above, we have

G(D)= [ 1 + D + D 2

1+D2

1.

(17.71)

An alternate description of the convolutional code is in terms of a state diugrum. The state diagram of our example convolutional encoder is shown in Fig. 17.7. In the state diagram, the two symbols that form the label of each vertex are (ui-l ~ ~ - 2 ) The . solid edges correspond to input bits equal to 0 and the dotted edges represent input bits equal to 1. The label on each edge represents the output of the encoder corresponding to the input associated with the particular edge.

Recursive Systematic Convolutional Code

The conventional convolutional encoders considered thus far have finite impulse response. Consider a convolutional encoder with one input {ut} and two outputs {vi')}, {v;')} whose associated power series u(D) = C z O u t D t , v(')(D) = E,"=, vil)Dt,d2)(D) = xEo vj2)Dt,are related by

v(')(D) = u(D)

(17.72)

(17.73)

zy

One method of implementing such an encoder is to introduce the auxiliary power series (17.74)

We then have u(D) = s(D)[l+D+D2 +D3 +D4], v(')(D)= u(D)and d2)(D) = s(D)[1 041 leading to the time domain relations: uf = st + st-' + s ~ + - ~ st-3 st-4, vj') = ut, vf2' = st ~ - 4 This . leads to the encoder shown in Fig. 17.8.

+

+

+

932

zyxwvu zyxwvu zyxwv zyxwvuts zyxwvu P. Vijay Kumar et al.

V/*)

Fig. 17.8 A recursive systematic convolutional encoder.

zyxwvutsrqp zyxwv

In the figure, the contents of the four-bit shift register correspond to the 4-tuple ( ~ ~ - 1 , ~ ~ - 2 s+3, , ~ ~ - 4 ) Note . that this encoder is systematic since one of the two outputs coincides exactly with the input. Such convolutional encoders are referred to as recursive systematic convolutional encoders (RSC encoders) [5]. Here, in place of the PGM we have a matrix G(D) with rational polynomial entries:

[

[v(’)(D) V(Z)(D)]= u(D) 1 \

zyxwv

1+ 0 4 1 + D + D ~ + D+04 ~

1.

(17.75)

I

W)

RSC encoders form the building blocks of turbo codes, see Section 17.9.

Decoding of ConvolutionalCodes The Viterbi algorithm [42,43] is an algorithm for carrying out maximumlikelihood codeword decoding of a convolutional code. It is of low complexity whenever the number of states in the state diagram of the convolutional code is small. Maximum-likelihood decoding of the information bits of a convolutional code via the BCJR algorithm [3] is discussed in Section 17.8.1.

17.8 Graphical Approach to ML Decoding of Binary Codes Claude Shannon has shown that given a communication channel, there is a quantity called channeZ capacity, C , [lo] such that it is possible to transmit information at rate R across the channel reliably, provided R < C . Reliable communication means communication with bit-error probability arbitrarily close to zero. Reliable communication calls for the use of codes of large block length as long block codes are able to average out random distortions introduced by the channel, and hence make the channel more predictable. If reliable communication is interpreted as communication at bit error rate on the order of then it has been shown that turbo and LDPC codes have

17. Error-Control Coding Techniques and Applications

933

come extremely close (within fractions of a dB) of achieving capacity on the AWGN channel. A second feature that both turbo and LDPC codes share in common is that in both cases, decoding is accomplished by passing messages iteratively around in a graph that represents the code. Efforts are currently underway at explaining the superlative performance of such a decoding scheme. Here we content ourselves with showing how the distributive law, applied in a more general setting, can be used to provide a heuristic justification for the use of message passing in a graph to approximate ML decoding of a code.

zy

zy zy zyxwvuts zyxwv zy

17.8.1 ML DECODllvG VIA THE DISTRIBUTNE LAW

In this rather long section, we lay down some principles that underline the decoding of turbo [5] and low-density parity-check codes [13]. The principal reference for the material in this section is the paper by Aji and McEliece [2], see also [8,23].

The Distributive Law

The distributive law may be viewed as a rule that allows a savings in computation. For example, the distributive law ab1

+ ab2 = a(b1 + b2)

(17.76)

reduces three operations down to two. A second example is given in Example 14. Example 14

Let A be a set of size q and let f and g be real-valued functions defined on 3-tuples and 2-tuples from A , respectively. Suppose it is desired to compute F(xlsx4) =

(17.77)

f(xl,xZ,X4)g(Xl~X3)-

XZ,x3&

Direct computation would require q2[q2(1)+ (q2 - l)] = 2q4 - q2 operations. However, the distributive law can be used to reorganize the computation as

zyx (17.78)

F ( x l ~ X 4 )= C f ( x l ~ x 2 9 x 4 )c g ( x l ~ x 3= ) /%l,X4h’(xl)~ X2 €A x3 4

zx3&

where B(xl,x4) = Ex2e,4f(X1 7x2, x4) and ?&l) = g(X1 x3). Computing ~ ( ~ 1 ~ for x 4 all ) (q,x4) pairs requires q2(q - 1) operations. Computing y ( q ) requires q(q - 1) operations. Thus a total of q2(4- 1) + 4(4 - 1) +

4” = q3 + q2 - 4

Y

(17.79)

934

zyxwvut zyxwvu zyxwvut P.Vijay Kumar et al.

operations is now required, which could be a significant saving in com putation.

zyxwvut zyxw zy zy zyx

The MPF Problem and ML Decoding

We next present the problem of marginalizing a product function (MPF) and show how the generalized distributive law (GDL) can be used to present an efficient solution. Let x1 ,x2, .. . ,x,, be variables taking on values from the set A1 ,A2, . .. ,A,, respectively. Let qi be the size of A i . Let

and let SI,S2, . ..,SM be subsets of S , not necessarily distinct. Each set Si will be called a local domain. We associate to each local domain Sia local kernel ai : Si+ B where B denotes the set of all real numbers and introduce a global kernel B(xl ,x2, .. .,xn) given by

By the Si-marginalizationof B(K) we will mean the sum

(1 7.82) and we will refer to this sum as the ifhobjectivefunction. (The notation S\Si is a reference to the subset of the elements in S that do not belong to Si.)Thus the MPF problem aims to efficiently compute the Si-marginalization of the product function p(.). Our earlier example can be recast in this notation. Example I5

The computation

can be viewed as the marginalization of a global kernel as follows: Set

and introduce the local kernels: Ul(S1) =f(x1,x2,x4),

az(S2)= g(x1,x3), a3(S3) = 1.

(1 7.85)

17. Error-Control Coding Techniques and Applications

Then since

zyx zy 935

zyxwvuts zyxwvuts 1 zyx zyxwvuts zy zyxwvuts

it is the &-marginalization of the global kernel

For our second example, we consider the decoding of a simple binary linear code. Example 16 (ML code symbol decoding of a block code)

Let C be the binary linear code having panty-check matrix

H=

[

1 1 0 1 0 0 0 0 0 1 1 0 1 0 . 0 0 0 1 1 0 1

(17.88)

Consider the problem of decoding the code over a BSC. Let x_ be the transmitted codeword, g the error pattern introduced by the BSC, andy- the received vector given by y=x_+g. -

(17.89)

The goal under ML code symbol decoding is to find the ith codeword symbol, 1,2,. . .,7, such that P(xily) is a maximum. Although this goal does not correspond to either ML codeword decoding or to ML message-bit decoding, it is sometimes easier to formulate, and it can be shown that under reasonable assumptions, this decoding technique will, with high probability, pick the code symbols of the transmitted codeword. Assuming all the codewords are equally likely, we can rewrite

xi E P2,i =

where the indicator function xc is given by:

zyxwvu

and where the cx sign indicates that we have ignored scale factors ( P o )in this case) that are independent of the symbol a.

936

zyxwvuts P. Vijay Kumar et al.

From the parity-check matrix, we have that

(17.92)

zyxwv zyx zyxwvutsr zyxwvuts (17.93)

and

(17.94)

We introduce the local kernel and domains in Table 17.9. Let Si-marginalization, 1 5 i 5 7,

q(xi)

be the

(17.95)

where

Then

(17.97)

Table 17.9 Local Domains and Kernels for ML Symbol Decoding Example Local Domain

Local Kernel

zy zyxw zyx zy zyxw zyx zyxw

17. Error-Control Coding Techniques and Applications

937

and thus the problem of ML code symbol decoding of the [7,4,2] block code can be viewed as an instance of the MPF problem. Iff = (21,22, ... ,27) is the decoded codeword, we set xi =

[ 1,

ifq(1) s ai@), 0, else.

Our next example considers the problem of ML decoding of a binary convolutional code.

zyxw

Example 17 (ML message-bit decoding of a convolutional code)

Let [ui}Lil, [si}Lil, and [ y i } L i l denote the sequence of inputs of a convolutional encoder, the sequence of states of the convolutional encoder and the sequence of channel outputs respectively. For simplicity, we assume that the convolutionalencoder is of rate R = l / n and memory u. Thus each ui is binary, each state si represents a binary u-tuple, and each output yi is an n-tuple. For ML message-bit decisions, we need to compute

a zyx

Figure 17.9 presents a graph known as a Bayesian network that depicts the statistical relationship between the various random variables.

... ... ...

@

YN.2

YN-I

Fig. 17.9 Bayesian network of a convolutional code.

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P. Vijay Kumar et al.

zyxwvu zyxw

Table 17.10 Local Domains and Kernels for ML Decoding of the Convolutional Code Local Domain

Local Kernel

ML message-bit decisions are made according to

With local domains and kernels as shown in Table 17.10and consequent global kernel

we see that the problem of ML message-bit decoding of a convolutional code can once again be recast as an MPF problem.

Junction Trees

zyx zyx zyxw zyxwvu

The first step in applying the distributive law to solve the MPF problem is to set up a labeled graph known as a junction tree, in which each node in the graph is associated to a local domain. If it is not possible to organize the local domains into a junction tree then one has to modify this approach. When it is possible to organize the local domains into a junction tree, an algorithm known as Primm’s greedy algorithm (see footnotes on p. 359 of [2]) may be employed to construct the junction tree. The label for a node in the graph is just the set of variables making up the local domain associated to that node. A tree may be defined as a graph in which there is a unique path between any two vertices. A junction tree satisfies the additional constraint that the subgraph consisting of all vertices whose label includes a fixed variable, say xl , is connected. Alternately, a junction tree can be characterized by the property that if nl belongs to the label of vertices vi and it also belongs to the label of every vertex lying on the unique path between vi and 5.

c

17. Error-Control Coding Techniques and Applications

939

Table 17.11 Local Domains and Kernels of Example 18 Local Domain

Example 18

zyx

Local Kernel

zyxwvuts zyxwv zyxwvu

Consider the MPF problem of S1-marginalization of the global kernel

where S = Ix~,x~,x~,x~}and the local given by B(SI)= &, B(xI,x~,x~,x~), domains and kernels are as shown in Table 17.11. The local domains can be organized into a junction tree as shown below:

zyxwv zyxwvutsrqpo zyxw

Let us ignore for the moment the arrows along the edges. To verify that the graph is indeed a junction tree, note that the subgraph consisting of vertices containing the variable, xi,1 5 i 5 4, are all connected, for instance, in case i = 1,we obtain the connected graph

2

940

zyxwvut zyxwvu zyxwv zyxwvu

zyxwv zyxw zyxwvut

P.Vijay Kumar et al.

Message Passing

Given thejunction tree, applicationof the distributive law amounts to message passing between the vertices of a junction tree. Loosely speaking, the message passed from vertex V;: to vertex 5 in a junction tree is a suitabZy marginalized product of the local kernels of all the local domains that vertex V;: has either directly or indirectlybeen in communicationwith. More precisely, the message p i jpassed from vertex V;: to vertex 5 is only a function of the variables in the intersectionSi n 4 and is given by:

zy zyx

where Nu is the set of all vertices connected to V;: other than 5,and where [ Isj denotes +marginalization correspondingto summation over the variables in

(17.104)

All messages pv(Sins,)are set equal to one initially, i.e., &Sins,) = 1, all i,j . A second operation carried out in thejunction tree is updating the state crj(Si) of each vertex 6 . Initially, the state of a vertex V;: is simply its kernel ai(&). The state is updated according to: (17.105)

where Ni is the collection of all vertices that are connected to vertex V;:. To compute the desired objective function, one passes messages in accordance with a message schedule, and at the end of the message schedule, the state of a vertex is updated. The savings in computation comes about because under an appropriate message schedule, the marginalization inherent in message passing constitutes an efficient application of the distributive law. In the present instance, we are interested only in computing the objective function at vertex V I .The next step in such cases is to direct all the edges in the graph so that they point toward vertex V I .Messages are passed only in the direction indicated by the arrows in accordance with the two rules below: (1) vertex fi will pass a message to 5 only when it has received messages from all of its other neighbors, (2) vertex V;: will update its state only when it has received messages from all of its neighbors.

zyx zyx zyxwvu

17. Error-Control Coding Techniques and Applications

941

When these rules are applied to our example, the sequence of messages passed reads as follows:

Phase 1

(17.106) (17.107) (17.108)

Phase 2 (17.109)

(17.110)

Phase 3

zyxw zyxwv zyxw zyx zyxwv

All the computations that comprise Phase 1 of the computation can be carried out simultaneously. However, the computations in Phase 1must be completed prior to carrying out any computation that is part of Phase 2, etc. The objective function computed given by cq(S1), when spelled out, reads as:

(17.112)

Clearly the computation when expressed in this fashion can be seen to make most efficient use of the distributive law. Suppose next, that in the same example, we were interested in computing the objective functions at more than one, perhaps all of the vertices VI,V2, . .., V5. In this case it takes more effort to describe what constitutes an appropriate message schedule. We begin with some notation: Let E denote the set of all edges in the junction tree. We will distinguish between edges (iJ) and (j,i)since reference to an edge ( i , j ) will

942

zyxwvut zyxwvu zyxwvuts zyx P.Vijay Kumar et al.

indicate our interest in passing a message from vertex V;: to vertex 5. In our example:

zyxwvuts zyx zyxwv zy zyxwvu (17.113)

A message schedule is a sequence of subsets of E, such as E1 = I(4, (5,213 (3,1>1and E2 = I(2, 111. With each message schedule we associatea message trellis. The trellis associated to message schedule { E l ,E z )is shown in Fig. 17.10. Each vertical column of vertices in the message trellis corresponds to the vertex V;: of the graph at successive time instants beginning with time t = 0. We use V;:(t)to denote vertex V;: at time t. In the message trellis, we connect the pair of vertices (V;:(t- l), c(t)) if and only if (1) i = j or (2) ( i , j ) E Et. We say that vertex &(t)knows c(0)if there is a path in the message trellis connecting Q(0)to V;:(t).In our examplemessage trellis we see that Vz(1) knows V4(0) and Vs(O), but not Vl(0). Also, Vl(2) knows V;:(O) for all i, 1 5 i 5 5. It can be shown that a vertex V,(t)is ready to compute its objective function pi(&) if K(t) knows Q(O), allj. Thus given that it is desired to compute the objective functions {pi (Si)I 1 5 i 5 M ) , setting up an appropriate message schedule can be accomplished by using the message trellis to check that at the desired time instant t, the vertices { V;:(t),i = 1,2, . . . ,M ) all know { allj}. We next show how the GDL can help solve the MPF problem associated to ML decoding of our example [7,4,2] code.

a,

c(O),

Fig. 17.10 Message trellis.

zyxwvuts zyxwv zyx zyx zyxw

17. Error-Control Coding Techniques and Applications

943

Example 19 (ML code symbol decoding of the [7,4,2] code (continued))

Here we are interested in computing for all i = 1,2, . . .,7, and xi = 0 , l the following objective function:

zyxw

zyxwvutsr (1 7.1 14)

We assume that the communication channel is a BSC having crossover probability E , E e 1/2. Thus for given b 1 , y 2 , . . . ,y7), P(yiIxJ E 11 - E , E). Our decisions will be based on the ratio /&(O)//$(l).The MPF nature of the problem is apparent. It will be found convenient to scale each local kernel P(yilxi) by the constant (1 - E ) (this will not affect the decision). Let us assume that the received vector y = (0110100) in a instance of transmission across the BSC. The local kernzl a1 ( S I )is then given by:

zyxwvu

Ql(S1) = -p (1y-l E' x l ) -

I

E1 9/ 1 - E ,

x1 = 0 , x1 = 1.

(17.1 15)

Let 8 = ~ / 1 E , then 8 e 1. Set

zyxwvutsrq

We similarly obtain g i = [L] for i = 4,6,7 and g i = [ y ] for i = 2,3,5. We will use VA, V g , VC to denote the vertices corresponding to the local domains 11,2,4}, {3,4,6), and {4,5,7}, respectively. Figure 17.11 shows the local domains organized into a junction tree. We are interested here in computing the objective functions at all vertices 6 , i = 1,. .. ,7. With regard to the message schedule, we will adopt an inward-outward schedule in which the outlying vertices send their messages inward first. Once the innermost vertex V4 has acquired knowledge of all the local kernels, the outward phase of message passing begins. The validity of this message schedule can be verified with the aid of a message trellis ifdesired. The messages passed are as follows: Phase 1

944

zyxwvut zyxwvuts P.Vijay Kumar et al.

zyxwvuts Fig. 17.11 Example ofjunction tree.

Similarly,

(17.117)

Phase 2

zyxw (1 7.118)

Similarly, p ~ , ~ (= 1 )1

zyxwvu zyxwvu

+ 8', which implies

Also,

zyxwvuts

Phase 3

P4,A (x4)

= P~P(X4>PC,4(~4)~4(40.

(1 7.120)

SO,P ~ J ( O ) = 28.28 = 402, ~ ~ , ~= (1 ( l+)e2)(1 + e2)8 = e(1 + e2)2 and 4ez

zyx zyx zyxwvuts 17. Error-Control Coding Techniques and Applications

Similarly,

945

Phase 4

and

EA,2

Phase 5

=

zyx zy

zyxwv

[ 4e3++ e2)2++e2)2 1 -e2(i

e(i

4.e2

EB.3

-

- EC.5'

+

Similarly, al(l) = Q3(l+ 02)2 403, so that

(17.125)

946

zyxwvut zyxwv zyxwvu zyxwvuts P.Vijay Kumar et al.

Similarly,

zyxwvut zyxwvu zyxw zyxw (17.126)

(17.127)

Note that a, could have been computed in Phase 3. Phase 6 (Decisions)

Since u1(0) = 403+ e( 1 + e*)‘ > 01 (1) = e3(1 + €J2)2

+ 403,we conclude that

P(Xl = Oly) - > P(x1 = lk). -

(17.128)

Denoting the decoded codeword as before by 2 = (21,i z , .. .,27), we therefore declare $1 = 0. Similarly, we get 26 = $7 = 0 and 22 = G = & = $5 = 1. It can be verified that [Ol1 1 lWITis a valid codeword. Example 20 (ML message bit decoding of convolutional codes (continued))

The local domains corresponding to the MPF problem in this case can be organized into a junction tree as shown in Fig. 17.12. The linear nature of the junction tree coupled with the fact that it is desired to compute the objective functions at vertices ui,i = 0,1,2,3 results in a message passing schedule that could be viewed as consisting of a forward wave of message passing and a second backward propagating wave. Part 1. Passing on A Priori Probabilities

4

7

10

3 6

9

SO 2

Fig. 17.12 Junction-tree representation of maximum-likelihood bit decoding of convolutional codes,

17. Error-Control Coding Techniques and Applications

Part 2. Forward Wave

zyx zyx 947

zyxwvuts

Part 3. Backward Wave

Part 4. A PosterioriProbabilities (17.130)

zyxwvu zyxwvutsr zy zy

Finally, since

(17.131)

we decide uo = 0 if q(0) > el(l), and similarly in the case of the other cj.The scheme just given for convolutional codes in which Parts 1, 2, 3, 4 are executed in sequence is clearly not optimized to yield the fastest decisions. The reader can fashion a message passing schedule that minimizes time. However, the schedule given does explain the commonly used terminology: forward-backward algorithm. This algorithm was discovered in a different

948

zyxwvuts zyxwvut zyxwvu P.Vijay Kumar et al.

setting by several researchers, independently, including Baum, Welch, Bahl, Cooke, Jelinek, and Raviv (BCJR), for details see [2]. It is also often referred to as the BCJR or the Baum-Welch algorithm.

zyxw zyxwvu zyx zyxw zyxwvuts

17.9 Turbo Codes

Turbo codes, also known as parallel concatenated convolutionalcodes, were discovered in 1993 by Berrou et al. [5], see also [15]. These codes presented a dramatic improvement in performance at low signal-to-noise ratios over an AWGN channel when compared with other codes existing at the time. An exampleturbo encoder is shown in Fig. 17.13. The encoder shown is composed of two identical rate 1/2 RSC encoders. The input to the first (top) encoder is a sequence {ui}Li’of binary symbols. It is assumed that the top shift register is initially in the all-zero state and that the last u input bits {uN-”,.. . ,U N - ~ } are designed to restore the encoder to the all-zero state. The input {wj}Ei’ to the second (bottom) encoder is the same set of input symbols but in a different order. Thus we may write: (wo...WN-1) = (UO u1 .. .U N - 1 ) P

(17.132)

for some ( N x N ) permutation matrix P.The second encoder is also initialized to the all zero state. The turbo encoder outputs three symbols (vi(1) ,vi(9,vi(3) ) per input symbol

ui,0 5 i 5 N - 1. Whereas vi‘” = uj, the remaining two symbols correspond

r.

Fig. 17.13 Example of turbo encoder.

zyx zyx zyxwvu zyxwvu zyxwv zyx zy 17. Error-Control Coding Techniques and Applications

949

to outputs of the top and bottom encoder. Thus the overall rate of the code is one-third. The input-output power series relationship of the two encoders may be expressed in the form 1+ 0 4 1+0+02+03+~4

]

(17.133)

The turbo encoder incorporates three novel features: (1) the use of two convolutional encoders to encode scrambled versions of the same input data, (2) the use of RSC encoders in place of conventional convolutional encoders and, (3) the use of a message passing decoding algorithm [23,28] that employs an iterative message-passing schedule. It is this decoder that gives the code its name. We explain with a simple example where N = 4, wo = u2, WI = U I ,wz = 1.43, andw3 = UO.Consider MLmessage-bit decoding of u2. Let { X ~ , ~ ~ , Zdenote ~};=~ the received symbols corresponding to the output streams {vi(1) ,vi(2) ,vi(3) }i=o, 3

zyxw

respectively. Then p (u2IIxi,yi,ziI~=o) a

p (tui,si,qi,xi,yi,zi}Lo) (17-135) uom 9%

Iqi);=o

zyxwvut 1 n1% 3

x

i= 1

Isi-1 ui-l)p(qi Iqi-lwi-~)]

n

p( yi Iuisi)p(ziIWiqi) ,

(17.137)

[ i=O 3

where si,qi denote respectively, the state of the top and bottom encoder. At this point, one should, strictly speaking, identify the local domains and kernels associated with this computation and then set up a junction tree. However, the turbo decoder operates using the graph shown in Fig. 17.14. The reader will observe that this graph is not a tree as it is possible to identify several pairs of nodes with each pair connected by two or more paths. Despite this,however, message passing is used for decoding, and the schedule runs as follows. It is evident that the graph is composed of two sections. The top section is the junction tree associated with the top encoder and similarly with the bottom section. The two sections are linked by edges designated by a dotted line. To begin with, let us pretend that the dotted edges are absent. The upper section employsmessage passing using a forward-backwardschedule and concludes by updating the states ai(uj) of the vertices labeled uo,u1,u2 and u3.

950

zyxwv zyxwv zyxwvutsrq P. Vijay Kumar et aL

zyxwvu zyxwvut zyx zyxwvutsrq Fig. 17.14 Junction-tree representation of turbo codes.

These states q ( u i )reflect the aposteriori probabilities of the symbols. The dotted edges then come into play. Each dotted edge indicates that the vertices at either end of the edge (such as, for example, vertices u3 and wz) should be viewed as being the same. Thus vertices u3 and w2 share the same state 4 u 3 ) = q(w2). The bottom section of the graph is now activated. Messages are passed into the bottom section from the vertices wi,i = 0, 1,2,3. Once again, we pretend that the dotted edges are absent and carry out fonvardbackward message passing, this time in the bottom section, concluding by updating the states of vertices wi,i = 0, 1,2,3. At this point, we repeat the earlier procedure of identifying the vertices wi with the vertices ui.The entire procedure described thus far constitutes one iteration. This procedure is iterated several times. It has experimentallybeen observed that with high probability, after several iterations, the probability ratio ai(0)/ai(l) can be taken to be a good estimate of P(ui = Oly)/P(ui = 1ly) and decisions on the ui made accordingly.

zyxwvuts

Performance of Turbo Codes At low signal-to-noise ratios, turbo codes have probability of bit error that is significantly lower than that of a comparable convolutional code. The explanation for this excellent performance lies in the difference between the weight distribution of a turbo code and that of a comparableconvolutional code. For details, the reader is referred to [30].

zyxw zyxwv

17. Error-Control Coding Techniques and Applications

951

17.10 Low-Density Parity-Check Codes

Thejunction tree of our earlier example [7,4,2] code can be redrawn as shown in Fig. 17.15. Such graphs are called bipartite graphs since the graph contains two classes of nodes. Each edge in the graph links a node with a second node belonging to the other class. In this particular bipartite graph, the two classes of nodes correspond to the code symbols and the parity checks on the code symbols, respectively. Such a graph is termed a Tanner graph [38]. Although the Tanner graph of our [7,4,2] code is a junction tree, in general, Tanner graphs are not junction trees. Clearly it is possible to associate every linear, binary block code with a Tanner graph. The Tanner graph of a [lo, 51 code along with its parity check matrix H is shown in Fig. 17.16. It can be verified that this Tanner graph is not a tree. Note that each row of H has six 1’s and each column has three 1’s Codes of large length, say of length 1000, with a small fixed number of 1’sin each column and each rowywere termed lowdensit): parity-checkcodes (LDPC codes) by Gallager [13,23,35]in the 1960s. Gallager showed how these codes could achieve reliable information transmission over a BSC with probability of error approaching zero as the length of the code approached infinity. The decoding algorithm employed by Gallager was a form of message passing and was of complexity linear in the length of the code. In recent years, followingthe successof turbo codes, there has been renewed interest in the decoding of these codes using various message passing algorithms, including those that correspond to message passing of the type carried out in our junction tree based decoding of the [7,4,2]code. The approach here, in essence, is to construct LDPC codes in which the cycles in the graph are not too short in terms of the number of edges along the cycles, ignore the fact that the graph is not a junction tree, and iteratively continue message passing from every node to its neighbor until at some point, hopefully, each node attains its associated objective function. For more details, we refer the reader to [25, 351.

zyx zyxw

zy

d

zyxw

Fig. 17.15 The Tanner graph of [7,4,2] code.

952

zyxwv zyxwv zyxwvutsrq [ Izyxwv P. Vijay Kumar et al.

1111011000 0011111100 = 0101010111 1010100111 1100101011

zyxwvuts zyxwvut zyxwv zyxwvu

Fig. 17.16 The parity-check matrix of a [lo, 51 code and the corresponding Tanner graph-

17.11 FEC Codes Proposed for Optical Fiber Communication

In this section, we discuss the applicability of the codes described in Sections 17.2 through 17.10 to the optical channel. We begin with some preliminaries. The rate R of an error correction code C is the ratio of the number of information-bearing message bits to the total number of bits transmitted. A code of rate R has redundancy p = 1 - R . The overhead w of a code of rate R is given by w = (1 - R)/R. The overhead is often presented as a percentage. In the case of an [n,k] block code, the rate, redundancy, and overhead of the code are given respectively by R = k / n , p = (n - k)/n, and w = ( n - k)/k. For example, a [255,239] block code has R = 0.937, p = 0.063, and an overhead of 6.7%. The complexity of a decoding algorithm is often measured in terms of the number of operations (addition, multiplication and division) over the relevant finite field. The fastest means of implementing finite field operations is via table lookup, which is feasible when the exponent m of the finite field F p is not too large.

Coding Gain Discussions of coding gain in the current optical-FEC literature usually take place in the setting of a WDM optical communication system in which the

zy zyxwvuts zyxwvu zyx 17. Error-Control Coding Techniques and Applications

953

dominant source of noise is the ASE noise introduced by the optical amplifiers present along the optical fiber. The modulation is assumed to be OOK and the receiver can be modeled as a symbol detector (see 17.1.3) followed by a hard-decisionFEC decoder. The symbol detector consists of a direct-detection photodetector followed by an integrate-and-dump filter with integration-time interval T chosen to capture most of the energy of the incoming pulse. The output x of the integrate-and-dump filter is fed to a threshold circuit which declares the transmitted message bit to be a “1” or a “0” depending upon whether x exceeds or does not exceed, a threshold Xth. The output of the threshold circuit is fed to the input of the FEC decoder. All distortions of the optical signal except that caused by the ASE noise are ignored. Thus an implicit assumption is made that the intersymbolinterference caused by the various sources of pulse dispersionhas been reduced to negligible levels through some form of optical or electronic equalization. The ASE noise can be assumed to be modeled as colored Gaussian noise obtained by passing additive white Gaussian noise through a bandpass filter whose single-sided bandwidth equals Bo,the bandwidth of the optical amplifier. Using this fact it is shown in [16] that statistically,x is a random variable having a probability distribution known as the chi-squaredistribution [32]with the exact distribution depending upon whether the transmitted bit is a ”1” or a “0”. The authors of [16] then go on to to show how one can determine the optimal threshold setting Xth that minimizes bit error probability (BEP)p and how this minimum BEPp can be computed. It is common in practice however, to assume that x has a Gaussian distribution. It is shown in [16], that while this assumption leads to an incorrect determination of the thresholdxth, it does yield an expression for a B E P j that is close to the true value p . Since it is the BEP that is of primary interest in this chapter, we will throughout use the approximationj for p given by the Gaussian assumption, Le.,

zyxwvu zyxwvuts ( 17.138)

where Q is called the Q-factor and turns to be given by [I61

(1 7.139)

where y = E/No is the S N R , i.e., the ratio of average signal energy E (per message bit) to the single-sided power density NO of the colored noise within the optical bandwidth Bo,and where Be = 1/T is the electrical bandwidth of the signal. The Q-factor is often expressed in terms of a quantity termed as

954

zyxwvuts zyxwvut zyxwvuts zyxwvu zyxw P.Vijay Kumar et aL

zyxwv

the optical-signal-to-noiseratio (OSNR)w given by w=y-

Be BO

(17.140)

so that in terms of the OSNR o,the Q-factor is given by

zyxwvu (17.141)

For large values of OSNR, Le., w

>> 1, the Q-factor is approximately given by

(17.142)

We will from now on make the approximation (17.143) The combination of physical optical fiber communication channel and the receiver described above, has resulted in the creation of a binary-input, binaryoutput channel. It turns out [ 161 that without significant loss in accuracy, we may assume the transition probabilities in this binary-input, binary-output channel to be equal. This leads to the binary-symmetric-channel (BSC) model shown in Fig. 17.1. In the context of a BSC, the BEP parameterp given by (17.143) is called the crossoverprobabiZity. The coding gain delivered by an FEC code is measured as follows. We assume in what follows, that the goal is to achieve a message-bit error probability of 10-l~or less. Let Euncodeddenote the average energy per message bit required in the absence of coding to achieve the target error rate. Note that in the uncoded case, there is no distinction between transmitted and message bits and hence E-ded also represents the average energy per transmitted bit. Next, ktpcoded be the crossover probability of the BSC at which the code C is able to deliver the target message bit error rate of Let R be the rate of the code. As in the uncoded case, let E c d e d denote the average received energy per message bit. Since there are R message bits per transmitted bit in the coded case, we have that (17.144)

zyx zyx zyxwvuts zyxwv zyxwvutsrqpo zyx

17. Error-Control Coding Techniques and Applications

955

The coding gain r] of the code C of rate R is then given by r]

= lolog,,

-.

~uncoded

(17.145)

Ecoded

In the optical FEC literature, the coding gain is also referred to as the net effective coding gain. Let yiulcoded Quncoded and ycoded , Qcoded denote the uncoded and coded SNR and Q-factor, respectively, defined via Yuncoded

Euncoded Ecoded (17.146) ycoded = = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC NO No ~

The equations below express the coding gain in terms of SNR and @factor:

zyxwvut r]

hncoded

= lolog,, _ _

(17.148)

ycoded

(17.149)

Example 21

Let the target BER= 10-j. Then since

Let the code C have rate R = 8/9 and letproded=

erfc,(7.942) =

(17.150)

e@..,(4.265) =

(17.151)

we have that Qimcoded = 7.942 and Qc&d = 4.265 so that the (net effective) coding gain of the code is given by

r]

= 20 log,,

(Am) 8 7.942

= 4.89 dB.

(17.152)

We next present an upper bound to the maximum achievable coding gain under hard-decision decoding, of the optical channel described above. As noted, the optical channel can be viewed as a BSC with crossover probability p given by (17.153)

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Table 17.12 Maximum Achievable Coding Gain on the BSC

Rate R

Maximum Achievable Coding Gain (BSC) (dB)

0.85 0.90 0.95

11.17 10.59 9.69

where R is the rate of the code. It is possible using information theory [lo] to determine the smallest value of S N R required to guarantee reliable communication at rate R. This value is obtained by solving the equation R = -p log, p - (1 -p ) log, (1 -p ) ,

where p =

(Jx). (17.154)

Let as before, Yuncoded denote the SNR needed to achieve reliable communication in the absence of coding. Interpreting reliable communication as we can determine l/w,c&ed by solving communicating with BEP erf* (JG;;)

= 1045

(17.155)

Then lOlog,, (YuncodedlYmin) is the maximum achievable coding gain at rate R. The maximum achievable coding gains at rates R = 0.85,O.g and 0.95 are tabulated in Table 17.12. By replacing hard-decision decoding with soft-decision decoding, it may be possible to gain something on the order of an additional 1-2 dB depending upon the rate R of the code.

BCH Codes (Section 17.6) BCH codes fall into the class of cyclic binary codes. From an optical standpoint, these codes offer certain advantages. They are efficient in having small overhead for given error correction capability, and are flexible in that they offer a trade-off to be made between overhead and error correction capability. When operated over a BSC, the codes can be decoded by a hard-decision decoding algorithm of reasonable complexity. If the BCH code has length n and is capable of correcting t errors, then decoding can be accomplished using roughly 4nt + 4t2 finite field operations, for details see [24]. A tabular listing of the coding overheadcoding gain trade-off offered by BCH codes is provided in Table 17.13. In deriving the coding gain of the BCH

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Table 17.13 Lower Bound on Coding Gain of Some BCH Codes Length n

t

Rate R

Overhead o (99)

Coding Gain (d3B)

2047

27 18 9 51

0.85 0.90 0.95 0.85 0.90 0.95 0.99

17.64 11.11 5.26 17.64 11.11 5.26 0.60

8.02 7.41 6.17 8.60 8.09 7.03 1.59

2047 2047 4095 4095 4095 2047

34 17 1

codes, it was assumed that the bit error probability at the output of the BCH decoder is equal to the probability given in (17.4) of incorrectly decoding the transmitted codeword using the bounded-distance decoding algorithm. This assumption is equivalent to saying that whenever a codeword is incorrectly decoded, all the message bits are erroneously decoded. For this reason, the “coding gain” entries in Table 17.13 are lower bounds on the actual coding gain realized by the respective BCH code. Application of the bounded-distance decoding algorithm requires knowledge of the minimum distance of the code. In this case, the minimum distance was set equal to the value given by the BCH bound, see [26]. The lengths of the BCH codes were chosen to be 2047 and 4095. The first length is comparable to that of the binary code in the ITU G.975 Recommendation, which involves a length 255 RS code, which upon conversion to bits, results in a binary code of overall length 8 * 255 = 2040. At both lengths, three sample codes are presented, corresponding to the code rates in the range 0.85-0.95. The bottom entry in the table corresponds to a BCH code with parameter t = 1, which corresponds as indicated in Section 17.6, to a single-error-correcting,cyclic Hamming code of length 2047. In the optical communication literature, BCH codes have appeared as constituent codes in the construction of product codes (see below). Hamming codes were proposed for use on the fiber-optic channel in an early paper by Grover [141.

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Product Codes (Section 17.6.1)

Product codes offer the benefits of large block length combined with ease of decoding. However, if it is desired to construct a product code C of high rate R, this forces the constituent codes C1 and Cz to have even higher rates. Typically in such cases the minimum distance d = dldz of the resulting product code will be low.

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A product code construction for optical communication, based on a pair of linear binary codes having parameters [128,113,6] is described in [l]. These binary codes are obtained by appending an extra parity symbol to the [127,113,5]double-error-correctingBCH code. An iterative soft-decision decoding algorithm is used to decode the code, resulting in a coding gain estimated at 9.7dB. The rate R of this product BCH code equals 0.78.

Reed-Solomon Codes (Section 17.5) RS Codes in Practice

For optical fiber submarine communication systems, ITU Recommendation G.975 [17] recommends the use of a [255,239] Reed-Solomon code. In the absence of interleaving, this code is capable of correcting eight random byte errors within each codeword. As noted earlier, this translates into a maximum guaranteed burst error correction capability of 57 bits. Interleaving of code bits across codewordscan be used to increase the burst error correction capability at the expense of an increase in delay in decoding. ITU G.975 allows for interleaving up to depth 16, which would result in a maximal guaranteed burst error correction capability of 8 x (7 x 16+ 15)+ 1 = 1017 bits. Decoding RS Codes

As discussed in Section 17.5, an [n = 2m- 1,k] RS code with code symbols lying in Fp, has minimum distancedmin = n-k+ 1 and is capable of correcting t = L&in - 1/2J errors. The Berlekamp-Massey algorithm [4] can be used to decode the RS code with a running time on the order of n2. Peformance of RS Codes

We provide a tabular listing in Table 17.14 of the error-correction capability, rate, overhead and correspondingcoding gain of length 255 and 51 1 RS codes in Table 17.14. The coding gains shown in the table assume a target BER of In deriving the value of coding gain, it was assumed that the biterror probability at the output of the RS decoder was equal to the probability of incorrectly decoding the RS codeword under a bounded-distancedecoding algorithm. This is equivalent to assuming that a decoding error causes all the corresponding message bits to be incorrectly decoded. Thus the value appearing in the table under “coding gain” is in actuality, a lower bound to the codinggain. The probabilityof decodingerror under the bounded-distance decoding algorithm was determined using (17.4). The last entry in the table corresponds to the RS [255,239,17] code appearing in the ITU G.975 Recommendation [17].

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Table 17.14 Lower Bound on the Coding Gain of Some RS Codes Length n

t

Rate R

255 255 255 511 511 511 255

19 13 6 38 25 13 17

0.85 0.90 0.95 0.85 0.90 0.95 0.937

Overhead o (%) 17.64 11.11 5.26 17.64 11.11 5.26 6.72

Coding Gain (dB) 7.42 6.70

5.40

8.04 7.53 6.56 5.99

Concatenated Codes (Section 17.5.1) The discussion here is restricted to the technique of concatenating codes presented in Section 17.5.1. Concatenated codes offer the benefits of large length and the ability to handle isolated errors as well as error bursts. Large code lengths improve performance as these tend to average out distortions introduced by the channel, making them more predictable, and hence more correctable. As pointed out earlier, the overall rate of the concatenated codes is the product of the rates of the outer and inner codes. There is a downside to the use of concatenated codes. With concatenated codes, the dimension of the inner code equals the number of bits in one bit of the outer code and thus is typically around the value 8. At dimension 8, the maximum rate of a block code equals 8/9. To construct a concatenated code of overall high rate, one is forced to use a very high-rate RS code, which drives down the overall error correction capability. RS Codes in the Literature

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It is shown in [21] that an increase in coding gain of about 1.2dB is observed when the ITU-recommended [255,239] RS code is replaced by the more powerful [255,223] RS code having 14.3% overhead. Most of the error correction schemes discussed in OFC 2001 were based on the Reed-Solomon code. In [l], an FEC scheme featuring a pair of concatenated RS codes with an interleaver in between is examined (see Fig. 17.17). Note that the method of code concatenation described in [l] is different from that discussed in Section 17.5. Two different example RS code pairs are considered. The first pair consists of two identical [255,239] RS codes. The overhead of the concatenated code in this case is 13.8% and a 7.2dB coding gain was estimated at a BER of when the interleaver depth equaled 32 bytes. In the second example, the RS codes have parameters [255,239] and [255,223],resulting in an overall

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overhead of 22%. A 7.7 dB coding gain was estimated when an interleaver of depth 32 bytes was used. The author also points out that an increase in coding gain results when the concatenated code is iteratively decoded. A third method of concatenation involving RS codes is discussed in [39]. Here the constituent RS codes have parameters [255,239]and [239,223]for an overall overhead of 14%. The authors of [39] point out that when operating at high power levels, the increase in symbol rate arising from the use of FEC can result in increased nonlinear effects which tend to reduce the amount of coding gain. If this nonlinearity penalty is ignored, then the serial concatenation scheme is able to produce (roughly) 3 dB gain over the ITU recommendation. However, since the nonlinear penalty observed by the authors of [39] is about 1 dB, the net coding gain of approximately 7.5 dB observed at a BER of is roughly 2 dB higher than that afforded by the ITU-recommended code. In [46], a new approach for enhanced PMD mitigation using a combination of polarization scrambling and FEC is presented. Due to the slow temporal dynamics of PMD, current systems have to be designed for the worst-case PMD constellation. By introducing polarization scrambling, these dynamics are accelerated such that bad PMD constellations can &ect only a limited number of bits per FEC frame. These erroneous bits can be corrected by the FEC scheme. The FEC scheme discussed in the paper is a RS [255,239,17] code. In [49], an alternative scheme for mitigating PMD using FEC coding and a first-order compensator is presented. A [255,241] RS code is used as FEC code. The measured OSNR gain due to FEC (as compared to using only a first-order compensator), in the presence of only PMD and noise, at an outage probability of was 5.7 dB at 31 ps average PMD and increased to 7.5 dB at 43 ps average PMD. Convolutional Codes (Section 17.7) When the memory of the convolutional encoder is not too large, the Viterbi and BCJR algorithms present efficient means of accomplishing either hardor soft-decision decoding of these codes. However, convolutional codes are typically low-rate codes. It is possible to puncture a low-rate convolutional code [44] to obtain a high-rate code that is also easily decodable, but this puncturing tends to decrease the Hamming distance between codewords in the code.

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A discussion on the use of a convolutional code as an FEC scheme for a pulse-position modulation-based optical fiber communication system may be found in [121. Turbo Codes (Section 17.9)

Turbo codes are also known as parallel concatenated convolutional codes. These codes tend to have low rates and also low values of minimum distance. Although these codes perform excellently at low SNR, at high SNR, the low minimum distance of these codes tends to degrade performance. It is also possible to iteratively decode convolutional codes that are serially concatenated [8,15] and these tend to have larger minimum distance and may therefore be better suited to the optical channel where very low bit errors are desired. Thus, it is desirable to identify serially concatenated convolutional codes, that in addition to having large minimum distance, also offer high rate.

zyxw

Low-Density Parity-Check Codes (Section 17.10)

LDPC codes are potentially of interest in optical channels. Of course, one does need to identify suitable high-rate LDPC codes that also possess large minimum distance. Nonbinary LDPC codes [25] could also be of interest.

Acknowledgment The authors would like to thank Habong Chung, Manini Shah, Ted Darcie, and Jack Winters for some very useful discussions.

References

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[l] 0. Ait Sab, “FEC techniques in submarine transmission systems,” OFC 2001, V O ~ .2, pp. T~Fl.l-T~F1.3,2001. [2] S. Aji and R. J. McEliece, “The generalizeddistributive law,” IEEE Trans.Inform. n e o r y , vol. 46, no. 2, pp. 325-343, March 2000. [3] L. R. Bahl, J. Cocke, E Jelinek, and J. Raviv? “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Zkuns. Inform. Theory, vol. 20, pp. 284-287, March 1974. [4] E. R. Berlekamp, Algebraic Coding Theory, Aegean Park Press, Laguna Hills, 1984. [4b] E. R. Berlekamp, “Bounded distance +1 soft-decision ReedSolomon decoding,” IEEE Trans. Inform. Theory, vol. 42, pp. 704-720, May 1996. [5] G. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error correcting coding: Turbo codes,” in Proc. 1993 Znt. ConJ: Commun., Geneva, Switzerland, pp. 1064-1070, May 1993.

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[6] R. Blahut, Theoryandpractice o f E m r ControlCodes, Addison-Wesley, Reading, Massachusetts, 1983. [7] A. E. Brouwer and T. Verhoeff, “An updated table of minimum-distance bounds for binary linear codes,” IEEE Duns. Inform. Theory, vol. 39, no. 2, pp. 662476, March 1993. 181 K. Chugg, A. Anastasopoulos, and X. Chen, Iterative Detection, Kluwer Academic Publishers, Boston, 2001. [9] G. Clark and J. Cain, Error-Correction Coding for Digital Communications, Plenum Press, New York, 1981. [lo] T. M. Cover and J. A. Thomas, Elements ofhformation Theory,John Wiley, New York, 1991. [111 E. Desurvire, Erbium-Doped Fiber Ampl$ers-Principles and Applications, John Wiley & Sons, Inc., New York, 1994. [12] E. Forestieri, R. Ganaopadhyay, and G. Prati, “Performance of convolutional codes in a direct-detection optical PPM channel,” IEEE Trans. Comm., vol. 37, no. 12, pp. 1303-1317, December 1989. [131 R. G. Gallager, “Low-density parity-check codes,” IRE Trans. Inform. Theory, V O ~ .8, pp. 21-28, January 1962. [14] W. D. Grover, “Forward error correction in dispersion-limited lightwave systems,” J.Lightwave Tech.,vol. 6, pp. 643654, May 1988. [14b] V. Guruswami and M. Sadan, “Improved decoding of ReedSolomon and algebraic-geometrycodes,” IEEE Trans. Inform. Theory,vol. 45, no. 6, pp. 17571767, September, 1999. [151 C. Heegard and S. Wicker, lttrbo Coding,Kluwer Academic Publishers, Boston, 1998. [16] P. A. Humblet and M. Azizoglu, “On the bit error rate of lightwave systems with optical amplifiers,”J. Lightwave Tech., vol. 9, no. 11, pp. 1576-1582, November 1991. [17] International Telecommunication Union Telecommunication Standardization Sector (ITU-T), Series G: Transmission Systems and Media, Digital Systems and Networks, G.975. [18] G. Jacobsen, Noise in Digital Optical Transmission Systems, Artech House, Norwood, MA, 1994. [19] R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding, IEEE Press, New York, 1998. [20] L.G. Kazovsky, S. Benedetto, and A. Willner, Optical Fiber Communication Systems, Artech House Publishers, Boston, October 1996. [21] H. Kidorf, N. Ramanujam, I. Hayee, M. Nissov, J. X. Cai, B. Pedersen, A. Puc and C. Rivers, “Performanceimprovement in high capacity, ultra-long distance, WDM systems using forward error correction codes,” OFC ’00, vol. 3, pp. 274276,2000. [22] R. Kotter, “A fast parallel implementation of a Berlekamp-Massy algorithmfor algebraiegeometry codes,” IEEE Trans. Inform. Theory, vol. 44,no. 4, pp. 13531368, July 1998.

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[23] F. R. Kschischang, B. J. Frey and H.-A. Loeliger, “Factor graphs and the sumproduct algorithm,” LEEE Trans. Inform. %ov, vol. 47, no. 2, p p 498-519, February 2001. [24] S. Lin and D. J. Costello Jr., Error Conml Coding:Fundamentals andApplications, Prentice-Hall, Englewood Cliffs, New Jersey, 1983. [25] D. J. C. Mackay and M. Davey, “Evaluation of Gallager codes for short block length and high rate applications,” in IMA Workrrhop on Codes, Systems and Graphical Models, 1999. [26] E J. MacWilliamS and N. J. A. Sloane, The lIeo7-y of Emr-Comcting Codes, Amsterdam, North Holland, 1977. [27] D. Marcuse, “Derivation of analytical expression for the bit-error probability in lightwave systems with optical amplsers,” J. Lightwave Tech.,vol. 8 , no. 12, pp. 1816-1823, December 1990. [28] R. J. McEliece, D. J. C. Mackay, and J.-E Cheng, “Turbo decoding as an instance of Pearl’s belief propagation algorithms,” IEEE J. Select Areas Comm., vol. 16, pp. 140-152, February 1998. 1291 J. B. H. Peek, “Communications aspects of the compact disc digital audio system,” IEEE Comm.Mag., vol. 23, no. 2, pp. 7-15, February 1985. [30] L. C. Perez,J. Seghers, and D. J. Costello, “A distance spectrum interpretation of turbo codes,” IEEE Trans. Inform. Theory, vol. 42, no. 6, pp. 1698-1709, November 1996. [311 V.S.Pless and W. C. Huf€man,Handbook of Coding Theory,Elsevier, New York, 1998. [32] J. K. Proakis, Digital Communications,4th edn., McGraw-Hill, Boston, 2000. [33] A. Puc, E m o o t , A. Simons, and D. Wilson, “Concatenated FEC experiment over 5000 km long straight line WDM test bed,” OFC ’99, vol. 3, pp. 255-258, 1999. [34] R. Rarnaswami and N. Sivarajan, Optical Networks: A Practical Perspective, 2nd edn., Morgan Kaufmann Publishers, San Francisco, 2002. [35] T. J, Richardson and R. L. Urbanke, “The capacity of low-densityparity-check codes under message-passing decoding,” IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 599-618, February 2001. [36] I. S. Reed and X . Chen, Error-Conirol Coding for Data Networks, Kluwer Academic Publishers, Amsterdam, Netherlands, 2000. [37] 0. Sab and J. Fang, “Concatenated forward error correction schemes for longhaul DWDM optical transmission systems,” in Tech. Dig., 25th European Conf. on Optical Comm. (ECOC’99), Nice, France, Paper Th C2.4. [38] R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inform. Theory, vol. 27, pp. 533-547, September 1981. [39] H. Taga, H. Yarnauchi, T. Inoue, K. Goto, N. Edagawa, and M. Suzuki, “Performance improvement of highly nonlinear long distance optical fiber transmission system using novel high gain forward error correcting code,” OF% 2001, vol. 2, pp. T~F3.1-TuF3.3,2001.

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[40] M. Tomizawa, Y Yamabayashi, K. Murata, T. Ono, Y Kobayashi, and K. Hagimoto, “Forward error correcting codes in synchronous fiber optic transmission systems,” J. Lightwave Tech., vol. 15, no. 1, pp. 43-52, January 1997. [41] S.A. Vanstone and l? C. Van Oorschot,An Introduction to Error CorrectingCodes with applications, Kluwer Academic Publishers, Boston, 1989. [42] A. J. Viterbi, “Convolutional codes and their performance in communication systems,” ZEEE Trans. Comm.,vol. 19,pp. 751-772,Oct. 1971. [43] A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding, McGraw-Hill, New York, 1979. [44] S. B. Wicker, E m r Control Systems for Digital Communication and Storage, Prentice-Hall, Englewood Cliff$ New Jersey, 1995. [45] S. B. Wicker and V. K. Bhargava, Reed-Solomon Codes and n e i r Applications, IEEE Press, New York, June 1994. [46] B. Wedding and C. N. Haslach, “Enhanced PMD mitigation by polarization scrambling and forward error correction,” OFC 2001 , vol. 2, pp. WAA1.1WAA1.3,2001. [47] J. Winters, R. Gitlin, and S. Kasturia, “Reducing the effects of transmission impairments in digital fiber optic systems,” ZEEE Comm. Mag., pp. 68-76,June 1993. [48] J. -H. Wu and J. Wu, “Performance of Reed-Solomon codes in CPFSK coherent optical communications,” J. Opt. Comm.,vol. 13,pp. 19-22,March 1992. [49] Y Xie, 0.Yu, L.-S Yan, Q. H. Adamczyk, Z. Pan, S. Lee, A. E. Willner, and C. R. Menyuk, “Enhanced PMD mitigation using forward-error-correction coding and afirst-order compensator,” OFC2001, vol. 2,pp. WAA2.1-WAA2.3, 2001.

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Chapter 18 Equalization Techniques for Mitigating Transmission Impairments Moe Z. Win and Jack H. Winters AT&T Labs-Research, Middletown, New Jersey

Giorgio M. Vitetta University of Modena and Reggio Ernilia, Modena, Italy

18.1 Introduction Most current multi-gigabit-per-second digital fiber-optic systems use simple modulation and detection techniques such as on-off keying with matched-filter receiver techniques. However, more complex techniques such as equalization, error control coding, and/or multilevel signaling can be used in lightwave systems to significantly increase the data rate and/or reduce the effect of transmission impairments and improve performance, and, in many cases, can be easily implemented [l]. There are numerous sources of transmission impairments in lightwave systems. These include chromatic dispersion and polarization-mode dispersion (PMD) in the fiber, laser and fiber nonlinearities, nonideal receiver response, echo, and distortion caused by semiconductor optical amplifiers. Fortunately, there are also numerous techniques to reduce these impairments, including error control coding, equalization, and modulation techniques with multilevel signaling. These techniques can be used for upgrading existing systems (e.g., reducing chromatic dispersion and PMD in systems with previously installed fiber) or as an alternative to the use of more costly transmitters and receivers (e.g., using coding to permit less stringent laser specifications[2]). The purpose of this chapter is to provide an overview of equalization techniques, which become increasingly important as device technology matures, in which case substantial increases in performance (especially for already installed systems) may only be achieved through these techniques.' We will examine the prospects for the application of digital equalization techniques to overcome these impairments, where the improvement is large and the implementation is relatively simple.

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Error control coding techniques are discussed in Chapter 17 of this volume.

965 OPTICAL FIBER TELECOMMUNICATIONS, VOLUME IVB

Copyright Q 2002, Elsevier Science (USA). All rights of reproduction in any form reserved. ISBN 0-12-395173-9

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18.2 Transmission Impairments in Lightwave Systems

Here we classify the transmission impairments in lightwave systems into three categories: (1) signal distortion with a single signal, (2) signal distortion between multiple signals, and (3) noise. These impairments are discussed in the following text. Signal distortion (with a single signal) refers to those impairments that distort and broaden the width of pulses, resulting in intersymbol interference (ISI) that limits the maximum bit rate. The key feature of signal distortion is that it is deterministic (can be calculated directly from the impairment), i.e., the distortion is bit-pattern dependent with the distortion for a given fixed pattern (or slowly varying). This distortion results in a narrowing or closing of the received signal eye in the vertical direction (a pattern-dependent signal level at the detector sampling time) and/or the horizontal direction (a pattern-dependent timing jitter). The most extensively analyzed distortion is chromatic dispersion (see, e.g. [3,4]) in long-haul systems. This is material dispersion in the fiber which causes a delay in the received signal spectrum that varies with frequency. The dominant delay distortion is a linear delay of about 17p s k d n m at a wavelength of 1.55 p.m in a standard fiber. Thus, the delay variation is linear with distance, but is fixed for a given length of fiber, i.e., it doesn’t vary significantly with time. A second source of distortion is PMD in long-haul systems (see, e.g. [4--71). PMD is generated by signal delays that are polarization dependent. These delays increase with distance and also vary slowly with time (due to temperature and other variations) [6,8-lo]. At a given frequency, two orthogonal polarizations have different delays. Thus, a pulse with a sufficiently narrow frequency spectrum can be received as two pulses with a time delay between them. For a study of the combined effects of chromatic and polarization dispersion in lightwave systems, see [l 11. We group laser nonlinearities and receiver bandwidth limitations as the third source of distortion. Note that this impairment is independent of distance, and varies only due to aging. A fourth possible source of dispersion is a semiconductor optical amplifier [121 (fiber optical amplifiers have negligible distortion), and a fifth source is fiber nonlinearities [13,14]. The previous impairments all increase in severity with the signal bandwidth. This bandwidth is lower bounded by the data rate, but may be much larger than this because of other factors. For a multimode laser, both mode evolution and mode hopping [15,16] increase the bandwidth of the signal to several nanometers. For an analysis of equalization techniques in multimode fiber systems, see [ 171. For a single-frequency(mode) laser, the laser linewidth (due to phase noise) and chirping or relaxation oscillation (with direct modulation of the laser) increase the bandwidth of the signal. A single-frequencylaser has a nonzero linewidth because of random variations in the phase of the laser (phase noise), as discussed below. Chirp is the variation in carrier frequency

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of the laser caused by changes in drive-signal amplitude. Similarly, relaxation oscillation is the variation (undesired oscillation) in amplitude of the laser caused by changes in drive-signal amplitude. Note that chirp (and relaxation oscillation) can be avoided if the laser itself is used in the cw mode with the modulation being done with an external modulator. The second impairment is interference between multiple signals in different frequency bands on the same fiber. This can be due to nonlinearities in the fiber [13,14]or in semiconductor optical amplifiers [12]. In addition, in duplex systems, echo also can degrade performance. Note that these distortions are deterministic. The third class of transmission impairment we consider is noise, which varies randomly from bit to bit. Noise in the received signal consists of shot noise, thermal noise, and, with optical amplifiers, amplified spontaneous emission (ASE) noise. Shot noise is the quantum noise due to the fact that the received signal is actually a series of photons. The number of photons received during each symbol interval has a Poisson distribution and, therefore, the received signal level vanes randomly from symbol to symbol. Thermal noise is introduced by the receiver preamplifier, and is usually assumed to be additive, white Gaussian noise. ASE is additive Gaussian noise in the optical signal that increases with the gain of the amplifiers. Although ASE is random, with direct detection the electrical signal at the receiver contains a noise times signal component, and thus the ASE noise level in the received electrical signal is signal-level dependent. Without optical amplifiers, thermal noise is the major limitation with direct detection, whereas shot noise is the major limitation with coherent detection if the local oscillator power is large enough. With large local oscillator power, however, the high-intensity shot noise can also be modeled as additive, white Gaussian noise. With optical amplifiers, ASE usually dominates the shot and thermal noise. Another source of noise is phase noise, which, as discussed previously, is the random variation in phase of the transmitting laser. The main parameter of interest with phase noise is the width of the phase-noise spectrum relative to the data rate. Wider spectra (or linewidths) result in more signal dispersion as discussed earlier. Also, wider linewidths require wider receive filters (if all the signal energy in the received signal is to be detected), which results in higher thermal noise. However, wider linewidths (if wide enough) can have beneficial effects. In particular, with multimode lasers the distortion caused by PMD is fixed, rather than time varying as with single-frequency lasers, where the worst-case dispersion is significantly greater than the fixed value. Also, with multimode lasers, the distortion due to chromatic dispersion is linear in the received electrical signal rather than nonlinear with direct detection of a single-frequencylaser signal. Both of these effects can make compensation of the distortion much easier.

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Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

18.3 Modeling of Fiber-optic Communications Systems

In this chapter we focus on direct-detection, long-haul, fiber-optic systems, such as that illustrated in Fig. 18.1,and we provide a quantitative description of some of the impairment affecting them. In this figure, the non-return-to-zero (NRZ) input data stream, c(t), depending on a symbol sequence { c k } , is filtered by a transmit filter having frequency response H ~ c f ) The . filtered data signal s(t) directly modulates a single frequency laser (SFL). Alternatively, the data stream can be used, as in the dashed path, to drive an external modulator (EM) controlling the optical power in order to avoid laser nonlinearity. For direct modulation the transmitted signal x(t) can be expressed as

+

zyx zyx

x ( t ) = m e x p [j(2nfct LsO)

+ 4c(t)ll,

(18.1)

where P(t) is the optical power [depending on 491, fc is the lightwave frequency’ and L s ( t ) is the phase of s(t). The phase variation d&(t)/dt is commonly referred to as chirp, whereas the amplitude variation of P(t) versus Is(t)l (the laser power is proportional to its input current) is referred to as relaxation oscillation. Both effects can be considered as laser nonlinearities[181. With external modulation, the transmitted signal x ( t ) is given by

z

where $(t) is the laser phase noise. It is worth noting that, in this case, the transmitted power Ix(t)l’ is proportional to the amplitude of the data signal c(t).

w

c .

zyxwv

Fig. 18.1 Block diagram of a long-haul, direct-detectionfiber-optic system.

The lightwave frequency is related to the wavelength by a = c / f , where c is the speed of light in the fibers.

zy zy zyxwvu zy zyxwvu zyxwvut zyxw zyxw 18. Equalization Techniques

969

The transmitted optical signal feeds a fiber, having frequency response H c ( f ) , which can introduce chromatic dispersion and PMD [18-201. Chromaticdispersion will have a significantimpact on system performance if the laser frequency is different from that of zero dispersion of the fiber [corresponding to a wavelength equal to 1.3 Fm in a standard single-mode fiber (SMF)]. In this case, the main portion of the chromatic dispersion is linear delay distortion, and the frequency response of the fiber is

where

12

= TCD-L,

(18.4)

C

where L is the fiber length, D is the chromatic dispersion parameterY3c is the speed of the light in the fiber, and h(=c/f) is the wavelength. Then, in the presence of chromatic dispersion, the optical received signal is expressed by

where hc(t) is the channel impulse response of the fiber, and it is the inverse Fourier transform of H&) given in Eq. 18.3; and 03 denotes convolution operation. With direct detection, the electrical signalse(t) at the photodetector output is related to so(t) as se(f) = a o e Iso(t)l

29

(18.6)

where aoeis the conversion constant between the optical and the electrical signals. The PMD can be characterized in terms of first- and higher-order (in fi-equency) effects. The first-order effect can be simply represented as a delay in the signal in one polarization relative to the delay in the signal in the other one. Thus, with first-order polarization dispersion and direct detection, the electrical signal se(t) at the photodetector output is given by

zyxwvu

where a, is the ratio of the signal strengths in the two polarizations and t is the time delay between propagation in the two polarizations.

For example, D = 17ps/km/nm for a SMF and D = 2.6 ps/km/nm for non-zero-dispersionshifted (NZDS) fiber at A. = 1.55 Fm.

970

zyxw zyxwvuts zyxwvu zyxwvu Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

The electrical signal se(t) at the photodetector output is amplijied and filtered [the frequency response HRcf)incorporates the characteristics of frequency selectivity of both the amplijier and the receive filter] to increase the signal-to-noise ratio of the decision variable. This produces the output signal

where hR(t)is the inverseFourier transform ofHRcf). The signal v(t)is detected by comparing the signal level to a decision threshold during a short time interval at the peak opening of the eye in the received digital signal. The quality of data decisions can be seriously afTected by ISI, i.e., by interference coming from data transmitted in adjacent bit intervals. As will become clear in the following sections, a key issue in the effectiveness of equalizationtechniques against intersymbolinterferenceis the lineariiy of the intersymbol interference, i.e., the linear dependence of the data signal applied to the decision device on the transmitted data. In the communication system of Fig. 18.1, linear distortions include the receiver frequency response HR(J) and first-order PMD. Chromatic dispersion is a linear distortion in the optical fiber; however, whether this distortion produces a linear dependence on the transmitted data at the detector input [i.e., on v(t)] depends on the transmission and detection techniques used. Specifically, chromatic dispersion appears as linear distortion in a coherent receiver, but as long as the laser linewidth is smaller than the data rate, this form of dispersion appears as nonlinear in a direct detection system. This is a critical point and we concentrate on this below, for both direct and external modulation systems. In a direct detection system using external modulation, the transmitted and the received optical signals are expressed by Eqs. 18.2 and 18.5, respectively. Then, after direct detection, the received electrical signal se(t)is (see Eqs. 18.5 and 18.6)

zyxwv zyxw

se(t) = aoe ~ x ( t8 ) hc(t11' 3

(18.9)

and the filtered received signal v(t) is

or, in baseband notation,

If we consider long-haul systems operating at a data rate of several Gbps the phase noise bandwidth is typically below 50 MHz, so that the phase noise distortion exp [j4(t)] can be deemed approximately constant over the memory

zy zyxwvu zyxwvu zyxwvuts zyx 18. Equalization Techniques

971

of the channel impulse response hc(t). Under this assumption Eq. 18.11 simplifies as 2

v(t) 21 a o e I ~ ~ x P [ ~ ~9 - hc(t)[ u ~ )~9 IhR(t).

(18.12)

The last result shows that the IS1 in the electrical signal at the input of the decision device is the square of the IS1 in the optical signal so that the overall distortion is nonlinear. However, even with this nonlinearity, linear equalization can be partially effectivein reducing ISI. In general, linear equalization will not improve performance with quadratic distortion. However, in lightwave systems, if the signalingis binary, on-off keying is used and the major portion of the IS1 is due to a single adjacent symbol, a linear equalizer can still be effective. In fact, under these assumptions, it can be shown that the IS1 consists of a linear component and a nonlinear component, with the former larger than the latter, if the IS1 is reasonably small (see [21], pp. 720-721). If the laser is directly modulated and the nonlinear amplitude variations in the laser output signal are negligible, the transmitted signal (Eq. 18.1) can be rewritten as x(t>

+ 4 )+ 4C(t))l ,

m e x p[ j

(18.13)

where the phase distortion expL&(t)] is mainly due to the chirp effect. Substituting Eq. 18.13 into 18.10 produces

In this case, the chirp variations are not slow as the chirp bandwidth of lasers is typically larger than that of the data signal [21]. Then the simplificationleading fromEq. 18.11to 18.12cannotbeappliedtoEq. 18.14. However, for arapidly varying &(t) it can be easily shown that Eq. 18.14 may be approximated as v(t>

a o e IS(~)I

~9

I ~ ~ ( o~9I~’

t ) .

(18.15)

The last result shows that the IS1 in the electrical signal at the input of the decision device is the sum of the squares of the IS1 in the optical received signal. The distortion described by Eq. 18.15 may be viewed as due to a linear system having impulse response Ihc(t)12and fed by Is(t)l. The insight provided by Eq. 18.15 is still not accurate. In fact, the chirp effect in the transmitted signal is caused by the signal level changes and, therefore, does not result in fast phase variations over the entire duration of each symbol. In addition, symbols surrounded by identical symbolsmay not experience chirp. Therefore, in general, in direct modulation systems, the IS1 is a combination of linear (Eq. 18.15) and nonlinear distortion (Eq. 18.11). This explains why, in direct detection systems employingdirect modulation, linear equalizationtechniques can only be partially effective in reducing ISI.

972

zyxwv zyxw

Mae Z. Win, Jack H. Winters, and Giorgio M. Vitetta

18.4 Equalization Algorithms and Their Applications

zyxw zyxw zyx zyx zyxwvu

In this section we delve into the field of equalization algorithms for digital communications and illustrate the application of some of them in the field of optical communications systems. Throughout this section we assume that 1. data decisions are based on the sequence of samples {Vk A v(kT)} (T being the symbol interval equal to the sample interval) of the electrical signal v(t) in Fig. 18.1; 2. the dependence of { V k } on the symbol sequence {dk}is linear and the noise4 samples Ink} form an additive, white Gaussian noise (AWGN) sequence, i.e.,

(18.16)

where {ql}is the discrete-time overall channel impulse response (CIR) and Ink} is a sequence of iid (independent identical distributed) Gaussian random variables having zero mean and variance ai. The channel symbols, in general, belong to an M-ary alphabet, but in lightwave systems M = 2 is commonly used. Nonetheless, in this scenario multilevel signaling could be used to decrease the symbol rate by a factor log, M, this would entail a reduction in the amount of dispersion and decrease the noise power in the detector.

18.4.1 MLSD It is known from the Equalization theory that, if the CIR is known, maximum likelihood sequence detection (MLSD) is the optimum sequence detection technique because it minimizes the error probability in making a decision on the transmitted data sequence. The ML sequence detector for the symbol A sequence c = [CO, c1, . . .,~ ~ - evaluates 1 1 ~ the Euclidean distance metric [22] (18.17) k=O

for each possible trial sequence C, where the quantity (18.18)

Thermal noise when direct detection is employed.

zy zyxw zyxw zyxwvu zyxwv zyxw 18. Equalization Techniques

973

A [Cm-L+1, depends on the data sequence through the vector E::-L+l Z,,-L+~, ...,&IT of L consecutive data symbols only, with the convention that Ci = 0 for i < 0 or i > N . The metric A(E) in Eq. 18.17 can be also rewritten as N-1

zyxwv zyx (18.19)

k=O

where 2

A.(X&,Xk+l)

(18.20)

= IVk - Zk(E)l ,

and Xk is the integer representation of the symbol vector ( Z ~ - L + I , Z~-L+Z, . .., consisting of (L - 1) consecutive data symbols. Equations 18.19, 18.20 express the optimal metric as a summation of partial metrics {h(xk,x~+l)}.The k-th of these terms, A(xk,xk+l), depends on X k and xk+l, Le., on the vectors of consecutive trial symbols (C~-L+I,Zk-L+2,. ..,Z k - 1 ) and ( Z R - L + ~ , Z k - ~ + 3 , . . .,Zk), respectively. These considerations suggest a recursive formula for the evaluation of A@). In fact, if we define the recursive relation &I),

NEk)

= NEk-1)

+

(18.21)

A.(Xk,Xk+l),

with Ei A [Eo, Z1, . . .,Zi] EN-^ = E) and A(E0) = 0, then we have A(E) = A(&-1)

(18.22)

after N iterations. A geometrical representation to the problem of searching over the optimal metric can be given as follows. A trellis diagram with N, = ML-' states is drawn, as illustrated in Fig. 18.2 for M = 2 and L = 3. In the k-th interval

I

k-2

I

zyxwvutsr

k- 1

I

k

I

I

&+l

+

time

Fig. 18.2 Four-state trellis (M = 2 is assumed).

974

zyxwvutsr zyxw zyxw zyxw zyxwvut zyxwvut zyxwvu Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

each trellis state represents one of the N, possible values that Xk can take and is connected via M branches to the next states {xk+1}. The branch connecting the state that couples Xk and Xk+l is labeled by the trial symbol zk and by the quantity h (xk,xk+l), dubbed the brunch metric. In this context each trial sequence E has a one-to-one correspondence with a sequence of states in the trellis diagram, Le., with a distinct path in the trellis. Moreover, looking for the optimal sequence decision is equivalent to searchingthe minimum distance path in the trellis. Such a search does not require an exhaustive analysis of all the possible trial sequences, but can be carried out recursively employing the so-called Eterbi algorithm (VA) [23-251. We apply now the VA to implement the MLSD with known CIR. The VA operates on the state trellis, which has already been defined. In the k-th symbolinterval, each branch, labeled by the pair of states (Xk,x~+I), is assigned the correspondingbranch metric h(xk,xk+l). The VAS task is to find the path (sequence of branches) through the trellis with smallest metric (i.e., the shortest path). The VA accomplishes this by (see Fig. 18.3):

1. maintaining one suwivor path per state Xk in the k-th symbol interval; 2. extending these paths one step along all the M branches (labeled by E,) emanating from it; 3. pruning these back by only retaining the path with smallest5metric A(&) into each state x~+I.

zyxwv

I I

I

I

I

k-2

k-1

k

k+l

I

*

time

Fig. 18.3 Example of time evolution of the VA. When a metric has to be maximized, the VA should be supplied with the negative metric instead.

zy zyxwvu zyx

zyxwvu zyxwvut zyxwv zyxw zyxw 18. EqualizationTechniques

975

In the k-th symbol interval, then, the Viterbi algorithm keeps track only of the one path (the so-called survivor) leading to each state Xk. Such a path, denoted as 2(xk), is the sequence of consecutive states belonging to the path, and it is characterized by an accumulated metric A(xk). The VAprocedure can be summarized in the following steps (k denotes the time variable): 1. Set

k = 0, ~ ( x o= ) (xo),

A(XO)= 0

(18.23)

to initialize the algorithm; 2. Repeat steps 3-7 until k = N ; 3. Extend path metrics according to Eq. 18.22, that is

for d l the allowed state transitions X k + xk+l; 4. For each destination state xk+l ,find the best (minimum metric) incoming path over all the previous states

2 k = arg min A(x,+l)

(18.25)

xk

5. Update and store survivor paths as

6. Store the new survivor metrics as

7. Set k = k + 1 (increment time counter); 8. Detect the ML decision for the symbol sequence as that associated with the survivor path ~ ( x N with ) minimum metric A ( q ) (termination). It is worth noting that (a) branch metrics evaluated for state transitions inconsistent with known (i.e., training or pilot) symbols are set to a large value (virtually inilnite), and (b) in any real implementation data estimates are generated by the VA with a fixed decision delay, K [23] by tracing back from the survivor with instantaneously best metric. In practice, however, there is little degradation if the final decisions are taken after a decision delay of about 5-10 L.

976

zyxwvutsr zyxwvu Moe 2.Win, Jack H. Winters, and Giorgio M. Vitetta

zyx zy zyxwvu zyxwvu

MLSD can be difficult to implement in optical communication systems, even though high-speed VLSI implementations of the VA have been available since the 1990s [26]. The complexity of the VA is governed by the total number of branches, which grows exponentially with the length of CIR. Therefore, for communications channels with IS1 over many symbols @e., large L) the VA is unreasonably complicated. Various schemes to reduce the VA's complexity have been proposed, and they usually involve searching only part of the trellis [27] or simplifying the trellis. In the latter case delayed decision feedback sequence detection (DDFSD) [28] or reduced state sequence detection (RSSD) [29] techniques can be employed. Both techniques exploit the typical behavior of the CIR, which may have a peak around its middle, referred to as the cursor, energy tailing away beforehand, the precursor, and energy tailing away afterwards, the postcursor (see Fig. 18.4). In DDFSD, a reduced state trellis is constructed. States in the VA's trellis, {xk = (Z,+L+~, . . .,&-I)), are collapsed together if they share the same "older" symbols. In other words, the DDFSD states are defined by the state vector

4= S

(Lm+l,.

.., Zk-1)

(18.28)

where Lm 5 L. The state definition leads to a trellis again, with branches and branch metrics associated with them. Trellis processing closely follows the VA, with survivor paths and survivor path metrics. For each state and state transition labeled by the channel symbol Ek, the symbols required in the evaluation of the branch metric (Eq. 18.20) are obtained partly from the DDFSD state xf and partly (those unspecified by the state from the corresponding survivor's path i This method represents an application of the decisionfeedback concept. As a first approximation, LRS is selected to span the precursor and cursor, and decision feedback is used for the postcursor. RSSD is an elegant but minor extension of DDFSD. Instead of a full trellis for the precursor and a single decision history per survivor for the postcursor,

4 '

4')

(e).

1

r

1

A

-

zyxwvuts r

zyxwvutsr zyxwvutsrq 0

0

0

2

1

' * '

...

L-2

k

zyx zyxwvuts 18. Equalization Techniques

977

set partitioning principles [30] are applied to steadily reduce the number of hypothesized symbols as more of the received pulse arrives The general idea behind it is to gracefully degrade performance with decreasing LRs. Another way of working around a large L is to adaptively prefilter the signal to obtain shorter duration of the overall impulse response by using a linear equalizer [31,32] or a decision feedback equalizer [33-351. A MLSD based on the VA is then applied to this prefiltered signal. However, the prefilter colors the additive noise, thereby reducing performance if noise correlation is not taken into account. There are also other techniques to implement simplified, approximate versions of MLSD that may be practical in optical systems operating at high data rates, if the sequence length N is small. One of these is a block-oriented ML detector [36] which aims at determining the bits of a short block of length N , based on N consecutive received signal samples. Specifically, the detector compares blocks of N received signal samples to each of the 2N (M = 2 is assumed) possible (stored) signal sample vectors, each corresponding to one of the possible 2N bit vectors. The performance of this detector is degraded by the edge effects of ISI. In fact, since ML detection makes decisions on block of N bits from N signal samples referring to these bits, bits at the edge of the block are more likely to be detected in error because of the IS1 coming from bits outside the block.

zyx zyxw zyx zyxwv

18.4.2 DECISION FEEDBACK EQUALIZATION

The decision feedback equalizer (DFE) can be viewed as the prefilter plus DDFSD, where LRS = 1 so that is an empty state vector. The trellis comprises one state with M branches, each returning to the same state. However, the DFE has a preeminent role in communications due to its nice balance between complexity and performance. Therefore we study it as a separate structure [37-391. In the DFE terminology, the prefilter is the feedforward filter (FFF), and the decision feedback of DDFSD is implemented via a feedback filter (FBF), as illustrated in Fig. 18.5. Since a DFE's trellis has one state, a memoryless quantizer is used as a decision device. As a simplification the FFF in an Lftap T-spaced FIR filter reduces precursor ISI, whereas the FBF an Ld-tap T-spaced FIR filter reduces the resulting postcursor ISI. The impulse responses of the FFF and the FBF are given by

4'

(18.29) and T

cIA [ & , 4 , . . . , & d, - ~ ]

(18.30)

respectively. The feedback filter is always symbol spaced (i.e., the tap spacing is equal to the symbol interval), whereas the feedforward filter may be

978

zyx zyxwvutsr

zyx zyxw zyx

Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

I

zyxwv I II

c

I

...

FBF

zyxwv zyxwvut I

I

Fig. 18.5 The decision feedback equalizer. The function Q( denotes the quantizer. a)

fractionally spaced (i.e.ythe tap spacing is a fraction of the symbol interval) [40, 411. If the FFF is fractionally spaced, r] samples per symbol interval are processed by the equalization algorithm. Then the received sample sequence turns into {Vk A v(kT,,)},where typically T,, 4 T/r], and r] is the number of samples per symbol. This increases the BW of the FFF to accommodate the signal whose BW is larger than the symbol rate [42]. In the k-th symbolinterval the received samples within the span of the FFF are expressed by (a symbol spaced FFF is assumed for simplicity) T

A

y k = [ v k - L J + l , vk-LJ+Zy

3

vk-1]

-

In any DFE, there is always a delay A (in symbol periods) between the first received sample containing energy from a symbol and that symbol being detected. Such a parameter is the decision delay or lag. Therefore, the past decision vector 4 employed in the FBF is given by ek

= [;k-A-Ld,

;k+l-A-&,..

.

Y

T

Zk-A-l]

Then from Fig. 18.5, the input to the DFE's quantizer, Ik

= fHVk - dH&.

-

(18.31)

e(-),is (18.32)

Ideally we would like to have (18.33) where A must satisfy 0 5 A

.e L

+ Lf - 2.

18. Equalization Techniques

979

zy

* >- 0.5 1.0

0.5

zyxwvutsrq zyxwvutsrq 2

zyxwvuts zyx .

0.5

-0.5

-

::

zyxwv

1

4

6

8

1 0 k

Fig. 18.6 Impulse responses involved in a DFE: (a) channel; (b) feedfoward filter; (c) cascade of CIR and FFF; (d) feedback filter; (e) channel and DFE.

zyxw

The DFE’s performance is optimized by appropriately choosing Lf , A, f and d. In known channels, Lf and L d should be chosen to be as large as possible (i.e., infinite, in which case A becomes arbitrary). It is usual to use a hard, nearest-neighbor quantizer (slicer) for Q( .) and then design the DFE’s filters so as to minimize the mean square error (MSE) between the quantizer’s input I k and its desired output C k - A under the assumption of correct past decisions, &, = c,,,: the corresponding equalizer is called minimum mean square error-decision feedback (MMSE-DFE) [43,44]. The “correct past decision” assumption has been repeatedly invoked, but it is important to recognize it as a strong assumption. In low SNR, noise may cause a “primary” error, which is fed back into the FBF. Instead of canceling Ld,

e(.),

980

Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

zyxw

the postcursor, the FBF can actually enhance it; in turn, this increases the likelihood of subsequent, “secondary” errors [45,46]. Since the beginning of the 199Os, DFE techniques have been proposed for use in long-haul direct-detection fiber-optic systems where it was shown that they can have more than double the maximum data rate of gigabit-per-second (Gbps) lightwave systems by canceling postcursors’ IS1 [47]. In this context, DFE can be implemented by the more general technique known as nonlinear cancellation (NLC) [47]. NLC can handle IS1 that arises from a variety of impairments, such as transmit laser chirp, chromatic dispersion, PMD, and nonideal receiver frequency response. The first implementation techniques for this equalizationstrategy are illustrated in [48]. Here, the proposed solution is based on a bank of 2 L d threshold detectors (where L d is the number of bits fed back), each having a difTerent threshold level that depends on the hypothesized postcursor ISI. The selection of the detector corresponding to the vector of selected symbols occurs after threshold detection. This is accomplished by choosing the output of the detector corresponding to the correct threshold rather than switching analog signals at the data rate in the feedback loop [47]. Since at high data rates, the propagation delay of the detector can exceed one symbol, another advantage of NLC is that the propagation delay of the detector is not an issue. Even if not shown in [48], a nonlinear canceler can also incorporate a feedforward section to mitigate the precursor IS1 (see, for instance, [21], p. 713). Due to the progress in high-speed integrated cicuits (ICs) [49], the realization of tunable analog linear and nonlinear filter functions has become feasible for high bit rates [50]. The electronic IC system for decision feedback equalizationof 10-Gbps signals is described in [50]. It is based on an eight-tap transversal filter (FFF) and a one-tap feedback section, and its tap weights are adjusted by external tuning voltages. It is interesting to note that in such a device (as in all the other linear and nonlinear electrical equalizers designed until now for optical communications),the FFF is an analog transversal filter, i.e., the input signal of the decision device is

zyxwvu zyxwvu zyxw zyxwvu I

(18.34)

where {fk}are the tap coefficients,T,,is the delay introducedby each stage in the tapped delay line (in [50],T,, = 55 ps, whereas the bit period is T = 100ps). The analog signal i(t) is sampled every T sec (ideally at the instant of maximum eye opening) in the decision circuit and each bit decision is fed back in a unique stage of the FBF. The equalizer, consisting of two ICs (one for the feedforward section and the other one for the feedback section), has been successfully tested in transmission experiments using standard SMF. It has been shown that the power penalties of long-distance links, mainly induced by the chromatic dispersion, can be substantially reduced.

zy zyxwvu zyxwvu zyxw 18. Equalization Techniques

981

With data rates larger than 10Gbps (say 40Gbps), PMD of the fiber becomes a serious impairment, and components and solutions for coping with this distortion become crucial issues. Moreover, since installed fibers are more or less exposed to environmental temperature changes, the actual PMD and, with that, the associated bit error rate (BER), fluctuates with time leading to outage events [51]. Since PMD is an optical property of the fiber, the most straightforward approach to overcome this limitation is the use of optical devices known as optical PMD compensators. However, in order to avoid the incorporation of slow bulk optical components, it is useful to move part of the processing from the optical domain to the more flexible electrical domain. For this reason opto-electronic compensators based on the use of multiple photo diodes have been proposed [52,53]. A winning alternative to optical and opto-electronic devices is the use of electrical equalizers (as electronic PMD mitigators), which offer the potential of a compact integration within the electronics of the optical receiver. Linear [54,55] (see the following section) and, in particular, decision feedback equalizers [56,57], have been proposed for combating PMD. A comparison between different equalization structures is illustrated in [56,58], where it is shown that the DFE (e.g., the concatenation of feedforward transversal filter with a one-tap feedback section) is the technical solution exhibiting the lowest residual penalty in high-data-rate systems. Once again, these results show the potential of postdetection signal processing for the reduction of distortion induced in the optical domain.

18.4.3 LINEAR EQUALIZATION The linear equalizer (LE) is a linear, normally transversal filter followed by a nearest-neighborquantizer. The LE is the simplestequalizer and, arguably, the most intuitiveas it is an adaptive filter compensatingfor the channel distortion. Its taps may be T-spaced or fractionally spaced (T,-spaced) [39]. The T-spaced structure of the LE is illustrated in Fig. 18.7.

zyxwvu

Fig. 18.7 Structure of the symbol-spacedLE.

982

zyxw zyxwvutsrq Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

LEs are also distinguishedaccordingto their design criteria. In applications, two criteria are usually considered zero forcing6 (ZF) and minimum mean square error (MMSE). The ZF method neglects the presence of the channel noise and minimizes the IS1 contribution in the equalizer time span. This is undesirable since the communication channel may be characterized by multiple, deep notches in frequency. In inverting these, a ZF equalizer inevitably causes undue considerable noise amplification (noise enhacement) and a degraded BER. For this reason MMSE is usually a better design criterion, where the combination of noise and IS1 are minimized. In the k-th symbol interval, the received samples within the span of an Lf-tap LE are expressed by (a symbol spaced LE is assumed for simplicity)

zyxw

Then the input to the quantizer of LE is given by

where f is defined in (Eq. 18.29).Then a ZF LE is designed according to (18.37) and MMSE LE is designed according to

zyxwvu (18.38)

where E{-}denotes expectation operator, i and A are trial values o f f and A, respectively, and Zk is the useful component of v k . At high data rates, symbol delays can be implemented by short transmission lines, and the taps can be implementedby variable gains amplifiers. Linear equalizerscan be used inserted between the receiver filter and the threshold detector of an optical receiver [42,54,59,60]. In any practical application the coefficients of an LE or a DFE must be adapted to the channel state. Equalizer tap weights can be adapted using either a single-step technique such as direct matrix inversion (DMI) or a gradient search algorithm (GSA) [21,61]. Although GSAs are much slower to convergethan the DMI technique, they are generally suitable for fiber-optic systems since their computational The ZF criterion can be also applied in the design of the DFE equalizers In this case the noise contribution in Eq. 18.32 must be neglected.

zyxw zy

18. Equalization Techniques

983

complexity is much lower, while the impairment changes with rate much less than the transmission rate. GSAs include both blind algorithms (see the following section) such as the constant modulus algorithm (CMA) and the least-mean-square (LMS) algorithm [62]or the zero-forcing algorithm [63]in conjunction with a training sequence. It is worth noting that the ZF algorithm minimizes the so-called peak distortion (ie., maximizes the opening of the eye diagram in the absence of thermal noise), whereas the MMSE algorithm minimizes the variance of the error signal. With modest amounts of linear IS1 and thermal noise, both equalizers produce distortion-free outputs and provide performance close to the optimum. To understand the technical problems associated with the use of adaptive LEs in optical systems, let us focus on the celebrated LMS and on the ZF algorithms. They can be expressed as [39] (real signals are assumed here) (18.39) and (18.40)

zyxwvutsrqpon

respectively, where f k is the tap vector in the k-th signaling interval, I is the step size (controlling the convergence speed and the stability of the algorithm), Ck = ICk-A-1, ck-A-2,. . . ,Ck-A-L, lT is a past data vector, and

is the error signal. In order to compute (Eqs. 18.39 and 18.40) the data symbols or very reliable estimates of them have to be available. This is generally achieved by initially using a known sequence to train the equalizer and, after the acquisition period of the equalizer, switch to data decision. In long-haul optical systems operating at high data rates, generating analog samples of the signals may be costly, and therefore may not be desirable. Thus single-bitaccuracy samples (correspondingto h l ) should be used wherever possible. Then an alternative to Eq. 18.39 is provided by the so-called sgn-sgn least mean square algorithm, fLMS kfl

zyx

= fLMS k - s&ekl

and the modified zero-forcing algorithm,

sgn[vkl,

ffT1 = fF - h Sgn[ek]ck.

(1 8.42)

(18.43)

Quantizing the signal samples reduces the rate of convergence of the algorithm. This is not a major concern, since channel impairments are expected to change

984

zyx zyxwvutsr Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

very slowly on optical channels. Of more concern, however, especially for the sgn-sgn LMS, are the steady-state weights. In fact, since the direction of the correction term sgn[vk] in Eq. 18.42 is different from that for the LMS (vk in Eq. 18.39), the equalizer taps may settle at different values in the two cases. On the other hand, the same considerations do not apply to the quantized version of the Z F algorithm (Eq. 18.43). In fact, the direction of the correction term in Eq. 18.43 is the same as for the unquantized algorithm (Eq. 18.40), and the former algorithm converges to the same weights as the latter when the eye diagram of the received signal is open (neither algorithm, however, works when the eye is closed). As already stated previously, the (unquantized) MMSE algorithm outperforms the ZF one when thermal noise is present and the improvement of MMSE increases with the noise power. Furthermore, unlike the Z F algorithm, when supplied with a training sequence the LMS algorithms can also work when the eye of the receiver is closed. However, the implementationpracticalities of Gpbs operation can preclude analog sampling of the signal and, as already mentioned, the quantized version of the LMS is not guaranteed to converge to the correct weights. In the DFE section it has been pointed out that modern advances in electronic technology have changed the perspective in the implementation of the equalizers. Linear electronic equalization can overcome the link-length limitation imposed by chromatic dispersion over more than 100-km SMF [60, 64-66]. An electronic LE compensating for PMD and chromatic dispersion after 100-km SMF at 10 Gbps is illustrated in [67]. In this case, a three-tap LE is realized with commercially available coaxial components, power splitters, tunable phase shifters, and broadband amplifiers and is preceded by an electrical low-pass filter using the dispersion supported transmission method to compensate for the chromatic dispersion of the fiber [65]. The magnitude of the tap weights in the LE is adjusted by the coaxial attenuator. This seemingly simple solution is shown to reduce the power penalty due to transmission via very high PMD fiber by 8.2 dB. A similar equalization scheme with the same penalty reduction is illustrated in [55]. More recently, advances in SiGe technology [68] have made it possible to implement integrated circuits, that can realize electronic processing functions for 1040-Gbps optical transmission systems. In particular, it has been possible to implement IC LEs using the continuous time LMS algorithm (Eq. 18.39) for tap adaptation [69]. This solution exhibits excellent properties in terms of speed of convergence as it can accommodateboth the slow environmental temperature changes (acting on the PMD properties) and the fast events (within a time scale of a few milliseconds) due to patch-cord moving or mechanical vibrations [57]. Further applications of SiGe tunable electronic equalizers in optical communications over SMF are illustrated in [70].

zyx

zyxw zyx

18. Equalization Techniques

18.5 Other Equalization Algorithms

985

zyxwvutsr zyxwvu zyxw

In the previous section the most important linear (LE) and nonlinear (MLSD, DFE) equalization techniques for optical communicationshave been described. In this section we briefly describe other classes of equalization algorithms that might be used in future optical systems.

18.5.1 MAPSD

zy zyxw zyxw

All previous equalization strategies can be easily incorporated in the receiver structure of Fig. 18.1. Whatever the selected solution, the detector will make a decision on each symbol of the sequence { c k } without providing any information about the reliability of the decision itself to a decoder. Reliability information can be extremely useful if channel coding is employed [71], since it can substantially improve the error performance of the system. If a vector v depending on the data vector symbol sequence c [coy c1, . .. ,cnr-11~is processed by the receiver, reliability (or SOB) information about the transmitted data is produced if the a posteriori probabilities (APPs) P(

~= k C~V),

k = 0,1, ...,N - 1

(18.44)

are evaluated for any possible choice of the symbol 2. These probabilities can be generated resorting to the so-called maximum a posteriori symbol detection (MAPSD) strategy which represent the optimum symboZ detection technique since it minimizes the probability of taking a wrong decision on each transmitted symbol. When the MAP criterion replaces the ML criterion, the MAP forwardbackward algorithm (MAP-FBA)replaces the VA [72]. The forward-backward procedure operates on the same state trellis as the VA, but it efficiently calculates the MAP symbol probabilities, instead of just finding the ML sequence. The forward-backward algorithm requires the complete vector v of received samples to be available before decisions can be made. If a large decision delay is to be avoided, a near-optimal,Jixed-Zag (forward-only) MAP (MAP-FLA) strategy can be adopted [73]. However, both the FB and FL MAP algorithms work with likelihoods rather than log-likelihoods,so that their branch metrics are generally more expensive to compute and their operations are multiplication and addition instead of the addition and minimization characterizing the Viterbi algorithm. Much work on reduced complexity implementations has been undertaken (see [22] and references therein), but this is outside the scope of this chapter. Let us now briefly describe the MAP algorithms mentioned above.

986

zyxwvutsr zyxwv zy

zyxw zyxw zy zyxwvu zy

Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

The Forward-Backward Algorithm

The FBA seeks the probabilities (Eq. 18.44) for any possible trial symbol Z. transmitted in the k-th signaling interval. As in Section 18.4.1 it is assumed here that the channel memory is not longer than (L - 1) symbol periods, so that any received signal sample depends on L consecutive channel symbols at most. Then the FBA operates on the same ML-'-state trellis as the VA and performs two basic recursions on the stream of received signal samples v in order to evaluate the probabilities (Eq. 18.44). In the following it is useful to keep in mind that: 1. each node in the trellis has M input branches and M output branches, with a branch correspondingto one of the A4 data symbols; 2. it is useful to associate the computed values of the FBA with nodes, states, and transitions in the trellis.

The evaluation of Eq. 18.44 requires the computation of intermediate quantities, known as state transition probabilities. Given the trellis states xk and xk+1 in the k-th and in the (k 1)-th symbol interval, respectively, the correspondingstate transitionprobability is given by

+

and equals zero if the states are not connected. This quantity can be evaluated as (18.46)

where C (xk, xk+l)is the subset (of the set C { E } ) consisting of all the possible trial sequencesthat traverse the trellis branch connecting the statesxk andxk+l, as illustrated in Fig. 18.8. In [22] it is proved that, given the signal model (Eq. 18.16) and under the assumption of independent symbols, Eq. 18.46 can be also rewritten as

where

zy

z

18. Equalization Techniques

987

J 0 0 0 0 0 0 0 0 0 I

k-2

4

zyxw 0 0

oXk-l

zyxwvuts zyxwvut

zyx

I

I

I

I

I I

k-1

k

Hl

k+2

k+3

time

Fig. 18.8 Subset Ck(xk,xk+l) of all the possible trial sequences traversing the trellis branch between the states x k and x k + l . M = 2 and L = 2 are assumed.

is a weightfunction depending on trellis branch connecting the states Xk and is the probability7of the event (Ck = &} and

Xk+l, p(&,)

Equation 18.47 shows that the evaluation of the state transition probabilities requires the computation of (a) the sum of the products of the weights associated with all the paths containing the branch going out of Xk and enteringXk+l (see the numerator), and (b) the sum of the products of the weights associated with all the paths in the trellis (see the denominator). A computationally efficient method to solve this problem is the following. Let us define the quantities {a!k(Xk)] and (Bk(Xk)] through the recursive formula ak(xk)= ~ak-1(xk-1)' yk(xk-l,xk)

(18.50)

xk

withk= 1y2y...,N-1,and Pk(xk) =

Bk+I(xk+l)

'

yk(xk,xk+l)

(18.51)

Xk+l

with k = N - 2, N - 3, ...,0, respectively. Here it is assumed that {ao(xo)) and {/~N-~(XN-I)} are known initial conditions. Such a probability is equal to 1/M for equiprobable channel symbols.

988

zyxwvu zyx zyxw zyxwvutsr zyxwv Moe Z. Win, Jack € Winters, I. and Giorgio M. Vitetta

The quantity a&) expresses the sum of the products of the weights along all paths originatingfrom all the possible past initial states { X O } and terminating at Xk in the k-th signaling interval. Similarly, /?k(Xk) represents the sum of the products of the weights along all paths ending in all the possible future terminal states {XN-l} and originating from Xk in the k-th signaling interval. Then the numerator of Eq. 18.47 can be evaluated as

zyxwvu N-1

whereas its denominator as

(18.53)

so that (18.54) The last result shows that all that is needed for the evaluation of the state transition probabilities are the quantities (a,&k, xk+l)}, computed as in Eq. 18.52. This, in turn, requires a forward (Eq. 18.50) and a backward recursion (Eq. 18.51) involving all the trellis states in each signaling interval, as illustrated in Fig. 18.9. It is worth noting that both recursions over the trellis only need to be performed once. For demodulation purposes, the quantity of interest is P(& Iv) for any possible value of the channel symbol &. This probability can be calculated by summing all the state transition probabilities (Eq. 18.54) that correspond to branches associated with the symbol Ek. Then if we define the set S(&) of all state transitions (xk,xk+l), such that the channel symbol labeling the correspondingbranch is &, P (Zklv) can be evaluated as

zyxw zyxwv

Finally, the FBA can be summarized in the following steps: 1. Evaluate the conditional probabilities { yk(xk, xk+l)} for all the trellis branches using Eqs 18.48 and 18.49; 2. Initialize the forward recursion setting

k = 1,

ao(x0) = 1

(18.56)

18. Equalization Techniques

I

I

989

z

zyxwvuts 1

. k

I

I

I

4

5

a,@>

I

I

y,(o,o)

I

zy zyxw

zyxwv

zyxwv zyxw zyx zyxwv I

6

P&)

0- o-o0/ o,(O,o)=a,(O).Y 3(0,0>.P4(0>

1 :

I

7

(c)

(4

?ig. 18.9 Application of the FBA to a two-state trellis (a) (A4 = 2, L = 1). The pantities {ak(xk)J and (Bk(xk)) are computed recursively in the forward (b) and in he backward (c) recursion, respectively, using the branch probabilities {yk(xk,xk+l)). ;inally, (d) the state transition probabilities {q(xk,xk+l)J are evaluated according to 3q. 18.52.

3. Repeat steps 4-5 until k = N ; 4. Compute and store the forward path probabilities ( a k ( x k ) ) using Eq. 18.50; 5 . Set k = k 1; 6 . Initialize the backward recursion setting

+

(18.57)

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zyx zyxwvutsr zyxwvuts zyxwv Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

7. Repeat steps 8-9 until k = 0; 8. Compute and store the backward path probabilities {Pk(Xk)}using

zyxw zyxwv

Eq. 18.51; 9. S e t k = k - 1; 10. For each trellis branch compute the quantity uk (&&+I) using Eq. 18.52; 11. Evaluate the a posteriori symbol probabilities {P (Zklv)} by means of Eq. 18.55.

Fixed-Lag MAPSD

The forward-backwardalgorithm is suited to short burst transmissionbecause, otherwise, its delay and storage requirements are unsatisfactory. The MAP makes decisions at a fixed ked-lag algorithm (MAP-FLA) detector [73,74] lag of Lfl symbols from the current received samples, as (18.58)

where the notation x,”denotes the vector [xa,xn+l,. . .,xblT. The parameter Lfl is akin to the decision delay in the VA, and so, for effectively optimal performance, it is expected to be as high as 5L or 7L.The decision rule may

be implemented via two good algorithms, both requiring a single forward has a pass only. The newer one, dubbed soft-output algorithm (or OSA) [75], smaller computationalcomplexity than the older one [73], since the number of quantities to be stored and recursively updated increases linearly, rather than exponentially, with the decision delay. A description of the MAP-FLA is not provided here. However, it is important, at this stage, to make some comments about the VA, the MAP-FLAYand the MAP-FBA. Each of these algorithms can be employed for the detection of data sequences in the presence of ISI. Among these algorithms, however, the VA has the smallest complexity and this makes it the most reasonable choice in uncoded communication systems where soft output information is not required. The MAP algorithms have the following relevant disadvantages: (1) they require the knowledge of the noise variance; and (2) they have large memory and computation requirements. In particular, as already stated, MAP algorithms accomplish computations in the probability, instead of the logarithm domain and, consequently, require a large number of multiply and exponential operations. The MAP-FBA detector performs two recursionsand, consequently, it operates in block mode. It memorizes all the received signal samples of each block and afterwards processes them. Its memory requirement grows linearly with the sequence length so that only short data sequences should be processed. The MAP-FLA requires only a forward recursion, so that it can operate in continuous-mode. Both the memory and computational

zy zyx zyxw

18. Equalization Techniques

991

requirements, however, grow exponentially with the decision delay so that this parameter should be kept to minimum. For this reason the FBA may have smaller computational requirements than the FLA. 18.5.2 BLIND TECHNIQUES AND CMA

The LE and the DFE equalization algorithms are commonly derived assuming a known CIR. In practice, such equalization algorithms learn the channel state in the training period during which a known data sequence is transmitted. An alternative to this approach is represented by blind equalization techniques. An equalizer can compensate for channel distortion even in the absence of known symbols, by using one of a number of blind deconvolution algorithms. These may be classiiied into four classes: algorithms explicitly using higher order statistics (HOS), subspace algorithms, Bussgang algorithms, and joint data detection and channel estimation techniques. Here we shortly discuss only Bussgang algorithms. Such algorithms employ a gradient descent algorithm that attempts to restore some property of the input data that was destroyed by the frequency selectivechannel [76,77]. Let us consider a linear equalizer with contents V k , coefficients f k , and quantizer input Ik defined by Eqs. 18.29,18.35 and 18.36, respectively, and update equation (see Eq. 18.39)

zyxw zyxwv zyxwvuts

where h is the step size and the error factor e( -) is a nonlinear, memoryless mapping that characterizes each Bussgang variant. There are two important variants for e( .) in the family of blind equalizers: (a) the Sat0 algorithm [76] and (b) the constant modulus algorithm (CMA) [77]. As we have previously shown with LMS-DFE, the error factor is evaluated as (18.60)

where Q( -)is the nearest neighbor quantizer. Given reliable (ideally correct) decisions, this choice minimizes the residual mean square error between the input and output of the quantizer, and thus it is well-suited to tracking. It is unsuitable for acquisition since typically many incorrect decisions are fed back initially, and the equalizer may converge to a closed-eye setting (i.e., the cost function has many local minima). For this reason, common practice is to use another blind algorithm until the eye diagram is opened and then operation is switched to decision-directed mode. Sato's algorithm pioneered the field of blind equalization. Given a real constellation and real received samples, it uses e (I,)

Ik - sgn(Ik).

(18.61)

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zyxwvutsr zyx Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

zyx

Essentially the symbols are quantized as pseudobinary, and this increases the decision reliabilitywhen large constellationsare employed. It is demonstrably less likely to converge to a local minimum than the decision directed version. However, it is known that it can get hung-up when initializing a DFE. The algorithm of choice is the CMA [78]. It attempts to ensure that the quantizer input lies as close as possible to a circlewith radius f i by minimizing

(18.62)

with

(18.63) It may be used for reaVcomplex signals and constantlnonconstantenvelope modulations. In recursive form the error factor is calculated as

zyxw

Given diversity (through fractional sampling for instance), a linite length equalizer adapted by the CMA can be shown to be globally convergent, i.e., to converge to the optimum setting whatever its initialization.

References J. H. Winters, “Reducing the effects of transmission impairments in digital fiber optic system,” IEEE Comm. Mag., pp. 68-76, June 1993. W. D. Grover, “Forward error correction in dispersion-limitedlightwave systems,” IEEE Journal ofLightwave Tech.,vol. 6, pp. 643-654, May 1988. A. F. Elrefaie, R. E. Wagner, D. A. Atlas, and D. G. Daut, “Chromatic dispersion limitations in coherent lightwave transmission systems,” IEEE Journal of Lightwave Tech.,vol. 6, p. 704, May 1988. H. Bischl and F. Derr, “Chromatic and polarization dispersion limitations in coherent optical bpsk and qpsk systems,” IEEE Journal of Optical Comm., vol. 12, pp. 42-46, June 1991. R. E. Wagner and A. F. Elrefaie, “Polarization-dispersionlimitations in lightwave systems,” in TechnicalDigest, Optical Fiber CommunicationsConference (New Orleans, LA), p. 37, Jan. 1988. C. D. Poole and R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-modefibres,” IEE Electronics Letters, vol. 22, pp. 10291030, Sept. 1986. C. D. Poole and C. R. Giles, “Polarization-dependent pulse compression and broadening due to polarization in dispersion-shifted fiber,” Optics Letters, vol. 13, pp. 155-157, Feb. 1988.

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[8] J. H. Winters, M. A. Santoro, and Z. Haas, “On the experimental measurement of pmd effects,” in Proc. of SPIE OE/Fibers’92, p. 1784.05, Sept. 1992. [9] C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization-mode dispersion,” IEEE Photonics Technology Letters, vol. 3, pp. 68-70, Jan. 1991. [lo] C. D. Angelis, A. Galtarossa, G. Gianello, E Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” IEEE Journal OfLightwave Tech.,vol. 10, pp. 552-555, May 1992. [l 11 M. Tsubokawa, M. Ohashi, and Y Sasaki, “Waveform degradation due to dispersion effects in an optical cpfsk system,” IEEE Journal of Lightwave Tech., vol. 8, pp. 775-779, May 1990. [12] A. A. M. Saleh, R. M. Jobson, and T. E. Darcie, “Compensation of nonlinearity in semiconductoroptical amplifiers,” IEE Electronics Letters, vol. 15, pp. 950-952, July 1988. [13] W. J. Tomlinson and R. H. Stolen, “Nonlinear phenomena in optical fibers,” IEEE Communicationsibfag.,vol. 26, pp. 36-44, April 1988. [14] A. R. Chraplyvy, “Limitations on lightwave communications imposed by opticalfiber nonlinearities,” IEEE Journal of Lightwave Tech., vol. 9, pp. 1548-1557, Oct. 1990. [15] R. Giles and J. Conradi, “Laser mode partitioning and mode evolution effects in high-speed fiber-optic transmission,” in TechnicalDigest of OFC’86, pp. 110-1 11, 1986. [16] K. Ogawa, “Analysis of mode partition noise in laser transmission system,” IEEE Journal of Quantum Electronics, vol. QE-18, pp. 849-855, May 1982. [17] B. L. Kasper, “Equalization ofmultimode optical fiber systems,” BellSyst. Tech.J., vol. 61, pp. 1367-1388, Sept. 1982. [18] L. Kazosky, S. Benedetto, and A. Willner, Optical Fiber Communication Systems. London: Artech House, 1996. [19] R. E. Wagner and A. F. Elrefaie, “Polarization-dispersion limitations in coherent lightwave systems,” in TechnicalDigest, Optical Fiber CommunicationsConference (New Orleans, LA), p. 37, Jan. 1988. [20] A. E Elrefaie, R. E. Wagner, D. A. Atlas, and D. G. Daut, “Chromatic dispersion limitations in coherent lightwave systems,” IEEE JournaI of Lightwave Tech., vol. 6, pp. 704-709, May 1988. [21] R. D. Gitlin, J. E Hayes, and S. B. Weinstein, Data CommunicationsPrinciples. New York: Kluwer AcademicPlenum Publishers, 1992. [22] A. E Molisch, Wideband wireless Digital Communications. Upper Saddle River, New Jersey: Prentice Hall, 2001. [23] D. G. Forney, Jr., “Maximum-likehood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. In$ Eheory, vol. 18, pp. 363-378, May 1972. [24] D. G. Forney, Jr., “The Viterbi algorithm,” Proc. IEEE, vol. 61, pp. 268-278, Mar. 1973.

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[25] J. A. Heller and I. M. Jacobs, “Viterbi decoding for satellite and space coII1II1uncation,” IEEE Trans. Commun. Tech., vol. COM-19, pp. 835-848, Oct. 1971. [26] G. Fettweiss and H. Meyr, “High speed parallel Viterbi decoding: Algorithm and VLSI-architecture,” IEEE Communications Magazine, vol. 29, pp. 46-55, May 1991. [27l J. B. Anderson, “Sequential coding algorithms: A survey and cost analysis,”IEEE Trans. Comm., vol. 32, pp. 169-176, Feb. 1984. [28] A. D. Hallen and C. Heegard, “Delayed decision-feedback sequence estimation,” IEEE Trans. Comm., vol. 37, pp. 428-436, May 1989. [29] M. V.Eyuboglu and S. U. H. Qureshi, “Reduced-state sequence estimation with set partitioning and decision feedback,” IEEE Trans. Comm., vol. 36, pp. 13-20, Jan. 1988. [30] G. Ungerboeck, “Channel coding with MultilevelPhase signals,”IEEE Trans. In$ Theory, vol. 28, pp. 55-67, 1982. [31] S. U. H. Qureshi and E. E. Newhall, “An adaptive receiver for data transmission over time-dispersive channels,” IEEE Trans. In$ Theory, vol. 19, pp. 448-457, July 1973. [32] D. D. Falconer and F. R. Magee, “Adaptive channel memory truncation for maximum-likelihood sequence estimation,” Bell Syst. Tech. J., vol. 52, pp. 1541-1562, Nov. 1973. [33] W. U. Lee and E Hill, “A maximum-likelihoodsequence estimator with decisionfeedback equalisation,” IEEE Trans. Comm., vol. 25, pp. 971-979, Sept. 1977. [34] Y. Gu and T. Le-Ngoc, “Adaptive combined DFEMLSE techniques for IS1 channels,”IEEE Trans. Comm., vol. 44,pp. 847-857, July 1996. [35] K. Wesolowski, “An efficient DFE & ML suboptimum receiver for data transmission over dispersive channels using two-dimensional signal constellation,” IEEE Trans. Comm., vol. 35, pp. 337-339, March 1987. [36] J. H. Winters and S. Kasturia, “Constrained maximum likelihood detection for high-speed fiber-optic systems,”in Proc. Globecom ’91,pp. 1574-1 579, Dec. 1991. [37l M. Austin, “Decision feedback equalization for digital communication over dispersive channels,” MIT Research Laboratory of Electronics Technical Report 461, Aug. 1967. [38] C. A. Belfiore and J. H. Park, “Decision feedback equalization,” Proc. IEEE, V O ~ .67, pp. 1143-1 156, Aug. 1979. [39] S. U. H. Qureshi, “Adaptive equalization,” Proc. ZEEE, vol. 73, pp. 1349-1387, Sept. 1985. [40] R. D. Gitlin and S. B. Weinstein, “Fractionally-spacedequalization: An improved digital transversal equalizer,” BelZSyst. Tech. J., vol. 60, pp. 856-864, Feb. 1981. [41] G. Ungerboeck, “Fractional tap-spacing equaliser and consequences for clock recovery in data modems,” IEEE Trans. Comm., vol. 24, pp. 856-864, Aug. 1976. [42] J. H. Winters, “Equalization in coherent lightwave systems using a fractionallyspaced equalizer,” IEEE Journal of Lightwave Tech., vol. 8, pp. 1487-1491, Oct. 1990.

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[43] J. Salz, “Optimum mean-square decision feedback equalization,” Bell Syst. Tech. J., V O ~ .52, pp. 1341-1373, OCt. 1973. [44] D. D. Falconer and G. J. Foschini, “Theory of minimum mean-squareerror QAM systems employing decision feedback equalization,” Bell Syst. Tech. J., vol. 52, pp. 1821-1849, Dec. 1973. [45] D. L. Duttweiler, J. E. Mazo, and D. G. Messerschmitt, “An upper bound on the error probability in decision-feedbackequalisation,” ZEEE Dam. ZnJ: Theory, vol. 20, pp. 490-497, July 1974. [46] R. A. Kennedy, B. D. 0. Anderson, and R. R. Bitmead, “Tight bounds on the error probabilities of decision feedback equalizers,” ZEEE Trans. Comm., vol. 35, pp. 1022-1029, Oct. 1987. [47l J. H. Winters and R. D. Gitlin, “Electrical signal processing techniques in longhaul fiber-optic systems,” ZEEE Trans. Comm., vol. 38, pp. 1439-1453, Sept. 1990. [48] S. Kasturia and J. H. Winters, “Techniques for high-speed implementation of nonlinear cancellation,”ZEEEJ.Sel. Areas Comm., vol. 9, pp. 711-717, June 1991. [49] A. Schiippen, H. Dietrich, U. Seiler, H. V. D. Ropp, and U. Erben, “A SiGe R F technology for mobile communication systems,” Microw. Eng. Europe, pp. 39-46, 1998. [50] E Buchali, H. Biilow, W. Baumert, R. Ballentin, and T. Wehreu, “Reduction of the chromatic dispersion penalty at 10Gbitls by integrated electronic equalisers,” in Optical Fiber Communication Conference, 2000, vol. 3, pp. 268-270, March 2000. [51] H. Biilow, “System outage probability due to first- and second-order PMD,” ZEEE Photon. Technol.Left.,vol. 10, pp. 696-698, May 1998. [52] H. Biilow, “Equalization of bit distortion induced by polarkition mode dispersion,” in Proc. NOC’97, 1997. [53] B. W. Hakki, “Polarization mode dispersion compensation by phase diversity detection,” ZEEE Photon. Technol.Lett., vol. 9, pp. 121-123, Jan. 1997. [54] J. H. Winters, “Experimental equalization of polarization dispersion,” IEEE Photon. Technol.Lett., vol. 2, pp. 591-593, Oct. 1990. [55] H. Biilow, D. Schlump, J. Weber, B. Wedding, and R. Heidemann, “Electronic equalization of fiber PMD-induced distortion at 10 Gbitls,” in Optical Fiber Communication Conference and Exhibit, 1998 (OFC ’98), Technical Digest, vol. 2, pp. 151-152, Feb. 1998. [56] H. Biilow, F. Buchali, W. Baumert, R. Ballentin, and T. Wehren, “PMD mitigation at 10 Gbit/s using linear and nonlinear integrated electronic equaliser circuits,” Electron. Lett., vol. 36, pp. 163-164, Jan. 2000. [57] H. Biilow, “PMD mitigation techniques and their effectiveness in installed fiber,” in Optical Fiber Communication Conference, 2000, v01. 3, pp. 110-112, March 2000. [58] J. Poirrier, A. Gnauck, and J. Winters, “Experimental nonlinear cancellation of polarization-modedispersion,” in Optical Fiber Communication Conference,2000, V O ~ .3, pp. 119-121,2000.

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996

zyx zyxwvutsr zyxwvutsr zy Moe Z. Win, Jack H. Winters, and Giorgio M. Vitetta

[59] D. G. Messerschmitt,“Minimum MSE equalization of digital fiber optic systems,” IEEE Pans. Comm., vol. 16,pp. 1110-1118,July 1978. [60] J. H.Winters and M. A. Santoro, “Experimental equalization of polarization diversity,”IEEE Photon. Technol.Lett., vol. 2,pp. 591-593, Aug. 1990. [61] J. G. Proakis, Digital Communications.New York, New York McGraw-Hill, Inc., Fourth ed., 2001. [62] B. Widrow, J. McCool, M. Larimore, and C. Johnson, “Stationary and nonstationary learning characteristics of the LMS adaptive filter,” Proc. IEEE, vol. 64,pp. 1151-1 162,Aug. 1976. [63] R. W. Lucky, “Automatic equalization for digital communications,” Bell Syst. Tech. J., vol. 44,pp. 547-588, April 1965. [64] D. Schlump, K.Koffers, W. Pohlmann, H. Reichelt, and B. Wedding, “10Gbitfs dispersion supported transmission field trial over 123 km standard single mode fibre for HDTV studio interconnection,” Electron. Lett., vol. 31, pp. 1854-1855, Oct. 1995. [65l B. Wedding, €3. Franz, and B. Junginger, “10-Gb/s optical transmission up to 253 km via standard single-modefiber using the method of dispersion-supported transmission,”IEEE JournaIofLightwave Tech., vol. 12,pp. 1720-1727,Oct. 1994. [66] T.Takahashi, T.Imai, and M. Aiki, “PMD mitigation at 10Gbitfs using linear and nonlinear integrated electronic equaliser circuits,” Electron. Lett., vol. 30, pp. 348-349, Feb. 1994. [67] D. Schlump, B. Wedding, and H. Biilow, “Electronic equalisation of PMD and chromatic dispersion induced distortion after 100km standard fibre at 10Gbitfs,” in 24th European Conference on Optical Communication, vol. 1, pp. 535-536, Sept. 1998. [68] €3. Wedding, W. Pohlmann, D. Schlump, E. Schlag, and R. Ballentin, “SiGe circuits for high bit-rate optical transmission systems,” in Proc. of the 1999 IEEE International Sjmposium on Circuits and Systems (ISCAS ‘99),vol. 2, pp. 492-495, May 1998. [69] B. Wedding, A. Chiarotto, W. Kuebart, and H. Biilow, “Fast adaptive control for electronic equalization of PMD,” in Optical Fiber Communication Conference and Exhibit, 2001 (OFC 2001), vol. 2,pp. TuP4.1-TuP4.3,March 1988. [70] H. Biilow, F. Buchali, and V. Nicolas, “Dispersion mitigation using a fiber-bragggrating sideband filter and a tunable electronicequalizer,”in Optical Fiber Communication Conference and Exhibit, 2001 (OFC 2001), vol. 3, pp. wdd34.1-wdd34.3, Jan. 2001. [711 W. D. Grover, “Forwarderror correction in dispersion-limitedlightwave systems,” IEEE JournalofLightwave Tech., vol. 6,pp. 643-654,Oct. 1988. [72] R. W.Chang and J. C. Hancock, “On receiver structures for channel having memory,”IEEE Dam. In$ Theory, vol. 12,pp. 463-468, Oct. 1966. [73] K. Abend and B. D. Fritchman, “Statisticaldetection for communicationchannels with intersymbol interference,” Proc. IEEE, vol. 58,pp. 779-785,May 1970.

zyxwvut zyxw

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zyx zyx zyxwv zyxwv zy zyxwv zyxwvu 18. Equalization Techniques

997

[74] K. Abend, T. J. Hartley, B. D. Fritchman, and C. Gumacos, “On optimum receivers for channels having memory,” IEEE Trans. In$ Theory, vol. 14, pp. 152-157, NOV.1968. [75] Y. Li, B. Vucetic, and Y. Sato, “Optimum soft-output detection for channels with intersymbol interference,” IEEE Trans. Inz neory, vol. 41, pp. 704-713, May 1995. [76] Y. Sato, “A method of self-recovering equalisation for multilevel amplitudemodulation systems,” IEEE Trans. Comm.,vol. 23, pp. 679-682, June 1975. [77] D. N. Godard, “Self-recovering equalisation and carrier tracking in twodimensional data communication systems,” IEEE Tram. Comm., vol. 28, pp. 1867-1875, NOV.1980. [78] R. Johnson, P.Schniter, T. J. Endres, J. D. Behm, D. R. Brown, and R. A. Casas, “Blind equalization using the constant modulus criterion: A review,” IEEE Proc., vol. 10, pp. 1927-1950, Oct. 1998.

zy zyxwvutsrqpon

Index to Volumes IVA and IVB 1 : 1 protection, A324, B:112, 113, 114 1 :Nprotection,B:112,113,114 APS protection switching in, B122-123 1 1 protection, A322,323, B62; 112,113,114 1.3 micron VCSELs, A671474 1.5micron VCSELs AlGaAsSb DBR approach to, A675-676 dielectric mirror approach to, A674675 metamorphic DBR approach to; A676677 wavelength-tunable, A677478 10Gbit/s standard, B:537 characteristics of, B549-550 fibers in, B:550 future of, B:558-559 need for, B:642,647 optional features of, B:55&551 XGMII Extender in, B:550-551 10 Gigabit transmission, A45 directly modulated lasers in, A6l.9425 evolution of Ethernet standard, A52-57 IOBASE-T: B:517,526,536 compatibility issues of, B:546547 userbase of, B:546 100BASE-T4and -T2, B540 100BASE-T, B:536 backward compatibility of, B:546-547 1000BASE-LX Ethernet, B:538,539 1000BASE-SX Ethernet, B:538,539 1000BASE-XEthernet, B:537 1310nm analog lasers, A605 applications of, A:605, 612 distortion by, A:605412 1480nm lasers characteristics of, A572-574 construction of, A:573-574 in EDFA pumping, A:575-576 160 Gbit/s systems demultiplexing in, B:283 OTDM in, B:281-284 practicability of, B:289-290 receiver for, B:282-284 sample system, B:283-284 single-channel transmission experiment, B:285-287 transmitter for, B:281-282 WDM in, B:287-289 16800GX, A:314 2R signal regeneration, A:720 3R signal regeneration clock recovery block for, A735-736,741-742 electrooptic vs. all-optical, A:771-775 hardware for, A:736741 implementation of, A:736744 input adaptation for, A:742-744 need for, A:73?-734 by nonlinear gates, A735756

+

SOA-MZI based, A744-748 by synchronous modulation, A:747-771 40 Gbit/s systems alternating polarization format in, B:280-28 1 dispersion compensation in, B:278-279 ETDM pseudo-linear transmission in, B:279-280 experiments in, B:276-279 reamplification in, B:276277 8B10B coding, B:541 8B6T coding, B:540 980 nm lasers beam characteristics of, A565-568 design of, A568-570 in EDFA pumping, A575-576 emissions spectra of, A:579-580 light output of, A57&572 mirror passivation in, A:564-565 waveguides for, 569-570 Abilene network, B:38 AboveNet, B:34-35 Access networks architectures for, E439 carrier systems in, B:439 described, A:36 dispersion compensation and reach in, A 3 9 4 0 fiber capacity limitations in, A 4 0 4 1 fiber choice for, A45 fiber economics for, A 4 3 4 l fiber requirements for, A 3 6 3 9 fiber use in, B:42&421,43b506. See also Optical access networks 1400nm market in, A 4 2 4 3 future trends in fiber use, A:44 history of, B:438440 SOAs in, A:722-723 1300nm market in, A:42 Acoustooptic filters, A467468 Adaptation grouping, B:6M7 and reconfigurability, B:68 Add/drop filters, A541-543 Add/drop multiplexers, B:6041 photonic B:58,67, 121 Addresses, Internet, B: 132 Adiabatic couplers, A427428 ADSL, B:503 in xDSL, E504 Al/Ge/Si glasses advantages of, A109-110 applications of, A 1 17-1 18 compositions of, A 1 1&112 in EDFAs, A130 erbium doping of, A: 110 fiber losses in, A 1 15-1 I6 fiber fabrication of, A: 11 4 115 fiber strength of, A 1 1 6 117 impurities in, A115-116

zyxwv zyxwvutsr

zyxwv

999

zyxwvut zyxwvutsrqp zyxwvutsr zyxwvutsr

1000

Index

A1f Gef Si glasses, continued phosphorus doping of, A 1 12 reliability of, A 117 synthesis of, A112-114 Alcatel Crosslight, A386 AlGaAs lasers design of, A568-570 mirror passivation in, A564565 waveguide patterns for, A566-567 All-optical islands, B:227-228 All-optical networks characteristics of, B226 feasibility of, B226 future of, B227 All-optical regeneration beyond 40 Gbitf s, A770-771 challenges facing, A:774-775 clock recovery block for, A735-736,741-742 electrooptic VL, A:771-775 experiments in, A769-770 hardware for, A736741 implementation of, A736-744 mechanism for, A748-749 need for, A733-734 by nonlinear gates, A735-756 prerequisites for, A773-774 regenerator configurations for, A768-769 by saturable absorbers, A749-756 by synchronous modulation, A:757-771 in WDM, A732-733, A767-771 All-optical signal processing cross-gain modulation, A 7 17-71 8 cross-phase modulation,A718-719 four-wave mixing, A719-720 optical time-division multiplexing (OTDM), A720-722 signal regeneration, A720. See also All-optical regeneration transmission speed using, A 8 2 2 wavelength conversion, A 7 17-720 All-pass dispersion compensation, B691,692-693 Alumina-doped silica EDFAs, A 8 0 Aluminosilicates advantages of, AlO9-110 applications of, A117-118 compositions of, A.110-I12 in EDFAs, A 130 erbium doping of, A.110 fiber lossesin, A115-116 fiber fabrication of, A l l 4 1 1 5 fiber strengthof, A l l 6 1 1 7 impuritiesin, All5-116 phosphorus doping of, A:ll2 reliability of, A 1 17 synthesis of, A112-I14 Aluminum in fluoride glasses, A107-108 in oxideglasses, A:108-118 Amplified spontaneousemission (ASE), A225, B160-161,201,905 accumulation of, B:236237 in an EDFA, A229-230, B202 excess, B161 filtering of, A540 in a passive fiber, A228-229 in a passive fiber followed by an amplifier, A230 in a Raman amplifier, A231-232 in a Raman amplifier followed by an EDFA, A:233-234

reduction of, B236 simulation of, B:572 source of, A705 Amplifier chains, length of, B:187-189 Amplifiers materials characteristics for, A.81-83 materials limitations for, A 8 4 8 8 pump schemes for, A82,83 Amplitude modulation (AM) in metro networks, B:415 modulator characteristics for, B:868-873 signal distortion in, BS67-868 signal representation in, B866-868 Amplitude transparency, defined, B86 Amplitude-modulated-nonreturn-to-zero (AM-NRZ) modulation, A276 Amplitude-modulated-return-to-xro (AM-R modulation, A276 Analog lasers history of, A601603 impairments of, A:60>604 Analog systems laser sources for, A595 SOAs in, A71 1 Analog-to-digital conversion, for cable systec B:42-26 Annealed proton exchange, A262 Anti-Stokes scattering, A216 Antimony silicates applications of, A:128 in C-band EDFAs, A132-135 composition of, A124-125 fiber fabrication of, A126128 history of, A124 in L-band EDFAs, 137-139 rare earths in, A125 synthesis of, A125-126 thulium-doped, A 145-149 Apodization in fiber gratings, A495 in nonunifom gratings, A513 ARPA (Advanced Research Project Agency), B:28 ARPANET, B:28-29 end of, B31 growth of, B30-31 Arrayed wavelengthgrating (AWG), B481 Arrayed-waveguide devices, B691 AT&T divestitures by, A.3, B:3 evolution of, A2, B:2 AT&T Northeast Corridor System, A2, B:2 ATM PON (APON), B446 Attenuation, defined, B:904 Attenuators midstage, A186188 in optical crossconnects, A338 Australia, Internet growth in,B:33, B34 Automated provision, modes for, B137-138 Autonegotiation evolution of, B548-549 importanceof, B:546547 and link integrity, B547-548 Avalanche photodiodes (APDs), A790-791 sensitivity of receiver using, A795796 simulation of, B582

zyxwvuts

zyxwvut Backscattering hardware for measuring, B759 to measure PMD, B759-761

Index Band filling, for index tuning, A65&652 Bandgap shrinkage, for index tuning, A650-652 Bandwidth trading, B:7%81 Bandwidth-on-demand service, B:85 BCH codes, B:915 for lightwave communications, B956-957 mathematics of, B:926928 product codes, B928-929 Beam-steering spatial cross-connects, A458-461 Beat noise, A.226 Bell System, breakup of, A2, B 2 Bellcore, founding of, A 2 , B:2 Beryllium fluoride, glass formation from, A:108-109 BFR (big fat routers), B:106 Bias voltage drift: A277 Bidirectional transmission achievement of, B:449 free-space optic modules, B:494-495 fullduplex, B 4 5 N 5 1 in optical access networks, B:494-496 PLC-based, B:495-496 using SCM, B:452453 using SDM, B450 using TCM, B451-452 using WDM, E453454 Binary ASK systems power spectral densities in, B:875-876 single-channel transmission simulations in, B:887489 Binary codes described, B907-910 linear, B:9 10-917 ML decoding of, B:932-948 Birefringence causes of, A:483484, B:727 characteristics of, B72G729 circular, B:727 magnitude of, A:484-485 Biterror rate (BER), A685697 estimation of, B:582-584 measurement of, B174177 and OSNR, B:238 related to Q-factor, B:173-174 Bit-interleaved WDM,B:486487 Bitrate distance product, B906 Black box EDFA model, B:575,581 Black-box optical regenerator (BBOR) systems, A764-765 advantages of, A765 characteristics of, A765-767 concerns regarding, A:767 for WDM application, A769-770 Block codes defined, B:907 linear, B:911-917 Border Gateway Protocol (BGP), B:133 Boron, as dopant, A483 Bounded-distance decoding algorithm, B:909 B r a g gratings See also Fiber gratings chirped, B:659469 coupled-mode theory on, A501-506 coupling in, A502-505 dispersion by, A:504-506 for fixed slope matching, B:69&699 illustrated, B:659 optics of, A498499 planar, A453454 for tunable slope matching, B:700-702 Bridges, function of, B:529

1001

zy

zyxw

Broadband, metallic media for, B:497 Broadband access facilities (BAF), B:446 Broadband amplifiers high bitrate, A824430 in MANS,B:345 need for, A:824825 transimpedance amplifier (TU), A826827 traveling-wave ampliier (TWA), A827430 Broadband OSSB, B : 8 W 8 6 BroadNED (Broadband Network Designer), B:570 Bromine, in tellurite glasses: A122 Bubble switches, A33%340 Burst error correction, B:924 Bursty data, amplification of, A:716 Bus architecture, compared to grid topology, B:405 Butt-joint growth, A599

C-band ampliien aluminosilicatesin, A130 antimony silicates in, A132-135 fluorozirconatesin, A:13&131 tellurites in, A123 Cable modems, B339 Cable TV systems coaxial bus system, B:406410 digitization in, B425-426 future of, E421425 history of, B:40546 hybrid fiber/coax networks, B:411-421 linear lightwave technologies in, B:430-431 low-cost lightwave technologies in, B:431-433 RF technologies in, B:415,427-430 simulation of: B603-604 SONET systems in, B:414,415 topology of, B:404-405 Carrier extension, in Gigabit Ethernet, B:524 Carrier hotels, B:78-79 Carrier Sense Multiple Access with Collision Detection (CSMA/CD), B:521-524 Carrier systems, B:439 Carrier-suppressed RZ modulation, A:816-818 Cascaded Raman fiber lasers, AM7-248 Cell phone industry, growth rate of, B:22-23 Cerium, as dopant, A:483 Channel capacity, B:932 Channel protection, A202-203 laser control, A205-206 link control, A20S205 pump control, A203 Chemical vapor deposition (CVD) history of, A:112-113 modified,A:113, 114: 115 China, Internet growth in, B:33-34 Chirp, B:968 calculation of, B242 in direct-modulated lasers, 409 in fiber gratings, A49-96 in nonuniform gratings, A:513 simulation of, B576-577 uses of, A509-510 wavelength, A:69&692 Chirped fiber Bragg gratings (chirped FBGs) advantages of, B:660 illustrated, B:659 multiple-channel, B:664-668 nonlinearly chirped, B682-686 polarization dependence of, B:662-663

zyxwvutsr zyxwv zyxwvutsr zyxwvutsrq zyxwvutsrqpon

1002

zyxwvutsr zyxwvut zyxwvutsr Index

Chirped fiber Bragg gratings (chirped FBGs), continued

ripple in, B66C-662 robustness of, B663 single-channel linearly chirped, B:664 single-channel tunable, B678488 temperature sensitivity of, B:662 tuning of, B:660 versatility of, B:663 Chirped return-to-zero (CRZ) pulse system, A815 advantages of, B:169-171 compared with DMS, B:309-310,322-323 described, B:169 and WDM,B:315-322 Chromatic dispersion, B214,979 compensation of. See Dispersion compensation cumulative effect of, B645 defined, B:904 effect of, B:645 figures for commercial fibers, B:647 historical perspective on,B545-651 importance of, B:708 linearity of, B:653 management of, B:215-220,651453 mathematics of, B:648 monitoring of, B:704-708 physics of, B64-5 time behavior of, B67M72 universalities of, B:643 Ciena CoreDirector, A386 Circuit switching, vs packet switching, B:516 Cladding pumping, A151 with broadstripe lasers, A151-152 Clamping, A708-709 Clipping, A 6 0 4 in cable systems, B:432 Clock and data recovery (CDR) circuits, high bitrate components of, A83C-831 function of, A832433 physical manifestation of, A835-836 using multiple-phase clocks, A83S834 Clock recovery block, A735-736 mechanism of, A:741-742 types of, A742 Clustering effects on gain, A:87 minimization of, A87-88 Coaxial bus system, B:405 characteristics of, B:407 described, B:40M07 distribution system of, B:409 evolution of, B411 headend of, B:40749 trunk system in, B409 upstream system of, B:410 Coaxial cable, properties of, B:535-536 Code-division multiplexing, B341 Codewords, defined, B:907 Coding error-control. See Error-control coding for Ethernet, B537,539-541 Coding gain, B:208,906 for lightwave communications, B:952 mathematics of, B:953-956 Coherent detection, defined, B905 Coherent optical time-domain reflectometer (COTD), B:186 Collision detection, B522,523 Commercial Internet Xchange (CIX), B31

Communications technology, predictions about,

B24-25

Compensation for PMD electrical, B:817-820,981 higher-order, B814-815 multichannel, B816817 multisection, B:81%816 optical, B809-817,981 Complex amplitude, calculation of, B242 Composite PONS (CPONs), B:484485 Concatenated codes, B:925-926,959-960 Conduits, B119 Connection attributes, B 138 Consolidation, B:72 reasons for, B:72-73 Constraint-based Routing Label Distribution h o t o w l (CR-LDP), B:135 Containment, in fault management, B:72 Control logic, for failure recovery, B: 110,111 Control plane, B97,99 alternative approaches to, B:143-144 alternative architectures for, B:128-131 enhancements to, B:142 Control register bit definitions, in Ethernet, B545 Convolutional codes, B:929 decoding of, B932 in lightwave communications,B:960-961 mathematics of, B:929-931 parallel concatenated, B948-950 recursive systematic, B93 1-932 Core network, A30lL302 bandwidth management in, A302-303 Coupled-mode theory, to analyze fiber gratings, A499-500 and Bragg gratings, A501-506 and nonuniform gratings, 509-519 and tilted gratin& A51%522 and transmission gratings, A506509 coupling in Bragg grating, A524-525 to cladding modes, A.522-525 radiation-mode, A:527-530 in transmission grating, A:525-526 Crossconnects architectures of, A312-315 beam-steering spatial, A 4 5 8 4 1 electrical, A314-315,385-389 optical. See Optical cross-connects port count and, A303-305 Cross-gain modulation (XGM), SOAs in, A717-718 Cross-phase modulation (XPM), A21,282 amplitude distortion penalty induced by, B:624625 collision-induced,B:625-629,635 compensation for, B:262-264 described, B548-649 effect of, B:257-261 intrachannel, B:257-264,629433 mathematics of, B:257-259,618 minimization through polarization interleaving, E798402 in NRZ systems, B:624425 pump-probe measurements of, B518-624 in RZ systems, B625629 simulation of, B:600 SOAs in, A 7 1 M 1 9 Crosstalk avoiding, A712-713 control of, A350-351,355,35%362

zyxwvutsrq zyxwvutsrq

zy zyxw Index

ganged per-stage control in, A:360-362 interchannel, A238-239,712-716 nonlinear, A25-26 and optical fiber design, A26 in optical switches, A:335-336 propagation of, A:352-355 pump-signal, A:240 in Raman amplifiers, A238-241 signal-pump-signal,A241 simulation of, B:599 suppression of, A713-716 Cyclic codes, B:915-917 BCH codes, B:915,92&929,957 generating polynomial of, B:916 Golay codes: B:915,917 Hammingcodes, B:915,917 Cyclic shift, B915

1003

VDSL, B:503-504 xDSL, B:502,504 Digital transmission, SOAs in, A710-711 Digital transparency, defined, B86 Dimension, of code, B:911 Diplex, B453 Direct detection, defined, E905 Direct matrix inversion, B:982 Direct modulation, in Ah4 transmission, B:868 Direct peering, B:76 Directional couplers, A:269,427; 428 types of, A270 Directly modulated distributed feedback (DFB) lasers arrays of, E486 in DWDM systems, A:618619 modulation efficiency of, A621 need for, A613 oscillation frequency of, A621 performance analysis of, A614618 in 10 Gbit/s transmission, A:619625 Directly modulated laser transmitters, A808409 Disk storage density of, B:47 innovations enabled by, B:4849 trends in, B:48 Dispersion calculation of, B:241-242,243 consequences of, B:163-165 cumulative effects of, B:244-245 deiined, B:163,904-905 leading to pulse broadening and chirping, B:244 simulation of, B:597,598 Dispersion compensation, A:23-25, B:236,652, 709-714 dynamic, A452453 figure of merit for, B:670 fixed, B657-670 in metro and access systems, A 3 9 4 0 with optical nonlinearities, B653457 slope matching, B:69&702 for subcarrier-multiplexed data, B:702-704 tunable, B:670496 using chirped FBGs, B659669 using dispersionxompensating fiber, B657459, 669-670 using FBGs in transmission mode, B:668669 wideband, A23-25 Dispersion length, B:214 calculation of, B242 Dispersion limit, B:214 formula for, B 163 Dispersion management, A:2&29, B:651453, 798 for land systems, A35 for undersea systems, A33-35 in WDM transmission, B633434 Dispersion mapping, B164165, B269-270, B:654 corrections to, B:654655 extreme, B:655657 optimization of, B:270-272 and precompensation choice, B:271-273,275 Dispersion monitoring, B:704 using duty cycle, B:707 using NRZ clock regeneration and RZ clock fading, B:705-706 using peak detection, B707 using phase shift, B707-708 using RZ power fading, B:705

zyxw

zyxwvutsrq zyxwvutsrqp

DARPA (Defense Advanced Research Project Agency), B:28 Data modulator, for wavelength switching, A398 Data rates, evolution of, A19 Data sheets, B:576 Data transmission growth rate of, B26 Moore’s law applied to, B:49-50 predictions about, B:25-26 Decision block for SOA-MZI-based 3R regeneration, A744745 for 3R regeneration, A:736-741 Decision feedback equalizer (DFE), B:817-819, B:977-981 Degree of polarization described, B:823424 to monitor PMD, B:824-825 Demultiplexers high bitrate, A836 simulation of, B:578 Deuterium loading, to increase photosensitivity, A482 Dielectric mirrors, for VCSELs, A674675 Differential group delay (DGD), B:221-222,725, 728-729 measured mean, B:761-762 polarization-mode coupling and, B:730-73 1 to predict PMD densities, B767 pulse broadening due to, B:735-736 simulation of, B:580 Differential mode attenuation (DMA), in plastic fiber, A63 Differential operation mode (DOM), A740-741 Digital Access and Cross-Connect Systems (DACS), A.309,311 evolution of, A:312-313 Digital cross-connect switch/system (DCS), A377, B 5 W in MANS B:334 types of nodes based on, B:334335 Digital loop carrier (DLC), B:439 Digital subscriber line (DSL) ADSL, B:503 described, B501-502 growth of, B:339-340 HDSL, B:503 standardization of, B:502 transmission techniques in, B:502-503

1004

zyxwvutsr zyxwvut Index

Dispersion-compensatingfiber (DCF), B216-218 adaptation to tunable compensators, B:677-678 characteristics of, B:657458 design of, B:218 higher-order, B:669-670 sites of application of, B:658459 slope matching based on, B:697498 Dispersion-compensatingmodules (DCM), A24 alternatives to, A25 Dispersion-compensation filters, A:543-546 Dispersion-managed soliton (DMS), B247-248 compared with CRZ, B309-310,322-323 PMD resistance of, B809 in singlechannel systems, B310-315 in WDM systems, B316-322 Dispersion-shifted fiber (DSF),A281, B:648 disadvantages of, B650 Distortion attenuation, B:904 dispersion, B904-905 dispersion management of, A26-29 limiting effects of, A25 miscellaneous sources of, B906 nonlinear, in cable systems, B432 between multiple signals, B967 noise, B905,967. See also Noise single-signal, B:966-967 types of, A28 1 Distributed Bragg reflector (DBR) lasers, A:398,462 AlGaAsSb for, A675476 characteristics of, A592 construction of, A591,64&641 function of, A641-642 metamorphic, A676477 variations of, A645-648 Distributed feedback (DFB) lasers, A590-591 advantages of, A640 characteristics of, A592 disadvantages of, A639640 mechanism of, A608 nonlinearities of, A609-610 Distributed photodetectors, A788-789 Distributed Raman amplification (DRA), A29-30 advantages of, A251, B:207 current research in, A:25&251 hardware for, B205 history of, B:204-205 to improve OSNR, B20S206 spontaneous emission in, A23 1-234 Distribution hubs architectures for, B417 multiplexing techniques for, B417-420 Distributive law,B933-934 DNS, origin of, B30-31 Domains, Internet, B:132 Domains of transparency, B67,89 complex, B:67 connectivity limitations associated with, B95 impairments and, 94-95 and networks, B:91-92 recoveryin, B:120-121 routing complications associated with, B: l a 1 4 1 routing and wavelength assignment in, B:92-94 Double-sideband suppressed carrier (DSSC) modulation, A276 DSL (digital subscriber line) ADSL, B:503 described, B:501-502 growth of, B:339-340

HDSL, B503 standardizationof, B502 transmission techniques in, B502-503 VDSL, B:503-504 xDSL, B502,504 Duobinary coding, A816 Duobinary signaling, B865 DWDM, B:890 power spectral densities in, B:877-880 Duty cycle calculation of, B240 dispersion monitoringusing,B:707 DWDM (dense wavelength-divisionmultiplexed) systems, A18 advantages of, B:390 characteristics of, A298 cost efficiency of, B330 difficulties in, A281 duo-binary, B:890 early, A298-299 economic issues of, B369-370 edge rings, B373-375 eye diagrams of, B241 history of, B198-199 laser use in, A:593 in MANS, B331-332,344,347-373,556 in metropolitan environments, A666 migration to, B:370-373 modem, A299 modified RZ,B891493 optical hybrid/mesh networks using, B:364369 optical switching in, A299-300 OSSB, B89&891 point-to-point systems, B224,348-351 in secondary hub architectures, B:419-420 simulation tools for, B571-572 spectra of, B241 subcarrierOSSB, B881-884 technologies enabled by, B:198 technologies enabling, B201 transparency of, B:330-331 use on PSPONs, B:457 wavelength budget of, A618419 wideband. See Wideband DWDM Dynamic dispersion compensators, A:452453 Dynamic gain equalization filters, A433435 Dynam!c passband shape compensators, A451452 Dynanuc rings engineering problems of, B36&361 indications for, B35M56 OADM nodes in, B356-357 self-healing,B:357-358 SPRING, B:358-359

zyxwvu zyxw zyxwvuts

E-mail, origin of, B29-30 EDFAs (erbium-doped fiber ampliiers) advantages of, A128,174, B159-160 Al/Ge/Siandvariants in,A:117-118 applications of, A179 ASE noise from, B:202 circuit noise in, A 8 0 M 0 1 control of, A181-182,202-206 conventional-band, A13&135 described, A176179 for DWDM, B:201 for dynamic WDM systems, A197-206 effect of optical filter bandwidth on, A79W00 erbium amplifier bands in, A:128-130

Index extinction ratio of, 801-803 gain dynamics of, A198-200 gain flatness of, A180-182 gain tilt in, A182 for high-capacity systems,A:183-197 history of, A176, B307 intersymbol interference in, A:803-805 L-band, 135-139,188-191 materials requirements for, A 8 0 midstage attenuators for, A:186188 noise calculations for, A 178-179 noise sources in, Al97-799 OSNR of, A179-180 physical parameters for, A177-178 p e r adjustment for, A:182 power transient behavior of, A198,200-202 reliability of, B 158 S-band, A140-158 sensitivity limit of, A:799 sensitivity of receiver using, A796805 SHB in, A185-186 signal photocurrent in, A796797 simulation of, B575,581 super-band,A139-140 ultrawideband, A191-193 use in undersea communication, B156163 versatility of, B: 158 Electrical cross-connects, A314 advantages of, A314315 disadvantages of, A 3 15 examples of, A:386 history of, A385 interconnections among, A388-389 scalability of, A387-389,391 state-of-the-art, A386 Electrical signal-to-noise ratio, A226,227 Electroabsorption (EA) modulators (EAMs), A:259-260, B:223 in AM transmission, B:868 chirp tuning of, B:691 simulation of, B:577 Electroabsorption modulator transmitters, A809-810 Electroabsorption-modulated laser (EML), A259 described, A625 design of, A632434 elements of, A:626 fabrication of, A:634 interactionswith modulators, A634437 parametersfor, A:626-629 performance of, A637-638 physics of, A629434 Elextrooptic effect, A:260 Electrooptic modulators compared with electroabsorption modulators, A259-260 lithium niobate, A260-278 need for,A:258 nonlinearity issues, A 2 8 1 performance assessment of, A279,281 polymeric, A283-288 system requirements for, A:278-282 Electrooptic polymers, A284 dekice fabrication using, A285 photobleaching property of, A287 Electrooptic switches, 34&341,343 Equalization algorithms for, B:972-992 decision feedback, B977-981

zyx zyx 1005

for high bitrate applications, A837-841 linear, B:981-984 need for, B965 using gain-flattening filters, B160 Equipment failures, B:108 Erbium amplifier bands of, A128-130 spectra of, A119-120 Erbiumdoped fiber amplifiers (EDFAs) advantages of, A128,174, B159-160 AI/Ge/Si and variants in, A:] 17-1 I8 applications of, A179 ASE noise from, B:202 circuit noise in, A800401 control of, A181-182,202-206 conventional-band, A:130-135 described, A176179 for DWDM, B201 for dynamic WDM systems, A:197-206 effect of optical lilter bandwidth on, A799-800 erbium ampliier bands in, A:128-130 extinction ratio of, 801-803 gain dynamics of, A:19M00 gain flatness of, A180-182 gain tilt in, A 182 for highcapacity systems,A183-197 history of, A176, B307 intersymbol interference in, A803-805 L-band, 135-139,188-191 materials requirements for, A 8 0 midstage attenuatorsfor, A:186188 noise calculations for, A:178-179 noise sources in, A797-799 OSNR of, A:179-180 physical parameters for, A177-178 power adjustment for, A 182 power transient behavior of, A198,200-202 reliability of, B: 158 S-band, A:14&158 sensitivity limit of, A:799 sensitivity of receiver using, A:796805 SHB in, A185-186 signal photocurrent in, A796797 simulation of, B:575?581 super-band,A:139-140 ultrawideband, A 191-193 use in undersea communication, B156163 versatility of, B:158 Erbium-doped fiber lasers, A104 Emr-control coding binary codes, B907-915 block codes, B911-917 convolutional codes: B:929-932,960-961 cyclic codes, B:91%917 lowdensity parity-check code&B951-952,961 need for, B:904-907 Reed-Solomon codes, B922-926,958 tree codes, B929-932 turbo codes, B:948-958,961 Ethernet, B:74 in access networks, B:448,500-501 addressing in, B:520-521 applications of, B:552-553 architecture of, B517-518,525-527 auto negotiation in, B:546551 bridges in, B:529-530 data rate supported by: B:515 development of, B:515 flow control in, B532-535

zyxwvuts zyxwvutsr zyxwv

zyxwvutsr

1006

zyxwvutsr zyxwvut Index

Ethernet, continued and FTTH, B500-501 full duplex operation in, B:526527 future of, B:551-559 Gigabit, A45,51-52,334, B52&525,553-559 history of, B:514 hubbed, B:525-527 line coding for, B:537,539-541 nomenclature of, B516-517 one-fiber, B493494 packet size of, B:524 physical architecture of, B:541-546 physical layer of, B:535-546 repeaters in, B527-529 routers in, B531-532 shared, B:521-524 sublayers of, B:542-546 switches in, B530-531 transmission media for, B535-537 upgrade issues of, B:553-555 Extinction ratio,801603 Eye closure penalty, B24S246 illustrated, B273,274,275 Eye monitor, of PMD, E822

Fiber gratings annealing of, A487489 applications of, A478,537-551,579-580 birefringence in, A:48?-485 coupling by, A.522-530 creating apodiiation and chirp in, A:494495 described, A477 diffraction in, A496-499 fabrication of, A489495 fiber photosensitivity and, A480439 history of, A:478480 importance of, A477 index modulation in, A495496 lifetime of, A:485487 limitations of, A478 in MANS,B:346 nonuniform, A509-519 optics of, A495-533 properties of, A533-537 strain effects on, A533-535 synthesis of, 530-533 temperature effects on,A:486,533-535 tilted, A519-522 types of, A:497499,501-522 versatility of, A477478 waveguide design for, A:535-537 Fiber nonlinearity, B247-248 dispersion mapping of, B:269-275 energy exchange and, B:252-253 intrachannelcross-phase modulation, B257-264 intrachannelfour-wavemixing, B:265-269 mathematics of, B248,250-252 precompensation for, B:271-273,275 self-phasemodulation, B:253-257 Fiber switches, B:69 Fiber-in-the-loop (FITL) systems, B:440 point-to-point, B44C-441 standardizationof, B : 4 4 3 4 Fiber-to-the-curb (arc)B:443 , Fiber-to-the-Exchange (FTTx), B:443 Fiber-to-the-home (FTTH)networks, B:440-441 assimilation of existing services by, B499 concerns regarding, BM2-443 Ethernet in, B50&501 future of, B497498 media for, B:497 overbuild vs new-build issues, B:498,499 powering of, E498 regulatory issues, B499 topologies for, B:499-500 Field-effect transistors, A822623 Filters See also Specifictypes of filter in MANS B:345-346 simulation of, B:576 Finite fields defined, B:919 importance of, B:917 mathematics of, B:918-922 Fixed DGD, to control PMD, B:812-813 Fixed spare protection, B:123 Fixed-lag MAPSD, B990-991 Flow control in full-duplex Ethernet, B533-534 in half-duplex Ethernet, B:532-533 MAC framing in, B533-535 Fluoride glasses fluoroaluminates, A 107-108 fluoroberyllates,A 108-109

zyxwvutsrq zyxwvuts zyxwvuts

Fably-Perot guiding filters, A:540-541 Fabry-Perot lasers c o d p a t i o n of, A:589 mirrors of, A569 oscillation characteristics of, A 6 2 4 4 2 5 properties of, A590 Failure protection and restoration from, A321-326, BlW-110 recovery from, Bl10-126 types of, B108-109 Fast Ethernet, A45 Fast link pulse (FLP), B:547 FASTAR@, B: 116 117 Fault detection, B 110,111 Fault localization, B110, B469 in central office,B471 in the field, B470-471 OTDR methods, B470 reference traces for, B:470 TDM/TDMA, B489492 Fiber cables, B:119-120 large-effective-area, B:635 in lasers, A549-550 simulation of behavior of, B:578-580 speed of light in, B:459 Fiber cuts, B:108 Fiber design dispersion compensation in, A23-25 dispersion management in, A 2 6 2 9 economic issues in, A43 future of, A44 for long-haul systems, A18,20-23 for metro and access systems, A 3 U 5 of microstructured fibers, A:67-70 for multimode applications, A:45-57 optical nonlinearities and, A 2 5 2 9 of plastic fiber, A:57-67 PMD and, A31-32 span loss and, A22-23 for trunk lines, A18 for undersea systems, A:18,33-35 wideband amplification and, A29-31

zyxwvutsr

Index

1007

zy

zyxwvutsr zyxwvutsr

fluorodrconates,A:89-106 optical characteristics of, A88-89 Fluorine, in tellurite glasses, A121-122 Fluoroaluminates applications of, A108 composition of, A107 fiber fabrication, A 108 history of, A:107 synthesis of, A:107-108 Fluoroberyllates, A 108-109 Fluorozirconates applications of, A 104106 compositions of, A90-91 devitrification of, A95 durability of, A103-104 in EDFAs, A130-131 fiber fabrication of, A:9>99 fiber losses of, A:99-103 fiber strength in, A103 impurities in, 100-103 reliability of, A104 studies of, A89-90, 106 synthesis and purification of, A91-93 thulium doping in, A:141-142 Forward error correction (FEC) advanced schemes of, B209-211 advantages of, B:178-180, 192,193 burst, 924 codes in, B:906 features of, B:177 importanceof, B:90&907 mechanisms of, B:208-209 and optical channels, B:100, 101 in optical communication, B952-961 to suppress PMD, B:819-820 Forward-backward algorithm (FBA), B:98&990 Four-port couplers, A427428 A22,40 Four-wave mixing (FWM), calculation of efficiency of, B:800 described, B265,266,649 dispersion mapping and, B:269 effects of, A41,281 intrachannel, B:265-269 mathematics of, B:267-269,61&617 mechanism of, B:265 minimization through polarization interleaving, B798-802 simulation of, B:570, 600 SOAs in, A719-720 sources of, A707-708 studies of, A:191 suppression of, B617 uses of, A719-720 Frame bursting, B:525 Franz-Keldysh effect, A259 Free-carrier absorption,A650 Free-space optic modules, B:494495 Frequency chirp, A:69&692 Frequency modulation (FM) transmission, in metro networks, B415 Frequencydivisionmultiplexing (FDM), B:405 in secondary hub architectures, B:417,418 Friss formula, A231 Full duplex transmission, B:450 Ethernet; B:52&527 implementation of, B:451 issues in, B:450451 Full wavelength-selectivecrossannects between-channels design of; A438-439

employing 2 x 2 switches, A438 interleave chirped design of, A 4 3 9 4 1 Full-service area networks (FSAN), B447-448 Fused couplers, B:493

GaAs, use in RF technology, B:429 GaAsSb, in VCSELs, A:673 Gain confinement factor and, A701 importance of, A700 Gain clamping, A708-709 Gain compression, A706-707 recovery from, 706 Gain control, in wideband amplifiers, A:183-188 Gain flatness filters to achieve, A181-182 importance of, A:180-181 Gain ripple, A701-702 effects of, B:211-212 management of, B:212-213 Gain tilt, A182 control of, A186-I88 Gain-flattening filters, A537-539, B:160, B:212-213 simulation of, B600-601 Gain-shifted pumping, in TDFAs, 142-145 Gain-transparentswitch, A721 GaInNAs, in VCSELs, A671472 Gas film levitation, A93 GCSR laser, A:644-645 Generalized distributive law (GDL), B934 Generalized Label Distribution Protocol (GMPLS) characteristics of, B:135-136 requirements of, B:136 Generator matrix, of code, B:911 Germanosilicates photosensitivity of, A480482 Raman gain in, A218-219 Gigabit Ethernet for backbone upgrade, B:553-555 carrier extension in, B:5Z frame bursting in, B:525 future of, B558-559 history of, A51-52 long-distance use of, B:556 in MANs, B:55>556 in multidwelling units, B:557-558 specifications for, A334 standard for, A45 Gigabit media-independent interfaces (GMII), B:543,544-546 Gigachannel, B:552 Gires-Tournois interferometers, B:69 1 for slope matching, E700 Glass systems antimony silicates, A 124128 fluoride glasses, A88-109 oxides, A109-124 Gnutella, B37 Golay code&B:915,917 GOLD (Gigabit Optical Link Designer), B:570 Gradient search algorithm (GSI), B982-983 Grating synthesis, A530-533 layer-peeling techniques of, A:532-533 matrix propagation techniques of, A531 Grating writing of complex structures, A530-533 using CW lasers, A:490

zyxwvuts

1008

zyxwvut zyxwvutsr zyxwvuts

Index

Grating writing, continued interferometer method,A491 phase mask method,A491494 using pulsed lasers, A:489490 Grating-assisted codirectional coupler (GACC) laser, A643644 Grid topology, E405 Grooming, OXCs in, A321 Group velocity dispersion (GVD), A282, B:726 calculation of, B242

HTML (HyperText Markup Language), B30 Hybrid fiber/coax (HFC) networks advantages of, B:412413 described, B:413421 evolution of, B411 Hydrogen loading, to increase photosensitivity, A482 Hydroxyl ion in Al/Ge/Si fibers, A 1 16 optical behavior of, A84-87

Hammingcodes, B915 cyclic nature. of, 917 Hamming distance, B:908 Hamming weight, B907 HDSL, B:503 Hierarchical networks, A30C-302 High saturation current photodiodes design of, A791-793 need for, A791 uni-traveling-carrier (UTC), A793-794 High-bitrateelectronics analog and mixed-function applications, A824-830 ASIC technologies for, A819424 broadband amplifiers, A:824-830 CDR circuits, A830436 demultiplexers, A836 equalizers, A:837-841 future of, A841 multiplexers, A836-837 High-bitrate receivers experimental data on, A805407 need for, A:78&785 sensitivity of, A:7%807 ultrawide-bandwidth photodetectorsin, A.785-79 1 High-bitrate transceivers hardware for, A819-821 high-speed IC technologies for, A:822-824 issues in, A821 High-bitrate transmitters carrier-suppressed RZ modulation in, A816-818 chirped return-to-zero modulation in, A815 design issues in, A81b819 directly modulated laser, A808409 duobinary coding in, A816 electroabsorption modulator, A809-8 10 lithium niobate, A:81&814 need for, A807-808 return-to-zero, A814815 types of, A 8 0 8 High-capacity, ultralong-haul networks challengesposed by, B:199-200 features of, B200-201 FEC in, B:208-211 noise issues in, B:201-204 optical networking in, B224-228 power issues in, B:211-213 prerequisites for, B 198 transmission impairments in, B:213-223 value of, B225226 High-speed TDM fiber nonlinearity and, B:247-275 pseudo-linear transmission of signals, B233-236, 275-289 sources of distortion, B:242-247 Higher-order compensation, for PMD, B:814815 Holmium-doped fiber lasers, A104

Impairment budget, B183-184 In-band ranging, B:461462 compared with out-of-band ranging, B462 in TCM TDM/TDMA system, B:462463 In-fiber gratings. See Fiber gratings Index tuning band filling and bandgap shrinkage for, A65Ck-652 bandgap independence of, A653 carrier-induced, A650 field effects for, A649450 free-carrier absorption, A.650 recombination, A554 thermal, A653 Index-guided microstmtured fibers, A 6 7 4 8 Indium phosphide waveguides advantages of, A:466 structure of, A457458 uses of, A.457465 Infinitesimal rotation, law of, B:733 InGaAs quantum dots active region of, A673 in VCSELs, A674 InGaAsP, lasers based on, A:572-573 Inner vapor deposition (IVD), A:ll3 limitations of, A 1 14 InP, nonlinearities in, A 4 6 4 6 6 Intel, financial figures for, B 5 2 Intensity modulation, A278 Intensity noise, in cable systems, B:432 Intensity-modulated direct-detection (IMDD) transmission formats, B:239-241 Intercarrier interface (IrDI), B:137 Interchannel crosstalk, A238-239 Raman gain, A239 Interferometers for grating writing, A491 Mach-Zehnder. See Mach-Zehnder interferometers to measure PMD, B 7 6 7 4 7 Michelson, A738,739 types of, A492,738-740 Intermodal dispersion, defined, B:905 International Telecommunications Union (rrv), and optical standards, B:139 Internet bandwidth for, B:7&75 bandwidth predictions for, B:53 connection length issues, B75-76 corporate traffic of, B:37 dominance of, B:27 and growth of metro networks, B:337 history of, B27-32 institutionaltraffic of, B:36-37 internationalexchange points of, B:35-36 killer applications in, B53 residential traffic of, B36 revenues from, B:23-24

zyxwvuts zyx zyxwvu

Index

1009

zy

zyxwvuts zyxwv zyxw

timing of changes of, B50 traffic figures for, B:18, B:19 traffic symmetry in, B 7 6 7 7 utilization issues, B:77 Internet Engineering Task Force (IETF), and optical standards, B:139 Internet growth aspects of, B:32-33 bandwidth growth, B:3341 causes of, B:42 disruptive innovation in, B:41-45 factors in, B32 issues in, B:20-22 predictions about, B:26 rate of, B17-19, B:51 traffic composition in, B:44-45 trends in, B:36-41 Internet protocol (IP), B:132 support for use of, B129-130 Intern&, B:38 Intersymbol interference (ISI), A:23 in optical preamplifier, A:803-805 linearity of, B:970 Intrachannel distortion, B:629 minimization of, B:631,633 W M , B:629-633 Ion-pair formation, A:87 IP (Internet Protocol), B:30 IP layer, recovery in, B:124 IP routers, evolution of, B:224 IP-over-glass architecture, B:224 IP-over-wavelength architecture, B:224 IP-over-WDM, protocol stacks for, B:104105 JANET, traffic figures for, B:20: B:21 Jones matrix, rotational forms of, B829 Jones Matrix Eigenanalysis (JME), B:736 concerns regarding, B:756 hardware for, B754 interleaving and, B:756-757 mathematics of, B:752-755 Junction trees, B:938439

birth of, A l , B:l catastrophic failure of, A564-565 and control of EDFAs, A20S206 directly modulated digital, A:613-625 distributed Bragg reflector (DBR), A:398,462, 591,592,64&642,645448,675-677

distributed feedback, A590-591, 502, 608410; 639-640 electroabsorption-modulated,A625-639 Fabry-Perot, A569, 589-590,624625 fast tunable, A461465 fiber grating technology in, A549-550 1480nm, A572-576 for grating writing, A489490 linewidth of, A:689-690 multifrequency, A462465 980 nm, A:564-572,575-576 1310nm, A605-612 pump, A564-583, B205-206 tunable, A397-398,599,638455,667468, 677478, B:346,486 use in telecommunications, A587-656. See also Telecommunication lasers VCSEL, A:601,668-697 Latching, A337-338 Layering ambiguities regarding, B:96 basics of, B:96 and planes, B:97,99 transport, B97,98 Lightwave communications capacity growth of, A 174 capacity trends for, A309-311 cumulative dispersion in, B:236,237 design challenges in, B:567 equalization techniques for, B:965-992 FEC codes for, B952-961 and growth of MANs, B:340-341 history of, A 2 4 B:24 modeling of, B968-971 origin of, A l , B:l recent history of, A:4, B:4 schematic of, A20, B:235 time-de endent effects in, B:67&672 LightWireqM ,B:422-424 costs of, B:424 Line coding, B:537 function of, B:539 types of, B539-540 Line-switched rings, B:113,115 Linear analysis, in photonic simulation, B597, 599-600 Linear binary codes block, B:911-912 choice of, B:914 concatenation of, B:925-926 cyclic, B:915-917 Hamming, B915 ML decoding, B914 minimumdistance of, B913414 modulo 2 arithmetic for, B:91&911 parity check matrix of, B:913 standard array decoding, B914 Linear electrooptic effect, A 2 6 0 Linear equalization, B:981-984 Linear lightwave technology, use in cable systems, B:430431 Linear PCM, in metro networks, B:415 Linewidth, A:689490

zyxwvutsrq zyxwv

Kerr coefficient, A650 Kerr effect, A:30, B:612 Kink, in lasers, A572

L-band amplifiers advantages of, A18&190 antimony silicates in, A137-139 characteristics of, A136137 nonlinearities in, A190-191 tellurites in, A123, 139 Label Distribution Protocol (LDP), B:135 Generalized (GMPLS), B135-137 Label switched paths (LSPs), B:133,135 Lambda services, B:338-339 Large strictly nonblocking cross-connects architectures of, A363-365 described, A363 performance of, A365 prototypes of, A.366 to restore mesh network, A.366368 using beam steering, A365-366 Lasers analog, A601412

1010

Index

zyxwvut

zyxwvutsr

Link control, of EDFAs, A203-205 Link state advertisements (LSAs), B:133 LINX (London Internet Exchange), growth rate of, B:33 Liquid crystal switches,A34Q-341 Liquid-phase epitaxy (LPE), A:596 Lithium niobate electrooptic effect in, A260 etching of, A267-269 optical properties of, A260-261 titanium diffusion in, A261,262 Lithium niobate amplitudemodulators bias stability of, A277 buffer layers for, A273 crystal orientation for, A272-273 directional couplers, A269 lumped-capacitance, 271-272 Mach-Zehnder, A269 modulation efficiency of, A273-277 modulation formats for, A276 temperatureperformance of, A278 traveling-wave, A271 Lithium niobate modulator transmitters lOGbit/s, A810 40Gbit/s, A811414 Lithium niobate optical modulators drive voltage for, A266-267 electrode fabrication for, A:262-263 electrooptic effect in, A260 manufacture of, A264-265 pigtailing and packaging of, A265-266 testing of, A266 waveguide fabrication for, A261-262 Lithium niobate switch arrays, A349-350 Lithium niobate waveguides advantages of, A468 structure of, A466 uses of, A46-68 Local -networks (LANs), speed trends in, A :46 Long-distance telephone service historical growth rates of, B22 Internet as fraction of, B73-74 revenue issues, B:74 Long-haul systems, A19, B:65-67 See also Ultralong-had networks hierarchy of, A300-301 impairments in, A21-22 OXCs in, A300-306 performance requirements for, A18 span loss in, A22-23 trafficfiguresfor,B18,B:19 typical link in, A20-22 Long-period gratings See Transmission gratings Loss-gain factor, calculation of, E242 Lowdensity parity-check codes, B:951-952 in lightwave communications, B961 Low-water peak fiber (LWPF), A37 advantages of, A45 LPoz mode dispersion compensation, A54a-549 Lucent founding of, A3, B:3 Lambdarouter product of, A386 Lumped-capacitance amplitudemodulators, 271-272

single-channel transmission simulations in, B:88&887 MAC framing in Ethernet, B519-520,533-535 in flow control, B:533-535 in TDMA, E463466 Mach-Zehnder interferometers (MZI), A269, B:223 in AM transmission, B:868473 cascaded, A42-3 1 described, A270-271 simulation of, B:577 for slope matching, B:699-700 switches using, A432433 with thermal phase tuning, B:691 in 3R signal regeneration, A73&739,744-748 Mail service, historical growth rates of, B:22 Management plane, B97,99 Manchester coding, B539, 540 Margin, measurement of, B174-175 Marginalization, of product function (MPF), B934938 Maximum a posteriori symbol detection (MAF'SD), B985 fixed-lag, B:990-991 Maximum likelihood (ML) decoding, B914 via distributive law, B933-9 junction trees in, B:938-939 message passing in, B:!XCb948 MPF problem and, B:934-938 Maximum likelihood sequence detection (MLSD), B:972-977 Media-independent interfaces (MII), B:543,544546 Medium access control algorithm for, B465 mechanisms of: B:463 protocols of, B463465 statistical multiplexing gain in, B:461-466 Memory chips Moore's law applied to, B:47 trends in, B52 MEMS (microelectromechanicalsystems) technology, A341-343,390 for dispersion compensation, B693 for MANs, B347 Merit Network, B38, B40 Mesh topologies described, A343-344 andfailurerecovery, B:113,115-116 compared to ring topologies, B:l17-118 hybrids with ring topologies, B364-369 and restoration, A327 restoration using OXCs, A366368 Message passing, B940-948 MetamorphicDBR, A67&677 Metro communications systems described, A36 dispersion compensation and reach in, A 3 9 4 0 evolution of, A666 fiber capacity limitations in, A w l fiber choice for, A45 fiber economics for, A 4 3 4 fiber requirements for, A 3 6 3 9 future trends in fiber usq A44 1400nm market in, A 4 2 4 3 13OOnm market in, A42 performance requirements for, A667668 VCSELs for, A668469 Metro core rings, B:335-336 Metro edge rings, B:333-335

zyxwvuts zyxwvutsrqpon

M-ary ASK systems B865 equivalent transmission bandwidth of, B876 power spectral densities in, B876-877

zy zyxwvuts zyxwv Index

1011

zyxwvutsrq

DWDM, B:373-375 migration strategies for, B:38 1-382 Metro networks (metropolitan area networks, MANS), B329-330 access technologies for, B:339-341 architecture of, B:348-349,413-417 asynchronous data transport in, E335 capacity issues, B342 channel provisioningin, B:383-384 component technologies for, 9344-347 domain interfacing in, B:385-386 DWDM in, B331-332,344,347-373,556 economic issues of, B:369-370 future of, B387-390 Gigabit Ethernet in, B:557 growing demands on, B:330-332,337-339 interoperability issues in, B:382-383 migration strategies for, B:370-373 network management for, B386-387 optical hybrid/mesh networks in, B364-369 packet switchingin, B:379-381 protection in, B556,384-385 protocols for, B:414 regulatory issues, B341-342 requirements for growth of, B:343-344 RF technologies in, B415 traditional architectures for, B:332-336 transport technologies in, B:414-417 Metro-core internetworking, and multiple routing domains, B:143 Michelson interferometers,A:738,739 Microelectromechanicalsystems (MEMS), A341-343,390 for dispersion compensation, B:693 for MANS,B:347 Microstructured optical fibers design of, A67 index-guided,A67-68 photonic bandgap, A:6!%70 Midspan spectral inversion, B69C-691 Midstage attenuators, A:186188 MILNET, B:31 Minifiber node (MFN) technology, B:421422 Minimum distance calculation of, B:912 defined, B:909 Minimum distance algorithm, B:908 Minimum mean square error (MMSE), B:982,984 Modified chemical vapor deposition (MCVD), A113,114,115 Modified return-to-zero DWDM, B:891-893 Modulation direct, A808-809 duobinary coding in, A816 electroabsorption and, A 8 0 W 1 0 lithium niobate and, A81&814 retum-to-zero, A:814-815 simulation of, B:577-578 Modulation formats, A276 choice of, 3:166-172 need for alternative, B362-866 Molecular beam epitaxy (MBE), A596,597 Moore's law application to photonics, B:421 background of, B:46 for data traffic, B46-51 effects of, B:51 proposed application to Internet, B19, B:32 Mosaic, B:32

MP Lambda S, B:135 Miieller matrix method (MMM), B752-I56 .~ hardware for, B:754 interleaving and, B:756-757 rotational forms of, B329-830 Multi protocol label switching (MPLS), B133-135 Multicarrier interconnection, and multiple routing domains, B:143 Multichannel compensation, for PMD, B:816-317 Multifrequency lasers, A:462465,648-649 in PONS, B486 Multilevel signaling duo-binary DWDM, B:890 efficiency gained by, B:893494 M - q ASK, B:865,87&877,88M87 modified RZ DWDM, B891493 OSSB DWDM, B:890-891 Multimode fiber (MMF), A45 characteristics of, 4-7 fiber and source characterization of, A:49-51 mechanism of, A:47-49 use in Ethernet, B:536-537 Multimode interferencecouplers, A:428 Multipath interference (MPI), in cable systems, B:432 Multiple access subcanier, B:46&l67 time-division, B:457466 wavelength-division, B:468 Multiplechannel Bra& gratings, B:664 long-length, B:664665 sampled discretechannel, B:66&668 Multiplexed semiconductor lasers, A:246 Multiplexing high bitrate, A:836-337 methods of, B:417420. See also specific types of multiplexing Multisection compensation, for PMD, B:815-816 Multiservice Provisioning Platform (MSPP), B:415416

Napster, B:37, B41 described, B:4243 history of, B:43 NCP protocol, B:30 Negative dispersion fiber (NDF): A37 advantages of, A:45 Neighbor discovery and maintenance, B:132, 139 Neodymium, in tellurite glasses, A 1 18 Neodymium-doped fiber amplifiers, A104,105 Neodymium-doped fiber devices, Al/Ge/Si and variants in, A117-118 Neodymium-doped fiber lasers, A:104 Netscape, B:32 Network Access Points, statistics on, B:35 Network management, B:386 for metro systems, B387 Noise assessment of, B:162-163 ME, A:225,228-234,705, B:160-161,201-202, 905 detection of, B905 excess, E161 sources of, B:905 total, B162 in ultralong-haul systems, B:201-204

zyxwvutsr

1012

zyxwvut zyxw zyxwvutsr Index

Noise figure calculation of, A227,705, B239 defined, A225-226 effective,A 2 2 8 Non-CVD (chemical vapor deposition) glasses, A80 Nonblocking connectivity, issues with, A:344 Nonlinear distortion, in cable systems, B:432 Nonlinear gates, in 3R regeneration, A735756 Nonlinear index reduction of, B166 of single-modefiber, B 1 6 H 6 4 Nonlinear optical loop mirrors (NOLMs), A738 Nonlinear Schrodinger equation, B305 generalized, B:247 Nonlinearities and analog lasers, A 6 0 4 4 0 5 cross-phase modulation. See Cross-phase modulation (XPM) fiber-based, B:247-275 four-wave mixing. See Four-wave mixing (FWM) intrachannel distortion, B629433 mathematics of, B612-613 origins of, B611412 self-phase modulation. See Self-phasemodulation (SPM) simulation of, B:579,600 suppression of, B:63%36 types of, B:250 Nonreturn-to-zero(NRZ) modulation, A278, B:222-223,865 enhancements to, A281 and PMD modulation, B807 in undersea applications, B:172 XPM-induced amplitude distortion in, B624625 Nonuniform gratings apodization in, A513 applications of, A509 spectrum calculation of, A510-519 Nonzero dispersion fiber (NZDF), A37,38 advantages of, A45 Nonzero-dispersion-shifted fibers (NZDSF), B:215-216,650,651 dispersion in, A:23,2425,281, B216,218 NPL network, B29 NRZ clock regeneration, dispersion monitoring using, B:705-706 NRZ format evolution of, B309 history of, B:307 and nonlinearities, B:308 NSFNet, B:28, B:31 Null fiber couplers, A 5 4 8

requirements for, B493 transmitters for, B493-494 OPALS simulation tool, B:568,569 Opaque interfaces benefits of, A:31C317 issues with, A317 Opaque optical networks, B 8 W O advantages of, B:361 disadvantages of, B362 recovery in, B120 wavelength conversion in, B361 Open Shortest Path First (OSPF), B 132 LSAs and, B132 neighbor discovery and maintenance, B132 Optical access networks, B420-421 bidirectional transmission issues, B449-454, 494-496 current state of the art of, B496-498 DSL in, B501-504 Ethernet, B:448 fiber-in-the-loop systems, BW1,443-444 FTTx systems, B:44243,497-498 full-service area networks, B:44748 future of, B:498499 multiplexingin, B:450-454 optical components for, B:488496 PONS, B:44142,445 PSPONs in, B:454479 m,B448 system architectures for, B499-501 transmission fiber for, B:448 wavelengths for, B:44849 WDM PONS in, B:479-488 Optical add-drop multiplexers (OADMs), A 174, B70 architecture choices for, B:71 in networks, A381 simulation of, B:578 in dynamic rinm B356-357 in static rings,B:352-354 technologies for, A.382-383 OptLal amplifiers, simulation of, B:581 Optical channel layer, B99 Optical channel monitoring, A:S46-547 Optical channels characteristics of, B100 proposed standard for, B10CM01 Optical cross-connects (OXCs), A174-175,315-321 applications of, A321-330 crosstalk in, A.335-336 evolution of, A306-309 features of, A307,311-312,389-391 fiber interface for, A337 granularity of, A331 internetworking of, A347 latching of,A337 in long-haul transport, A30C306 multivendor operation, A312 nonlinear effects and, A338 and OAMM features, A312 in optical hybrid/mesh networks, B365 optical performance properties of, A330-339 optical switching for, A295-300 performance features of, A:338-339 polarization-mode dispersion in, A336 port count and, A330 positioning of, A329 power issues with, A337 power loss and, A333,335

zyxwvuts zyxwv

zyxwvuts

OADMs (optical add-drop multiplexers), A 174, B:70 architecture choices for, B:71 in networks, A381 simulation of, B578 in dynamic rings, B356-357 in static rings, B352-354 technologies for, A.382-383 OAMBtP (organization, administration, maintenance, and provisioning), A312 OC48 interface specifications, A.334 OG192 interface specifications, A334 On-offkeying (OOK),A278 One-fiber Ethernet point-to-point receivers for, B:494

zy zyxwvuts Index

reliability issues of, A338 scaling and, A.331 simulation of, B:578 size issues with, A:337 small optical switch fabrics, A:343-347 strictly nonblocking, A363-368 switch technologies for, A339-343, B:36 switching frequency and, A332-333 switching speed of, A332 wavelength dependence of, A.337 wavelength-selective, A347-363 Optical Domain Services Interconnect (ODST), and optical standards, B:139 Optical fibers nonlinearity of, B:247-275 parameters of commercial products, B:249 performance requirements of, A17-18,19, 389-390 technologies for, A390-391 Optical Internetworking Forum (OIF), and optical standards, B:139 Optical layer ambiguities regarding, B96 basics of, B:96 and planes, B:97,99 recovery in, B:124,125 role of?B:101-108 sublayers of, B99-100 Optical layer crossconnects (OLCCS, OLXCS), B:106 advantages of, B:107-108 types of, B:69-70 Optical layer switching, B:105-106 alternatives for, B:105-106 Optical loopback, B482-483 optical multiplex section (OMS) layer, B:99 Optical network architectures transparency or opacity of, B 8 a 9 unit costs of, B86 Optical network services advantages to be offered by, B:82-85 growth of, B.224-225 ISP needs, B:82 issues in, B:81-82 types of, B:85 Optical packet switch, A:393-394 Optical phased array (PHASAR), B:481 Optical preamplifiers circuit noise in, A80&801 effect of optical filter bandwidth on: A799-800 extinction ratio of, 801-803 intersymbol interference in, A803405 noise sources in, A:797-799 sensitivitylimit of, A:799 sensitivity of receiver using, A796805 signal photocurrent in, A796-797 Optical receivers, simulation of, B582 Optical signal-to-noise ratio (OSNR), B202-203 calculation of, A Z O , 179-180, B:237,239 effects of, A180-181 improvement of, B:203-204,20%206 relation to bit-ermr rate, B:238 Optical single-sideband (OSSB) generation, B:865 broadband, B884886 DWDM, B:89C-391 with Hilbert-transformed signals, B:889490 power spectral densities in, B88C-386 single-channeltransmission simulations in, B:88!9-890

1013

subcarrier, B881-884 Optical switching fabric advantages of, A319-320 cross-connectswith, A:315-316 disadvantages of, A:320 need for, A374 with opaque interfaces, A316-317 requirements and technologies of, A329-343 with transparent interfaces: A31&319 Optical TDM in 16OGbit/s systems, B281-284 SOAs in, A720-722 for ultrahigh data transmission rates, A818 Optical timedomain reflectometry (OTDR), B:470 polarization, B:471 WDM-based, B471 Optical transmission section (OTS) layer, B:99 Optical transport systems advantages of, B:83 capacity trends of, B : M 5 defined, B57 described, B:64 domains of transparency in, B:91-92 failure management in, B71-72,109-126 intelligent, B:70-71, 83 intercity, E78 layering of, 96101 local, B:78 multivendor internetworking in, B:64 opaque, B88-90 polarization effects in, B180-183 reconligurabilityof, B68-70 recovery in, B120-123 relationship between needs and functionality, B84 service issues for, B:73-74 signalingformats of, B 167 SONET and SDH, B:5743 standards for, B:139-140 testing of PMD-induced problems in, B772-784 transparent, B 8 N 8 types offailures in, B:108-109 Optical virtual private networks, B 8 5 Optoelectronic transceivers, high bitrate, A819424 Optomechanical switches, 343 Organic nonlinear optical (NLO)polymers, A:283 Organometallicvapor-phase epitaxy (OMVPE), A:596,597,598-600 Orthogonal polarization pairwise, B:166 to suppress distortion, B:635 Oscillation frequency calculation of, A621 minimum requirements for 10Gbit/s transmission, A:621-625 OS1 (Open Systems Interconnection) reference model, B:517-518 Ethernet architecture in, B:542 repeaters in, B527-529 Out-of-band ranghg, B:46C461 compared with in-band ranging, B:462 Outcoupling devices for optical channel monitoring, A546547 for polarization monitoring, A547-548 Outer vapor deposition (OVD), A 1 13 Oxide glasses A/Ge/Si, A:109-118 characteristics of, A109 OXiomm, B424-425

zyxwvutsrq zyxwvutsrq zyxwvutsrq zyxwv zyxwvutsr

1014

Index

zyxwvut

P-I-N diodes, simulation of, B:582 Packet rings, B38C381 Packet switch, A:377, B:530 application of, A391 capacity of, A392 vs. Circuit switching, A:37M76 optical, A394395 schematic diagram of, A393 state-of-the-art, A:391-393 switch fabrics for, A394 Packet switching vs Circuit switching, B:516 future of, B387-389 in metro networks, B379-381 optical, B:387-389 Pairwise orthogonal polarization, B:166 PAM 5 x 5 coding, B:540,541 Parallel concatenated convolutional codes, B948-950 Parity check matrix, of code, B:913 Passive bus, B:442 Passive double star (PDS), B:441,442 Passive optical networks (PONS),B:44142 ATM, B445-446 availability issues of, B:472 broadcast replication in, B474 channel broadcasting on; B475476 compared to WDM PONS, B:487 composite (CPON), B:484485 fault location in, B:469471 hybridized with WDM PONs, B488 integrated baseband broadcast on, B 4 7 U 7 7 narrowband, B445 one-fiber FSAN-compliant, B 4 8 8 4 9 power-splitting, B:454479 privacy issues in, B468 protection for, B:471474 vs point-to-point, B:477478 reliability of, B471-472 security issues in, B468-479 splitters in, B492-493 SuperPONs, B:478-479 WDM, B:479488 Path-switchedrings, B:6142,113,114-115 PAUSE frames, B:533-534 Payload overhead (POH), B63 Peak detection, dispersion monitoring using, B:707 Peak distortion, B:983 Perfect codes, B:915 Persuasion, in fault management, B:72 PFBVE fiber, A.58 applications of, A 6 5 4 7 attenuation of, A m 1 bandwidth of, A 6 1 4 3 differential mode attenuation in, A:63 geometry of, A:5%59 mode coupling in, A 6 2 4 3 reliability of, A.63-64 Phase diversity detection, B:819 Phase masks properties of, A493494 to write gratings, A:491-493 Phase shift dispersion monitoring using, B:707-708 Pockels effect and, A:431-432 use of, A510 Phase-modulated (PM) modulation, A276 Phase-only filters, B:692 for slope matching, B699-700

Phosphorus, as dopant, A483 Phosphosilicate fibers, in cascaded Raman fiber lasers, A:247-248 Photodetectors, A785 distributed, A:78%789 efficiency issues, A786787 structure of, A785 Photodiodes avalanche, A:790-791 high saturation c u m t , A791-794 resonant cavity, A789-790 saturation currents of, A794 waveguide, A:787-788 Photonic add/drop multiplexers (PADM), B:58,67 recovery in, 121 Photonic bandgap fibers, A:69-70, B:694-695 Photonic cross-connects, B58 Photonic integrated circuits, A:599 Photonic simulation advantages and disadvantages, B:605 analog, B603-604 automated analysis in, B:595403 automated optimization of, B:589 automated parameterization of, B:589,591-592 automated synthesis in, B:59M95 benefits of, B:565 BER estimation, B:584 black box model for, B:575 component sweep, B:588-589,590,592 control of, B:585-589 customization of, B:572-573 data exchange in, B573 Design assistants in, 595, 596, 599 evolution of, B566-568 graphical user interfaces for, B568-569,57>574 hierarchy in, B584585 of higher-order functions, E585 model development for, B574-576 of modulators, B:577-578 module interfacing for, B569-571 multiple signal representations in, B571-572 need for, B:605 of optical amplifiers, B581 of optical receivers, B:582 of optical sources, B:576-577 parameter sweep, B586588 of passive components, B578 physical model for, B:575 of regenerators and wavelength converters, B:581-582 of topologies, B:589,591 uses of, B:566 Photonic transport networks, B58 Photosensitivity birefringence, A483485 boron-induced, A483 ceriumbinduced, A483 hydrogen-induced, A482 in germanosilicateglass, A480482 in phosphorus-doped silicates, A483 tin-induced, A483 type 11, A:481 to U V light, A481482 Ping-pong multiplexing, B:451 Planar Bragg gratings, A453454 Planar couplers, B493 Planar lightwave circuitry, in bidirectional modules, B:495496 Planar waveguide filters, B:345-346

zyxwvutsrq zyxw

zyxwvutsrq

Index Plastic optical fibers applications of, A:6S67 attenuation of, A:5!9-51 bandwidth of, A61-63 chemistry of, A:59 connectability of, A 6 4 6 5 geometry of, A58-59 history of, A57 reliability of, A:63-64 PMD nulling, B811412 Pockels effect, A260,649 for index tuning, A:649 phase shifters based on, A:431432 Point-to-point transmission systems FITL systems, B:440-441 metro systems, B:348-351 vs PONs, B:477478 Polarization hole-burning (PHB), B:180, 181-182, 221 counteracting, B:183 illustrated, B182 Polarization interleaving, B:798-802 Polarization monitoring, A 547-548 Polarization multiplexing PMD impairments to, B:795-798 polarization beam splitters for, B:796 Polarization-dependent chromatic dispersion (PCD), B737-738,794 Polarization-dependent gain (PDG), B:220,221 in Raman amplifiers, B:802403 Polarization-dependent loss (PDL), B 180, B220, B:663 Polarization-dependent signal delay method, B:747-749 hardware for, B:749 issues in, B:75&752 mathematics of, B:749 Polarization-mode coupling, B:729-730 correlation length and, B:730-731 Polarization-mode dispersion (PMD), A31, B:180, 182! 220-221.233 backscattering measurements of, B759-761 birefringence and, B:727-729 calculation of, A:32 causes of, A:336 characteristics of, B:725726 correlation functions for, B:771-772 defined, B:905 distinguished from GVD, B:726 electrical compensation for, B817420,981 emulation of fiber-based, B:777-779 emulation of first-order, B:774-776 emulation of second-order, B:776 fibers low in, B:80M07 frequency-domain behavior of, B:728 gain effects of: B:802403 higher-order, B:222, B739 impairment due to fist-order, B:784-785 impairment due to second-order, B:791-795 interferometric measurement of, B:746-747 intrinsic or short-length, B:729 JME analysis of, B:752-757 launch penalties from, B787-788 measurements of: B740-742 mitigation of, B:803425 models of, B:773-774 modulation formats and, B:807-809 monitoring of, B820-825 numerical simulation of, B779-784

zyx zyx 1015

optical compensation for, B809-817,981 origins of, B:725 and polarization interleaving, B:798402 in polarization multiplexing, B:795-798 power penalties from fist-order, B:78S787 Principal States model of, B:731-733 probability densities of, B:763,764-767, 768-769 PSD measurement of, B:747-752 in Raman amplifiers, B:802-803 relation between vectors of, B828-829 scaling of, B:767-771 second-order, B:736-739 simulation of, B:579-580,601603 statistical issues regarding, B:762-764 statistical theory of, B:730,731 system outages due to, B:788-791 time-domain behavior of, B:728-729,804-806 Polarization-mode dispersion (PMD) vectors, B:733-736 characterization of, B745-762 concatenation of, B:742-745 correlation functions of, B:742 second-order, B736-742 second-order measurement of, B:757-758 Polymer waveguides advantages of, A:455 structure of, A454 uses of, A454455 Polymeric electrooptic modulators, A:283 design of, A284285 manufacture of, A285-288 Polymethylmethacrylate (PMMA), optical characteristics of, A284 Polynomials defined, B:918 degree of, defined, B918 irreducible, B:918-9 19 operations on, B:918 primitive, B:920-922 Port count, A:303-304 approximation of, A:305 Positive dispersion, B:652 Power management for long-haul networks, B:Zll-212 simulation of power budget, B:596,598 Power scaliig optimal fiber for, A 155-1 58 tapered multimode oscillators in, A152-154 Yb transitions and, A:149-152 Power spectral densities, B:873475 in binary ASK systems, B:875476 in duo-binary systems, B:877480 in multilevel ASK systems, B:876-877 in OSSB systems, B:880-886 Power splitters, for OX&, A:338-339 Power transients in EDFAs, A.198 in EDFA chains, A20C-202 Power-splitting PONs (PSPONs), B454 distinguished from WDM PONs, B:479-480, 501 downstream multiplexing in, B:456457 optical split ration in, B:455456 splitting strategies for, B:454455 upstream multiple access of, B:457468 Praseodymium, in tellurite glasses, A 118 Praseodymium-dopedfiber lasers, A 105 Principal states of polarization (PSP), B:732-733 bandwidth of, B:74C-742

zyxwvuts

1016

Index

zyxwvut zyxwvut

Principal states of polarization (FSP), continued depolarization of, B738 Privacy, in access networks, B468 Processor speed, Moore's law applied to, B:47 Product codes, B:928-929 for lightwave communications, B:957-958 Protection, B:109 events covered by, A325-326 importance of, A321-322 OMS-level, B:121-122 of PONS,B:471474 signaling of, B:384385 types of, A:322-325 Provision, automated, B:137-138 Provisioned bandwidth service, B:85 Provisioning, OXCs in, A:321 Pseudo-linear transmission, B:233-234 defined, B:234-235 experiments in, E275289 in 40 Gbit/s systems, B276281 need for, B:235-236 in 160Gbit/s OTDM systems, B:281-289 precompensation and, B:271-273,275 propagation of short pulses in, B:255-256 PSP transmission, to control PMD, B:81&811 F'TP (point-to-point), in access networks, B:448 Pulse broadening, B244 Pulse chirping, B:244 Pulse compression, to control PMD, B814 Pulse system CRZ, B:169-171 NRZ,B172 optical solitons, B171-172 unipolar, B167-168 Pulse width, calculation of, B:242,243 Pump control, of EDFAs, A203 Pump depletion, in Raman amplifier, A237 Pump lasers equivalent noise figures for, B:205-206 history of, A563-564 invention of, A:563 980nm, A564-572 980 vs 1480nm, A575-576 packaging of, A581-583 reliability of, A576578 wavelength and power stabilization in, A:578-581

zyxwvutsrqp zyxwvutsrqp zyxwvutsrqp zyxwvutsr zyxwvuts gain characteristics of, A194 in high-bitrate receiver, A807 history of, AZ48-249, B206205 to improve SNR, 207 multiplexed semiconductor lasers in, A246 noise in, A:225-236 path-averaged power of, A23S235 polarization-dependent gain in, B:802-803 pump depletion in, A237 rate equations for, A219-223 Rayleigh scattering and, A:241-244 signal effective length of, A236235 simulation of, B:581 speed of, A580 spontaneous emission in, A228-234 to suppress distortion, B635 temperature dependence of, A244246 theory behind, A21%224 undepleted pump approximation of, A223- -224 and undersea communications,B:191 Raman gain calculation of, A193 coefficient of, A.30,217 in single-mode fiber, A216-219 Raman lasers and amplifiers, fiber grating technology in, A550 Raman scattering, A213 physics of, A:215-216 Ranging,B:459-460 in-band, B:461462 out-of-band, B:460461 Rayleigh scattering, A223 characteristics of, A241-242 noise caused by, A.225,242-244 and Raman amplification, B206207 Reamplification, SOAs in, A720 Receiiers high bitrate, A784407, B:282-284 for onefiber Ethernet, B494 simulation of, B:582 TDMA PON, B491-492 tunability of, B68 using avalanche photodiodes, A795-796 using EDFAs, A796405 for wavelength switching, A398-399 Reconfigurability importance of, B:68 methods of ensuring, B:68 multiplexing and, B70 OLXCs and, B69 Recovery, B:109 conceptsof,BllO-111 methods of, B:lll-117 multilayer considerations in, B:123-126 options in optical networks, B:12&123 topologyand, B:ll&lll Reed-Solomon codes burst error correction using, B:924 changing length of, B:925 codeword error probability, B:924 coding gain of, B:959 concatenation of, B:959-960 decoding of, B925,958 generator matrix for, B:923-924 for lightwave communications,B:958 minimum distance in, B922-923 performance of, B958 uses of, B:922 Reflection filters

zyxwvut

Q-factor and bit-error rate, B:17>174 formula for, B:172 limitations of, B:176-177 Quantum well disordering, A599 Quasi-phase matched wmlength conversion, A 4 6 8 Radiation-mode coupling, A527-530 suppression of, A529 Radio frequency. See R F Raman amplification advantages of, A213-214 benefits of, A194197 cascaded Raman fiber lasers in, A247-248 constraints of, A236241 counterpropagating vs copropagating, B208 crosstalk in, A238-241 discrete, A249-250 distributed (DRA), A29-30,231-234,251, B:204-207

zy zyxwvutsr Index

addldrop, A541-543 dispersion-compensation,A543-546 Fabry-Perot guiding, A:540-541 Reflection gratings. See Bragg gratings Refractive index, modulation of, in fiber gratings, A:495496 Relative intensity noise (RIN), A:687-689 Relaxation oscillation, B968 Repeaters characteristics of, B528 in Ethernet, B:527-529 in star topology, B:528 Reservoir channel, A715 Reshaping of signal, SOAs in, A720 Resilient packet ring (RPR), 416 Resonant cavity photodiodes, A789-790 Resource discovery, B 139 Restoration, B:109 failure scenario and recovery, A:328 network node and cross-connects, A327 topology and, A327, B:l10-111 Restoration and Provisioning Integrated Design (RAPID), B116 Return-to-zero (RZ) modulation, A282,814815, B:223 carrier-suppressed,A816-8 18 chirped, A 8 15 collision-induceddistortion in, B62M29 and PMD modulation, B:808 Reverse dispersion fibers (RDF): B:219 R F power, use to monitor PMD, B822 R F power fading, dispersion monitoring using, B:705 R F spectrum, use to monitor PMD, B:82&822 R F technology feed-forward hybrids, B428,429 future of, 429430 GaAs technology in, 429 power-doubling hybrids, B:427429 push-pull hybrids, B:427,428 Right-of-way topology, B l l 9 , 120 Ring gateway interconnection, B364 Ring resonators, tunable, B:691 Ring topologies advantages of, B:368-369 compared to mesh topologies, Bll7-118 described, A343-344 diversity in, BI19-I20 dynamic, B355-361 examples of, E 117 hybrids with mesh topologies, B366369 in metro networks, B:351-364,413414 self-healing, B357-358 SPRING, B358-359 static, B352-355 transparency issues, B:361-364 using OXC fabrics, A348 virtual, B l l b 1 1 9 Ring tributary interconnection, B366 Ripple, B660 characteristics of, B662 multipl-hannel, E664668 sources of, B66(M61 Route failures, B:108 Routers, A 3 0 0 described, B:531 function of, B:531-532 modem advances in, B532 ports of, A344

1017

transparency of, A383 Routing effects of impairments on, B:9495 hierarchical vs. nonhierarchical, B:76 Routing and wavelength assignment problem, B:92-93 RWA algorithms, in all-optical rings, B363-364 RZ clock fading, dispersion monitoring using, B705-706

zyxwvut zyxwvutsrq S-band amplifiers gain-shifted pumping in, A 142-145 power scaling in, A149-158 thulium-doped, A14&149 Sampled-gratingDBR (SG-DBR) laser, A645-647 Saturable absorbers in optical regeneration, A74%750 properties of, A752.754 and regeneration of pulse marks, A752-754 technologies of, A750-752 in 2R regeneration, A:756756 Schawlow-Tomes linewidth, A689 Schottky's formula, A226 SDH (Synchronous Digital Hierarchy), B59 See also SONET contrasted with SONET, B:63 Secondary hubs architectures for, B417 multiplexing techniques for, B:417420 Security, of access networks, B:468469 Selective area growth (SAG), A599 Self-healing ring?(SHRs), B60,357-358 Self-phase modulation (SPM), A21, 282, B253-257 described, B:648 illustrated, B:615 mathematics of, B613-614 Semiconductor optical amplifiers (SOAs), A:461 in access networks, A722-723 advantages of, A724 in all-optical signal processing, A:716722 applications of, A710-723,739-740 future of, A723-724 gain in, A700-702,706-709 history of, A699 mechanism of, A699-700 noise figures of, A705-706 output power of, A703-705 phase shift in, A739 polarization properties of, A:703 simulation of, B581-582 in 3R regeneration, A744748 Sensitivity of avalanche photodiode, A795-796 of optical preamplifier, A796-805 of p-i-n detector, A794795 Service discovery, B:139 Service layer, recovery in, B12S124 Set partitioning, B976977 Set-and-forgetstrategy, B:482 SETIBhome, B:44 sgn-sgn least mean square algorithm, B983 Shared protection, A:324,325-325 in SOSFs, A347 Shared protection rings (SPRING), B:358-359 Short-haul systems, lasers in, A594595 Short-period gratings. See Bragg gratings Short-wave VCSELs, A45 Shot noise, A226, B905

zyxwvutsrq

1018

Index

zyxwvut zyxwvuts

Signal regeneration all-optical, A732-775. See also All-optical regeneration SOAs in, A720 3R, A733-775 2R, A:720 Signal splitting, in fault management, B:72 Signal-to-noise ratio (SNR) dehed, B905 estimation of, B:162-163 optical (OSKR), A20,179-181, B:202-203, 237-239 simulation of, B:59&597 types of, A226227 Signaling formats, B187 Silica waveguides advantages of, A454 dynamic dispersion compensators, A452453 dynamic gain equalization filters, A433435 dynamic passband shape compensators, A451452 planar Bragg gratings, A453454 Pockels-based phase shifters, A431432 structure of, A406-4Q9 topology of, A409-413 using Mach-Zehnder interferometers, A429430, 432-433 vertical tapers and segmentation of, A416418 waveguide grating routers in, A42W23 wavelength add-drops, A444-451 wavelength-selectivecross-connects, A 4 3 5 4 4 Silicon-on-insulator waveguides advantages of, A457 structure of, A456 uses of, A 4 5 U 5 7 Single sideband (SSB) modulation, A276 Single-channel amplification analog transmission, A71 1 digital transmission, A710-711 Single-mode fiber chromatic dispersion in, B:644-645 in MANS,B:346 nonlinear index of, B:163-164 Single-sideband modulation optical use of, B:865,880-891 PMD tolerance of, B:808 Size, of code, B:907 Slope matching DCF-based, B:697-698 FBG-based, B:698-699,700-702 Mach-Zehnder-based. B:699 need for, B69&697 using Gires-Tournois interferometers, B:700 using phase-only filters, B699 VIPAIbased, B:699 Small-scale optical switch fabrics (SOSFs) described. A345-347 and intemetworking, A347 and protection, A347 Small-signalmodulation (SSM), A:682-685 SOA-MZI-based 3R regeneration decision block for, A:744-745 mechanism of, A:747 transmission properties and, A:745-747 Soda-lime glasses, A109 Sol-gel processing, of fluorozirconates, A92-93 Solitons DC, B:254 dispersion-managed, B247-248,30%323

evolution of systems using, B:309 history of, B305-310 mathematics of, B306 nonlinearities and, B614 PMD resistance of, B80W09 SPM and, B:253-254 in undersea systems, B:171-172 SONET (Synchronous optical network), B57 See also SDH (Synchronous digital hierarchy) advantages and disadvantages of, B:342-343 alternatives to, B:lM characteristics of, B62-63 components of, B:59-62 contrasted with SDH, B:63 described, B:332-333 future of physical layer functions, B:103-105 history of, B224 interface specifications, A:334 and IP services, B102-103 layers of functionality of, E62 in metro networks, B332-333,414: 415 multiplexing issues in, B:101-103 next-generation, B:375-379 recovery mechanisms for, B:61,112-117 signal rates in, B:59 survivability features of, B108 SONET-based systems features of, A345 in metro networks, B:414 in secondary hub architecture, B417 Space-division multiplexing (SDM), B:450 Span length and power consumption, AZO-22 Span loss, A22-23 Span protection, A322,323 Spare capacity, for failure recovery, B: 110,111 Spatial mode conversion devices fiber lasers, A549-550 LPOZmode dispersion compensation, A548-549 null fiber couplers, A548 Raman lasers and amplifiers, A:550 Spectral efficiency, B:240 Spectral hole burning, A185 consequences of, A185-186,6G9-611 Spectral holography, B692 Spectral sampling, A:424427 Spectral slicing downstream, B:485 upstream, B:483484 Splitters, B:492493 in fault management, B:72 fused couplers, B493 for OXCs, A:338-339 planar couplers, B:493 Square mesh network, A:3M Standard array decoding, B:914 Standard single-mode fiber (SSMF), A37 advantages of, A45 Star coupler, A414416 size of, A418420 use of, A417 Star topology, B:404 in Ethernet, B:525-527 repeaters and, B528 in secondary hub architecture, B:417 State-of-polarization (SOP) drift, B:180 Staticrings components of, B:352-353

zyxwvuts

zyxwvutsr

zy zyxwvutsr Index

OADM nodes in, B:352-354 WDM in, B354-355 Step-index PMMA fibers, A57 production of, A58 Stimulated Brillouin scattering (SBS), A281 in cable systems, B:432 Stimulated Raman scattering (SRS) in cable systems, B:432 in EDFAs, A193-197 effect of, A29, 193 efficiency of, A29 equation for, A29 in power management, B:213 Stimulated scattering, B:612 Stitching error, B:661 Stokes scattering, A:215,216 mechanism of, A219 Storage area networks (SANS),B338 Strict transparency, defined, B86 STS-I (Synchronous Transport Signal-1), B:59 Subcarrier multiple access (SCMA), B:46&467 Subcarrier multiplexing (SCM), B:405, B:452453 dispersion compensation in, E702-704 Subrate TDM grooming, B364 Super-band amplifiers, A139-140 SuperFQNs, B:47M79 Superstructure-grating DBR (SSG-DBR) laser, A54548 Survivability:B108 OXCs in, A:321 protection, A:321-326 restoration, A:327-329 Switch fabric, for failure recovery, B:lIO, 111 Switch technologies, for MANs, B347 SWITCH network, B:38, B39 Switches, A295-300; 344-368 circuit vs. packet, A375-376 in Ethernet, B530-531 function of, B:529,530 future of, A308-309 need for, A296-300 technologies for, A339-343 Switching arrays crosstalk control in, A350-351,355,359-362 crosstalk propagation in, A352-355 destination addresses of level-o and level-1 sign2 A355-357 discussed, A351 LN, A349-350 output leaf addresses, A357-359 Switchingfabrics, B:530-531 and reconfigurability, B:68 Switching nodes functionalities of, A378 types of, A376-378 Sycamore SN16000,A386 Synchronous modulation black-box optical regenerator approach to: A:764-761 optimization of systems, A761-764 principles of, A757-759 in singlechannel transmission, A7.59-761 System design, for undersea communications, B183-186

1019

TDFAs (thulium-doped fiber ampliiers), A121-122 antimony silicate, A145149 gain-shifted pumping in, A142-145 S-band, 140-142 TDM (time-division multiplexing), A19, B:66 decline of, B:102 described, B:198 economic issues of, B:369-370 evolution of, E862463 high-speed, B232-295. See also Pseudo-linear transmission history of, B:232 increasing efficiency of, B:863-865 in secondary hub architectures, B:417 SOAs in, A:720-122 TDM grooming, subrate, B:364 TDM/TDMA PON power requirements for, B:489 receivers, B:491492 transmitters, B:489-491 Telecommunication lasers analog, A:601-612 applications of, A592-595 design of, A589-591 directly modulated digital, A613425 electroabsorption-modulated, A:625439 fabrication of, A595401 factors affecting evolution of, A:655 function of, A590-591 history of, A587-588 importance of, A587 tunable, A638455 in WDM systems, A 5 8 8 Telecommunications industry, structure of, B:78-81 Telephone service compared to telegraph service, B25 historical growth rates of, B22 Tellium Aurora, A386 Tellurite glasses applications of, A123-124 composition of, A: 11b l 2 2 fiber fabrication of, A123 history of, A118 introduction of halides into, A121-122 in L-band EDFAs, 139 limitations of, A120 in super-band amplifiers, A139-140 synthesis of, A122 Tellurium, as codopant, A121 Telstra, growth rate of, B:33, B:34 Thermal noise, A.226, B:905 in cable systems, B:432 Thermooptic switches, 343 Thin-film filters, B:345 Thulium as dopant, A121-122 spectra of, A119-120 Thulium-doped fiber lasers, A105 Tilted gratings characteristics of, A519-521 coupling in, A529 uses of, A522 Time-compressionmultiplexing (TCM), B:451452 Time-division multiple access (TDMA) described, B:457 MAC in, B463466 ranging, B459-460 upstream overhead in, B:458459

zyxw zyxwvut zyxw

Tapered multimode oscillators, A152-154 threshold power of, A153 TCP (Transfer Control Protocol), B:30

1020

zyxwvutsr zyxwvut zyxwv Index

Time-division multiplexing (TDM), A19, B:66 decline of, B:102 described, B:198 economic issues of, B:369-370 evolution of, B:862-863 high-speed, B:232-295. See also Pseudo-linear transmission history of, B232 increasing efficiency of, B863-865 in secondary hub architectures, B:417 SOAs in, A720-722 Tin, as dopant, A483 Titan 6500. A:314 Topology dkovew, B139 Transceivers high bitrate, A819-824 in optical access networks, B:494-496 Transimpedance ampliier (TTA), A 8 2 M 2 7 Transistors capacitance of, A825 field-effect, A822423 frequency response of, A825 Translucent routing, B364 Transmission Hters ASE, A540 gain-flattening, A537-539 Transmission gratings coupled-mode theory on,A506-509 coupling in, A505-506 optics of, A498 Transmission impairments, B:213-224 CBUS~SOf, B213-214,784-785,795-798,965 chromatic dispersion, B:214 classificationsof, B966967 effects of, B:94-95 from polarization, B22CL222 related to modulation formats, B222-223 Transmitters directly modulated, A808409 electroabsorption modulator, A809410 high bitrate, A807-819, B281-282 for one-fiber Ethernet, B:494495 TDMA PON, B489-491 Transparency advantages of, B:87 defined, B86 domains of, B:89 economic issues regarding, B90-91 hitations on,B87-88 types of, B86 Transparent interfaces benefits of, A318 issues with, A318-319 Transparent LANs PLANS), B:338 Transparent networks advantages of, B:362-363 disadvantages of, B36M64 Transport control plane, B126 need for, B:127-128 objectives for, B130-131 Transport layering, B97,98 Transport management alternative architectures for, B:128-131 concerns regarding, B:128 enhancements to, B142 protocols related to, B127 traditional view of, B127-128 Transversal filters PF), B:817-819 Traveling-wave amplifier W A )

zyxwvutsr advantages of, A.828-829 application of, A:827 concept behind, A827428 Traveling-amplitude modulators, A271 Tree codes, B92%932 Tree-and-branch topology, B404,407 Triangular mesh network, A,304 Trunk lines, performance requirements for, A18 Tunability, of lasers and receivers, B:68 Tunable dispersion compensation, B:709-714 need for, B673-678 using electronic integrated devices, B694 using integrated optical devices, B690-694 using singlechannel tunable FBGs, B:678488 using VPA, B:689-690 l h a b l e FBGs with low third-order dispersion, B:686488 multiple&annel nonlinearly chirped, B685486 nonlinearly chirped, B:682485 single-channel,B678 using nonuniform mechanical strain,B678-680 using thermal gradients B:680-682 Tunable lasers cantilever-VCSEL, A678 fast, A461465 index tuning in, A649454 and MANs, B:346 in PONs, B486 for reconfigurable networks, A667468 structure of, A599 types of, A639-649 uses of, A638-639 VCSEL, A677478 and wavelength switching, A397-398 Tunable ring resonators, B:691 Tunable spare protection, B:l23 Tunable virtually imaged phase array (VIPA), B689-690 for slope matching, B699 llubo codes, B:94&950 in lightwave communications, B961

zyxwvutsr

Ultrafast nonlinear interferometer (UNI), A739 Ultralong-haulnetworks, A19, B:65-67 challengesposed by, B199-200 features of, B:200-201 FEC in, B:208-211 noise issues in, B201-204 optical networking in, B22&228 power issues in, B211-213 prerequisites for, B:198 transmission impairments in, B213-223 value of, B:225-226 Ultrawide-band wid^ photodetectors, A785 avalanche photodiodes, A79CL791 distributed, A788-789 efficiency issues, A786787 high saturation current photodiodes,A791-794 resonant cavity photodiodes, A78%790 structure of, A.785 waveguide photodiodes, A787-788 Ultrawideband EDFAs A191-193 Undersea communications dispersion issues in, A33-35, B163-I66 EDFAs in, B:156163 equipment for, B:185-186 future trends in, B189-193 history of, B:154-157,200

Index modulation formats for, B:166-172 performance assessment of, B172-177 performance improvement of, B204 performance requirements for, A18 polarization effects in, B18C183 Raman gain and, E191 system design for, B18~186,191-192 temperature conditions in, A:578 transmission experiments in, B186-189,190 Uni-traveling-carrier (UTC) photodiodes, A793-794 Unipolar pulse system, defined, B167-168 User-network interface (UNI), B137-138

1021

silicon-on-insulator,A456 star coupler in, A414416,417420 structure of, A4064409 topology of, A409413 Wavelength add-drops (WADS),A.444-445 difEculties of, A450-45 1 large-channel-count, A446-45 1 smallchannelcount, A446 Wavelength assignment problem, B:92,93 Wavelength blockers, A 4 4 1 4 2 advantages of, A442 experiments on,A443 refinements of, A 4 4 2 4 3 wavelength chirp, A690692 Wavelength conversion and reconligurability,B:68 SOAs in, A717-720 Wavelength grating router (WGR), B481482 Wavelength switching components for, 39C399 demonstration of, A399 theory behind, A395-396 Wavelength tracking, B:482 Wavelength-divisionmultiple access (WDMA), B468 Wavelength-divisionmultiplexing (WDM) advantages of, A174 bit-interleaved, B48-87 capacity growth in, A174-175,732 concatenation of systems, B:225 described, B:453454 dispersion managementin, B633434 EDFAs in, A197-206 evolution of, B:862-863 gain-equaliid, A183-188 growth of, B:611 history of, B:224,308 increasing efficiency of, B363-865 and Internet, B27 lasers foq A588, 593 nonlinearities in, B:611436 in 160Gbit/s system, B287-289 planar lightwave devices for, A 4 0 5 4 9 in secondary hub architectures, B418 simulation tools for, B:569-571 Wavelength-interchangingcrossconnect (WIC), A377 applications of, A383,385 system boundaries for, A384 Wavelength-selectablelasers. See Tunable lasers Wavelength-selectivecross-connects (WSC), A37C377, B:69-70 advantages of, A379 architecture of, A347,348,37%379,435437 and crosstalk control, A350-351 described, A435437 drawbacks of, A37S380 examples of, A381 full, A438-441 optical add/drop as,A381-383 small lithium niobate switch arrays, A34%350 wavelength blockers and, A4414M Wavestar, A309,314,315 WDM (wavelength-divisionmultiplexing) advantagesof, A 174 bit-interleaved, B486-487 capacity growth in, A174-175,732 concatenation of systems, B225 described, B453454

zy

zyxwvuts zyxwvutsr zyxwvuts zyxw zyxwvutsrq

Vapor-phase epitaxy (VPE),A596 VCSELs (vertical cavity surface emitting lasers), A601 advantages of, A669 bit-error rate of, A685497 chirp in, A690692 continuous tuning of, A678481 described, A668-669 design issues,A669471 developments in, A681482 history of, A692493 linewidth of, A689490 materials for, A670 1.5 micron, 674682 1.3 micron, A571474 relative intensity noise of, A687489 small-signal modulation (SSM) response in, A682485 SONET specifications for, A 6 8 6 transmission characteristics of, A.682492 tunable cantilever, A678 tuning speed and, A681 wavelength locking of, A 6 8 1 wavelength-tunable,A677478 VDSL, B503-504 Vernier effect, A398 Vestigial sideband (VSB), A604 Virtual LANs (VLANs), B:338 Virtual line services, B338-339 Virtual private networks, optical, E85 Virtual rings, B:118-119 Virtually imaged phase array (VIPA), B:689490 Viterbi algorithm, B932,974 Voice telephony, growth trends in, B:339 VPI simulation environments, B571,594

Waveguide grating multiplexer, N x N arrayed, A396-397 Waveguide grating router as mux/demux, A420-422 N1 x N2, A422423 spectral sampling by, A424427 Waveguide photodiodes, A787-788 Waveguides fabrication-robust arrays of, A:42%424 four-port couplers and, A427428 index tuning in, A649454 indications for use of, A405 indium phosphide, A457466 lithium niobate, 466-468 polymer, A455-456 silica, A405454

1022

zyxwvutsr zyxwvut zyxwvu zyx Index

WDM (wavelength-divisionmultiplexing), continued dispersion management in, B633-634 EDFAs in, A197-206 evolution of, B862-863 gain+qualiized, A183-188 growth of, B611 history of, B224,308 increasing efficiency of, B863-865 and Internet, B27 lasers for, A588, 593 nonlinearities in, B:611-636 in 160Gbit/s system, B:287-289 planar lightwave devices for, A405469 in secondary hub architectures, B:418 simulation tools for, B569-571 WDM amplification, SOAs in, A712-716 WDM PONS alternatives to WDMA in, B:482484 architectures of, B480 assessment of, B:488 brute folce, B:480481 distinguished from PSPONs, B:479480,501 distributed routings in, B487 s o m alternatives for, B:485487 temperatureissues, B:482 variations of, B487-488 wavelength muter for, B481482 Web hosting sites, B:79 Weight distribution,of code, B:908 Wideband ampliication, A29-31,191-193 DWDM, A19 Wireless and growth of MANs, B:340-341 historical growth rates of, B:22 Wrapster, B:37 xDSL, B:502 implementation of, B:504 XGXS inputs and outputs of, B:552 in 10 Gbit/s Ethernet, B:549-550

XPM (crossphase modulation), A21,282 amplitude distortion penalty induced by, B624-625 collision-induced, B625429,635 compensation for, B262-264 described, B:648-649 effect of, B:257-261 intrachannel, B:257-264,629633 mathematics of, B257-259,618 minimization through polarization interleaving, B:7984302 in NRZ systems, B:624425 pumpprobe measurements of, B518-624 in RZ systems, B525-629 simulation of, B600 SOAs in, A718-719

Y-branch couplers, A428 Ytterbium BS codopant in tellurite glasses, A 1 18-119 doubleclad fiber for 980nm, A15S158 electronic configuration of, A 150 978nm behavior of, A150-155 980nm transition of, A149,15>158 Ytterbiumdoped fiber lasers, A104-105 ZBLANs applications of, A104-106 compositions of, A90-91 devitrification of, A95 durability of, A103-104 in EDFAs, A13&131 fiber fabrication of, A93-99 fiber losses of, A9%103 fiber strength in, A 103 impurities in, 100-103 reliability of, A104 studies of, A89-90, 106 synthesis and p d c a t i o n of, A91-93 Zero forcing equalization (ZFE), B982,983 modified, B:983 Zirconium, in fluoride glasses, A89-106

zyxwvutsr