Integrated Optics: Characterization, Devices, and Applications, Volume 2 1839533439, 9781839533433

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IET MATERIALS, CIRCUITS AND DEVICES SERIES 77

Integrated Optics

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Analogue IC Design: The current-mode approach C. Toumazou, F.J. Lidgey and D.G. Haigh (Editors) Analogue–Digital ASICs: Circuit techniques, design tools and applications R.S. Soin, F. Maloberti and J. France (Editors) Algorithmic and Knowledge-Based CAD for VLSI G.E. Taylor and G. Russell (Editors) Switched Currents: An analogue technique for digital technology C. Toumazou, J.B.C. Hughes and N.C. Battersby (Editors) High-Frequency Circuit Engineering F. Nibler et al. Low-Power High-Frequency Microelectronics: A unified approach G. Machado (Editor) VLSI Testing: Digital and mixed analogue/digital techniques S.L. Hurst Distributed Feedback Semiconductor Lasers J.E. Carroll, J.E.A. Whiteaway and R.G.S. Plumb Selected Topics in Advanced Solid State and Fibre Optic Sensors S.M. Vaezi-Nejad (Editor) Strained Silicon Heterostructures: Materials and devices C.K. Maiti, N.B. Chakrabarti and S.K. Ray RFIC and MMIC Design and Technology I.D. Robertson and S. Lucyzyn (Editors) Design of High Frequency Integrated Analogue Filters Y. Sun (Editor) Foundations of Digital Signal Processing: Theory, algorithms and hardware design P. Gaydecki Wireless Communications Circuits and Systems Y. Sun (Editor) The Switching Function: Analysis of power electronic circuits C. Marouchos System on Chip: Next generation electronics B. Al-Hashimi (Editor) Test and Diagnosis of Analogue, Mixed-Signal and RF Integrated Circuits: The system on chip approach Y. Sun (Editor) Low Power and Low Voltage Circuit Design with the FGMOS Transistor E. Rodriguez-Villegas Technology Computer Aided Design for Si, SiGe and GaAs Integrated Circuits C.K. Maiti and G.A. Armstrong Nanotechnologies M. Wautelet et al. Understandable Electric Circuits M. Wang Fundamentals of Electromagnetic Levitation: Engineering sustainability through efficiency A.J. Sangster Optical MEMS for Chemical Analysis and Biomedicine H. Jiang (Editor) High Speed Data Converters A.M.A. Ali Nano-Scaled Semiconductor Devices E.A. Gutie´rrez-D (Editor) Security and Privacy for Big Data, Cloud Computing and Applications L. Wang, W. Ren, K.R. Choo and F. Xhafa (Editors) Nano-CMOS and Post-CMOS Electronics: Devices and modelling S.P. Mohanty and A. Srivastava Nano-CMOS and Post-CMOS Electronics: Circuits and design S.P. Mohanty and A. Srivastava Oscillator Circuits: Frontiers in design, analysis and applications Y. Nishio (Editor) High Frequency MOSFET Gate Drivers Z. Zhang and Y. Liu RF and Microwave Module Level Design and Integration M. Almalkawi Design of Terahertz CMOS Integrated Circuits for High-Speed Wireless Communication M. Fujishima and S. Amakawa System Design with Memristor Technologies L. Guckert and E.E. Swartzlander Jr. Functionality-Enhanced Devices: An alternative to Moore’s law P.-E. Gaillardon (Editor) Digitally Enhanced Mixed Signal Systems C. Jabbour, P. Desgreys and D. Dallett (Editors)

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Negative Group Delay Devices: From concepts to applications B. Ravelo (Editor) Characterisation and Control of Defects in Semiconductors F. Tuomisto (Editor) Understandable Electric Circuits: Key concepts. 2nd Edition M. Wang Gyrators, Simulated Inductors and Related Immittances: Realizations and applications R. Senani, D.R. Bhaskar, V.K. Singh and A.K. Singh Advanced Technologies for Next Generation integrated Circuits A. Srivastava and S. Mohanty (Editors) Modelling Methodologies in Analogue Integrated Circuit Design G. Dundar and M.B. Yelten (Editors) VLSI Architectures for Future Video Coding M. Martina (Editor) Advances in High-Power Fiber and Diode Laser Engineering I. Divliansky (Editor) Hardware Architectures for Deep Learning M. Daneshtalab and M. Modarressi Cross-Layer Reliability of Computing Systems G. Di Natale, A. Bosio, R. Canal, S. Di Carlo and D. Gizopoulos (Editors) Magnetorheological Materials and Their Applications S. Choi and W. Li (Editors) Analysis and Design of CMOS Clocking Circuits for Low Phase Noise W. Bae and D.K. Jeong IP Core Protection and Hardware-Assisted Security for Consumer Electronics A. Sengupta and S. Mohanty Phase-Locked Frequency Generation and Clocking: Architectures and circuits for modem wireless and wireline systems W. Rhee (Editor) MEMS Resonator Filters R.M. Patrikar (Editor) Frontiers in Hardware Security and Trust: Theory, design and practice C.H. Chang and Y. Cao (Editors) Frontiers in Securing IP Cores; Forensic detective control and obfuscation techniques A. Sengupta High Quality Liquid Crystal Displays and Smart Devices: Vol. 1 and Vol. 2 S. Ishihara, S. Kobayashi and Y. Ukai (Editors) Fibre Bragg Gratings in Harsh and Space Environments: Principles and applications B. Aı¨ssa, E.I. Haddad, R.V. Kruzelecky and W.R. Jamroz Self-Healing Materials: From fundamental concepts to advanced space and electronics applications, 2nd Edition B. Aı¨ssa, E.I. Haddad, R.V. Kruzelecky and W.R. Jamroz Radio Frequency and Microwave Power Amplifiers: Vol. 1 and Vol. 2 A. Grebennikov (Editor) Tensorial Analysis of Networks (TAN) Modelling for PCB Signal Integrity and EMC Analysis B. Ravelo and Z. Xu (Editors) VLSI and Post-CMOS Electronics Volume 1: VLSI and post-CMOS electronics and Volume 2: Materials, devices and interconnects R. Dhiman and R. Chandel (Editors)

Integrated Optics Volume 2: Characterization, devices and applications Edited by Giancarlo C. Righini and Maurizio Ferrari

The Institution of Engineering and Technology

Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no. 211014) and Scotland (no. SC038698). † The Institution of Engineering and Technology 2021 First published 2020 This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the authors and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the authors nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library

ISBN 978-1-83953-343-3 (Hardback) ISBN 978-1-83953-344-0 (PDF)

Typeset in India by MPS Limited Printed in the UK by CPI Group (UK) Ltd, Croydon

Dedicated to two exceptional women: Prof. Vera Russo, who 50 years ago got me involved in integrated optics, and my wife, Marta, who for as many years went with me with her love and great patience. – Giancarlo C. Righini To Profs. Georges Boulon, Eugene Duval, Andre Monteil, and all the friends of the PCML laboratory in Lyon, where I started to develop my passionate interest for glass photonics. – Maurizio Ferrari

Contents

About the editors Preface

xv xvii

Part I: Characterization techniques

1

1 Optical characterization techniques Lidia Zur

3

1.1 1.2

Introduction Ellipsometry 1.2.1 Theory 1.2.2 Types of ellipsometers 1.2.3 Analysis of the data 1.2.4 Applications 1.3 Fluorescence spectroscopy 1.3.1 Apparatus 1.3.2 Data analysis 1.3.3 Fluorescence lifetimes 1.3.4 Fluorescence quenching 1.4 Fourier transform infrared spectroscopy (FTIR) 1.4.1 Theory 1.4.2 Apparatus 1.4.3 Data analysis 1.4.4 Applications 1.5 Raman spectrometry 1.5.1 Theory 1.5.2 Apparatus 1.5.3 Data analysis 1.5.4 Applications 1.6 Optical waveguide characterization 1.6.1 General 1.6.2 Refractive index measurements 1.6.3 Geometrical characterization 1.6.4 Optical loss measurement 1.7 Summary Acknowledgments References

3 3 4 5 6 8 10 11 11 12 13 14 14 15 16 18 18 19 20 20 21 22 22 22 24 24 25 25 26

x 2

Integrated Optics Volume 2: Characterization, devices, and applications Structural and surface-characterization techniques Giorgio Speranza

35

2.1 2.2

37 39 39 41 43 46

X-ray-based analytical techniques and X-ray diffraction Examples of characterization of optical materials by X-rays 2.2.1 Application of XRD to photonic crystals 2.2.2 Application of XRD to nanostructures 2.2.3 Application of XRD to detect material strain and stresses 2.2.4 X-rays and computed tomography 2.2.5 EXAFS and XANES applied to glass, glass ceramics, and nanostructures 2.2.6 X-ray photoelectron spectroscopy applied to optical materials 2.3 Conclusion References

3

Integrated spectroscopy using THz time-domain spectroscopy and low-frequency Raman scattering Tatsuya Mori and Yasuhiro Fujii 3.1 3.2 3.3 3.4

Terahertz light and excitations in the THz region Terahertz time-domain spectroscopy Light-scattering spectroscopy Boson peak investigation via THz spectroscopy and low-frequency Raman spectroscopy 3.5 Conclusion References

48 52 56 57

65 66 67 71 75 80 80

Part II: Integrated optical waveguides, devices, and applications

89

4

Plasmonic nanostructures and waveguides Tong Zhang

91

4.1 4.2

91 92

4.3

4.4

Introduction to plasmonics Plasmonic nanostructures 4.2.1 Scattering, absorption and extinction of plasmonic nanostructures 4.2.2 Active tuning of plasmonic resonance 4.2.3 Applications based on plasmonic nanostructures Plasmonic waveguides and devices 4.3.1 Plasmonic waveguide circuits for subwavelength light transmission 4.3.2 Plasmonic modulators 4.3.3 Plasmonic hot-carrier-based photodetector Plasmonic metamaterial and metasurface 4.4.1 Anomalous reflective and refractive material 4.4.2 Beam-splitter and polarization controller

92 94 97 98 98 102 105 108 109 109

Contents

xi

4.4.3 Sub-diffractive limit superlens and metalens Quantum plasmonics 4.5.1 Quantum properties of surface plasmon 4.5.2 Quantum plasmonic integrated circuits 4.6 Barriers and perspectives References

111 113 113 115 117 118

5 Crystalline thin films for integrated laser applications Gurvan Brasse and Patrice Camy

129

4.5

5.1

General context 5.1.1 State of the art and overview of the main techniques to produce thin films 5.1.2 Thin film growth by the liquid phase epitaxy method 5.2 Growth of single crystalline thin films by liquid phase epitaxy 5.2.1 The liquid phase epitaxy 5.2.2 Fluorides epitaxial thin films 5.2.3 Oxide epitaxial thin films 5.2.4 Shaping of the LPE grown crystalline thin films 5.3 Photonic application of RE-doped crystalline thin films grown by liquid phase epitaxy 5.3.1 Laser oscillator in a waveguide configuration 5.3.2 Laser emission in the visible domain 5.3.3 Laser emission in the NIR around 1 mm 5.3.4 Laser emission in the MIR around 2 mm and above 5.3.5 Laser oscillator in a thin-disk configuration 5.3.6 Crystalline thin films for saturable absorbers 5.4 Conclusion References 6 Integration of optical microcavities Andrey B. Matsko 6.1 6.2

Introduction Overview of coupling techniques 6.2.1 Input-output formalism and critical coupling 6.2.2 Prism couplers 6.2.3 Angle-cut fiber couplers 6.2.4 Tapered fiber couplers 6.2.5 Planar coupling 6.3 Ultra-high-Q PIC microcavities 6.3.1 High-Q Si PICs 6.3.2 High-Q SiN PICs 6.3.3 High-Q fused silica PICs 6.3.4 High-Q lithium niobate PICs 6.4 Integration of bulk microcavities for PIC applications

130 130 132 134 134 135 143 146 148 148 149 150 151 153 154 154 156 161 161 163 164 168 172 172 173 173 174 174 176 177 179

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Integrated Optics Volume 2: Characterization, devices, and applications 6.4.1 Integration of bulk lithium niobate and tantalate resonators on an SOI platform 6.4.2 Integration of bulk calcium fluoride resonators on a polymer platform 6.4.3 Integration of bulk magnesium fluoride resonators on a SiN platform 6.5 Conclusion Acknowledgments References

7

Electric and magnetic sensors based on whispering gallery mode spherical resonators Tindaro Ioppolo 7.1

8

180 181 183 185 185 185

197

Sensor concept 7.1.1 Tethered sensors 7.1.2 Untethered sensors 7.2 Stress and strain tuning of an optical spherical resonator 7.3 Electric field induced WGMs 7.4 Magnetic field induced WGM 7.5 Conclusions References

197 198 199 199 202 209 212 212

Nonlinear integrated optics in proton-exchanged lithium niobate waveguides and applications to classical and quantum optics Marc De Micheli and Pascal Baldi

215

8.1 8.2

8.3

8.4 8.5 8.6

Introduction Proton exchange in LiNbO3 8.2.1 The first discoveries: High dne, low loss 8.2.2 Combination with birefringence phase matching 8.2.3 Cerenkov configuration 8.2.4 Destruction of the c2 and strain-induced losses in channel waveguides Periodic poling 8.3.1 Surface domains: Titanium diffusion and heat treatment 8.3.2 E-Field poling 8.3.3 The different PE processes and their impact on the nonlinearity of the crystal 8.3.4 PE and periodic poling 8.3.5 Components Single photon pair generators Quantum photonics integrated circuits on PPLN 8.5.1 Quantum relay 8.5.2 Squeezed states Further improvements

215 218 218 219 219 221 222 222 223 225 229 233 239 241 242 243 244

Contents 8.6.1 Power-resistant materials 8.6.2 Highly confining waveguides 8.7 Today’s issues 8.7.1 Control of the domains 8.7.2 Insensitive phase-matching configurations 8.8 Conclusion Acknowledgments References 9 Next-generation long-wavelength infrared detector arrays: competing technologies and modeling challenges Marco Vallone, Alberto Tibaldi, Francesco Bertazzi, Andrea Palmieri, Matteo G.C. Alasio, Stefan Hanna, Detlef Eich, Alexander Sieck, Heinrich Figgemeier, Giovanni Ghione and Michele Goano 9.1 9.2

Introduction Lower cost, large FPAs with subwavelength pixel pitch 9.2.1 Comprehensive electromagnetic and electrical simulations 9.2.2 Small pixels and inter-pixel crosstalk in planar FPAs 9.2.3 Modeling photoresponse for non-monochromatic illumination 9.3 HOT HgCdTe detectors: Technologies and modeling approaches 9.3.1 Defects- and tunneling-related dark current 9.3.2 Auger-suppressed and fully carrier-depleted detectors 9.3.3 Compositionally graded HgCdTe detectors 9.4 Conclusions References 10 Arrayed waveguide gratings for telecom and spectroscopic applications Dana Seyringer 10.1 Arrayed waveguide gratings 10.1.1 AWG principle 10.1.2 Different types of AWGs 10.2 AWG design 10.2.1 Focusing 10.2.2 Dispersion 10.2.3 Free spectral range 10.2.4 Performance parameters 10.2.5 AWG design parameters 10.3 AWGs for telecom applications 10.3.1 SoS-based 8-channel, 100-GHz AWG 10.3.2 SoS-based 64-channel, 50-GHz AWG

xiii 244 245 246 246 247 250 251 252

265

265 270 272 273 275 278 279 282 284 287 288

295 297 298 299 302 302 302 303 303 306 307 308 315

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Integrated Optics Volume 2: Characterization, devices, and applications 10.4

AWGs for spectroscopic applications 10.4.1 Optical coherence tomography 10.4.2 AWG-spectrometer for SD-OCT system 10.5 Conclusion Acknowledgments References

316 317 319 327 329 330

11 Integrated quantum photonics Devin H. Smith, Paolo L. Mennea and James C. Gates

337

Acronyms 11.1 Introduction 11.2 Applications 11.3 Quantum states of light 11.3.1 ‘True’ single-photon sources 11.3.2 Heralded photon sources 11.4 Low-loss components 11.5 Material platforms 11.5.1 Silica 11.5.2 Silicon-on-insulator 11.5.3 Silicon nitride 11.5.4 Lithium niobate 11.5.5 III–V semiconductors 11.5.6 Hybrid systems 11.6 Conclusion References 12 The optical reservoir computer: a new approach to a programmable integrated optics system based on an artificial neural network Sendy Phang, Phillip D. Sewell, Ana Vukovic and Trevor M. Benson 12.1 Introduction 12.2 Some applications of genetic algorithms in integrated optics design 12.3 Functional integrated optics powered by a reservoir computer 12.3.1 Introduction to an algorithmic reservoir computer 12.3.2 An optical reservoir computer as a temporal signal discriminator 12.3.3 Chaotic cavity as a reservoir computer kernel 12.3.4 ORC training and validation 12.4 Conclusions References Index

337 337 338 340 341 344 346 349 349 352 352 353 354 354 355 356

361 361 363 364 364 367 371 373 376 376 381

About the editors

Giancarlo C. Righini is former director of the Enrico Fermi Center and of the National Department on Materials and Devices, National Research Council of Italy (CNR). He was also research director at the Nello Carrara Institute of Applied Physics, CNR, and vice-president of the International Commission for Optics. His research interests concern fiber and integrated optics, glass materials, and microresonators. He has published over 500 research papers. He is fellow of OSA, SPIE, and Italian Physical Society (SIF), and also founding member and fellow of European Optical Society (EOS) and Italian Society of Optics and Photonics (SIOF). Maurizio Ferrari is the director of research with the Institute for Photonics and Nanotechnologies, CNR, Italy, where he is also head of the Caratterizzazione e Sviluppo di Materiali per la Fotonica e Optoelettronica Lab and the Institute for Photonics and Nanotechnologies (IFN-CNR) Trento unit. He is coauthor of more than 400 publications in international journals, of several book chapters, and he is involved in numerous national and international projects concerning glass photonics. He is a OSA and SPIE fellow.

Preface

The birth of integrated optics is commonly associated with the publication, in 1969, of the article by Stewart E. Miller titled “Integrated Optics: An Introduction”. In reality, as discussed in more detail in Chapter 1, Volume 1, of this book, the confinement of light in thin-film structures had been experimentally demonstrated in earlier works, in 1963, and its potential for new optical devices and applications had already been imagined. It was in 1968, for instance, that Shubert and Harris brought up the idea of realizing an integrated data processor based on twodimensional refractive lenses and thin-film modulators. Whatever it be, it is sure that the 1960s have represented a decade of extraordinary advances for optics, where the fundaments of the modern photonics were laid. Begun with the invention of laser, those years saw the birth of semiconductor laser industry, the seeds of the fiber optic telecommunications, and the first envisioning of compact, lightweight, multifunctional guided-wave optical devices. A long way has been travelled since those early works, and great advances have been made in both the materials and the technologies for integrated optics. As an example, let us just refer to the case of glassy materials: since the very beginning, low-loss optical waveguides have been produced by using oxide glasses. Commercial optical glasses, e.g., borosilicates, were first exploited using both deposition processes (mostly, RF-sputtering) and diffusion processes, either at low energy (ion exchange) or at high energy (ion implantation). Even soda–lime glasses (commercial microscope slides) were frequently used in the laboratories for the preliminary tests. Such waveguides were purely passive, so the researchers started to search for a proper approach permitting to add functionalities to glass. Excellent results were obtained, for instance, with the doping of glasses with semiconductor particles, to enhance nonlinear properties, or with rare earth ions, leading to the development of integrated optical amplifiers and lasers. By the way, the laser cavity could be produced by direct UV writing of gratings in glasses containing photorefractive oxides, like germanium or tin oxides. The subsequent efforts to optimize the rare-earth-doped glasses and the devices based on them have led to the use of transparent glass-ceramics, which combine the properties of the homogeneous matrix with those of the nanocrystals embedded in it. Then, after consideration that the transmission window of oxide glasses was not suitable for important applications in the mid-infrared wavelength range, the research moved toward non-oxide glasses, and chalcogenide glass thin films have proven to be very good for integrated optical devices operating up to 10 mm. More recently, the same chalcogenide glasses have been deposited onto plastic substrates, demonstrating the

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Integrated Optics Volume 2: Characterization, devices, and applications

potential of flexible and stretchable glass-integrated photonic devices. At the same time, also in response to requests by the microelectronics industry, major glass companies have developed ultrathin flexible glasses, thus opening the way to a monolithic glass flexible photonics. Analogous developments have occurred for other materials and technologies, so that nowadays various material platforms (some of them are fully compatible with CMOS (complementary metal-oxide semiconductor) fabrication processes) are available for the fabrication of on-chip photonic devices. Due to these exceptional advances in integrated optics, we considered that it could be worth to collect in a new book some novel scientific contributions from both top and emerging researchers, with the aim of—on one side—illustrating some fundaments to newcomers in this field and—on the other—presenting to the experts a state of the art and some recent achievements. The vastity of the field, of course, prevented us from providing an exhaustive review; a hard decision we had to take, for instance, was to leave out details of semiconductor integrated optics. Besides this, the collected material was massive, and the publisher considered more convenient to split the 25 chapters of the book into two volumes. Volume 1 begins with a short summary of the chronological development of integrated optics in the last 50 years. Then, since the development of highperformance integrated optical circuits providing complex functionalities requires an accurate modeling of their components, the following three chapters discuss numerical and analytical tools to model waveguides, devices, and nanophotonic metasurfaces, with particular attention to nonlinear effects. The second section takes most of Volume 1, discussing material platforms and fabrication techniques. Two introductive chapters (Chapters 7 and 8) present the fundaments of thin-film deposition methods, by a physical and a chemical route, respectively. Five chapters review the fabrication methods and the applications in integrated optics of different materials, rare-earth-doped glasses (Chapter 5), lithium niobate (Chapter 6), photorefractive glasses, crystals, and polymers (Chapter 9), liquid crystals (Chapter 10), and silicon nitride (Chapter 11). Fabrication of channel waveguides and integrated optical structures is then analyzed in detail in two more chapters, dealing with femtosecond laser writing and with ion beam techniques (Chapters 12 and 13, respectively). Volume 2 begins with a section devoted to optical (Chapter 1) and structural (Chapter 2) characterization techniques of materials and surfaces; Chapter 3 outlines the novel information that can be obtained by performing spectroscopic measurements in the THz spectral domain, a crucial step to acquire the knowledge of material properties at these frequencies, in view of a future THz photonics. Finally, the second and last section of Volume 2 includes a group of chapters more related to guided-wave structures, devices, and applications. It begins with a discussion of plasmonic nanostructures and waveguides (Chapter 4) and continues with a review of the growth or deposition processes of dielectric crystalline thin films; the liquid-phase epitaxy process of rare-earth-doped fluoride and oxide crystalline films is described in detail, together with their applications, especially in the laser field (Chapter 5).

Preface

xix

The two chapters that follow deal with different aspects of whispering gallery mode microcavities, namely, with the integration of open-ring microresonators and with the use of microspherical resonators for sensing (Chapters 6 and 7, respectively). The applications are at the core of the last five chapters: nonlinear phenomena in proton-exchanged lithium niobate waveguides and their applications to classical and quantum optics are described in Chapter 8. Technologies and modeling challenges of next-generation long-wavelength infrared detector arrays are the subject of Chapter 9, whereas Chapter 10 presents an in-depth analysis of arrayed waveguide gratings for telecom and spectroscopic applications. The status of integrated quantum photonics, namely, of integrated systems where the photons themselves act as carriers of quantum information, is reviewed in Chapter 11; so far, most quantum photonics has not yet achieved monolithic integration, but much work is being done and progress is fast. The conclusive chapter (Chapter 12) in some way goes back to the fundaments of integrated optics and to the need of designing and optimizing each component of the circuit: with today’s complex functionalities required, genetic algorithms and neural networks may become necessary. As an example, an optical reservoir computer is presented, which is used as a programmable optical signal information processing device for a sensing application. We are aware that some excellent books on integrated optics are available, but none very recent; so, we sincerely hope that the readers will appreciate our effort to provide an updated overview of integrated optics. We apologize for the incompleteness, even if almost unavoidable when dealing with a so-wide R&D area, and for any omission, possible but certainly unintentional. Last but not least, we want to thank all the authors of the chapters for their excellent work and precious collaboration. We also wish to remember Marc De Micheli, who passed away abruptly in July 2019, when still working on his contribution, and to thank his friend and colleague Pascal Baldi, who completed the chapter on nonlinear integrated optics in lithium niobate. Finally, thanks are due to the editorial staff of The IET, especially Olivia Wilkins and Sarah Lynch, for their full support. Giancarlo C. Righini Maurizio Ferrari

Part I

Characterization techniques

Chapter 1

Optical characterization techniques Lidia Zur1

1.1 Introduction Optical characterization techniques have always been a fascinating tool for researchers to reveal and study the fundamental properties of materials. Novel optical materials are designed and synthesized for applications in various fields, including Information and Communication Technology, Health and Biology, Structural Engineering, and Environment Monitoring Systems. The optical properties of a material can tell us valuable information about its physical properties. However, they can also reveal valuable information about the electronic properties of a material using spectroscopy. In this chapter, different optical characterization techniques have been presented and discussed. Starting from the ellipsometry, fluorescence spectroscopy, through Fourier transform infrared spectroscopy, Raman spectroscopy to optical waveguide characterization, readers can get some necessary information about the discussed techniques.

1.2 Ellipsometry Ellipsometry is a non-destructive and non-invasive optical technique that is based on the change in the polarization state of light as it is reflected obliquely from a thin film sample. Ellipsometry requires only a low-power light source. Thus, it does not affect most processes, which makes ellipsometry a convenient tool for in situ studies. It is well known that P. Drude built the first ellipsometer around the 1980s. The earliest ellipsometry measurements were used to determine the optical functions, such as refractive index n and extinction coefficient k, or absorption coefficient a for some materials. After Drude, the technique was not widely recognized. This had changed in the 1940s when a single-wavelength nulling ellipsometry measurement was used to determine the thickness of certain thin 1 Institute of Photonics and Nanotechnologies (IFN-CNR) CSMFO Lab., and FBK Photonics Unit, Trento, Italy

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Integrated optics Volume 2: Characterization, devices, and applications (5)

(1) (2)

(4)

(3) Sample

(a)

(5)

(1) (2)

(4)

(3) Sample

(b)

(5)

(1) (2)

(4)

(6) Sample

(c)

Figure 1.1 Diagrams of ellipsometer in use, where (1) light source, (2) polarizer, (3) compensator, (4) polarizer (analyzer), (5) detector, and (6) photoelastic modulator films very accurately. In 1945, the term “ellipsometry” had been coined by Rothen. In the 1970s and 1980s, ellipsometry became widely utilized; during that time, technical papers and books were written to describe this technique. Since then, multiple wavelength ellipsometry has been used in spectral scanning and multichannel configurations. Spectroscopic ellipsometry has become the standard methodology of thin films characterization for a variety of industrial applications.

1.2.1 Theory Thanks to the advances in theory, the tools to understand spectroscopic ellipsometry data and interpret them in terms of material and structural properties are available. The first crucial theoretical contribution related to the discussed topic comes from Fresnel [1], who, with the assistance of Poisson, proved the wave theory of light. Clausius [2] and Mossotti [3] first connected an optical response

Optical characterization techniques

5

function, the refractive index, to atomic-scale properties, the atomic polarizability a and the atomic density n. Generally, in ellipsometry, the measured quantity is the ratio (r) between the ~ and perpendicular complex reflection coefficients with polarization parallel (Rp) ~ to the plane formed by the incident and reflected light beams. (Rs) r¼

~ jðdpdsÞ ~ jRpj Rp e ¼ ~ ~ jRsj Rs

~ and Rs, ~ and j ¼ where dp and ds are the phases of Rp This ratio is usually written as r ¼ tan YejD

(1.1) pffiffiffiffiffiffiffi 1. (1.2)

where Y and D are called ellipsometric angles. To obtain the optical properties of the characterized material from the ellipsometric angles, it is necessary to construct a physical model of the sample and fit the calculated values of Y and D from the model to the ones obtained experimentally.

1.2.2 Types of ellipsometers With the development of the ellipsometry, different types of ellipsometers have been built. The most common are presented schematically in Figure 1.1. The oldest known type of ellipsometer is the nulling ellipsometer (Figure 1.1 (a)). The source of light for a nulling ellipsometer is usually a small laser, but other monochromatic sources can also be used. The polarization state generator (PSG) is a polarizer-retarder pair, while the polarization state analyzer (PSA) is a linear polarizer, traditionally called the analyzer. Nulling ellipsometry measurements are performed by rotating the PSG polarizer and the PSA analyzer until the light intensity reaching the detector is at a minimum. This ellipsometer is known as one of the simplest ellipsometers, and it is capable of very accurate measurements with proper calibration. However, it commonly uses a single wavelength source. Additionally, measurement times are long, so this ellipsometer is not useful for spectroscopic ellipsometry or fast time-resolved measurements. Nowadays, the most common type of commercially produced spectroscopic ellipsometer is the rotating compensator ellipsometer (RCE), presented in Figure 1.1(b) [4–6]. Typically, the PSG is made up of a linear polarizer followed by a rotating compensator before the sample. The PSA is a fixed linear polarizer (analyzer). For an alternative configuration, the rotating compensator can be placed after the sample in the PSA. In both configurations discussed above, the physically rotated compensator makes the light intensity at the detector a periodic function of time. When a rotating compensator is placed before the sample, dynamically elliptically polarized light is incident upon the sample. The instrument configuration with only a single rotating compensator enables the measurement of information contained within the first three rows of the Mueller matrix (N, C, and S for isotropic samples), but it is not able to measure the fourth row. Information contained within the fourth row of the Mueller matrix is redundant for isotropic

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Integrated optics Volume 2: Characterization, devices, and applications

samples, but it is vital for a full assessment of anisotropic samples. More advanced instrumentation in which two rotating compensators [7] are implemented and are placed before and after the sample and rotated at specific integer frequency ratios, has been developed to measure the complete Mueller matrix in one optical cycle. Thanks to a complete characterization of the Mueller matrix, the extraction of the generalized ellipsometric ratios, detection of anisotropic optical response, and characterization of depolarization are possible. The rotating polarizer, single rotating compensator, and dual rotating compensator instruments have all been successfully made spectroscopic in either spectral scanning or multichannel configurations. The polarizers are independent of the wavelength, while the compensator(s) and sample will have spectrally dependent properties. Therefore, it is essential to incorporate spectral variations in retardance of the compensator(s) during instrument calibration and data reduction. In multichannel instruments [8], a spectrograph is placed after the PSA, and light is detected by a photodiode array or CCD array. In this way, spectroscopic information is gained in parallel during a single optical cycle of the instrument. The measurable spectral range in ex situ configurations of rotating compensator and polarizer (analyzer) instruments has been extended to the vacuum ultraviolet (VUV) [9], infrared [10], and THz regions [11]. VUV data provides sensitivity to ultra-thin films and the optical response of wide bandgap materials. Fourier transform infrared (FTIR)-extended ellipsometric spectra provides sensitivity to chemical bonding vibrational modes and the free-carrier absorption characteristics of metals, transparent conducting oxides, and heavily doped semiconductors. THz range spectroscopic ellipsometry is useful for determining the free-carrier absorption characteristics of more lightly doped semiconductors. Another spectroscopic ellipsometer is based on the photoelastic modulator (PME) [12], presented in Figure 1.1(c). Typically, the PSG consists of a polarizerPEM pair, where the polarizer is oriented at 45 concerning the vibration axis of the PEM. The well-known complication of the PME is that the modulation amplitude of the PEM must be calibrated, and the small, but significant, static retardation measured at all wavelengths used. Additionally, the frequency of the PEM is about 500 times faster than the rotation speed of the RCE; this improves the time resolution to ~1 ms but requires faster electronics for data collection. In the standard configuration presented above, the PME can measure S and either N or C. Another implementation of the PME [13] uses two polarizer-PEM pairs, one before the sample (PSG) and another after the sample (PSA), where the operating frequencies of the two PEMs are set to different frequencies. This implementation measures only eight elements in the reduced sample Mueller matrix. For the investigation of the systems where significant depolarization is not present, this is sufficient. If all 15 elements are required, then four PEMs can be used, two both in the PSG and PSA [14].

1.2.3 Analysis of the data Speaking about the advantages of the spectroscopic ellipsometry, one can quickly tell that it is a fast, non-destructive, and very sensitive method which possesses a

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wide application area. However, the spectroscopic ellipsometry data demands mathematical analysis to obtain the required parameters, such as the thickness of thin films, surface roughness, the refractive dispersion index, and extinction coefficient values versus wavelengths. To correlate the measured parameters with actual characteristics, it is necessary to construct the model, based on which the Fresnel reflection coefficients (Rp and Rs) can be calculated [15]. Usually, the analysis of the data consists of three steps. The first step is based on the construction of the optical model. The second step concerns the parameterization or selection of the spectroscopic optical functions used in the model. The third step refers to a fitting procedure allowing to determine the fitted parameters, associated errors, and a measure of the “goodness of fit” [15]. The procedure is schematically presented on the chart (Figure 1.2). After the measure of the selected sample, using a computer, a model is constructed to describe the sample’s optical properties. During the model’s construction, assumed values of properties are placed, and an optical dielectric function is employed to describe the dielectric properties of the sample’s material. If the dielectric function of a sample is unknown, it is necessary to construct it. Looking at the optical properties of the examined sample, it is necessary to select the appropriate dielectric function model. There are several dielectric functions models, such as Sellmeier, Drude, Cauchy, etc. [16], which are used for different samples properties. The Cauchy or Sellmeier [16] model can be used in the transparent region (e2 ~ 0). The Drude model can be used for the data analysis when there is freecarrier absorption. This model is used to calculate the estimated response from

Experimentl data Measurement

Model

n n–1

n, K

Generated data

1 0 Comparison Fit Fit parameters n, K Results

Thickness roughness uniformity

Figure 1.2 Flowchart of the process from the raw data to the results

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Fresnel’s equations, which describe each material with corresponding thickness and optical constants. If the values are unknown in advance, a prediction is given for the purpose of the preliminary calculation. Next, the obtained values from the model are compared with experimental ones with the all wavelength spectrum. Then, the unknown material properties can be extracted by varying the parameters to improve the match between the experimental and calculated spectrum. Furthermore, the best match between the model and the experiment data can be achieved only through regression analysis. An estimator, like the Chi-squared Error (c2), is used to quantify the difference between the discussed curves. The unknown parameters can vary until the minimum Chi-squared is reached. At the end of the procedure, after achieving a good fit, one can extract the investigated parameters, such as refractive index n, extinction coefficient k, surface, interface roughness, thickness, etc. [15].

1.2.4 Applications From the very beginning, spectroscopic ellipsometry has been applied to evaluate optical constants and thicknesses of thin films. However, with the time and the technological and computational development, the applications of the ellipsometry have been broadened. Figure 1.3 presents different physical values, which can be determined based on ellipsometry measurements. With the spectroscopic ellipsometry, the spectra of Y and D for photon energy or wavelength are measured. It is important to note that the direct interpretation of obtained results is difficult from the absolute values of Y and D. As was already discussed in the paragraph above, to analyze the obtained data, the construction of an optical model is needed. After the data analysis, different physical properties such as optical constants and film thicknesses of the sample can be obtained. One of the advantages of the ellipsometry is that it allows the direct measurement of the refractive index n and extinction coefficient k. From their values, it is possible to determine the complex refractive index:  pffiffiffiffiffiffiffi N  n  ik i ¼ 1 (1.3) Additionally, based on n and k, the complex dielectric constant e and absorption coefficient a can be obtained, based on simple relations, as follows: e ¼ N2 and a ¼ 4pk/l. Using the obtained thin film thickness and optical constants, one can calculate the reflectance and transmittance at a different angle of incidence. Based on the measurements performed in the UV/Vis region, the band structure of the investigated system can be are characterized. Notably, the bandgap Eg can be assumed from the variation of absorption coefficient with photon energy. It is well known that the band structure differs depending on surface temperature, alloy composition, phase structure, and crystal grain size. Thus, all these properties can be determined based on the spectral analysis of optical constants. In the IR region, the free electrons in solids induce free-carrier absorption. When carrier concentration is higher than > 1018 cm–3, some electrical properties can be determined, such as carrier mobility, carrier concentration as well as

UV/Vis region

Infrared absorption LO and TO phonons Local structures (Si–H, –OH)

Free-carrier absorption Carrier concentration (cm–3) Carrier mobility (cm2/Vs) Conductivity (S/cm)

Reflectance, R Transmittance, T

Film thicknes (structure) Surface roughness layer Bulk layer Multilayer

Figure 1.3 Possible application and information which can be taken from the ellipsometry measurements

Band structure Bandgap (Eg) Direct transition: α = A(hv – Eg)1/2 Indirect transition: α = A(hv – Eg)2 Surface temperature (ºC) Alloy composition (at.%) Phase structure (crystal, amorphous, void) Grain size (Å)

Optical constants Complex refractive index n(hv), k(hv):N = n – ik Complex dielectric constant ε1(hv), ε2(hv): ε = ε1 – iε2 Absorption coefficient a = 4κ/λ

Contruction of optical model

Measured values Ψ(hv) Δ(hv)

IR region

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conductivity. Additionally, in the IR region, lattice vibration modes (LO and TO phonons) and local structure (Si-H and -OH) can be examined.

1.3 Fluorescence spectroscopy Scientists in many disciplines widely use fluorescence spectroscopy. Among other applications, it is essential to mention the new lasers’ materials. When an active material is considered as a potential laser gain media, is fundamental to know its spectroscopic properties, including the absorption, emission, excitation scheme features, and the upper-state lifetime of the photoluminescence at the target wavelength. Thus, in this part of the chapter, our attention will be focused on fluorescence spectroscopy, and some part of its aspects will be discussed more in-depth. Luminescence is the emission of light from any substance and occurs from electronically excited states. Luminescence is formally divided into two categories – fluorescence and phosphorescence – depending on the nature of the excited state. In excited singlet states, the electron in the excited orbital is paired (by opposite spin) to the second electron in the ground-state orbital. Consequently, return to the ground state is spin allowed and occurs rapidly by the emission of a photon. The emission rates of fluorescence are typically 108 s–1, so that a typical fluorescence lifetime is near 10 ns (10  10–9 s). The lifetime (t) of a fluorophore is the average time between its excitation and return to the ground state. It is valuable to consider a 1-ns lifetime within the context of the speed of light. Light travels 30 cm in one nanosecond. Many fluorophores display sub-nanosecond lifetimes. Because of the short timescale of fluorescence, measurement of the time-resolved emission requires sophisticated optics and electronics. Despite the added complexity, time-resolved fluorescence is widely used because of the increased information available from the data, as compared to stationary or steady-state measurements. Additionally, advances in technology have made time-resolved measurements easier, even when using microscopes. Phosphorescence is the emission of light from triplet excited states, in which the electron in the excited orbital has the same spin orientation as the ground-state electron. Transitions to the ground state are forbidden, and the emission rates are slow (103 to 100 s–1), so that phosphorescence lifetimes are typically milliseconds to seconds. Even longer lifetimes are possible, as is seen from “glow-in-the-dark” toys. Following exposure to light, the phosphorescence substances glow for several minutes, while the excited phosphors slowly return to the ground state. Phosphorescence is usually not seen in fluid solutions at room temperature. This is because there exist many deactivation processes that compete with emissions, such as non-radiative decay and quenching processes, that will be mentioned further. It should be noted that the distinction between fluorescence and phosphorescence is not always clear. Transition metal-ligand complexes, which contain a metal and one or more organic ligands, display mixed singlet-triplet states. These complexes display intermediate lifetimes of hundreds of nanoseconds to several microseconds. Fluorescence typically occurs from aromatic molecules. It is essential to mention a widely encountered fluorophore, quinine, which is present in tonic water.

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If one observes a glass of tonic water that is exposed to sunlight, a faint blue glow is frequently visible at the surface. This glow is most apparent when the glass is observed at a right angle. Fluorescence spectral data are generally presented as emission spectra. A fluorescence emission spectrum is a plot of the fluorescence intensity versus wavelength (nanometers) or wavenumber (cm–1). Emission spectra vary widely and are dependent upon the chemical structure of the fluorophore and the solvent in which it is dissolved. The spectra of some compounds, such as perylene, show significant structure due to the individual vibrational energy levels of the ground and excited states. Other compounds, such as quinine, show spectra devoid of vibrational structure. An essential feature of fluorescence is high-sensitivity detection. The sensitivity of fluorescence was used in 1877 to demonstrate that the rivers Danube and Rhine were connected by underground streams [17]. This connection was demonstrated by placing fluorescein into the Danube. Some 60 h later, its characteristic green fluorescence appeared in a small river that led to the Rhine. Today fluorescein is still used as an emergency marker for locating individuals at sea, as has been seen on the landing of space capsules in the Atlantic Ocean. Readers interested in more profound knowledge in the history of fluorescence are referred to as the summary written by Berlman [17].

1.3.1 Apparatus All fluorescence instruments contain three essential items: a source of light, a sample holder, and a detector. Besides, to be of analytical use, the wavelength of incident radiation needs to be selectable, and the detected signal capable of precise manipulation and presentation. In simple filter fluorimeters, the wavelengths of excited and emitted light are selected by filters that allow measurements to be made at any pair of fixed wavelengths. Simple fluorescence spectrometers have a means of analyzing the spectral distribution of the light emitted from the sample, the fluorescence emission spectrum, which may be employed either a continuously variable interference filter or a monochromator. In more sophisticated instruments, monochromators are provided for both the selection of exciting light and the analysis of sample emission. Such instruments are also capable of measuring the variation of emission intensity with exciting wavelength, the fluorescence excitation spectrum. In principle, the most significant sensitivity can be achieved by the use of filters, which allow the whole range of wavelengths emitted by the sample to be collected, together with the highest intensity source possible. In practice, to realize the full potential of the technique, only a small band of emitted wavelengths is examined, and the incident light intensity is not made excessive, to minimize the possible photodecomposition of the sample.

1.3.2 Data analysis Alongside the classical sampling techniques using different types of cuvettes, there are several excellent ways of detecting the fluorescence signal. The use of fiber optics allows the measurement of fluorescence in whole organs in vivo. When

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Table 1.1 Several spectroscopic methods for different parameter characterization Spectroscopic method Steady-state fluorescence Time-resolved fluorescence Fluorescence correlation spectroscopy

Basic parameter characterized

Quantum yield Lifetime Particle number and diffusion time Fluorescence recovery after photo bleaching Rate and extent of recovery Application of total internal reflection fluor- Dependent on the combined escence method

References [18] [19,20] [21] [22] [23]

looking at cells, one can use cell culture plates or flow cytometry. Due to the fact that each of the measurement techniques provides different information based on different ways of detecting the fluorescence signal, the data evaluation is different for each method. Table 1.1 lists the references dealing with the mathematical data treatment and evaluation of the basic fluorescence techniques.

1.3.3 Fluorescence lifetimes The fluorescence lifetime and quantum yield are perhaps the essential characteristics of a fluorophore. Quantum yield is the number of emitted photons compared to the number of absorbed photons. The fluorescence lifetime determines the time available for the fluorophore to interact with or diffuse in its environment, and hence the information available from its emission. Several techniques are used to measure fluorescence lifetimes. One approach is to excite a sample repeatedly with short pulses of light and measure the times at which individual emitted photons are detected after the excitation flashes. This is called single-photon counting or timecorrelated photon counting. The emitted light is attenuated so that, on average, there is a relatively small probability that a photon will be detected after any given flash, and the chance of detecting two photons is negligible. The results of 105 or more excitations are used to construct a histogram of the numbers of photons detected at various times after the excitation. This plot reflects the time dependence of the probability of emission from the excited molecules. The signal-to-noise ratio in a given bin of the histogram is proportional to the total number of photons counted in the bin. If a sufficiently large number of photons are counted, the time resolution is limited by the photomultiplier and the associated electronics and can be about the order of 5  10–11 s. Fluorescence decay kinetics also can be measured by exciting the sample with continuous light whose intensity is modulated sinusoidally at a frequency (w) about the order of 1/t, where t again is the fluorescence lifetime. The fluorescence oscillates sinusoidally at the same frequency, but the amplitude and phase of its oscillations compared to the oscillations of the excitation light depend on the product of w and t. If wt is much less than 1, the fluorescence amplitude tracks the excitation intensity closely; if wt is larger, the oscillations are delayed in-phase and

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damped (demodulated) compared to the excitation [24–26]. Fluorescence with multiexponential decay kinetics can be analyzed by measuring the fluorescence modulation amplitude or phase shift with several different frequencies of modulated excitation. A third technique, fluorescence up-conversion, is to focus the emitted light into a material with nonlinear optical properties, such as a crystal of KH2PO4. If a separate short pulse of light is focused on the same crystal so that the two light beams overlap temporally and spatially, the crystal emits light at a new frequency that is the sum of the frequencies of the fluorescence and the probe pulse. The time dependence of the fluorescence intensity is obtained by varying the timing of the probe pulse compared to the pulse that excites the fluorescence, in the manner typical for pump-probe absorbance measurements. As with absorbance measurements, the time resolution of fluorescence up-conversion can be about the order of 10–14 s. This technique is well suited for studying relaxations that cause the emission spectrum of an excited molecule to evolve rapidly with time.

1.3.4 Fluorescence quenching Another important process that should be mentioned while discussing fluorescence spectroscopy is fluorescence quenching. Quenching can occur by different mechanisms. Collisional quenching occurs when the excited-state fluorophore is deactivated upon contact with some other molecule in solution, which is called the quencher. Collisional quenching can be explained based on the modified Jablonski diagram. In this case, the fluorophore is returned to the ground state during a diffusive encounter with the quencher. The molecules are not chemically altered in the process. For collisional quenching, the decrease in intensity is described by the well-known Stern–Volmer equation: F0 ¼ 1 þ K ½Q ¼ 1 þ kq t0 ½Q F

(1.4)

In this expression, K is the Stern–Volmer quenching constant, kq is the bimolecular quenching constant, t0 is the unquenched lifetime, and [Q] is the quencher concentration. The Stern–Volmer quenching constant K indicates the sensitivity of the fluorophore to a quencher. A fluorophore buried in a macromolecule is usually inaccessible to water-soluble quenchers so that the value of K is low. Larger values of K are found if the fluorophore is free in solution or on the surface of a biomolecule. A wide variety of molecules can act as collisional quenchers. Examples include oxygen, halogens, amines, and electron-deficient molecules like acrylamide. The mechanism of quenching varies with the fluorophore-quencher pair. For instance, the quenching of indole by acrylamide is probably due to electron transfer from indole to acrylamide, which does not occur in the ground state. Quenching by halogen and heavy atoms occurs due to spin-orbit coupling and intersystem crossing to the triplet state. Aside from collisional quenching, fluorescence quenching can occur by a variety of other processes. Fluorophores can form nonfluorescent complexes with quenchers. This process is referred to as static

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quenching since it occurs in the ground state and does not rely on diffusion or molecular collisions. Quenching can also occur by a variety of trivial, i.e., nonmolecular mechanisms, such as attenuation of the incident light by the fluorophore itself or other absorbing species.

1.4 Fourier transform infrared spectroscopy (FTIR) FTIR is a universal analytical tool for the evaluation of a wide range of materials [27,28], mostly used for the identification of unknown materials [29]. The FTIR technique has been widely used to identify pure substances [30], mixtures [31], impurities [30,32], and compositions of various materials [33,34]. In the specialist literature, the application of infrared spectroscopy for the analysis of structural changes [35] as well as for monitoring production (bioproduction) processes [36–38] are well discussed. Advance techniques of FTIR are as follows: Fourier transform infrared-attenuated total reflectance (FTIR-ATR), Fourier transform infrared-photo acoustic spectroscopy (FTIR-PAS), Fourier transform infrared imaging spectroscopy (FTIR spectrometer combined with an optical microscope, FTIR-Microscopy), Fourier transform infrared microspectroscopy, and Fourier transform infrared nanospectroscopy (nano-FTIR spectroscopy), which achieves nanoscale-level spatial resolution by combining IR spectroscopy and scatteringtype near-field scanning microscopy [27,28,35,36,39,40]. Infrared nano spectroscopy opens up new possibilities for chemical and structural analysis and quality control in various fields, ranging from materials’ sciences to biomedicine [40].

1.4.1 Theory Infrared spectroscopy probes the molecular vibrations. Functional groups can be associated with characteristic infrared absorption bands, which correspond to the fundamental vibrations of the functional groups [41,42]. For a nonlinear molecule with N atoms, there are 3N-6 vibrational motions of the molecule atoms, or 3N-6 fundamental vibrations or normal modes. A normal mode of vibration is infrared active (i.e., it absorbs the incident infrared light) if there is a change in the dipole moment of the molecule during the course of the vibration. Thus, symmetric vibrations are usually not detected in infrared. In particular, when a molecule has a center of symmetry, all vibrations which are symmetrical concerning the center are infrared inactive. In contrast, the asymmetric vibrations of all molecules are detected. This lack of selectivity allows us to probe the properties of almost all chemical groups in one sample, and notably of amino acids and water molecules which can hardly be observed by other spectroscopic techniques. Strong IR absorptions are observed for groups with a permanent dipole (i.e., for polar bonds). As such, the carbonyl groups of the polypeptide backbone contribute largely to the infrared absorption spectra of proteins. In the mid-infrared region (4000–1000 cm–1), two main types of vibrations are observed: vibrations along with chemical bonds, called stretching vibrations (n), which involve bondlength changes; and vibrations involving changes in bond angles, and notably

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bending vibrations (d-in-plane, p-out of the plane). The stretching vibrations can be modeled using the harmonic oscillator model, in which a chemical bond is represented by two point-masses linked by a spring. The bond strength (or molecular force field) is the spring tenseness k, and the point masses (m1 and m2) model the masses of the atoms or chemical groups involved in the bond. The equation gives the oscillation frequency n: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1.5) n ¼ ð1=2PcÞ ðk ðm1 þ m2 Þ=m1 m2 Þ The vibration frequency n depends on the bond strength, with higher frequencies for triple or double bonds as compared to single bonds. A consequence of the dependence of stretching mode frequencies on the bond strength is that the frequencies are very sensitive to the group environment, the electronegativity of neighboring atoms or groups, or to hydrogen-bonding interactions. The involvement of one of the atoms in a hydrogen bond will induce a weakening of the bond strength, and thus a frequency downshift of the stretching mode of the chemical group. The sensitivity of this method is high and corresponds to changes in bond length ° [43,44]. For a carbonyl group, the formation of a hydrogen bond smaller than 0.2 A induces downshifts up to 20 cm–1. The inspection of stretching mode frequencies of chemical groups, and specifically of a carbonyl or carboxylic groups in proteins, reveals information on fine structural details. Formation or disruption of hydrogen bonding interactions is one of those. The vibration frequency n also depends on the mass of the atoms involved in the vibration. Consequently, it is possible to specifically alter a vibration frequency by isotope labeling of one of the atoms involved in the vibration. The substitution of hydrogen by deuterium has been widely used to identify and analyze groups with exchangeable protons. Specific isotope labeling (13C, 15N, 18 O, 2H) is also a compelling approach to identify the frequency of one specific group in a complex infrared spectrum. In summary, the vibrational frequencies of a given chemical group are expected in specific regions, which depend on the type of atoms involved and the type of chemical bonds. Tables are available for the main chemical groups [45–48]. Within these vibration regions, the frequencies of the chemical groups are modulated by the specific environment of the group. Therefore, to establish a clear relationship between the infrared mode frequency and the structural properties of a given material, or when there are no data available in the tables, it is necessary to perform a detailed IR analysis on simplified model compounds in different environments and/or to analyze experimental results using theoretical chemistry approaches.

1.4.2 Apparatus The FT spectrometer design is based on light interference rather than diffraction. Instead of using diffractive optics to separate the wavelength components of the light spatially, the FT spectrometer uses a Michelson interferometer with a movable mirror moving at a fixed frequency and directs all wavelengths at once to the detector. The frequency of this mirror’s movement is constantly monitored and calibrated using a reference laser, which grants the FTIR its greater precision and accuracy. The laser also serves as a real-time wavelength reference, which is acquired simultaneously to data

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collection. Its principle of operation lies in the interference between the light traveling through the two different arms of the interferometer. For a monochromatic light beam, when the path difference (Dl) between the two arms of the interferometer is an integer multiple of the wavelength, the beams will interfere constructively, and when it is an integer multiple plus half of the wavelength, they will interfere destructively and cancel each other. This will generate an oscillatory signal on the detector as a function of time. Different wavelengths interfere differently for given positions of the movable mirror. When monochromatic light passes through the interferometer, it creates an oscillating response on the detector. With polychromatic light, the presence of multiple wavelengths results in a superimposed signal oscillating in time with different frequencies. This combined signal is called an interferogram. To recover the frequency domain spectrum, a Fourier transforms to the interferogram is applied. The simpler moving parts of the instrument and the use of a fixed wavelength laser for monitoring and calibrating the FTIR spectrometer mirror’s movement grants the technical accuracy and precision that cannot be easily achieved with dispersion opticsbased spectrometers. The fact that the optics do not change during the experiment (no changing filters or gratings for different wavelengths) means that the FTIR spectra do not have the discontinuities that arise from those changes. New approaches for FTIR difference spectroscopy involve the use of attenuated total reflectance (ATR), coupled with the perfusion of samples with buffers containing a triggering reagent or a metal cofactor [49]. With an ATR setup, the infrared beam is reflected within the ATR crystal. At each reflection, the evanescent wave probes a layer of the sample deposited on the crystal, within a thickness of about 1 mm. In contrast with transmission FTIR difference spectroscopy, in which reactions must be induced in the thin path length sample by external methods, without modifying the sample volume and content, this approach has the advantage of minimizing global absorption changes, when the protein layer deposited on the ATR crystal is exposed to reactants administrated at the top of the sample. This approach was applied to the recording of FTIR difference spectra of different redox cofactors of PSI or bacterial reaction centers dried as stable films on the ATR crystal [50]. The difference spectra obtained by the perfusion of buffers poised at different redox potentials were identical to spectra recorded using light-induced FTIR difference spectroscopy [50]. This approach was also extended to the analysis of soluble proteins maintained on the ATR crystal by a dialysis membrane [51,52].

1.4.3 Data analysis Infrared spectroscopy is used to characterize many materials. Looking at the literature, it is evident that glass-based rare-earth-activated optical structures represent the technological pillar of a huge of photonic applications covering health and biology, structural engineering, environment monitoring systems, and quantum technologies. Among different glass-based systems, a strategic place is assigned to transparent glass-ceramics, nanocomposite materials, which offer specific characteristics of capital importance in photonics. In this part of the chapter, some first results concerning silica tin-dioxide glass-ceramics will be discussed.

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105 100 95

Transmittance (%)

90 85

10.0SnO2

80 75 70 65 60 55 50 400

800

1,200 1,600 2,000 2,400 2,800 3,200 3,600 4,000 Wavenumber (cm–1)

Figure 1.4 Infrared spectra recorded for silica tin dioxide sol-gel system (containing 10 mol% of SnO2) doped with Er3þ ions

Figure 1.4 presents infrared spectra recorded for SnO2-SiO2 sol-gel system doped with Er3þ ions in the 4000–400 cm–1 spectral region. Generally, the registered bands in the 1400–400 cm–1 frequency region correspond to the vibrational modes of silicate tetrahedral, whereas the infrared bands in the 4000–1400 cm–1 frequency region are related to the vibrational modes involving O-H groups of water and organic solvents [53,54]. The recorded infrared bands in Figure 1.4 (1087, 800, 463 cm–1) confirmed the creation of an amorphous silicate matrix in the obtained samples as a result of the polycondensation reaction. Moreover, the weak broadband observed around 3300 and 1630 cm–1 (bending and stretching vibrations of O-H groups, C¼O groups vibrations) indicated the absence of water and organic solvents in pores inside the silicate matrix [55,56]. The intense infrared band at around 1087 cm–1 is attributed to the asymmetric stretching vibration of Si-O-Si linking bonds. Additionally, this band has two shoulders at 1200 and 998 cm–1 corresponding to vibration SiO4 tetrahedron in Q4 units and Q2 units or stretching vibration of Si-OH, respectively [57,58]. The amorphous structure of silica is also characterized by the absorption bands located at 800 and 449 cm–1. The appearance of these bands in all samples is assigned to the Si-O-Si symmetric stretching (800 cm–1) and the vibrational bending mode between adjoining SiO4 rings (463 cm–1). The infrared bands in the 500–720 cm–1 frequency region are attributed to the presence of tin dioxide in the silica matrix. The band located at 657 cm–1 is typical of O-Sn-O vibrations of SnO2, which confirm the formation of the SnO2 crystalline phase, whereas the absorption band at 558 cm–1 is related to the terminal oxygen vibration of Sn-OH [59].

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1.4.4 Applications As illustrated above, infrared spectroscopy is a valuable technique for the analysis of pharmaceuticals, polymers and plastics, food, environment, and falsified materials, including medicines [39,60,61]. It is worth to mention that FTIR spectroscopy has also helped to perform more advanced analyses, such as the characterization of artistic materials [62] and disease diagnosis [63,64]. FTIR spectroscopy is a crucial technique for the characterization of polymeric and biopolymeric materials [65,66]. The FTIR technology has proved to be useful in the identification and characterization of homopolymers, copolymers, or polymer composite, and it has been successfully applied in the evaluation of polymerization process, characterization of the structure, surface, and degradation and modification of the polymers [65,67,68]. More common applications of FTIR methodology include the quality verification of materials; analysis of thin films and coatings [69]; decomposition of polymers and other materials, often through thermogravimetry combined with FTIR [70,71] and mass spectrometry; microanalysis of materials to identify contaminants; monitoring of emissions; and failure analysis [72–74]. In the literature, different optical materials were analyzed employing the FTIR spectroscopy. Among them, the modifications occurring in the glass network as a consequence of the heat treatments performed near the glass-transition temperature and their effect on devitrification behavior of the glasses with different composition have been studied [75]. The speed of FTIR analysis makes it particularly useful in screening applications, while its sensitivity allows many advanced research applications.

1.5 Raman spectrometry In 1928, Sir Chandrasekhara Venkata Raman observed that for a material illuminated with monochromatic light, in addition to the light scattered elastically (Rayleigh scattering), a small portion of the light was inelastically scattered, having its energy changed. The difference in energy of the emerging photons compared to the incident photons corresponds to the energy that is absorbed or released by collective vibrations of the atoms in the sample, phonons in solids, normal vibration modes in molecules, liquids, or gases. This scattering is now known as the Raman effect. For its discovery and the development of the theory behind the effect, Sir Raman was awarded Nobel Prize in Physics in 1930. For years, the Raman spectroscopy has been a powerful tool for the investigation of molecular vibrations and rotations. Before the laser era, its main drawback was a lack of sufficiently intense radiation sources. After the laser introduction, this field of spectroscopy has been revolutionized. Lasers have enhanced the sensitivity of spontaneous Raman spectroscopy, and they have kicked off new spectroscopic techniques based on the stimulated Raman effect, such as coherent anti-Stokes Raman scattering (CARS) and hyper-Raman spectroscopy. Nowadays, the Raman spectroscopy is a versatile and non-destructive technique to study the structure of a wide range of different optical materials, including

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polymers, multicomponent glasses [76], and glass-ceramics [77] at both micro- and macro-scale [78].

1.5.1 Theory Raman and Rayleigh scattering can be understood as the light generated by oscillating electric dipoles in the material, induced by the incident excitation radiation. The induced dipole moment tensor m can be considered, in a first-order approximation, a linear function of the applied field E: m ¼ aE

(1.6)

The a tensor is the polarizability of the material. Considering its modulation by the normal atomic vibrations of the material, for small amplitude oscillations near the equilibrium, the polarizability dependence on the normal coordinate Q associated with a normal mode of vibration can be written as:   @a 0 Q ¼ a0 þ a Q a ¼ a0 þ (1.7) @Q Where a0 is called the derived polarizability tensor. Treating the normal vibrations as harmonic: Q ¼ Q0 cos wt

(1.8)

and with the incident electric field being given by: E ¼ E0 cos w0 t

(1.9)

the time dependence of the induced dielectric moment will be given by: 1 0 0 m ¼ a0 E0 cos w0 t þ a Q0 E0 ½cos ðw0  wÞt þ cos ðw0 þ wÞt 2

(1.10)

This means that the dipole will oscillate simultaneously with three frequencies, w0, w0w, and w0 þ w. The first term of m0 describes the Rayleigh scattering while the second and third terms account for the anti-Stokes and Stokes Raman scattering corresponding to the normal mode of vibration Q. It can also be seen that while the Rayleigh scattering depends on the polarizability of the material at its equilibrium configuration, the Raman scattering depends on the sensitivity of the polarizability to changes in the atomic configuration along the direction of the usual coordinates of vibration, reflected by a0 . That means that if for a particular normal mode Q, a0 ¼ 0, that mode of vibration is not Raman active. For IR absorption, a particular mode of vibration is active if the dipole moment changes with that vibration, i.e., when   @u Q 6¼ 0 (1.11) @Q

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Since the Raman and IR activities are subject to different selection rules, as presented above, the techniques are used as complementary characterization tools.

1.5.2 Apparatus Being a versatile characterization tool, applicable to the analysis of gases, liquids, and solids, the Raman spectroscopy instrumentation is available in a great variety of different setups. Some equipment are more adapted to a specific application, and some intended for broader use. The typical setup is composed of an excitation laser source, which is directed at the sample to generate the scattering. The scattered light is collected by a lens or system of lenses, filtered to eliminate the Rayleigh scattered light, dispersed in photon energies, and directed to a detector.

1.5.3 Data analysis

Normalized intensity (a.u.)

In this paragraph, the Raman spectra of the SiO2-SnO2 glass-ceramic planar waveguides will be analyzed as an example of the characterization of an optical material. Looking at Figure 1.5, one can observe the presence of typical Raman modes at 440, 489, 600, and 800 cm–1. The intense broadband at about 440 cm–1 can be assigned to SiO4 tetrahedra deformation vibrations in the silica network [79,80]. Henderson [81] specified this band as symmetric stretching of Si-O-Si bonds predominantly with 6-membered rings of SiO4 tetrahedra with a minor contribution from 5-membered and higher than 6-membered rings.

pure SiO2 10%

30%

pure SnO2 200

400

600 800 Raman shift (cm–1)

1,000

1,200

Figure 1.5 Visible micro-Raman (lexc ¼ 632 nm) spectra of (100-x)SiO2xSnO2:0.5%Er3þ planar waveguides (where x ¼ 10, 30) compared to SnO2 and SiO2

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It was already observed [82] that the presence of SnO2 in the glass-ceramics leads to the narrowing of this band. According to the literature [83], the width of this band is related to the disorder-induced distribution of angles in the Si-O-Si units connecting the SiO4 tetrahedra. On the other hand, McMillan [84] correlates the narrowing of this band, together with a higher-frequency shift with the narrower average Si-O-Si angle in a more compact SiO2 structure. Thus, the band narrowing observed on micro-Raman of planar waveguides can be explained as follows: the introduction of SnO2 in SiO2 matrix may prevent the formation of highermembered rings or induce a narrower Si-O-Si angle of SiO4 tetrahedra. The following two bands, at about 489 and 600 cm–1, recognized as the D1 and D2 defect bands, are attributed to the presence of local defects of four-fold and three-fold rings in the regular six-fold rings of SiO2 network [80,85,86]. It is seen that the intensity of the D1 defect band centered at 489 cm–1 assigned to the four-fold rings present in the SiO2 network [85,86] is much higher than in pure SiO2. Comparing the Raman features of the pure SnO2 pellet with the investigated planar waveguides, a very small contribution of A1g crystal-mode SnO2 at 630 cm–1 is revealed as in [87]. This band is feeble and covered by the defect band D2, which is due to the high distortion of SnO2 nanocrystals, as suggested by Die´guez in [88]. Furthermore, a small contribution of B2g mode at 760 cm–1 integrated with the S3 (or Au2) mode appears as a consequence of disorder activation. Also, a new weak band centered at 770 cm–1 was observed, assigned to B2g, one of the nondegenerate vibration modes of the plane vibration perpendicular to the c-axis of the 6-atom unit cell of tetragonal rutile crystalline structure of SnO2 [88,89]. Next, the band at 800 cm–1, the w3 band, is assigned to a complex motion of Si atoms against the bridging oxygen atoms in O-Si-O in silica network [90]. The Raman spectra are characterized by the presence of bands at 1063 and 1170 cm–1, attributed, respectively, to symmetric and anti-symmetric Si-O stretching vibrations [83].

1.5.4 Applications The ability to investigate the vibrational spectrum of the of the molecular systems makes Raman spectroscopy an ideal technique to complement the IR spectroscopy. It has to be mention that the Raman spectroscopy is one of the most versatile and powerful optical characterization techniques. A wide range of applications exist, from materials structural and chemical characterization [91] to medical diagnostics [92], to applications in the fields of forensics and crime prevention [93], food sciences [94], biology [95], nanotechnology [96], industrial process and quality control [97], and space exploration [98,99]. By using the Raman spectroscopy, we are able to differentiate between the various phases of a material with the same chemistry or regions of the different chemical composition of a sample. It can be used to study the incorporation of impurities on a crystalline matrix, to measure stress distribution in a sample, or monitor phase transitions, with temperature or pressure. In some optical materials, like glass-ceramics, the resonance Raman spectroscopy, that uses excitation frequency higher or close to the electronic transition frequency of the investigated

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materials, allows for an improvement of the sensitivity and especially selective enhancement of some vibration modes associated to specific chemical groups [100]. These scattering signals may be silent or extremely weak in the conventional non-resonance Raman spectra, which has a sensitivity of the order of 1 over 10 million photons [101]. Using the UV resonance effect, one can observe the presence of the SnO2 phase in glass-ceramics that can be seen on the conventional Raman spectroscopy but is improved by the mentioned effect.

1.6 Optical waveguide characterization 1.6.1 General Since optical waveguides are fundamental elements for constructing integrated optical devices, the characterization of such light wave guiding structures plays an essential role in the design and manufacturing processes. Besides the fundamental material assessments in terms of the structural, morphological, chemical, and spectroscopic properties to ensure the required optical quality of optical waveguides, another mandatory characterization is placed on their waveguiding properties. Critical features of optical waveguides need to be inspected are: ● ● ●

refractive index and index profile; geometrical features such as thickness, width and surface morphology; and optical loss.

In the following content, a brief introduction to various characterization techniques for each of the features, as mentioned above, is presented.

1.6.2 Refractive index measurements In general, an optical waveguide is a structure that consists of a dielectric medium with a higher refractive index than its surrounding dielectric media. The refractive index is among the foremost parameters of an optical waveguide. To determine the refractive index of an optical waveguide, different non-destructive methods can be utilized, such as: m-line spectroscopy [102–105], reflectometry [106,107], ellipsometry [108], surface plasmon resonance spectroscopy [109], and techniques of propagation-mode near-field [110] and refracted near-field [111,112]. A detailed description of the physics, experimental setups, features, and applications of each method can be found in the corresponding mentioned publications. In the scope of this chapter, to compare these methods, a summary of their working principle, features, and applications is listed in Table 1.2. From Table 1.2, one can see that m-line and ellipsometry appear to be complementary techniques for the measurement of the refractive index of planar waveguides with high accuracy. Moreover, they provide the simultaneous determination of the waveguide thickness as well. Concerning the acquisition of the refractive index profile of optical waveguides, the techniques of propagation-mode near-field and refracted near-field are more applicable.

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Table 1.2 Several techniques of refractive index measurements for optical waveguides Method

Working principle

Features and applications

M-line

Prism coupling

–

– – Reflectometry

Ellipsometry

Based on the measurement of the reflected light intensity ratio

– – –

Based on the change in the – polarization state of reflected light – – –

Surface plasmon Based on surface plasmon resonance resonance reflectivity spectroscopy measurement

– –

– Propagationmode near-field technique

Based on the measurement of – the near-field mode intensity profile – – –

Refracted near-field technique

Based on the measurement of – the near-field intensity of the refracted beam

Allows simultaneous measurement of refractive index and thickness of waveguides in planar forms High accuracy (up to  10–4) [105] Applicable only to waveguides thick enough to support at least two guided modes Generally yielding an approximation of the real part of the refractive index Accuracy about  0.01 [106] Not applicable to thin transparent films Allows measuring the refractive index, extinction, and thickness of waveguides in planar forms Accuracy up to  510–3 [108] Applicable also to very thin films ° ) [106] (less than a few thousand A Requires accurate advance knowledge of the complex refractive index of the substrate Applicable to dielectric films deposited on noble metal surfaces Requires choosing the complex permittivity of the metal layer correctly with respect to the measured dielectric films to excite the surface plasmon resonance Reported relative accuracy of about ~1% [113] Allows acquiring the profile of refractive index of optical waveguides Applicable to any cross-sectional symmetry of the waveguides Requires a weakly waveguiding, and only the fundamental propagation mode to be excited Need for multiple acquisition times of near-field mode intensity profile for the refractive index approximation Allows acquiring the profile of refractive index of optical waveguides

(Continues)

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Table 1.2 Method

(Continued) Working principle

Features and applications – – –

Applicable to planar and channel waveguides supporting either single- or multimodes Complicated experimental setup Existing issue of the accuracy related to the uncertainty of refractive index calibration

1.6.3 Geometrical characterization For applications in integrated optics, optical waveguides are usually in geometrical plane forms, such as planar waveguides and channel waveguides. To have strong light confinement and contemporary optimize the device performance [e.g., in terms of losses], it is required to have a high refractive index contrast of the waveguide core versus cladding and a single-mode propagation regime at the working wavelength. In other words, besides the refractive index, another critical parameter defining light confinement is the dimension (thickness and width) of optical waveguides, which is generally on the micron scale. Apart from the mentioned m-line and ellipsometry techniques, one can use other non-destructive methods to measure the waveguide thickness, such as stylus surface profiling [114], and noncontact optical profiling [115]. Scanning electron microscopy can be used as another means of measuring the waveguide dimension and topography; but in this case, the limitation is that it is a destructive method. Concerning the surface morphology of optical waveguides, surface imperfections can induce loss due to mode conversion [116]. For general optics applications, the limit of the rough mean square (rms) surface roughness can be defined based on the Rayleigh smooth-surface criterion [117], and the maximum amplitude allowed for the surface roughness is less than 10 nm. However, according to the optical specification of high-quality manufacture in integrated optics, surface roughness ° [106]. To analyze the surface roughness, the foremost should be in the range of 5 A technique is atomic force microscopy (AFM), but both the above-mentioned surface profilers (stylus and noncontact optical ones) can also be employed. A comparison of surface roughness characterization by the three techniques can be found in 115.

1.6.4 Optical loss measurement When a light wave travels in a medium, it suffers a loss due to many factors, the most important being material loss due to absorption, and scattering loss due to surface roughness or volume imperfection. Another source of loss is due to out-ofguide radiation, which becomes significant in bent optical waveguides or when the optical waveguides have either small core/cladding refractive index contract or thickness close to the cut-off condition [118]. All these losses induce the

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attenuation of the propagating light wave, generally called propagation loss: it can be described by the following equation: a I ðzÞ ¼ I0 10ð10Þz

(1.12)

where z is the distance in the longitudinal propagating direction (usually in cm), I(z) is the optical power remaining after the propagation length z, and I0 is the initial optical power at the first point of the propagation. To measure the propagation losses, several approaches have been used, including scattered light measurement [105], sliding-prism [119,120], end-fire coupling with waveguides of different lengths, or cutback method [106,121]. Each method has its merit and limitation. The mentioned end-fire coupling/cutback method is the most fundamental and accurate since it uses the approach of introducing a known input power into one end of the optical waveguides and measuring the output at the other end. However, the method is destructive since the waveguides must shortened by cutting and polishing: it is excellent for optical fibers, but not really suitable for integrated optics. The sliding-prism is a versatile and non-destructive technique, where the optical power input is introduced in the guide by a fixed prism and the output is extracted by a movable sliding-prism. However, it is less precise and hardly reproducible than the end-fire coupling. The scattered light measurement is a convenient and non-destructive alternative to measure the propagation loss of optical waveguides. It usually exploits a transversely oriented fiber optic probe and a photodetector to measure the light scattered out from the plane of the optical waveguide, either planar or channel. This method provides an accurate solution for loss measurement of dielectric waveguides, where the scattering loss dominates the propagation loss.

1.7 Summary In this chapter, different optical characterization techniques have been discussed. It clearly appears, based on the literature, that these techniques are flourishing, bringing novel applications and allowing characterization of new, sometimes exotic, materials. The limited scope of this chapter precluded a complete discussion on the use of different characterization techniques, but should have permitted the reader to be acquainted with the principles and basics that are behind each of the applied techniques. Having this knowledge, new directions can be set and the limitations of existing techniques can be removed.

Acknowledgments The support of the projects ERANet-LAC “RECOLA” (2017–2019) and Centro Fermi MiFo (2017–2020) is gratefully acknowledged. The author thanks Thi Ngoc Lam Tran (IFN-CNR, Trento, and Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, Vietnam) and Marta Kuwik (University of Silesia, Katowice, Poland) for their invaluable contribution while writing this chapter.

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[83] Montagna M, (2004) “Characterization of sol–gel materials by Raman and Brillouin spectroscopies,” In: Sakka S, (ed.), Handbook of Sol-gel Science and Technology: Processing, Characterization and Applications. Volume II: Characterization and Properties of Sol-Gel Materials and Products, Kluwer Academic Pulishers, pp. 99–117. [84] McMillan PF, and Remmele RLJ, (1986) “Hydroxyl sites in SiO2 glass: A note on infrared and Raman spectra,” Am. Mineralogist, 71: 772–778. [85] Bouajaj A, Ferrari M, and Montagna M, (1997) “Crystallization of silica xerogels: A study by Raman and Fluorescence spectroscopy,” J. Sol-Gel Science and Techn. 395: 391–395. [86] Kinowski C, Bouazaoui M, Bechara R, and Hench LL, (2001) “Kinetics of densification of porous silica gels: A structural and textural study,” J. Non-Cryst. Solids, 291: 143–152. [87] Van Tran TT, Si Bui T, Turrell S, et al., (2012) “Controlled SnO2 nanocrystal growth in SiO2-SnO2 glass-ceramic monoliths,” J. Raman Spectr., 43(7): 869–875. [88] Die´guez A, Romano-Rodrı´guez A, Vila` A, and Morante JR, (2001) “The complete Raman spectrum of nanometric SnO2 particles,” J. Appl. Phys., 90 (3): 1550–1557. [89] Fazio E, Neri F, Savasta S, Spadaro S, and Trusso S, (2012) “Surfaceenhanced Raman scattering of SnO2 bulk material and colloidal solutions,” Phys. Rev. B – Cond. Matt. Mat. Phys., 85(19): 1–7. [90] Okuno M, Zotov N, Schmu¨cker M, and Schneider H, (2005) “Structure of SiO2–Al2O3 glasses: Combined X-ray diffraction, IR and Raman studies,” J. Non-Cryst. Solids, 351(12–13): 1032–1038. [91] Dutta B, Tanaka T, Banerjee A, and Chowdhury J, (2013) J. Phys. Chem. A, 117: 4838. [92] Feng S, Lin D, Lin J, et al., (2013) Analyst 138: 3967. [93] Tripathi A, Emmons ED, Guicheteau JA, et al., (2010) Chemical, biological, radiological, nuclear, and explosives (CBRNE) sensing XI, 76650N. Proceedings of SPIE 7665, 27 April 2010. doi:10.1117/12.865769 [94] Mohamadi Monavar H, Afseth NK, Lozano J, Alimardani R, Omid M, and Wold JP, (2013) Talanta 111: 98. [95] Bansal J, Singh I, Bhatnagar PK, and Mathur PC, (2013) J. Biosci. Bioeng. 115: 438. [96] Chrimes AF, Khoshmanesh K, Stoddart PR, Mitchell A, and Kalantar-zadeh K, (2013) Chem. Soc. Rev. 42: 5880. [97] Sarraguc¸a MC, De Beer T, Vervaet C, Remon J-P, and Lopes JA, (2010) Talanta 83: 130. [98] Strazzulla G, Baratta GA, and Spinella F, (1995) Adv. Space Res. 15: 385. [99] Jaumann R, Hiesinger H, Anand M, et al., (2012) Planet Space Sci. 74: 15. [100] Rossi B, and Masciovecchio C, (2018) “GISR 2017: Present and future of Raman researches in Italy,” J. Raman Spectroscopy, 49: 909–912. [101] Woodward LA, (1967) Raman Spectroscopy, New York: Plenum Press. [102] Tien PK, (1977) “Integrated optics and new wave phenomena in optical waveguides,” Rev. Modern Phy., 49(2): 361–420.

32 [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113]

[114] [115] [116] [117] [118] [119]

Integrated optics Volume 2: Characterization, devices, and applications Ulrich R, and Torge R, (1973) “Measurement of thin film parameters with a prism coupler,” Appl. Optics., 12(12): 2901–2908. Monneret S, Huguet-Chantoˆme P, and Flory F, (2000) “M-lines technique: Prism coupling measurement and discussion of accuracy for homogeneous waveguides,” J. Opt. A: Pure App. Opt., 2(3): 188–195. Metricon Corporation, (n.d.). https://www.metricon.com/model-2010-moverview/ Tong XC, (2014) “Chapter 2: Characterization Methodologies of Optical Waveguides.” In: Advanced Materials for Integrated Optical Waveguides, Springer International Publishing. pp.53–102. Sultanova NG, Nikolov ID, and Ivanov CD, (2003) “Measuring the refractometric characteristics of optical plastics,” Optical Quant. Elec., 35: 21–34. Tompkins HG, (1993) A User’s Guide to Ellipsometry, Boston: Academic Press. Raether H, (1988) “Chapter 2: Surface plasmons on smooth surfaces.’ In: Surface Plasmons on Smooth and Rough Surfaces and on Gratings. Berlin, Heidelberg: Springer, pp. 4–39. Yip GL, Noutsios PC, and Chen L, (1996) “Improved propagation-mode near-field method for refractive-index profiling of optical waveguides,” Appl. Opt., 35(12): 2060–2068. White KI, (1979) “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Optical Quantum Elec., 11(2): 185–196. Go¨ring R, and Rothhardt M, (1986) “Application of the refracted near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Comm., 7(3): 82–85. Del Rosso T, Sa´nchez JE, Carvalho RD, Pandoli O, and Cremona M, (2014) “Accurate and simultaneous measurement of thickness and refractive index of thermally evaporated thin organic films by surface plasmon resonance spectroscopy,” Opti. Express., 22(16): 18914–18923. Bennett JM, and Dancy JH, (1981) “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt., 20(10): 1785–1802. Poon CY, and Bhushan B, (1995) “Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler,” Wear, 190(1): 76–88. Dietrich M, (1969) “Mode conversion caused by surface imperfection of a dielectric slab waveguide,” Bell System Tec. J., 48(10): 3187–3215. John CS, (2012) “Chapter 2: Quantifying surface roughness,” In: Optical Scattering: Measurement and Analysis, 3rd edn., SPIE Press, pp. 23–46. Hunsperger RG, (2009) “Chapter 6: Losses in optical waveguides.” In: Integrated Optics, 6th edn., New York, NY; Springer, pp. 107–128. Weber HP, Dunn FA, and Leibolt WN, (1973) “Loss measurements in thinfilm optical waveguides,” Appl. Opt., 12(4): 755–757.

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Tien PK, Ulrich R, and Martin RJ, (1969) “Modes of propagating light waves in thin deposited semiconductor films,” Appl. Phy. Let., 14(9): 291–294. Merz JL, Logan RA, and Sergent AM, (1976) “Loss measurements in GaAs and AlxGa1-xAs dielectric waveguides between 1.1 eV and the energy gap,” J. Appl. Phy., 47(4): 1436–1450.

Chapter 2

Structural and surface-characterization techniques Giorgio Speranza1,2,3

The optical characteristics of a material refer to a list of properties which substantially mirror the solid-light interaction. This, in turn, depends on the electronic structure of the solid, which is intimately bound to the material structure and chemical properties. Then, the interaction of radiation with matter is strongly influenced by the presence of crystalline/amorphous structures, size confinement in 1D, 2D systems and if they are isolated or embedded in a bulk matrix, the material chemical composition, density, etc. An accurate characterization of these parameters is a prerequisite for an exact description of the material optical properties. For this reason, generally, their characterization is made using a list of complementary techniques. These may be roughly classified in two groups: those using photons as probes and those relying on electrons. In this section, we will focus our attention on the photon probes and in particular X-photons, to investigate the material properties. X-radiation describes photons with wavelengths in the range 10–0.01 nm, corresponding to soft and hard rays, respectively. This rather wide spectral range corresponds to different kinds of solid-light interactions. For this reason, since the discovery of X-rays, a list of different techniques has been developed probing materials at different levels, from macroscopic to atomic scale range, thus providing bulk and local information about the nature of the probed sample. In the following, we will give some salient descriptions of the use of X-rays to investigate the properties of optical materials. The section is organized in a brief introduction on X-ray-based techniques, including X-ray diffraction and some selected examples: application of X-ray diffraction to photonic crystals, application to nanostructures, detection of strain-stress, X-based tomography, extended X-ray absorption fine structure, X-ray absorption near-edge spectroscopy, and finally X-ray photoemission spectroscopy.

1

CMM – Fondazione Bruno Kessler (FBK), Trento, Italy Institute of Photonics and Nanotechnologies (IFN – CNR), CSMFO Lab., Trento, Italy 3 Department of Industrial Engineering, University of Trento, Trento, Italy 2

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Integrated optics Volume 2: Characterization, devices, and applications

(a)

Optical Luminescence

Incident X-ray micro-beam

X-ray Flourescence

Absorbed photons

Electron emission Sample

Scattered/diffracted beam Transmitted beam (b) XEOL

XRF

XAS (XANES, EXAFS)

XMCD XMLD

MicroSpectroscopy

XPEEM

Modalities: Full-Field XTM Scanning XTM

(Spectro-) Microscopy

XTM

Contrast formation: Absorption Phase Contrast Fluorescence Magnetic Dichroism Scattering/Diffraction Coherent Diffraction (ptychography, SXDM)

XPS

Principal methods/ variants: powder diffraction Laue diffraction protein diffraction magnetic diffraction surface diffraction

CrystalXRD

Space-Resolved X-ray Analytical Methods (principal techniques)

Topography

MicroDiffraction

Imaging

Laminography Radiography

Principal variants: WAXS SAXS

Diffuse Scattering

Ptychography

Tomography

Figure 2.1 (a) Schematic representation of the principal X-rays and matter interactions. (b) Classification of most popular X-ray-based space-resolved analytical tools with micrometric and submicrometric resolution; four main categories are represented: microspectroscopy, microdiffraction, (spectro)microscopy, and imaging. Reprinted, with permission, from [3]

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37

2.1 X-ray-based analytical techniques and X-ray diffraction X-photons are generally utilized to obtain structural information. The discovery of X-rays by Roentgen dates back to 1895 [1], and it was soon realized that X-rays deeply penetrate into the matter since have wavelengths in the angstrom range [2]. This discovery led to the development of a few useful techniques for materials’ characterization. The X-ray fluorescence (XRF) analysis is a method of quantitative element analysis based on the ionization of the atoms induced by a X-ray probing beam. X-rays induce ionization of the probed atoms, and the radiation emitted upon relaxation contains information regarding the nature and the abundance of those elements in the sample. With the advent of synchrotrons, other forms of X-ray spectroscopies requiring highly monochromatic photons have also been made available. Using the X-ray absorption spectroscopy (XAS), it is possible to determine both the local geometry and the electronic structure of matter. Upon spectral energy, three main regions may be identified in XAS spectra: the absorption threshold determined by the transition to the lowest unoccupied states; the X-ray absorption near-edge structure (XANES), which is dominated by core transitions in the range 10–150 eV, providing information about vacant orbitals, the electronic configuration, and site symmetry of the absorbing atom; the extended X-ray absorption fine structure (EXAFS), which probes transition energies in the range 50–1000 eV. In this range, X-ray absorption induces electron photoemission. The wave associated to the photoelectron Ye interferes with the backscattered equivalents caused by atoms surrounding the photoemitter. So, the final state of Ye can be described by the sum of the original and scattered waves. EXAFS is one of the most appropriate spectroscopies to be applied to characterize amorphous solids, liquids or gels, molecules, and biomolecules as proteins, nanostructures, and catalysts. Wide-angle X-ray scattering (WAXS) or small-angle X-ray scattering (SAXS) are diffraction-based techniques which can be applied to study amorphous materials. X-diffraction-based 3D ptychography is an emerging technique to map the electron density distribution using coherent microfocused beams. Finally, thanks to the brilliant intense and tunable synchrotron sources and the possibility to collimate them on the sample, X-ray microscopy has gained even more popularity. Figure 2.1 summarizes the X-based space-resolved techniques available for characterizing materials. Among the X-techniques, X-ray diffraction (XRD) is one of the most important widely utilized techniques for its easy use. XRD provides the structural and phase composition analyses and information about the geometry of the crystal lattice and its unit cell. In practice, when photon wavelengths are similar to the spacing of planes in a crystal lattice, as in the case of X-rays, the materials behave as 3D diffraction gratings. Diffraction patterns are generated by multiple constructive/destructive interferences produced by the various crystalline plains. Depending on the inclination of the sample with respect to the incident X-ray beam,

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Integrated optics Volume 2: Characterization, devices, and applications

θ

θ

d

Figure 2.2 Schematic representation of the Bragg law the photons scattered by different plains can emerge in phase with the incident radiation, thus giving a constructive interference. This happens if the Bragg relation is satisfied: nl ¼ 2dsin q as shown in Figure 2.2. This simple law relates the wavelength l of the impinging photon to the lattice spacing d of the crystalline sample and the diffraction angle q, which is the angle between the incident beam and the normal to the reflecting lattice plane. The scattered X-photons are then detected to reconstruct the diffraction pattern of the material by tilting the sample through a range of 2q angles, in order to identify all the possible diffraction directions of the crystalline lattice. Alternatively, this may be accomplished by analyzing powders, where the same result is obtained thanks to the random orientation of the powder grains. For a crystalline solid, each diffraction pattern is composed by a unique set of peaks, i.e. d-spacing, making possible to recognize any kind of crystallographic phase, among the others. However, clear diffraction peaks are generated only when the sample is characterized by an adequate long-range order. In high-quality crystals, the diffraction lines are very narrow and well defined. Reducing the system dimensions, as in the case of crystallites or nanoparticles (NPs) with sizes below 100 nm, there is a loss of long-range order, and the spectral lines broaden. This occurs because of the partial constructive/destructive interference along the scattering directions where the X-rays are in or out of phase. To obtain information regarding the crystal size, one can use the Scherrer equation relating the crystal size to line width: ¼ kl=w sin q

Structural and surface-characterization techniques

39

where represents the average dimension of crystallites or NPs in the direction perpendicular to the reflecting plane, l is the X-ray wavelength, w is the line width at half the maximum intensity, q is the diffraction angle, and k is shape factor which is often taken close to unit. The Scherrer equation is an easy method to estimate the particle size, but it suffers from some uncertainties [4]. Apart the line broadening due to instrumentation, errors derive from nonspherical particle shapes ( is the dimension perpendicular to the diffraction plane) and not appropriate values for k. In addition, the contribution of strain and/or disorder is neglected, although they contribute to the diffraction line width. Thus, the application of the Scherrer equation easily leads to an underestimate of the coherently diffracting domain size. More sophisticated versions of this equation are applied to account for these aspects [4]. XRD is widely utilized for assessing the optical properties of different materials. Concerning materials for photonics, XRD was used to get the structural properties of a large class of network glass formers [5] such as SiO2 [6–9], GeO2 [10–13], P2O5 [14–16], and B2O3 [17–19], as well as tellurites [20–22], fluorides [23–25], chalcogenides [26–29], and glasses obtained by mixing these formers; some example are given in [30–40]. Generally, these glasses are doped with some rare earth ions to induce specific optical properties, and some reference to this broad topic can be found in [41–43].

2.2 Examples of characterization of optical materials by X-rays Due to the easiness of use and the possibility to analyze almost any kind of material, the literature regarding the application of XRD is huge. Here we will describe a few of the XRD applications showing some of the peculiarities of this technique, with particular attention to materials or systems used in photonics.

2.2.1 Application of XRD to photonic crystals Photonic crystals (PC) are structures in which the refractive index varies periodically in one, two, or three dimensions. This comes out from lattice parameters comparable to the wavelength of light, thus influencing the propagation of photons. In this respect, PCs are photonic bandgap materials characterized by a range of forbidden frequencies. Thus, a photonic bandgap material can be considered as the optical analogue of an electronic bandgap in semiconductors. Thanks to the strong interaction with light, photonic bandgap materials display an unprecedented control over both the emission and the propagation of light [44–47]. This, in combination with nonlinear optical effects, enables important applications in optical integrated circuits, infrared telecommunications [48,49], photon manipulation in optics and quantum optics [50,51]. The range of forbidden frequencies intimately depends on the PC lattice parameters. It is then crucial to know how the single units are organized. However, determination of the structure by visible light is hampered by the interaction with photonic crystals, leading to multiple scattering [52]. In addition, in laser diffraction experiments, refractive-index matching and diffraction

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Integrated optics Volume 2: Characterization, devices, and applications

angles correction for refraction at the sample-air interface are required. Differently, X-rays allow inspection of the internal 3D structure of samples operating in air. In X-rays diffraction, photons are allowed to propagate freely through the PC, after which the transmitted and diffracted beams are focused by a refractive lens to collect the diffraction pattern. Another advantage of XRD is that it can probe the 3D structure in situ. Furthermore, it yields macroscopically averaged structural data, whereas scanning electron microscopy (SEM), for instance, only provides information on a small part of the surface. In addition, the relatively weak interaction of X-rays with matter makes X-ray scattering an excellent probe to investigate the internal 3D structure of PCs, also in the case when the refractive-index contrast is large in the visible region. However, problems can arise because of the dramatic difference between the X-ray wavelength (ca. 0.1 nm) and the lattice unit cell dimension of the PCs (of the order of 1 mm), that leads to diffraction angles as small as 104 rad. Nevertheless, it is possible to obtain this resolution utilizing small-angle X-ray scattering (SAXS) with a synchrotron radiation facility. In [53], authors were able to characterize the crystalline structure of a 2D PC. In this ° are selected using a double experiment, X-rays with wavelength l ¼ 0.443 A crystal monochromator. In another experiment, at the q-space resolution needed to measure Bragg reflections at very small angles, an image of the source was created at the detector screen [54].

(a)

(b) (300)

(220)

(220) (300)

(110)

(100)

(100) beam stop

beam stop

1,000

(110)

10,000

40,000

1,000

10,000

40,000

Figure 2.3 (a) Diffraction pattern at normal incidence of an approximately 6-layer PC crystal made of 1.1-mm diameter silica spheres in air. (b) Normal-incidence diffraction pattern of a closed packed crystal with approximately 20 layers after partial infiltration with amorphous silicon. The white scale bar in both images is 10 mm1. The numbers below the intensity scale bar are detector pixel values. Reprinted, with permission, from [55]

Structural and surface-characterization techniques

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In 2D PCs, the reciprocal lattice of a single plane can be generated by two basis vectors, b1 and b2. In 3D PCs, the reciprocal lattice depends on the stacking of the layers, and any scattering vector q can be decomposed into q ¼ hb1 þ kb2 þ jb3, where b3, along the z-direction, is associated to the interplanar spacing d through the relation: b3 ¼ (2p/d). This description of the nonprimitive, reciprocal-space unit cell makes the comparison between the scattered light patterns and the PC structures easy. Figure 2.3(b) shows the diffracted maps obtained by synchrotron radiation of an approximately 20-layer closed packed crystal. To further enhance the refractive-index contrast, the crystal can be infiltrated with amorphous silicon. Figure 2.3(a) and (b) displays the dominant features, namely the six reflections of the (110) family and the six reflections of the (220) family, demonstrating that silicon infiltration does not cause any significant damage.

2.2.2 Application of XRD to nanostructures X-ray diffraction is traditionally utilized to obtain detailed knowledge of the atomicscale structure of materials, to understand and predict their properties. A material exhibiting a long-range order irradiated with X-rays acts as a grating and generates a diffraction pattern formed by numerous sharp spots, thus allowing the determination of the spatial 3D arrangement of atoms. This technique, over the years, has been successfully applied to determine the structure of crystalline materials, complex proteins and also to study the structure of materials where atoms are ordered only at short distances (i.e. less than a nanometer), such as glasses and liquids. In this latter case, however, these materials act as very imperfect gratings and produce XRD patterns that are highly diffuse. Particular approaches, such as the atomic pair distribution function (PDF), [56] can therefore be applied to obtain important structural information such as nearest neighbor atomic distances and coordination numbers. Nanostructures fall somewhere between regular crystals and noncrystalline materials, because they are characterized by a structural coherence length from one to several tens of nanometers. The limited reflection power offered by nanosized structures leads to diffraction patterns showing few, if any, Bragg peaks and pronounced diffuse components. This renders traditional (Bragg) X-ray crystallography of these materials very difficult, if not impossible [57]. However, a combination of high-energy XRD and sophisticated data-analysis techniques such as PDF [58] or surface-sensitive X-ray diffraction (SXRD) [59] can be used to successfully tackle the problem. In [55], for example, the authors were able to work out the atomic structure of crystalline faceted NPs. Then, the use of SXRD has opened unique opportunities for the in situ characterization of surfaces and nanostructures even in operando conditions [60,61]. In the case of single crystals, information about the surface structures are obtained from the analysis of intensity variations along sets of so-called crystal truncation rods (CTR), namely lines in the reciprocal spaces. However, the measure of the integrated intensities of the CTRs needs to probe the sample in different orientations, which requires long acquisition times. A similar problem is encountered when characterizing epitaxially grown NPs, where retrieving the average NP shape and size needs an extended reciprocal-space mapping [62,63].

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Integrated optics Volume 2: Characterization, devices, and applications

High-energy surface X-ray Diffraction (HESXRD) is a novel tool to investigate the atomic structure of surfaces, interfaces, and ensembles of NPs [64,65]. It became available with the advent of third-generation synchrotron radiation sources, providing intense, microfocused, hard X-ray beams with energy >70 keV [66]. In combination with a large 2D detector, it allows, without scanning the detector, an immediate and nearly distortion-free mapping of vertical planes in reciprocal space, also containing, among others, CTR and NP facet diffraction signals [59]. As an example, Figure 2.4 shows the scenario of Rh NPs epitaxially grown on a MgAl2O4 substrate. The nanostructures display an angular in-plane mosaicity distribution DQ, well described by a Gaussian distribution (inset at the figure top). At the figure bottom, the sketched orange particles are perfectly aligned to the given orientation Q, whereas the blue (green) particles are rotated counterclockwise (clockwise) with respect to the substrate normal. The map was probed in a single snapshot with the sample aligned to the (111) Bragg peak of the untilted (here: orange) particles.

[001] (002)Rh

I(Θ)

→

∆ki

(111)RhPd

Θ ∆qD

(111)Rh

(111) → kf

→

→

G┴

γ ∆Θ

δ

→ ki

→

K=G →

→

Z

∆

[110]

c* θ → → b* G╨ → a* (000) θ

L

(c)

L (001)

Θ

(111)

D

(a)

(002) (111) (111)

(111) (b)

(100) H = K (220)

L

Figure 2.4 High-energy diffraction measurement scheme for epitaxial nanoparticles: (a) perspective view of the diffraction geometry for nanoparticles with an in-plane angular distribution and finite diameter D; (b) diffraction pattern from epitaxial Rh nanoparticles on MgAl2O4 (100) recorded by a 2D detector in stationary geometry with fixed sample rotation qS; (c) (left) schematic view of a (100)-oriented, truncated octahedral nanoparticle with (001) top and (111) side facets, (right) corresponding reciprocal lattice with facet rod signals indicated. Reprinted, with permission, from [67]

Structural and surface-characterization techniques

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Accordingly, as illustrated in Figure 2.4(a), the Ewald sphere intersects the rod of the untilted particles (vertical orange bar) at the position of the (111) Bragg peak leading to the (111) reflection. To illustrate the richness in information, Figure 2.4 (b) displays the reciprocal space map of Figure 2.4(a). Such a 2D map provides quantitative information on the main particle epitaxy which consists of (001)oriented and truncated octahedral-shaped particles, as illustrated in Figure 2.4(c). The NP size can be deduced from the full widths at half maximum of the indicated (111) and (002) Bragg reflections [59]. This kind of analysis may in principle be applied to any kind of NP important for photonic applications.

2.2.3 Application of XRD to detect material strain and stresses X-rays are also successfully utilized to obtain information about presence of strain and stresses, and their effect on the material’s optical properties. For example, in [68], the authors characterized the optical properties of ZnO thin films deposited by RF magnetron sputtering at different deposition temperatures. Experiments showed that films deposited at higher temperatures displayed redshift of the optical bandgap. The shift in the bandgap calculated from the size effect cannot explain the experimental values. As XRD spectra demonstrate, the redshift may be attributed to compressive stress: the films deposited at lower temperatures (50–150  C) are characterized by a large strain, which relaxes as the temperature of the substrate is increased. In another work [69], authors synthesized CoAl2O4 NPs for their optical properties. They utilized a Pechini method using citric acid as a chelating agent and a different temperature T ranging from 600 to 900 to calcinate the nanostructures. XRD peak broadening was analyzed to estimate both the CoAl2O4 NPs size and the presence of lattice strain. Authors applied the Williamson–Hall plots [70] coupled with different models (the uniform deformation (UD), uniform deformation stress (UDS), the uniform deformation energy density (UDED), and size-strain plot (SSP) to evaluate the internal strain as a function of the calcinations temperature. While NP size’s estimates provided by all the methods increase with the temperature, a clear trend of the stress as a function of T was provided by only the SSP method. The Williamson–Hall formalism combined with the Rietveld refinement method were utilized also in [71] to characterize BaF2 NPs by XRD powder diffraction spectra. These results demonstrated that the lattice parameters are dependent on the NP size. As a consequence, the photoluminescence spectra showed a slight shift in the self-trapped exciton for samples with higher particle sizes, while the bandgap energy (Eg) was found to be around 10.5 eV for all samples. To better elucidate the effect of the internal stress on the optical properties of ZnO thin film, in [72], the authors used glass, quartz, and silicon substrates. XRD spectral analysis was utilized to determine the internal stress and correlate it with the substrate utilized. The authors found that the lattice parameters decrease going from glass to quartz, to silicon. Similarly, the internal strain and stress show the same trend. Concerning optical properties, all the films displayed a high transmittance, but the absorption edge was shifted toward lower wavelengths for the film deposited on the quartz

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Integrated optics Volume 2: Characterization, devices, and applications

substrate. In another study [73], the authors synthesized ultrathin (15 nm) and thin (100 nm) ZnO nanowires, and found that the nanowire aspect ratio depends on the compressive stress because of the lattice mismatch between the nanostructure and the substrate. XRD results show that the polycrystalline ZnO nanowires have a wurtzite structure. After annealing at 873 K in ultrahigh vacuum, the crystallite size and compressive stress in as-grown 15- and 100-nm wires are 12.8 nm and 0.2248 GPa, and 22.8 nm and 0.1359 GPa, respectively. A variation in the internal stress induces changes in the electron spin interaction, and thus modifies the optical, electrical, and magnetic characteristics. Raman spectra show an increase in E2 (high) phonon frequency, ascribed to the higher compressive stress. Additionally, there is a significant shift in magnitude of full width at half maximum (FWHM) E2 phonon vibration modes of approximately 8.6 and approximately 25.8 for the asgrown ultrathin and thin ZnO NWs, compared to the vacuum-annealed sample. These results support the XRD investigation of variation in the crystallite size and compressive stress for well-aligned ultrathin and thin ZnO NW arrays. In particular, there is a higher shift in the [002] peak intensity for 15-nm nanowires than that for 100-nm as-grown and thermally treated nanowires arrays. As a consequence, the ultrathin ones are much better suited for optical emission-based applications than 100-nm nanowires.

ZSr3 ZSr1

0.006 ZSr0 0.003

10

0.003

0.004

ZSr5 ZSr3 ZSr1

4

(c)

0.0008

0.003

20

u

0.0004

8

(4sin θ/(Ehkl/2)1/2)

10

ZSr0 (d)

0.0003

Strain

0.0002

Stress

6

0.0004

0.0006

ZSr0 ZSr1 ZSr3 ZSr5

0.002

0.006 ZSr0 0.003

15

4sin θhkl/Ehkl

(b)

Strain (ε)

βhklcos θhkl

0.003

ZSr1

2.0

4sin θhkl

(a) 0.003

0.003

ZSr3

0.006 ZSr0 0.003 1.5

1.0

0.003

ZSr5

Stress (σ)

0.003

0.003

Energy Density (μ)

0.003

ZSr5

βhklcos θhkl

βhklcos θhkl

0.003

ZSr1 ZSr3 ZSr5 Sample Code

Figure 2.5 The W–H analysis plots of pure and Sr-doped ZnO nanostructures assuming (a) UD model, (b) UDS model, and (c) UDED model. (d) Variation of micro strain, stress, and deformation energy density with the Sr content used in the synthesis process (0.0, 0.001, 0.003, and 0.005 M of Sr corresponding to ZSr0, ZSr1, ZSr3, and ZSr5, respectively). Reprinted, with permission, from [78]

Structural and surface-characterization techniques

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Among the techniques available for stress analysis, XRD methods employing medium-energy X-photons (E ¼ 5–15 keV) are very suitable for the analysis of films, nanostructures and surface layers. XRD allows the characterization of the full mechanical stress tensor of all crystalline phases and, in addition, also the analysis of stress gradients is possible [74]. Standard methods of analysis applicable to bulk aggregates include the traditional sin2y analysis [75], Williamson–Hall (W–H) [70,76] strain–size plot (SSP), and Warren–Averbach methods [77]. Semiconducting ZnO nanorods have been synthesized for their potential use as UV and visible light-emitting devices, as well as for catalysis, gas sensors, solar cells, and life science applications [73]. The bandgap of ZnO can be tuned by either modifying the size of the NPs or doping with different atoms. In particular, the authors studied the effect of incorporation of Sr in ZnO nanorods on their optical properties. The incorporation of the dopant-induced local vibrational mode in Raman spectra. In addition, while the ZnO nanorods fluorescence covers the entire visible region, the characteristic exciton displays an UV luminescence. These optical properties were found to strongly depend on the crystallite size variation, defects formation, and relaxation of micro strain after doping of the prepared samples. Strain stress induced by Sr nanorod doping was estimated using the Williamson–Hall plots which are shown in Figure 2.5. The induced changes in crystallite size, lattice parameters, and microstrain are observed from XRD studies. Relaxation of micro strain after Sr doping leads to an increase in unit cell volume

1.0×105

1.0×105 2.0×105

1.5×106

2.0×105 3.0×105

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) (nm on ati cit Ex

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m)

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ssio Emi

Figure 2.6 Excitation-dependent photoluminescence studies of the as prepared and Sr-doped ZnO nanorods. Reprinted, with permission, from [78]

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Integrated optics Volume 2: Characterization, devices, and applications

and crystallite size which can be ascribed to variations of the ionic radii of the host and dopant. Optical absorption studies display a red shift of the bandgap induced by the Sr doping. Pure ZnO photoluminescence reveals the characteristic ultraviolet emission, while the emission in the visible range is related to various defects inducing states in the bandgap. Strong enhancement of the emission of a near-white light fluorescence in the 400–600 nm range is obtained by Sr doping of the ZnO nanorods, as shown in Figure 2.6. XRD analysis of the ZnO NPs shows a relaxation of the microstrain induced by the Sr insertion. The increase of the nanorod luminescence upon doping can be explained by the increase of the defect density due to the random substitution of Sr, and are also favored by the relaxation in micro strain [79]. Essentially, the presence of the strain at microscales influences band edges and modifies the energy levels, thus changing absorption and luminescence of the sample. Then, as the photoluminescence measurements demonstrate, the relaxation of micro strain plays an important role in enhancing the near-white luminescence from the samples.

2.2.4 X-rays and computed tomography Another special application of X-rays is the computed tomography. Information about this technology and base principle of operation may be found in [75,76]. Thanks to the availability of hard highly penetrating X-rays with the advent of the third generation of synchrotron sources, a highly collimated and monochromatic X-ray beam is focused on a sample. This latter is translated or rotated along a given directions, and the diffracted X-rays are recorded with a 2D detector. Generally, the photon energies span from a few hundred electronvolts to several tens of kilo-electronvolts, corresponding to wavelengths from few nanometers to angstrom fractions. Such a kind of probe may identify elements and chemical bonds by imaging with photon energies near the absorption edge. Furthermore, also relatively thick samples can be imaged thanks to the large penetration depth of X-rays. X-ray microscopy is a powerful technique which, applied to materials science, allows a deep characterization of a variety of materials such as magnetic materials for storage devices, solar cell defects, battery chemistry, and nanomaterials. X-ray microscopy is also applied to photonic materials, for example to probe photonic crystals [80,81]. The detailed morphology of photonic crystals is commonly characterized directly using SEM imaging of their surfaces and cross sections, and indirectly, probing the optical properties and making diffraction measurements. However, photonic crystals may be studied also by direct electromagnetic 3D tomography at length scales substantially shorter than those of optical wavelengths did. The large penetration depth of the X-rays allowed angle-resolved 2D images to be analyzed in order to reconstruct the full 3D morphology of a holographic photonic crystal via computed tomography (CT). This enables the non-destructive investigation of structure deformation induced by material processing and to study the presence of structural defects. An example is shown in Figure 2.7 presenting a 3D rendering corresponding to two different methods (inscribed blobs and water

Before heat treatment

Structural and surface-characterization techniques (a)

Volume rendering of i-PhC

(b)

5 2.6

μm

Macro pores

(g)

(f) After 1400° C – 4h

(c)

Max. inscribed blob at macro pore

(h)

Max. inscribed blob at connection points

47

(d)

3D skeleton Nano pores

(i)

m

5μ

2.6

Figure 2.7 3D rendering of selected volume of interest, extracted from the ptychographic X-ray computed tomography data sets of the mullite inverse opal photonic crystals, (a–d) before, and (f–i) after heat treatment at 1400  C for 4 h. It shows the structural features evidenced during image analysis: (a, f) inverse opal photonic crystal phase; (b–d, g–i) macro pores pictured blue and inscribed blobs in green; contact points in yellow; nano pores in purple and image skeleton in red. A perpendicular cutting plane was applied to allow the visualization of all the structural features. Volume of interest in (a, f) equals 18.6 mm3. Reprinted, with permission, from [82] shed-segmented pores), where one can clearly see the differences concerning the macropores diameters computed by both methods. The effect of heat treatment of the photonic crystal can be easily measured using the ptychographic image, leading to an estimation of an overall 8% structural shrinkage. Because of the possibility of non-destructive 3D analysis of microstructured materials, X-ray tomography was successfully applied to study optical fibers and multimaterial optical fibers (e.g. incorporating different glasses, metals, and polymer elements) [83]. Tomographic images may be used to detect possible longitudinal inconsistencies in the arrays of capillaries (i.e. twist, bend, or misplaced elements) of a hollow core photonic bandgap fiber. Figure 2.8 shows an example of CT analysis performed at different stages of preparation of an optical fiber. A preform with some structural deformations of the outer ring of holes as highlighted by the yellow oval is displayed in Figure 2.8(a). Important is to observe that this structural defect is not visible from the free ends of the preform. In Figure 2.8(b), the X-ray CT shows the image of a cane approximately 130 mm in diameter. The tomography reveals a perfect longitudinal uniformity and consistency. Finally, Figure 2.8(c) displays a tomographic image obtained from a 19-cell hollow core

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(a)

Integrated optics Volume 2: Characterization, devices, and applications

(b)

(c)

Figure 2.8 X-ray CT images: (a) first-stage preform of a 37-cell hollow core incorporating a core tube with capillary arrangement drift highlighted, (b) cane of a 19-cell hollow core, and (c) a 19-cell hollow core photonic bandgap fiber. Reprinted, with permission, from [83] photonic bandgap fiber. Post-processing allows making a section to inspect inner regions of the fibers.

2.2.5 EXAFS and XANES applied to glass, glass ceramics, and nanostructures To control nanomaterial properties, exact knowledge at the atomic level is required; this may also permit to regulate their organization in desired sizes and shapes. This complex task may be afforded using different complementary experimental techniques [84] and advanced computational methods [85]. XAS is one of the direct structural probes providing information on the local environment around a photoabsorber [86]. However, XAS analysis is complicated by the influence of undercoordinated atoms at the surface and the limited size of the NPs making this technique not reliable. Then, alternative experimental methods are needed for the determination the coordination numbers in nanocrystalline metals and oxides, which are of crucial importance for application in catalysis, in energy, in sensing, in photonics, and in other areas. Agostini et al. [87] emphasized that a combination of transmission electron microscopy (TEM), chemisorption measurements, and EXAFS makes obtaining detailed structural information up to the fourth coordination shell possible. In addition, several effects such as charge-transfer effects under the influence of ligands, or the existence and type of vacancies, can be analyzed using XANES [88]. EXAFS describes the absorption of a given orbital as the difference between the measured X-ray absorption and the contribution of both the background absorption and the atomic-like absorption due to an isolated absorbing atom [89]. Because the timescale of the photoabsorption process is ~1015–1016 s, two orders shorter than the characteristic excitation time of thermal vibrations (~1013 s), atoms may be considered as frozen. As a consequence, EXAFS spectra represent the configurational average of all atomic positions during a single excitation process, although the effect of thermal disorder can be accounted for by different additional terms and specific methods [90].

Structural and surface-characterization techniques

49

An example showing how EXAFS can be utilized to characterize materials for photonics is shown in the paper by van Tran et al. [91]. Silica-based materials doped with rare-earth ions may find widespread applications such as laser emitters, highbrightness displays, and erbium-doped fiber amplifiers used for optical communication at 1.5 mm. However, one of the main concerns with these materials is the limited Er concentration, since above a certain threshold Er3þ ions tend to clusterize, thus limiting the emission efficiency. To face this problem, glass-ceramic materials can be utilized, where a crystalline phase is uniformly dispersed in a glassy matrix. In this way, the rare earth dopant can be embedded in the crystallites, thus allowing to increase Er concentration without formation of clusters. A set of (100-x)SiO2-x SnO2 nanocomposite sol-gel thin films (with x ¼ 25 and 30 mol%) were produced by varying the Er3þ-dopant concentration in the range 0.5, 1, and 2 mol%, followed by different annealing temperatures [87]. AFM maps show that annealing at 800  C for 1 h led to a smooth surface, indicating the presence of few SnO2 crystals. Formation of SnO2 crystals was obtained when increasing the temperature to 900  C and continued steadily until 1100  C. Surprisingly, a further heat-treatment at 1200  C caused an almost total disappearance of surface crystals. Crystallite size of ~10 nm was estimated by applying the Sherrer equation to XRD spectra and was independent from the Er concentration. EXAFS was utilized to model the local environment of the Er ion. EXAFS indicates that Er is substitutional for Sn in the SnO2 matrix. In particular, both the annealing at 800 and 1200  C lead mainly to an ° region), while the second coordination shell (3–4 A ° ) may Er–O first shell (1–2 A consist of Sn and/or Si atoms. At 1200  C, the substitution is not complete, leading to different fractions of Er entering in the crystals while the rest remains in the amorphous phase. This is confirmed by the shrinkage of the first coordination shell radius with respect to that for the sample at 800  C. In this latter case, EXAFS indicates that Er environment is that corresponding to an amorphous silica structure, whereas for the higher annealing T, the Er–O distance values corresponds to six coordinated Er3þ ions. A similar detailed analysis was performed in [92]. In this work, authors studied the strontium molybdate, SrMoO4 system, where the stimulated Raman scattering (SRS) effect can be utilized for laser radiation conversion. The SrMoO4 crystal matrix allows introduction of sufficient amounts of active rare earth ions, such as Pr3þ, Nd3þ, Tm3þ, and Ho3þ, making possible to obtain laser generation near 2 mm at room temperature. EXAFS and XANES analysis led to the determination of the coordination shell of Sr and Mo in both pure and doped samples. The two techniques indicate a reduction of the coordination number of Mo in Hoand Tm-doped samples by the presence of O vacancies. This was confirmed by XRD spectra. In particular, Ho3þ and Tm3þ ions occupy different sites in the SrMoO4 crystal structure: the Ho3þ ions replace the Sr2þ ones in the dodecahedral sites (HoSr•), and Tm3þ ions are located in interstitial sites while (Tmis•) are in the vicinity of the Sr sites. This causes an increase in interatomic distances in the MoO4 tetrahedra in the structure of undoped crystal, as compared with SrMoO4: Tm/Ho.

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Integrated optics Volume 2: Characterization, devices, and applications

Among the wide literature on this topic, other examples of application of EXAFS and XANES to glasses and glass ceramic materials may be found in [93–99]. EXAFS was also utilized to characterize the optical properties of MgO-based NPdoped optical fiber performs [100]. Rare earth-doped optical fiber amplifiers fabricated using novel materials require continuous improvements of their spectroscopic properties, for reducing the device size and lowering their cost. However, some degradation of spectroscopic properties can easily arise form clustering or inappropriate local environment of the dopants when they are inserted into silica, thus limiting the potential applications. A possible solution consists in supporting the fiber waveguide in a silica matrix and making a dispersion of the dopant ions within NPs of appropriate composition and structure. Since silicate and phosphate systems display a pronounced immiscibility toward divalent metal oxides, a phase-separation mechanism was utilized to form NPs. These are composed by alkaline ions such as Mg, Ca, and Sr [101], and are incorporated into a porous fiber core doped with P2O5. This also prevents the clustering of Er3þ, as it occurs in phosphate phases. To study the optical properties of the pure and separated-phase fibers, a series of samples containing Mg concentrations ranging from 0 to 1.5 mol/l were produced. Figure 2.9(a) shows the emission spectra of Mg-doped preforms as a function of the Er concentration at room temperature. Three Mg-concentration domains can be identified to explain the different fluorescence of Er3þ, as identified by the trend of the FWHM and wavelength of fluorescence vs Mg concentration reported in Figure 2.9(b). At low concentration (0 and 0.1 mol/l), the Er emission is peaked at 1536 nm and the FWHM is about 20–25 nm, corresponding to those measured in a P-doped silica fiber. At intermediate Mg concentrations (0.3 and 0.5 mol/l), the peak position shifts to shorter wavelengths (~1531 nm) and FWHM increases up to 45–50 nm. Contrary to what could be expected by reabsorption effects induced by an increase of the Mg nanostructures sizes, for the highest Mg concentrations (1–1.5 mol/l), FWHM and peak position values are 35–40 and 1533 nm, respectively. To explain the spectroscopic behavior of Er3þ ions’ dependence on its concentration, the authors studied the local order around rare earth ions by EXAFS. Results displayed in Figure 2.9(c) and (d) indicate that Er environments change as the Mg fiber content changes. In the Mg-0 mol/l sample, P builds a well-organized solvation shell around Er. In the low Mg-doped samples, Er ions are located in the Mg NPs which contain P ions also. In this ° . At case, the coordination number NO ~ 7 and Er-O bond length REr-O is ~ 2.31 A Mg-0.3 and Mg-0.5 mol/l concentrations, the results could be explained by assuming a P-rich and/or well-polymerized environment, NO ~ 6.9 and REr-O ~ 2.3 ° . At highest Mg concentrations, the phosphate network depolymerizes and A °. NO ¼ 6.3 and REr-O ¼ 2.26 A

2.2.6 X-ray photoelectron spectroscopy applied to optical materials X-rays can also be utilized to induce electron emission from the material surface (photoelectric effect). Here the material properties are probed not just directly

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Structural and surface-characterization techniques 2,5

–0,2 50

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Figure 2.9 (a) Emission spectra of Mg-doped preforms (continuous lines) and fibers (dashed lines) recorded at room temperature. Excitation wavelength is 980 nm; (b) FWHM (triangles) and wavelength of the maximum of fluorescence intensity (squares) vs Mg concentration. Open symbols are related to the samples without P; (c) EXAFS spectra of the various Mg-doped samples (0.1–1.5) compared with a sample without divalent codopant (Mg-0). For Mg-1.5 also, the fit is shown (þ) with the residual (); (d) Fourier Transforms of the spectra shown in Figure 2.10(c). For Mg-1.5 also, the fit is shown (þ) with the residual (). Reprinted, with permission, from [102] analyzing how X-photons interact with matter, but looking at the photoelectrons resulting from that process. In particular, the photoelectron energy is intimately related to the electronic structure of the material, thus making the X-ray photoelectron spectroscopy (XPS) a powerful, information-rich technique to probe the sample properties. XPS can be applied to any kind of material provided it may be placed under vacuum. Then, XPS may be utilized to characterize solid matter. However, XPS was recently utilized to characterize materials at near ambient pressure allowing analysis of liquids or high pressures for gaseous phases or materials in operando conditions [103]. Furthermore, the recent evolution of XPS instruments allows the characterization of materials with lateral resolution on the micron scale; this result is achieved

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by acting on the X-source [104] or on the analyzer performances [105]. Referring to photonics, the emission properties depend on the nature of the luminescent material, on its chemical state, on the host chemical composition and structure, on the presence of defects, etc. Synthesis conditions, heat treatments, and any kind of processing affecting the dopant and host energy levels strongly affect the material emission properties [106–108]. Hence, XPS probing the electronic structure of the elements and their oxidation state is one of the primary techniques to assess their optical properties. XPS is widely utilized to determine the material composition. Describing the composition of a material means identifying the chemical elements together with their atomic concentrations. It has to be observed that the XPS sensitivity amounts to ~1% atomic concentration although this number strongly depends on the chemical element probed. This makes sometimes difficult to

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Figure 2.10 (a) Si 2p, (b) Hf 4f, and (c) oxygen core lines of SiO2–HfO2 glass ceramic waveguides, with different HfO2 molar concentrations, normalized at the same height. Dark and grey spectra represent the pure SiO2 and HfO2 references and O in these oxides, respectively. (d) XPS crystalline HfO2 concentration (right) and bandwidth of the of the 4I13/2 !4I15/2 emission of Er3þ ions (left) for the SH10, SH20, and SH30 GC waveguides, as a function of the HfO2 molar concentration. Reprinted, with permission, from [109]

Structural and surface-characterization techniques

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determine the abundance of dopants such as rare earth ions, if their concentration is maintained low to avoid photoluminescence quenching. Determination of the element abundance is also important to verify the presence of contaminations which, depending on the material synthesis method, may account for a non-negligible fraction of the composition. In the following, we will present some examples showing how XPS is crucial to explain the optical properties of materials. An XPS analysis more sophisticated than the simple quantification can be performed adding the identification of chemical bonds. A good example is shown in [109]: the authors studied the xHfO2–(100-x) SiO2 (x ¼ 10, 20, 30 mol %) glassceramic planar waveguides doped with 0.3 molpercentage Er3þ ions. Hf is incorporated in the SiO2 glassy matrix with the aim to form a glass ceramic matrix. A spinodal decomposition with Hf nanocrystals nucleation was obtained by heating the waveguides at 1000  C. A detailed identification of the different bonds formed by oxygen with silicon and hafnium as a function of the Hf concentration was performed. Results are shown in Figure 2.10(a-c), where Si, Hf, and O core lines are decomposed in their components corresponding to different chemical bonds. In particular, Si and O components experience a shift toward lower binding energy as the concentration of Hf increases in the waveguide, while the opposite holds for hafnium. These evidences, together with the bandwidth of the of the 4I13/2 ! 4I15/2 emission of Er3þ ions in Figure 2.10(d), enabled authors to unambiguously state that, when increasing the Hf concentration, Er segregates in the nanocrystals generated from the decomposition. The crystalline Hf environment of Er3þ ions explains the improved optical properties of the waveguide. In another work, the XPS technique was applied to characterize silver NPs embedded in soda-lime glass [110]. The work was stimulated by the need to overcome (1) the limitations arising from the small oscillator strength of the 4I13/2-4I15/2 of Er3þ at 1.54 mm, and (2) the concentration quenching and up-conversion in Er-doped glasses. The presence of Ag NPs can be utilized to enhance the Er3þ luminescence induced by the presence of small silver particles embedded in the matrix [111]. XPS was utilized to understand the changes of the electronic structure of silver NPs in the glassy network upon the different Ag concentrations. Results are shown in Figure 2.11; a strong interaction between oxygen of the glassy matrix and silver was identified by analyzing their core lines. At the lower Ag concentrations, Ag is in oxidized state and mainly dispersed in the glass matrix, while a minor part is in form of nanoclusters. At intermediate silver concentrations, more nanoclusters are formed, leading to marked changes of the binding energy and FWHM of Ag3d 5/2, of the Fermi cutoff position, and of the value of the Auger parameter. Finally, at higher silver abundance, the core line position and valence band shape, together with the Fermi cutoff position, reflect an increasing metallic character of the silver clusters. In particular, the position of the Ag3d core line at the intermediate and higher silver concentrations mirrors the quantum confinement effects corresponding to clusters with an average diameter of about 2 nm. Results are in agreement with the estimates obtained from the plasmon-resonance frequency and TEM analyses. Another example regards silicon nanocrystals embedded in a SiO2 host matrix, displaying interesting luminescence properties. In [112], nanocrystalline silicon

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Figure 2.11 (a) XPS Ag3d core-level spectra for the ion-exchanged soda-lime glasses (SAg) and for the bulk silver reference (AgRef). The spinorbit components, 3d5/2 and 3d3/2, are labeled. Solid and broken lines indicate the BE of Ag nanoclusters and silver oxide, respectively; (b) XPS valence band of the SAg and AgRef samples upon subtraction of the pure soda lime VB contribution. (c) Position of the Fermi cutoff (&) and values of the VB width (VBW) for the SAg ion-exchanged samples (■); (d) Amount of bridging oxygen atoms (&) and nonbridging oxygen atoms (■) for the SAg ionexchanged samples. Reprinted, with permission, from [110] was produced by annealing silicon-rich oxide films deposited by a chemical vapor deposition process. The material optical properties, such as the refractive index n, may be estimated using the Bruggeman’s theory as a combination of the dielectric constants of amorphous silicon and silicon dioxide. Hence, n can be correlated with the oxygen concentration of the film, namely the local bonding environment of silicon. This latter, in turn, can be described using two different models, the random bonding model (RBM) [113], and the mixture model (MM)[114]. Results can be compared with experimental values of n obtained from ellipsometry and with the oxygen bulk concentration measured by time-of-flight elastic recoil detection analysis (TOF-ERDA), the energy-dispersive X-ray (EDX), and the surface composition by XPS. An extended analysis of the Si 2p core line was utilized to describe the oxygen distribution at the material surface. This analysis led to the conclusion that the random-bonding network model does not give a satisfactory description of the system, while the mixture model is in almost perfect agreement with

Structural and surface-characterization techniques

55

experimental data. Following this model, all of the samples were found to exhibit rather complete separation into amorphous silicon and silicon dioxide components. This kind of analysis is of paramount importance to design and optimize synthesis processes for fabrication of materials with superior optical properties. Swart provided a list of case reports where XPS has a crucial role in explaining the luminescent properties of phosphors [101]. Thanks to the capability of describing the chemical state of elements, XPS was utilized to detect the oxidation state of Zn in ZnS phosphors exposed to electron beams. A reactive electronstimulated surface chemical reaction was proposed to describe the ZnS degradation. In this model, oxygen molecules adsorb on the surface of the ZnS phosphor and are dissociated to reactive atomic species by the electron beam. This results in the formation of volatile SO2 and of a nonluminescent ZnO/ZnSO4 layer, which was identified in the irradiated area using X-ray chemical mapping. Another system which undergoes degradation is Y2SiO5:Ce3þ: the inspection of the Si 2p core line

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Figure 2.12 (a) The simplified energy-level diagram of Bo3þ and Bi2þ species on photographs of their respective luminescence. (b) Bi 4f high-resolution deconvoluted XPS spectrum of a 1200  C post-annealed CaO:Bi phosphor powder; (c) cathodoluminescence spectra at different beam voltages (1–3 keV). Reprinted, with permission, from [106]

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Integrated optics Volume 2: Characterization, devices, and applications

indicated the transformation of yttrium silicate in SiO2. The presence of electron bombardment causes formation of defects inside the SiO2 network, thus making it luminescent. Emission properties arising from presence of SiO2 were confirmed by cathodoluminescence measurements. The presence of luminescent SiO2 causes a change of the phosphor color, with degradation of the original performances. Interesting is also the capability of XPS in identifying the different valence states of Bi2þ, Bi3þ in CaO:Bi powder. The powder was synthesized by the sol-gel combustion method followed by sintering at a temperature of 1200  C. PL spectra show a yellow orange emission corresponding to 2P3/2(1) ! 2P1/2 transition of Bi2þ and a blue emission corresponding to 3P1 ! 2P1/2 and 3P0 ! 2P1/2 transitions of Bi3þ[115], as shown in Figure 2.12(a). This was confirmed by XPS analysis. The two different oxidation states of Bi are clearly identified by analyzing the Bi 4f core line (Figure 2.12(b)), corresponding to BiO and Bi2O3, respectively. Degradation was observed during cathodoluminescence measurements, with a reduction of the blue intensity and a correspondent increase of the orange-yellow emission (Figure 2.12(c)). On the basis of the XPS analysis, this effect is explained as an electron-induced reduction of Bi3þ to Bi2þ ions.

2.3 Conclusion The use of X-rays as a probe for the non-destructive analysis of materials is well consolidated since many years. In this chapter, we focused our attention on few selected examples of X-rays utilized to study materials of interest in photonic applications as dopants in glassy matrix, glass ceramics, plasmonic structures, thin films, planar and channel waveguides, and photonic crystals. XRD can be applied to bulk, nanostructures, and photonic crystals to detect and evaluate strains and stresses; X-ray-computed tomography to reconstruct the full 3D morphology of complex structures; EXAFS and XANES make possible obtaining detailed material structural information, and, finally, XPS provides chemical, compositional, and electronic structure information. The aim here was to illustrate the importance of the X-radiation-based techniques to better understanding of the nature of the probed samples. Thanks to the short wavelength, X-photons can easily penetrate into the matter providing a full characterization of materials at different size scales and complex photonic devices, which can be beneficial for optimizing their optical properties.

References [1] W.C. Roentgen, On a new kind of rays, Ann. Phys. Chem. 64 (1898) 1–11. [2] W. Friedrich, P. Knipping, and M. von Laue, Interferenz-erscheinungen bei roentgenstrahlen, Sitzungsber Math-Phys Cl. Koeniglich Bayer. Akad. Wiss. Muenchen. (1912) 303–322.

Structural and surface-characterization techniques [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

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Chapter 3

Integrated spectroscopy using THz time-domain spectroscopy and low-frequency Raman scattering Tatsuya Mori1 and Yasuhiro Fujii2

Materials are fundamental for the development of photonic devices, and a hot topic is the search for material systems suitable for the fabrication of integrated photonic devices. It is well known that Raman spectroscopy is the most effective spectroscopic tool to assess the structural properties of a material and, in particular, its nanostructure, including the structural fluctuation at the nanoscale. By the way, the first research to provide information about the transparency of glass ceramics was performed by Duval and co-workers on the glass ceramic ZERODUR in 1986 [1]. This pioneering research allowed to better calibrate the nanocomposite materials for photonics, and the approach developed by Duval and co-workers is still largely used to get information about the structural properties of the materials. Typical is the case of transparent nanoceramics-based integrated laser sources and amplifiers operating in the visible and near-infrared (NIR) region. Nowadays, the interest towards the THz application is a hot topic, mainly for the quantum cascade laser (QCL) availability and the applications in security and environmental control. At this regard, some years ago, Hu¨bers discussed about THz-integrated photonics in an article published in Photonics Nature [2]. In this article, the demonstration of an integrated terahertz transceiver featuring a QCL and a Schottky diode mixer promises new applications for compact and convenient terahertz photonic instrumentation. It is clear that, for any kind of photonic systems operating in the THz domain, it is crucial to know the behaviour of the material system at these frequencies, especially the characteristics of the vibrational modes which fall in the THz region. For this reason, in this chapter we discuss in detail the so-called low-frequency Raman scattering region and we put in evidence the novel information that can be obtained by performing spectroscopic measurements in the THz spectral domain.

1 2

Division of Materials Science, University of Tsukuba, Tsukuba, Japan Department of Physical Sciences, Ritsumeikan University, Kusatsu, Japan

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3.1 Terahertz light and excitations in the THz region The term ‘terahertz light’ often refers to electromagnetic waves having a frequency ranging from approximately 0.1 to 10 THz. This frequency band is located in the intermediate region between visible light and radio waves. Electromagnetic waves in the terahertz region have been regarded as being within the so-called ‘terahertzgap’ because THz light is difficult to generate and detect. However, along with recent advances in semiconductor fabrication technology and the development of femtosecond lasers, studies of the fundamental characteristics of THz light and technological applications in the terahertz field have been actively reported [3–5] across various research fields including information communication, biology, medicine, security, environment, space, etc. A 1-THz photon represents 4.14 meV in terms of energy and 48 K in terms of temperature and has a wavenumber of 33 cm
1. Therefore, terahertz light is the optimum type of light for detecting electronic states in the extremely low-energy region in the vicinity of the Fermi level with respect to a material’s electronic properties [6]. On the other hand, as for the physical properties of lattices, the photon energy of the terahertz light corresponds to the energy of the end of the acoustic wave or to low-frequency optical phonons [7–9]. Interesting phenomena that occur in the terahertz region include superconductivity, charge density wave, spin density wave, Mott insulator transition, etc. [6]. In addition, the relaxation of free carriers in semiconductors [10–13], anharmonic vibrations [14], rattling phonons [7,9,15] and soft modes [16–18], all occur in the THz region. As will be described later, it is possible to detect broad peaks using terahertz light, owing to the vibrational density of states in glassy materials, and also the boson peaks (BP) [19], which are a universal excitation feature in amorphous materials. In 1984, a method for generating terahertz waves using a femtosecond laser was developed by Auston et al. [20], and this method was applied in terahertz timedomain spectroscopy (THz-TDS). From the late 1980s to the early 1990s, THz-TDS was mainly developed by Grischkowsky et al. at IBM [10,21], and by Nuss et al. at Bell Labs [22,23]. An exemplary study about superconductors using THz-TDS was carried out by Nuss et al. and involved the observation of Nb thin films with a superconducting gap of approximately 1 THz [22]. Another example of a study concerning the direct observation of the superconducting gap of Nb is the research carried out by Pronin et al. [24]. They determined the size of the superconducting gap and the penetration depth of a magnetic field from their experimental results. As for strong-coupling superconductors, for example, THz-TDS was performed on a Pb thin film, and its behaviour in the superconductor terahertz region was reviewed from the modern viewpoint of optical self-energy [6]. Another example of a study of semiconductors using THz-TDS is the research reported by Exter and Grischkowsky [10] for moderately doped silicon, in which the probability of scattering is very close to 1 THz. The frequency dependence of the complex conductivity from 0.1 to 2 THz was derived from their measurement

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results, and they reported that the behaviour of the carriers in silicon matches the simple Drude model well. They also found a small experimental deviation from the simple Drude model and explained it by using the extended Drude model, which considers the energy-dependent scattering probability. In addition, THz-TDS has been applied to various substances such as ferroelectric materials [16–18,25–30], drug-related materials [31–34], polymers [35–38], liquids [39,40] and amorphous materials [19,41–49]. The research on glasses, in particular [44,46,47], may indicate a possible way to get more information on the structural characteristics of glasses for integrated optics.

3.2 Terahertz time-domain spectroscopy In THz-TDS [23,50], a terahertz pulse wave generated using a femtosecond laser pulse impinging on a suitable element is transmitted through a sample. The time waveform of the terahertz electric field is then recorded, and information about the amplitude and phase of each frequency is obtained via the Fourier transform. THzTDS can be said to be a new spectroscopy method in the terahertz band because the time waveform of the amplitude of the electric field of the terahertz wave itself can be measured. As a result, it is possible to simultaneously determine the real and imaginary parts of the complex permittivity without using the Kramers–Kronig transform. To illustrate how THz-TDS can be applied to determine the complex permittivity of a material, an experiment was carried out using an RT-10000 terahertz time-domain spectrometer manufactured by Tochigi Nikon Corporation [16,33,39]. The configuration of the optical system of this apparatus is shown in Figure 3.1.

Delay stage Sample

THz emitter

THz detector

Femtosecond Laser

Beam splitter

Figure 3.1 Schematic of THz-TDS system used (RT-10000)

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During the measurements, dry air was injected into the optical chamber to prevent the absorption of the terahertz light by water vapour. A photoconductive antenna using a low-temperature grown GaAs was used as the generation and detection element for terahertz waves. A Ti: sapphire femtosecond laser (Spectra Physics, Inc., Mai Tai) was used for exciting the photoconductive antenna. The centre wavelength of the optical pulse was 780 nm, the pulse width was 100 fs or less, the repetition frequency was 80 MHz and the measurement frequency range was approximately 0.2–4.5 THz. The optical pulses generated by the femtosecond laser were divided into the pump light (excitation light) and probe light (detection light) using a beam splitter. The pump light was incident on the terahertz pulse-generating element, and a terahertz pulse wave with a time width of approximately 2 ps was radiated. The radiated terahertz pulse wave was focused on the specimen using an ellipsoidal mirror (or two off-axis parabolic mirrors), and the transmitted terahertz wave was converged on the detection element using an ellipsoidal mirror (or two off-axis parabolic mirrors). Photoconductive antennas are used for the generation and detection of the terahertz waves. The photoconductive antenna used in this experiment consisted of a semiconductor substrate for generating a terahertz pulse wave and a hyperhemispherical lens for collimating the generated terahertz light (Figure 3.2). High-resistivity silicon with low absorption loss was used for the hyperhemispherical lenses. The semiconductor substrate consisted of GaAs grown at low temperature (LT-GaAs) with semi-insulating GaAs (SI-GaAs) as a base, and a parallel electrode made of an alloy was attached on top of it.

Figure 3.2 Schematic diagram of photoconductive antenna with hyperhemispherical lens

Integrated spectroscopy using THz-TDS and LF Raman scattering Photoconductive antenna

69

GaAs

~1.5 eV (780 nm) LT-GaAs

Figure 3.3 Schematic diagram of photoconductive antenna of a THz wave generator and a photoexcited carrier in GaAs The protruding portion at the centre of the antenna operated as a micro-dipole antenna. At the centre of the two parallel electrodes, there was a small gap of a few micrometres, and a voltage was applied between the gaps (left side of Figure 3.3). When a light pulse having a photon energy higher than the energy gap of the semiconductor was irradiated onto this minute gap region, photoexcited carriers were generated in the semiconductor, and a pulsed instantaneous current flowed. The photon energy of the femtosecond laser (pump light), which had a centre wavelength of 780 nm, was approximately 1.5 eV, which corresponds to the energy gap of GaAs (right side of Figure 3.3). Therefore, by irradiating GaAs with the pump light, photoexcited carriers were generated in the semiconductor, and an instantaneous current flowed. At this time, a terahertz wave was generated by the accelerated motion of the photoexcited carriers. In the photoconductive antenna, on the detection side, an ammeter was connected instead of a voltage applied (Figure 3.4). The photoexcited carriers generated by irradiating a femtosecond laser (probe light) on the gap of the antenna on the detection side were accelerated by the electric field of the terahertz pulse wave transmitted through the sample and incident on the detection antenna. As a result, an instantaneous current flowed between the gaps. Because the magnitude of this current is proportional to the electric field of the terahertz pulse wave, the strength of the oscillating electric field of the terahertz pulse wave can be measured by measuring the current. By moving the delay stage and measuring the instantaneous current at each point, while shifting the timing at which the probe light reaches the detection antenna, it is possible to obtain the time waveform of the electric field of the transmitted terahertz pulse wave (Figure 3.5). Hereafter, the analysis method for the amplitude and phase information obtained through the measurements will be described [33,39]. First, the time waveform (reference wave) Eref(t) when the sample is not in place and the time waveform (sample wave) Esam(t) when the sample is in place are measured. Next, the fast Fourier transform (FFT) is applied to these data to obtain the intensity and

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Integrated optics Volume 2: Characterization, devices, and applications Photoconductive antenna

A

LT-GaAs

Figure 3.4 Schematic diagram of a THz wave detector

∆τ = t1 → t2

∆τ = t1

∆τ = t2

∆τ = t2 → t3

∆τ = t3 → t4

∆τ = t4 → t5

∆τ = t4

∆τ = t3

∆τ = t5

THz wave

t1 t2 t3 t4 t5

∆τ

Figure 3.5 Conceptual diagram of the detection of THz time-domain waveform phase spectrum of each frequency for both the reference wave and the sample wave.

  Eref ðtÞ ! Eref ðwÞ ¼
Eref ðwÞ
exp iqref (3.1) Esam ðtÞ ! Esam ðwÞ ¼ jEsam ðwÞjexpðiqsam Þ Figure 3.6 shows the time waveform of the terahertz pulse wave of the reference wave and the sample wave measured using the RT-10000 and the power

71

Integrated spectroscopy using THz-TDS and LF Raman scattering 0.05

Glassy glucose Reference Sample

0.04

Glassy glucose Reference Sample

E(ω)2 (a.u.)

E(t) (a.u.)

0.03

10–2 10–3 10–4 10–5 10–6 10–7 10–8 10–9 10–10 10–11 10–12 10–13 10–14 0

0.02 0.01 0.00

–0.01 –0.02 10

20

40 30 Time (ps)

50

60

1

2

3

4 5 6 Frequency (THz)

7

8

Figure 3.6 THz time waveforms and power spectra of reference wave and sample wave measured via THz-TDS (RT-10000) spectrum obtained after applying the Fourier transform. From the amplitude and phase data obtained via the measurements, the complex amplitude transmission coefficient of the sample is obtained using the following equation. t ðw Þ ¼

  Esam ðwÞ jEsam ðwÞj
exp i qsam ðwÞ
qref ðwÞ : ¼

Eref ðwÞ Eref ðwÞ


(3.2)

On the other hand, when a terahertz pulse wave passes through a parallel flat plate sample with thickness d, the theoretical value of the complex amplitude transmission coefficient is expressed as   Esam ðwÞ 4~n ð~n
1Þ ¼ exp i wd ; (3.3) t ðw Þ ¼ Eref ðwÞ ð~n þ 1Þ2 c where ~ n is the complex refractive index and c is the speed of light. If t(w), which depends on ~ n , has the same value as the measured complex transmission coefficient, then ~ n becomes the complex refractive index of the measured sample. The following relational expression can be used to obtain the real part and the imaginary part of the complex permittivity ~e of the sample: ~ n 2 ¼ ðn þ ikÞ2 ¼ ~e ¼ e þ ie’’: 0

(3.4)

3.3 Light-scattering spectroscopy Light-scattering spectroscopy as an in situ probe with non-destructive and noninvasive characteristics has been widely used in many research fields [51,52]. We briefly overview the principle of light scattering in solids. The light propagating

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Integrated optics Volume 2: Characterization, devices, and applications

inside a material induces some electromagnetic radiations with the same or different frequencies from that of the incident light source. The former is known as Rayleigh scattering and the latter corresponds to Raman and Brillouin scattering. As is explained comprehensively elsewhere [53], within the framework of classical electromagnetic theory, the light-scattering phenomena are explained in terms of the secondary radiation of light arising from the fluctuating dipole moment stimulated by the incident electric field. The alternating electric field EðtÞ of an incident light induces a dipole moment mðtÞ ¼ aEðtÞ, where a is the electron polarizability tensor of the material. Considering temporal-modulation of the polarizability due to molecular vibrations, phonons, polaritons, magnons, etc., we obtain

P @a a ¼ a0 þ s Qs ; (3.5) @Qs 0 where a0 and Qs denote the time-independent component and the normal coordinates of the vibrational modes, respectively. Thus, the dipole moment along j induced by an incident electric field along k is described as mj ðtÞ

¼ aik Ek cos wi t ¼

a0ik Ek cos wi t

þ



P s

@ajk @Qs

0

Q0s cos Ws tEk cos wi t;

(3.6)

where j,k indicate Cartesian coordinates. The trigonometric addition formula derives the time-dependent terms of the dipole moment with angular frequencies of wiþWs and wi
Ws, and, thus, the first term of (3.6) corresponds to Rayleigh (elastic) scattering and the second one corresponds to inelastic light scattering. The light-scattering process that causes scattered light with a higher frequency than the incident frequency is called the Stokes process, and the other is called the antiStokes process. The inelastic peaks corresponding to the Stokes and anti-Stokes processes appear symmetrically with respect to the zero-frequency-shift in the light-scattering spectrum. (See Figure 3.7.) Since the electric field radiating from the oscillating dipole moment is proportional to d 2 mðtÞ=dt2 , the intensity of radiation corresponding to the ðwi  Ws Þ term is proportional to a cycle-averaged intensity. As the scattering intensity  depends on

@ajk @Qs 0 ,

this term is called the Raman polarizability tensor, or simply

the Raman tensor. Regarding the scattering of light that originates from the thermally fluctuating dipole moment, the power spectrum of the scattered light is described by the Fourier transformation of the time-correlation function of the dipole moment according to the Wiener–Khinchin theorem, i.e., 1 I ð WÞ ¼ 2p

1 ð

dte
iWt < m ðtÞmð0Þ > :

1

(3.7)

Integrated spectroscopy using THz-TDS and LF Raman scattering

73

Furthermore, according to the fluctuation-dissipation theorem, we obtain

kB T X 00 c ðWÞ; I ð WÞ / (3.8) pW s s where we introduced the susceptibility cs , which corresponds to the polarizability attributed to the s-th vibrational mode, in accordance with the convention, and the double prime denotes the imaginary part. By the quantum-mechanical treatment, the power spectra due to the Stokes and anti-Stokes processes are described as IS ð W Þ / IAS ðWÞ /

X 00 ℏ ðnðWÞ þ 1Þ cs ðWÞ; p s X 00 ℏ nðWÞ cs ðWÞ; p s

(3.9) (3.10)

 
1 respectively, where nðWÞ ¼ exp kℏW
1 is the Bose–Einstein factor. As is BT clear from (3.9) and (3.10), the intensity ratio of the Stokes to anti-Stokes determines the temperature of the sample. Note that the Raman intensity to be observed in the experiments is also proportional to the factor of wi w3s , which is involved in the quantum-mechanically derived spectral differential cross section. Thus, the Stokes to anti-Stokes ratio is given as

IAS ðwi þ WÞ3 ℏW (3.11) : ¼ exp
kB T IS ðw i
W Þ3

When we consider the light scattering to be a scattering phenomenon of photons by some elementary excitation, both the energy and momentum conservations should be satisfied, i.e., ℏws ¼ ℏwi  ℏW;

(3.12)

ℏks ¼ ℏki  ℏq;

(3.13)

where q is the quasimomentum of the elementary excitation, and the suffixes i and s of w and k denote the incident and scattered light, respectively. The minus signs in (3.12) and (3.13) correspond to the Stokes process, and vice versa. Note that the momentum conservation in the light-scattering process shown in (3.13) gives the phase-matching condition of the scattered light, which is attributed to the translational symmetry in the crystal. Figure 3.7 shows a schematic of the light-scattering spectrum. As we have already seen, the inelastic light scattering originates from the elementary excitations such as phonons, magnons, etc. It is worth stressing here that it is of less importance to distinguish the Brillouin and Raman scattering because they are seamless and essentially the same phenomena in the low-frequency light-scattering regime, while in a narrower sense they are classified as light scattering by acoustic and optical phonons, respectively. As for the quasi-elastic light scattering, whose

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Integrated optics Volume 2: Characterization, devices, and applications

Brillouin (Acoustic Phonon, ˂~ a few cm–1) Raman (Optical Phonon, –1 Molecular vib., > ~ a few cm )

(Anti-Stokes)

Frequency shift

(Stokes)

Figure 3.7 Schematic of the light-scattering spectrum peak frequency is zero, we actually observe broad spectra across the Brillouin and Raman regimes [54,55]. Furthermore, since the power spectrum is described using c’’, the ultralow-frequency spectrum is continuous to the dielectric-loss dispersion. In a practical sense, the light-scattering measurement employing a grating spectrograph is called Raman spectroscopy, while the ultralow-frequency measurement using an interferometer is called Brillouin spectroscopy. Since the Raman peaks show a much weaker intensity than the elastic scattering, attenuation of the elastic spectral component is indispensable even for a measurement of a spectral region that does not include the laser wavelength. The incidence of the excitation laser into a spectrograph results in not only a serious damage to the detector but also a false spectrum due to stray light caused by diffuse reflection inside the spectrograph. Thus, many types of optical filter have been developed and employed for Raman spectroscopy. Representative types of such equipment often employed nowadays are holographic notch filters (HNFs) [56–59], dielectric multilayer filters [60,61] and subtractive spectrographs with a zerodispersion [62,63]. For the investigations of glassy systems, structural phase transitions, etc., a low-frequency Raman analysis in the vicinity of the excitation laser frequency is essential because spectroscopic anomalies in such systems, e.g., the BP in inhomogeneous systems and soft modes accompanying ferroelectric phase transitions, and intermolecular vibrations in liquids, tend to be observed in the low-frequency region. To achieve a Raman measurement down to 10 cm
1, a rather large subtractive triple-spectrograph equipped with three gratings or a double-monochromator consisting of a long focal length and high spectraldispersion gratings have usually been employed. These types of instrument tend to show a low throughput, and especially the latter one cannot attain a lowfrequency measurement near the laser frequency using multi-channel detectors. Recently, HNFs based on the Bragg diffraction by a three-dimensionally recorded

75

Integrated spectroscopy using THz-TDS and LF Raman scattering (a)

Relative frequency/THz

(b)

HNF

Sample

Normalized intensity

To spectrograph

–1.5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

–1.0

–40

–0.5

0.0

0.5

1.0

–20 0 20 Relative frequency/cm–1

1.5

40

Figure 3.8 (a) Schematic of micro-Raman system utilizing a holographic notch filter. (b) Spectrum of black body radiation from a halogen lamp near 532 nm. Note that the spectrum at the higher frequency shows the higher intensity as the positive side of the relative frequency corresponds to the longer wavelength interferometric pattern inside a photo-thermo-refractive glass are often utilized in the low-frequency Raman spectroscopic measurements to reject strong elastic scattering. The ultranarrow-band HNFs enable the low-frequency Raman analysis using relatively small spectrometers because such filters diffract the elastically scattered light within a very narrow bandwidth of a few cm
1 [55–57]. Figure 3.8(a) shows a typical setup for the low-frequency Raman measurement employing an ultranarrow band HNF. The incident laser beam is efficiently reflected (diffracted) by the HNF, which works as a bandpass filter, and focused on the sample using an objective lens. The backscattered light is collected using the same lens, and, next, the HNF works as an ultranarrow band notch filter. Since the recent HNFs have a rejection band width of typically about 5 cm
1 or 150 GHz, the transmitted light with a higher frequency shift than the bandwidth contains the very spectral component of the Raman scattering, as shown in Figure 3.8(b) [55]. The Raman spectra shown in Figures 3.9 and 3.10 were obtained using this optical setup. Rapid acquisition of the Raman scattering spectrum across the Stokes and anti-Stokes regimes is another advantage of the system employing HNFs, which enables us to estimate the local temperature in the vicinity of the focal point using the Stokes to anti-Stokes intensity ratio according to (3.11).

3.4 Boson peak investigation via THz spectroscopy and low-frequency Raman spectroscopy The BP is an excitation that universally appears in the THz region of glass-forming materials and has been both experimentally and theoretically studied as one of the

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Integrated optics Volume 2: Characterization, devices, and applications (d)

(a)

3

3.6

Glassy glucose Intensity (a.u.)

Glassy glucose

ɛ'(v)

320 K

3.4 14 K

2

297 K

1 215 K

(b)

3.2 (e)

Glassy glucose

χ"(v) (a.u.)

6

0.2 14 K

0.0 Glassy glucose

α/v2 (cm–1THz–2)

40 30

14 K

10 0 0.0

(f)

0 Glassy glucose 297 K

320 K

20

215 K 4 2

10 χ"/v (a.u.)

(c)

Glassy glucose 297 K

320 K

ɛ"(v)

0.4

0 8

BP

5

215 K

BP 0 0.5

1.0 v(THz)

1.5

2.0

0

1

2

3

4

5

6

v(THz)

Figure 3.9 (a) Real part e’(n), (b) imaginary part e"(n) of the complex permittivity of glassy glucose, and (c) its BP plot using a(n)/n2. (d) The Raman spectrum I(n), (e) the imaginary part of Raman susceptibility c"(n), and (f) the BP plot using c"(n)/n of glassy glucose unresolved problems of glass physics [64–90]. It is known that the BP appears in the form of excess states in the spectrum of the vibrational density of states divided by the square of the frequency, which indicates a deviation from the threedimensional Debye model. Because the BP universally appears in structural glasses, many efforts have been carried out to elucidate its origin. An easy-tounderstand interpretation involves a theory that states that the BP originates from

77

Integrated spectroscopy using THz-TDS and LF Raman scattering

24 22

E (meV)

20 18

INS [95] Violini et al.

INS [95] Violini et al.

α/v2 (cm–1 THz–2) χ"(v)/v (a.u.) 40

30

20

10

0

THz-TDS

Raman

THz-TDS Crystalline

6 5 4

16 14

3

12

v(THz)

g/v2 (a.u.)

10 2

8 6

BP

4 2 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Q (Å)–1

BP

0 0.6 0.5 0.4 0.3 0.2 0.1 0.0

0.5 0.4 0.3 0.2 0.1 0.0

g(v) (a.u.)

ɛ"(v)

1

χ"(v) (a.u.)

ɛ"(v)

Figure 3.10 (a) Dispersion relations of the deuterated glassy glucose. The data depicted are from [95]. (b) Vibrational density of states g(n) and g(n)/n2 of hydrogenated glassy glucose. The data depicted are from [95]. (c) THz-TDS results and (d) Raman scattering results for glassy glucose. (e) e"(n) spectrum of polycrystalline D-(þ)-glucose the local vibration mode and the transformation of the transverse acoustic (TA) van Hove singularity [64,82,86,87,91–93]. As a result of recent advances in molecular dynamics simulation, an interpretation of the BP based on elastic heterogeneity has also been presented [88–90], and the characteristic properties of the vibrational modes of the BP are currently being clarified. The most popular methods for detecting the BP are the inelastic neutron scattering (INS) [66–68,94–96], low-frequency Raman scattering [71–74,97,98] and low-temperature specific heat approaches [65,75–77]. Via the INS approach, the vibrational density of states can be directly determined, making it possible to directly observe the BP in the spectrum of g(n)/n2 spectrum. In the Raman scattering approach, since the BP appears in the experimental spectrum at room temperature, the BP can be easily detected using a Raman spectroscopic system capable of observing the terahertz frequency region. In the case of specific heat measurements, because heat capacity C is the temperature differentiation of internal energy, the BP appears in the plot of C/T3 at approximately 10 K. Is it then possible to detect the BP via infrared spectroscopy, which is generally a complementary spectroscopic technique used along Raman scattering? In particular, can the BP be detected via THz-TDS, whose performance has been remarkable in recent years? Unfortunately, there have been almost no reports stating that the BP can be detected via THz-TDS, which had been established since c. 2000 as a powerful spectroscopic method [99–103]. As we describe below, it is easy to detect the BP via THz spectroscopy [19,34,41–49]. In order to understand how the BP is detected via THz spectroscopy (infrared spectroscopy), it is necessary to consider the following equation obtained from the

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Integrated optics Volume 2: Characterization, devices, and applications

linear response theory for amorphous materials [104,105]. aðnÞ ¼ CIR ðnÞgðnÞ

(3.14)

where a(n) is the absorption coefficient and CIR(n) is the infrared light-vibration coupling coefficient. In this equation, it is assumed that the selection rule of the wavenumber is broken, and if the glass forming material can be regarded as one giant molecule without translational symmetry, any mode (even the acoustic mode in a crystal) will essentially become infrared-active. Because the BP is a peak appearing in the g(n)/n2 spectrum and not in g(n) itself, we transform (3.14) as follows, to observe the BP from the infrared spectroscopy results: aðnÞ=n2 ¼ CIR ðnÞgðnÞ=n2 :

(3.15)

It is evident from (3.15) that the BP does not directly appear in the spectrum of a(n) but is expected to appear in the plot of a(n)/n2. In this chapter, in order to show that the BP can be detected via infrared spectroscopy, glassy glucose, which has its BP at approximately 1 THz, is selected as a model glass substance for the purpose of acquiring a high-accuracy spectrum in the frequency range detectable via THz-TDS. For this experiment, D-(þ)-glucose was purchased from Sigma-Aldrich Co. Its glass transition temperature Tg is approximately 310 K [19,106]. The measurement sample was prepared via the melt-quenching method. A terahertz timedomain spectrometer (RT-10000 manufactured by Tochigi Nikon Corporation) was used for the THz-TDS measurements [19]. For Raman scattering spectroscopy, a single-monochromator spectrometer (HR 320 manufactured by JobinYvon) was used along with Nd: YAG laser (LMX-300S manufactured by Oxxius Corporation) with a wavelength of 532 nm for the excitation laser [19]. Brillouin scattering was carried out using a 90-degree scattering arrangement of a six-pass tandem Fabry–Pe´rot interferometer, and the transverse-wave sound speed was directly determined [19]. Figure 3.9(a) and (b) shows the real part e’(n) and the imaginary part e"(n) of the complex permittivity obtained via THz-TDS, respectively. The absorption coefficient and the imaginary part of the dielectric constant are related by a(n) ¼ ne’(n) 2p/[cn’(n)]. Here, c is the speed of light and n’(n) is the real part of the complex refractive index. At 1 THz in the e"(n) plot, we can see that only a hump structure is observed and that there is no absorption peak. However, as can be seen from Figure 3.9(c), the a(n)/n2 spectrum, which is proportional to e"(n)/n, has a clear peak at 1.17 THz at low temperatures. This is the BP seen in the infrared spectrum. The BP is not directly a peak in g(n) but it has a peak structure in g(n)/n2, and this also applies to the absorption coefficient. Furthermore, the appearance of a peak in the a(n)/n2 plot means that the BP in the infrared spectrum does not involve only a single mode but is the result of the reflections in the whole structure of g(n) in the glassy state. Next, we evaluated the results of the Raman scattering measurements. Figure 3.9(d) shows the measured Raman intensity spectrum I(n) and Figure 3.9(e)

Integrated spectroscopy using THz-TDS and LF Raman scattering

79

shows the spectrum converted into the imaginary part c"(n) of the Raman susceptibility using the following equation: I ðnÞ ¼ ðnðnÞ þ 1Þc00 ðnÞ:

(3.16)

Here, n(n)¼ [1þexp (hn/kBT)]-1 is the Bose–Einstein distribution function. Figure 3.9(f) shows the c"(n)/n spectrum obtained by dividing c"(n) by the frequency. As in the case of the infrared spectrum, no peak appears in c"(n), but the BP clearly appears in c"(n)/n (1.24 THz at 215 K). This situation is virtually the same as for the peak that appears in a(n)/n2. The major difference with infrared spectrum is that the BP peak clearly appears in the experimental Raman intensity spectrum I(n). Because of this, low-frequency Raman scattering has become more popular as a BP detection method. However, it should be noted that the peak seen in this experimental spectrum I(n) is the ‘universal artifact peak’ created by the temperature factor [19,107]. The reason why this peak forms is the temperature factor ‘n(n) þ 1’ in (3.16). As mentioned in Section 3.1, the energy of a photon at 1 THz is 4.14 meV and its temperature is 48 K, which is a sufficiently low temperature (low energy) compared to 300 K, i.e., room temperature. Therefore, if a Taylor expansion is performed with n(n) þ 1 as a high temperature approximation, the factor is expressed as 1/n. Namely, it can be seen from (3.16) that the experimental spectrum I(n) has the same spectral shape as the so-called BP plot, which has the spectral shape of c"(n)/n. This effect disappears at low temperatures (approximately 20 K or less). In many cases, experiments involving the Raman scattering of glasses are performed at room temperature; however, it is difficult for researchers who are not Raman experts to understand the influence of the temperature factor, which affects the observed spectral shape in the THz region. Finally, the results of the INS studied by Violini et al. [95] are compared with the results of our THz-band infrared and Raman spectroscopy measurements, as shown in Figure 3.10. The BP can be clearly observed in the plots of a(n)/n2 and c"(n)/n. However, it does not appear in the g(n)/n2 spectrum. This is a roomtemperature spectrum, close to the Tg of glucose (310 K). Therefore, the existence of a fast relaxation tail obscures the BP. If a low-temperature measurement (approximately 200 K or less) was carried out, the BP in the g(n)/n2 spectrum would be observable at approximately 0.9 THz. On the other hand, the g(n), e"(n) and c"(n) spectra showed similarities. This is due to the fact that the light-vibration coupling coefficient in the frequency region higher than the BP is proportional to the frequency. From the results of the dispersion relation obtained via INS [95], a localized flat mode called the L mode, shown in Figure 3.10(a) and a dispersive mode called the H mode were observed. The L mode is considered to be the origin of the BP of glucose, but its energy is approximately 1.7 THz, which corresponds to the position of the hump in g(n), as shown in Figure 3.10(b). This is slightly higher than the BP frequency and can be explained by considering that information about the lowfrequency region is emphasized when calculating g(n) from g(Q, n).

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Integrated optics Volume 2: Characterization, devices, and applications

Furthermore, compared with the infrared spectrum of the crystal shown in Figure 3.10(e), the L mode corresponds to the lowest-order optical phonon energy. On the other hand, the kink structure at 2.6 THz seen in the H mode in Figure 3.10 (a) is consistent with the optical phonon energy of that frequency, and it can be interpreted as the structure that appears as a result of the hybridization of these two modes. Figure 3.10(a) shows the modes of the longitudinal and transverse waves obtained via Brillouin scattering by extrapolation with broken lines and straight lines, respectively. Although the longitudinal mode is connected smoothly with the H mode, the transverse mode does not coincide with the L mode, suggesting a hybrid of the transverse acoustic mode and the L mode.

3.5 Conclusion The integration of THz-TDS and low-frequency Raman spectroscopy may provide a valid tool to acquire deeper information of structure of materials, including some of interest for integrated optics. The experiment reported here using glassy glucose as an example shows that the BP of glassy materials, which has been an object of study for a long time, can be clearly detected via THz spectroscopy. In order to understand the interaction between THz light and the vibrational density of states, it is generally important to compare the theoretical calculation result of CIR(n) with the experimental results. However, there have been very few studies regarding CIR(n) in the vicinity of the BP frequency in both the experimental and theoretical fields and, thus, further research in this area should be expected in the future. As for the applications of detecting the BP using THz light, it allows for evaluating the degree of crystallinity of a substance by monitoring the absorption coefficient in the vicinity of the BP frequency, taking advantage of the fact that infrared spectroscopy can be used to determine the absolute value of the absorption coefficient. An advantage of THz spectroscopy over Raman scattering is that the former can be applied to opaque glasses in the visible light region, and THz light is less likely to cause photo-induced damage to substances. The development of evaluation methods and applications for various physical properties related to the BP using THz light will be a future challenging research topic.

References [1] Duval E., Boukenter A., and Champagnon B. ‘Vibration eigenmodes and size of microcrystallites in glass: Observation by very-low-frequency Raman scattering’. Phys. Rev. Lett. 1986, vol. 56, pp. 2052–55. [2] Hu¨bers, H. ‘Towards THz integrated photonics’. Nat. Photonics 2010, vol. 4, pp. 503–504. [3] Dragoman D., and Dragoman M. ‘Terahertz fields and applications’. Prog. Quant. Electron. 2004, vol. 28(1), pp. 1–66.

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[13] [14] [15] [16] [17] [18]

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Parrott E.P.J., and Zeitler J.A. ‘Terahertz time-domain and low-frequency Raman spectroscopy of organic materials’. Appl. Spectrosc. 2015, vol. 69(1), pp. 1–25. Dhillon S.S., Vitiello M.S., Linfield E.H., et al. ‘The 2017 terahertz science and technology roadmap’. J. Phys. D. Appl. Phys. 2017, vol. 50(4), p. 043001. Mori T., Nicol E.J., Shiizuka S., et al. ‘Optical self-energy of superconducting Pb in the terahertz region’. Phys. Rev. B. 2008, vol. 77(17), pp. 174515/1–6. Mori T., Goshima S., Iwamoto K., et al. ‘Optical conductivity of rattling phonons in type-I clathrate Ba8Ga16Ge30’. Phys. Rev. B. 2009, vol. 79(21), pp. 212301/1–4. Matsumoto H., Mori T., Iwamoto K., Goshima S., Kushibiki S., and Toyota N. ‘Optical conductivity from local anharmonic phonons’. Phys. Rev. B. 2009, vol. 79(21), pp. 214306/1–8. Mori T., Iwamoto K., Kushibiki S., et al. ‘Optical conductivity spectral anomalies in the off-center rattling system b-Ba8Ga16Sn30’. Phys. Rev. Lett. 2011, vol. 106(1), pp. 015501/1–4. Exter M.V., and Grischkowsky D. ‘Carrier dynamics of electrons and holes in moderately doped silicon’. Phys. Rev. B. 1990, vol. 41(17), pp. 12140–9. Nagashima T., Takata K., Nashima S., Harima H., and Hangyo M. ‘Measurement of electrical properties of GaN thin films using terahertz-time domain spectroscopy’. Jpn. J. Appl. Phys. 2005, vol. 44(2), pp. 926–31. Miyasaka H., Motokawa N., Matsunaga S., et al. ‘Control of charge transfer in a series of Ru2II,II/TCNQ two-dimensional networks by tuning the electron affinity of TCNQ units: A route to synergistic magnetic/conducting materials’. J. Am. Chem. Soc. 2010, vol. 132(5), pp. 1532–44. Iwamoto K., Mori T., Kajitani S., et al. ‘Optical conductivity spectra of rattling phonons and charge carriers in the type-VIII clathrate Ba8Ga16Sn30’. Phys. Rev. B. 2013, vol. 88(10), pp. 104308/1–9. Walther M., Fischer B.M., and Jepsen P.U. ‘Noncovalent intermolecular forces in polycrystalline and amorphous saccharides in the far infrared’. Chem. Phys. 2003, vol. 288(2–3), pp. 261–8. Iwamoto K., Kushibiki S., Honda H., et al. ‘Anomalous infrared spectra of hybridized phonons in type-I clathrate Ba8Ga16Ge30’. J. Phys. Soc. Jpn. 2013, vol. 82(2), pp. 024601/1–7. Mori T., Igawa H., and Kojima S. ‘Progress of ultrafast terahertz timedomain spectroscopy: Raman inactive soft mode in quantum paraelectric SrTiO3’. IOP Conf. Ser. Mater. Sci. Eng. 2014, vol. 54, pp. 012006/1–5. Helal M.A., Mori T., and Kojima S. ‘Softening of infrared-active mode of perovskite BaZrO3 proved by terahertz time domain spectroscopy’. Appl. Phys. Lett. 2015, vol. 106(18), pp. 182904/1–4. Kojima S., and Mori T. ‘Terahertz time-domain spectroscopy of Raman inactive phononpolariton in strontium titanate’. Ferroelectrics 2016, vol. 499, pp. 100–06.

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Part II

Integrated optical waveguides, devices, and applications

Chapter 4

Plasmonic nanostructures and waveguides Tong Zhang1

With the unprecedented ability of shrinking photons into dimensions far below the optical wavelength, plasmonic architectures can surpass the classical diffraction limit, providing more degrees-of-freedom to integrated optical devices. Localized surface plasmon excited in plasmonic nanostructures enable high localized light intensity and strong light-scattering effects, opening possibilities for single-molecule sensing, wide spectral absorbers and enhanced photoelectric conversion. Propagating surface plasmon polaritons in plasmonic waveguides can be used to guide, couple and modulate light under subwavelength dimension. Besides, plasmonic nanostructures could also function as electron-transport paths or hot carrier generators, pouring new insight into integrated optoelectronics. Based on the plasmonic nanostructures and waveguides, plasmonic metamaterials and metasurfaces were further proposed to manipulate light wave at will. When the scale of the nanostructure is decreased to atomic-scale, quantum effects arise and new applications are in the way. In this chapter, we will introduce the fundamentals and applications of plasmonic nanostructures and waveguides, especially focusing on the recent advances of subwavelength control of photons and electrons. At the end of this chapter, we will prospect the potential directions of plasmonic integrated optics.

4.1 Introduction to plasmonics During the past three decades, plasmonics has become a vibrant field in integrated optics research [1,2]. Surface plasmons (SPs) are the light-induced collectiveelectron oscillations confined to the surface of the conductive material [3]. When plasmons are excited in a nanostructure, which can be localized surface plasmon (LSP). By the contrast, if surface plasmons are bounded to an extended metaldielectric surface forming a propagating electron density waves, such a condition is referred to surface plasmon polaritons (SPPs) [4]. Plasmonic nanostructures and waveguides, as the carriers of surface plasmon, enable brand-new physics, unprecedented functions as well as disruptive applications [5–7]. 1 Joint International Research Laboratory of Information Display and Visualization, School of Electronic Science and Engineering, Southeast University, Nanjing, China

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The most eye-catching features of surface plasmons were the unparallel plasmonic light manipulation properties at subwavelength scale [8]. Plasmonic nanostructures show optical cross-section orders of a magnitude larger than physical cross section [9]. Besides, plasmonic waveguides can route and compress light at volumes far below the diffraction limit, which decrease the size of optical devices to the scale of the electronic circuit, facilitating the integration of light path and electronic path on one chip. Furthermore, plasmonic metamaterials and metasurfaces constituted by the plasmonic nanostructures or waveguides could pave the way for optical devices which could never be achieved under classical optical methods by introducing abrupt amplitude, phase and polarization [10]. When the feature size further decreases to the atomic-scale, permittivity, the parameter describing the material optical property, turns to be nonlocal [11]. Permittivity model and theory should be modified to describe the quantum effect in those atomic-scale structures. In this chapter, we will introduce the recent advances of plasmonics into four part: plasmonic nanostructures, plasmonic waveguides, metamaterials and metasurfaces, and quantum plasmonics. At the end, we want to discuss the perspectives of plasmonic nanostructures and waveguides.

4.2 Plasmonic nanostructures The subwavelength resonant nature of plasmonic nanostructures permits lightmatter interaction at nanoscale. In this section, we will discuss the advances on research of optical properties of nanostructures. First, we start by introducing the basic absorption, scattering and extinction behaviours of nanoparticles. We then discuss the tuning approaches of plasmonic resonance. At the end of this section, we will review the plasmonic nanostructure-enabled applications.

4.2.1 Scattering, absorption and extinction of plasmonic nanostructures When shedding light on nanostructured plasmonic materials (e.g. Au, Ag), light absorption and light scattering phenomenon occur, owing to the excitation of surface plasmons. Absorption and scattering originate from electromagnetic energy dissipated and reradiated from the nanostructure, respectively. The sum of absorption and scattering is defined as extinction of plasmonic nanostructure [4]. The scattering coefficient, absorbing coefficient and extinction coefficient of a nanoparticle are [12]: ssc ¼

1 ∯ ðn  Ssc ÞdS pR2 I0

sabs ¼

1 ∰ QdV pR2 I0

sext ¼ ssc þ sabs

(4.1) (4.2) (4.3)

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where I0 is the incident optical intensity, n is the vector normal to the surface of nanoparticle (pointing outwards), Ssc is the Poynting vector of scattered filed, the integral in (4.1) is taken over the surface of the nanoparticle, Q is energy-loss density; the integration space of (4.2) is the volume of the nanoparticle, and R is the radius of a sphere with same volume of the nanoparticle. Additionally, the absorption coefficients, scattering coefficients and extinction coefficients are defined as: Qsca ¼

ssc p  R2

(4.4)

Qabs ¼

sabs p  R2

(4.5)

Qext ¼

sext p  R2

(4.6)

where R is the radius of nanosphere with the same volume as the nanostructure. Localized surface plasmon resonance (LSPR) occurs when the incident electromagnetic wave is in resonance with the surface plasmons in the nanostructure. The LSPR properties is highly dependent on the shape, size and material properties of plasmonic nanostructures. As illustrated in Figure 4.1, Ag nanostructures with different shapes exhibit distinct scattering and absorption spectra [13]. For example, the scattering coefficients of Ag nanosphere and nanocube are comparable to absorption coefficients, while tetrahedron and octahedron show a negligible scattering coefficient. The scattering of a nanostructure could contribute to the radiative damping process of surface plasmon [14]. Time-dependent induced dipole (or high-order) moment of nanostructure, determined by the particle size and electron density of the plasmonic material [15], is the main influential factor of scattering. When the induced moment oscillates in phase, the scattering coefficient increases with the increased size. And the scattering coefficient decreases with the increased size while the electrons oscillated out of phase. Furthermore, mode hybridization of LSPR in nanocavities gives rise to the formation of superradiant mode and subradiant mode [16]. The superradiant located at red-side results in an increase in net dipolar moment and a broaden line width, while the subradiant mode at blue-side gives a decrease in dipolar moment with a narrow resonance, as shown in Figure 4.2 [17]. Breaking the symmetry of the coupling system in those nanocavities could result in Fano resonances, giving further modulating methods for scattering spectra. Symmetry-breaking nanostructures exhibit a strong anisotropic scattering phenomenon in the wavelength of Fano-dip. Under the measurement of single-particle scattering spectra with a polarizer, the results show strong polarization-related scattering intensity in the Fano-dip compared to the peak wavelength of Fano resonance [18]. Complex structures supporting more than one type of resonance could achieve a better light concentrating performance. For instance, as shown in Figure 4.3, a nanoflag, consisting of a localized surface plasmon resonator (nanotriangle) and a

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(b) 40 nm

8 Sphere

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0

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0

600 800 Wavelength (nm)

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600 800 Wavelength (nm)

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8 Tetrahedron 4

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Optical coefficient

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4.2.2 Active tuning of plasmonic resonance In the study of radio-frequency antennas, reconfigurable radiation wavelength and radiation pattern is the newly developed tendency [20]. The main regulation mechanism of a reconfigurable antenna design at microwave frequency is to optically or electrically change the structural parameters of radiation elements [21]. A similar principle can be applied in nano-antennas for more versatile radiative performance. Nano-mechanical methods (Figure 4.4(a)) can be integrated into plasmonic devices to regulate the coupling of two adjacent nanowires [22]. When the voltage is applied to the electrodes, a repulsive Coulomb force Fc¼ kc Q2 =d 2 is formed at the end of each nanowire, causing the distance change between the two nanowires. Thus, a peak-shift of 15 nm in the scattering spectrum was found (applied electric potential: from 0 to 40 V). These reversible and continuous modulation methods can be applied in nanoelectromechanical systems.

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The development of chemical nanocrystal synthesis methods has given precise control on the morphology of nanocrystals [3,13,23]. Oxidation-reduction chemistry using electrochemical method provides reversible and striking changes in the scattering spectral lines. Byers et al. reported electro-induced oxidation and reduction between Ag shells and AgCl shells [24]. A conductive electronic mechanism was proposed to explain Au@Ag dimmer resonance, while capacitive electronic coupling mechanism was attributed to Au@AgCl dimmer optical property (Figure 4.4(b)). This method turned to be reversible but, having only two distinct states, it may be used in switching or plasmonic storage. The above two reconfigurable designs are based on the structural change of the nanostructures. Another featural modulation route is built upon near-distance dielectric index sensibility of electromagnetic response of plasmonic nanostructures (Figure 4.4(c)). The most representative example also relies on a core/ shell nanostructure made by metallic/nonlinear optical material [25]. Dynamic control, obtained by applying an external electric field on the Au rods capped by polyaniline, permits active modulation of the plasmonic resonance peak. Under an electric field from 0 to 10 V/mm, the plasmonic resonant peak varies from 613 to 624 nm. Besides, when the direction of external electrical field is parallel to the light polarization direction, the modulation performance is the best. Similar principle can be used in the phase-change material capped plasmonic nanostructures [26].

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4.2.3 Applications based on plasmonic nanostructures In this part, we will give a fast glance at the applications of the plasmonic antenna effect and provide some design thoughts for those applications. Detailed reviews could be found in [27–29]. Surface-enhanced Raman scattering (SERS) is one of the most mature plasmonic applications. ‘Hot spots’ located at the corners and the nanogaps of metallic nanoparticles dramatically enhance the Raman scattering cross section [30]. Furthermore, superhydrophobic coatings together with micropillar structures have propelled the analyte concentration detection limit to 1 fM [31] (Figure 4.5(a)). Besides, the interface property should be considered, where electrons transfer between the plasmonic nanostructure and the analytes, showing different Raman enhancement factor [32]. The plasmonic antennas absorb more light energy, which could be used to design a perfect absorber material [33]. Au nano-island deposited on multiple-pore AAO templates with multiple resonance modes have been designed and demonstrated [34]. Further, a chemical synthesis method of Ag nanoplates-aggregations (Figure 4.5(b)) was also demonstrated. This three-dimensional film showed perfect light absorption effect in the wavelength region from 300 to 1000 nm. The plasmonic coupling between the nanoplates and the defects in the nanoplates intensely trap the incident light of the wide range [35]. Plasmonic-enhanced photodetectors (Figure 4.5(c)) are another representative application of plasmonic antenna [28]. In the design of plasmonic-enhanced devices, both scattering efficiency and absorbing efficiency of plasmonic nanostructures should be considered. Additionally, directional scattering (forward scattering or backward scattering) is preferred when the plasmonic architectures cannot be embedded in the active region (P-N junction) in the photodetectors [36]. Since plasmonic structures are dramatically sensitive to the localized dielectric Plasmonic nanostructure (a) Laser

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Figure 4.5 Applications of plasmonic nanostructures. (a) Surface-enhanced Raman scattering based on superhydrophobic structure, (b) broadband absorber based on nanoplates-clusters, (c) plasmonicenhanced photodetector and (d) photo-thermal sintering of nanostructures

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index, the thin multilayers in the devices need special attention, which may cause plasmonic hybridization and redirected scattering [37]. Some recent researches pay attention to aluminium nanoparticles, with the interband absorption at infrared wavelength, which have smaller absorption loss for incident light energy [38,39]. The absorption of plasmonic antenna is the main energy-loss mechanism in plasmonic-enhanced photovoltaic devices. However, in a plasmonic heating utility, the ‘energy loss’ can reversely turn into gain [40]. Plasmonic heating was first used in the light heating therapy, killing the cancer cells without hurting the normal cells [29]. Recently, the plasmonic heating is used to desalinate the sea water [41]. Besides, it also shows particular superiority on the photonic sintering, circumventing the energy-consuming high-temperature treatment. Under illumination, strong localized electric fields and large quantities of heat are generated at the junctions of nanostructures. Treated by the localized thermal source, the nanostructures undergo quick melting and sintering (Figure 4.5(d)) [42]. Li et al. demonstrated that nanowire inks sintered by only shedding a flash light on them. A touch pad sensor was achieved on paper-based substrate [43]. To meet the requirement of flexible electronic devices, bonding strength and conductivity are comprehensively studied in their further research [44].

4.3 Plasmonic waveguides and devices As medium of information, photons have many advantages. For example, photons can travel at the fastest speed, and hardly be affected by ambience. With the development of telecommunication and data-routing applications, the aim which could confine photons into a smaller mode volume is pursued [45–47]. However, compared with their electronic counterparts, photons are much more difficult to be confined. The main reason is that there are few interactions between photons and their surroundings. Perhaps, the only parameter that could be used to manipulate photons is the refractive index of the materials, which is typically ranging from 1.3 to 4 [2]. In addition, the diffraction limit, one of the intrinsic properties of light wave, ensures that the ultimately confined volume achievable by traditional optical circuits shares the same order of magnitude with wavelength, far huger than the electronic circuits’ volume [48]. Consequently, in order to acquire the extreme capabilities to manipulate photons in nanoscale, new principles are indispensable. One of the most potential candidates is SPPs.

4.3.1 Plasmonic waveguide circuits for subwavelength light transmission SPPs is a surface electromagnetic wave propagating along the interface between metal and dielectric. It provides a spatial squeezing of super-intense optical field which is far below the diffraction limit. According to this, a silver nanowire waveguide, transmitting SPPs, was first proposed by Takahara et al. in 1997 [49]. In 2005, researchers from Australia and Germany studied the propagating and resonant characteristics of silver nanowire waveguide by using scanning near-field

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longest propagation distance (defined as the length where the intensity becomes the 1/e of the initial value) which can be several centimetres at the telecommunication wavelength [57]. The longest propagation distance is obtained by paying the price of low confinement (micrometres), which shares a similar size with dielectric waveguides. Even so, the unique configurations, especially the material properties of LRSPP waveguide, make it possible for many specialized applications in optics. For example, by using an organic cladding material, flexible LRSPP devices can be fabricated, which are promising for chip-scale interconnection [57,58]. Another application is optical sensors. The propagation properties of LRSPP waveguides are sensitive to their surroundings. Any perturbation will induce huge changes, which will be reflected in the output signal simultaneously. Meanwhile, the single polarized property (holding TM mode only) of plasmonic waveguide makes its polarization noise and pump noise much lower than other waveguide structures, which renders LRSPP waveguide an excellent candidate for high-precision sensors [59–61]. Channel plasmon polariton (CPP) waveguides, consisting of sharp V-shaped groove on metal surface, are a typical example of SPP waveguides with not only small mode volume (blow the diffraction limit) but also long propagation length (about 100 mm) [62]. Here, the electromagnetic field distributed in the groove is formed by coupling SPPs from its opposite sides. Nanoscale dimensions of plasmonic mode in its cross section have been reported with typical propagation lengths of tens of micrometres [62,63]. However, there is a fatal problem that needs to be pointed out. In order to obtain strong confinement, grooves with extremely sharp angle must be fabricated; as a result, the actual volume is relatively large. Usually, the size of the CPP waveguide is sub-micrometre scale, which is comparable to standard optical architectures such as silicon on insulator (SOI) waveguides. The inverse structure of the CPP waveguide is a metallic wedge waveguide, which

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shares the same problems of CPP waveguide, but it is expected to produce stronger field enhancement [64,65]. Metal-insulator-metal (MIM) SPP waveguides have similar characteristics as the CPP waveguides but offers much stronger confinement. The SPP modes in MIM waveguides are bound at the metal-insulator interface and Fabry-Pe´rot (FP) resonance is formed in the cavity of two metal film (or nanostructure). Since light could be strongly concentrated in the insulator layer contributed to the two resonance, the losses are relatively low. The confinement increases when the gap is narrowed down, along with the decrease of effective in-plane wavelength [66]. Meanwhile, as the size of gap decrease below 2 nm, quantum effects dominates, which will be discussed in Section 4.5. Recently, Chen et al. demonstrated a threedimensional plasmonic antenna architecture integrating features of nanogaps and nanotips [67]. Tightly confined light field was found at the interface of the tip and gap, achieving an focusing spot volume of ~l3/106, with an enhancement in electric field exceeding 50 times. Choo et al. also reported a tapered MIM waveguide with a rectangular cross section which consists of a gradually varied silica core layer between two 50-nm-thick gold layers [68]. The cross section of this sandwich structure continually decreased from 500  200 to ~80  14 nm2, leading to the compressed propagating mode and thus producing three-dimensional nano-focusing. In this case, ~400 times intensity enhancement was achieved at the end of the taper, which was proved by two-photon luminescence measurements. Dielectric-loaded SPP (DLSPP) waveguide is another important plasmonic waveguide structure. The dielectric strip with a higher refractive index supports a bounding SPP mode at the metal-dielectric interface, similar to the confinement of guiding modes in optical fibres or dielectric waveguides. However, the trade-off between higher confinement mode and lower propagation loss must still be considered when designing a DLSPPW. Here, different effective index between the guiding modes supported by metal-dielectric and the unguiding mode at the metalair interface leads to good propagating and confinement properties of DLSPPWs. This means that waveguides with smaller bending radius (few micrometres) at telecommunication wavelengths can be achieved [69]. The main advantage of DLSPPWs is that their dielectric strips can be easily functionalized to provide thermo-optical or electro-optical adjustment. It makes DLSPPW a potential candidate for the development of active nanophotonic devices, such as high-speed modulators [70], all-optical switches [71,72] and on-chip lasers [73]. Compared with above-mentioned SPP waveguide configurations, hybrid plasmon polariton (HPP) waveguide, proposed in [74–76], supports a low-loss and deep subwavelength mode with much longer propagation distance. Such mode is formed by coupling a plasmonic mode with a photonic mode from a high refractive index ridge waveguide which are separated by a spacer with low refractive index. Since most portion of optical field of the hybrid mode distributes in the spacer layer with low refractive index, the total losses of HPP waveguide is low. It is theoretically predicted that the optimized structured HPP waveguide enables subwavelength bending modes and micro-size optical cavity (Figure 4.8) which show great potential in the construction of ultra-high-density integrated optical circuits

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4.3.2 Plasmonic modulators Plasmonic waveguides also manifest excellent electron management property due to their made-up material supporting free electron movement. More importantly, when the material size is shrunk to nanoscale, surface electron becomes the main contributor of the electromagnetic response. High-speed, compact and powerefficient optical modulators are key elements for a variety of integrated optic device applications such as photonic transceivers for optical communications, radio-over-fibre (ROF) links, microwave photonics, low-noise microwave oscillators and so on [78]. The modulation of light in a material can be attributed to the change of its dielectric constant or complex refractive index induced by external signals. Generally, optical modulators can be phenomenally classified into refractive or absorptive modulators depending on the change of real part or imaginary part of the complex refractive index. For a refractive modulator, optical modulation is generally realized by the Pockels effect, the Kerr effect, and thermal and acoustic waves modulation of the refractive index. While in an absorptive modulator, an absorption material is always introduced and controlled by the quantum-confined Stark effect, the Franz-Keldysh effect, saturable absorption or electro-absorption. According to the principle of operation, optical modulators can be categorized as electro-optic (EO), thermo-optic, magneto-optic, acousto-optic modulators, etc. Among these kinds of modulators, the EO approach based on Pockels effect by using the nonlinear optical (NLO) materials is mostly used in current optical modulators. The key for an EO waveguide modulator is to create a strong interaction between the propagating optical signals and the electrical signals. So far, there are three generations of EO waveguide modulators that all utilize NLO materials to encode an electrical signal onto an optical carrier [79]. Figure 4.9 shows the three generations of modulators.

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The first generation is an optical waveguide modulator which is composed by strip waveguide. It is bulky and inefficient due to the optical diffraction limit and weak light-matter interactions. The p-voltage-length product is about 5 Vcm for lithium niobate EO modulators [80] and about 1 Vcm for organic EO modulators [81]. The second one is a high-index silicon waveguide EO modulator with a slot waveguide structure filling with organic NLO materials [82]. The size of the modulators decreases from centimetres to millimetres. The p-voltage-length product of 320 Vmm is achieved for state-of-the-art silicon-organic EO modulator [83]. The third one is a plasmonic modulator with a length of a few tens of micrometres. Different with the previous proposed modulators, the plasmonic modulators use the Au contact electrodes to directly form a MIM slot waveguide. At the interfaces between the gold and the NLO materials, the optical signal is guided as surface plasmon polaritons. This approach has many advantages offered by plasmonic MIM slot waveguides such as sub-diffraction confinement of light, enhanced lightmatter interaction, small RC time constants and reduced plasmonic losses [84]. The plasmonic modulator was first demonstrated in 2014 which has a length of only 29 mm and operates at 40 Gbit/s [85], as shown in Figure 4.10. It consists of two metal tapers and a phase modulator section. One of the most outstanding advantage of the plasmonic modulator is optical field enhancement in the slot

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4.3.3 Plasmonic hot-carrier-based photodetector After excitation, surface plasmons experience damping in two paths: radiative damping through reemitting photons and nonradiative damping through generating non-equilibrium hot carriers. The radiative damping is the origin of optical antennas as well as metasurfaces discussed in Section 4.2. When the surface plasmons damp nonradiatively, plasmonic nanostructures generate non-equilibrium hot carriers; if no electron-transport path exists, the hot carriers will lose ‘heat’ by transferring the energy to crystal lattice at the timescale of picosecond. As the hot electrons are routed in a certain direction by introducing a semiconductor material or forming a MIM structure [90], a photo-induced current generates, which depicts the basic ideas behind plasmonic hot carrier photodetectors.

4.3.3.1 General physical process in plasmonic hot-carrierbased photodetector The basic energy band diagram of plasmonic hot carrier generation is illustrated in Figure 4.12. Compared to bulk metal-semiconductor heterojunction, the plasmonic nanostructures exhibit high light absorbing ability in an ultrathin layer and, thus, make the design of nanoscale photodetectors with dimensions far below diffraction limit possible. Another characteristic distinguishing plasmon-induced hot carrier and the direct light-excited hot carrier in bulk material is the electronic initial states: the plasmonic hot carrier is typically excited through intraband transition of electrons located near Femi energy level, while the direct light-excited electrons come from the intraband transition of d-band electrons [91]. As shown in Figure 4.12(b), we can also conclude from the band diagram that the intraband pump needs extra momentum for transition but interband pump occurs directly

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Figure 4.12 Band gram of plasmonic hot-carrier-based photodetector. (a) Band gram of plasmonic metal-semiconductor heterojunction and (b) the relation of energy (E) versus wavevector (k) [92]. The energy of the plasmonic-induced hot electrons could be higher than the interband electron excitation in bulk material, which makes plasmonic nanostructures and waveguides unique candidates for high-efficiency Shockey-junction devices such as on-chip detectors. A metallic bulk material shows a high reflection at visible-light and infrared frequencies, generating negligible current when forming Schottky contact with a semiconductor material. Plasmonic materials and nanowaveguides efficiently couple the incident light into the devices across broadband wavelengths through tuning the geometrical parameters. And the intraband transition property of plasmon-induced hot carriers makes a great promise for bandgap-free devices working at infrared region, such as photodetectors working at telecom wavelength compatible to CMOS technology. The Au nanowaveguide-Si heterojunction structure showed by Sobhani et al. gives a light-current response of 0.6 mA/W and an external quantum efficiency (EQE) of 0.05 per cent [93]. Later, Au–Si metasurface was demonstrated for perfect absorption and photodetection in infrared regime under excitation of SPP mode, increasing the value of EQE to 0.31 per cent [94]. A three-dimensional nanopillar nanostructure was further proposed to increase the light-matter interaction path, resulting in an EQE of 3.5 per cent [95]. A circular-polarized light detector was also demonstrated by proper metasurface design without adding traditional polarizers or wave plates [96]. Electron transport is another important process in typical plasmonic photodetector devices. A recent research deconvoluted the light absorption and the electron transport process by exploring the internal quantum efficiency (IQE) of the photodetector [97]. The IQE is the ratio of number of electrons detected divided by the absorbed phonon number, which eliminates the influence of light absorption process. Both the quantum theoretical results and the experimental results show a band-related IQE response. The interband transition will result in a

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relatively lower IQE compared to the intraband transition despite of higher photon energy of the interband excited electrons, which explained the failure of Fowler theory when applying to the visible-light region [91]. Dark current, another important parameter describing the performance of photodetector, could be reduced without obvious change of photocurrent by incorporating a 0.7-nm layer of WO3 deposited by atomic-layer-deposition method [98]. The main advantage of this strategy is to increase the signal-to-noise ratio of this plasmonic photodetector. The reason behind it is the increasing barrier height induced by the WO3 material. Barrier height management was also achieved by the utility of bimetallic MIM structure to facilitate the electron transport [99]. The contact manner of above-mentioned configurations is direct planar contact, allowing only 50 per cent electrons transport to semiconductor layer to the most. Omni– Schottky junctions collecting all direction scattered electrons are designed to get a high-efficiency device [100]. A new one-step plasmonic hot carrier conversion mechanism based on plasmon-interfacial electronic states hybridization was proposed in 2015, showing great potential to further improving the performance of hot-carrier-based photodetector performance [101]. Plasmonic nanodetectors enable over 100 GHz plasmonic photodetection, where the capacitance of the device is in the order of about fF due to the ultra-small volume. Besides, plasmonic nanostructures and waveguides confine the electron draft path at nanoscale, permitting a very short transporting time of light-induced carriers [102].

4.3.3.2 General physical process in plasmonic hot-carrierbased photodetector It should be noted that the maximum EQE of the plasmonic hot carrier-based photodetector was about 5 per cent. In a sense, the physical origin of the relative lower EQE are momentum mismatch on electron wave functions between plasmonic structure and Si substrate as well as the short lifetimes of hot electrons [103]. To further enhance the performance of the plasmonic on-chip photodetector, dual detecting mechanism or multiple mechanism were proposed recently. One of the hottest topics among them is the combination of twodimensional material with plasmonic material. Graphene-based photodetectors show a broadband absorption from visible-light to mid-infrared regime duo to its zero-bandgap property, but the absorption coefficient is not large enough due to its atomic thickness. Incorporating plasmonic nanomaterials into those devices could enhance the light absorption as well as form new hot-electron transport path, obviously increasing the current response [104]. In 2018, N. J. Halas’s research group reported a dual mechanism plasmonic hot carrier-based photodetector: the first one was the traditional plasmonic hot electron mechanism from metallic nanowaveguide-Si heterojunction, and another one was free-carrier absorption mechanism in highly doped p-type Si (Figure 4.13(a)). The former mechanism generates wavelength-dependent light response, while the latter greatly reduces the heavy-hole mass and enhances the mobility of carriers, resulting in >1 A/W responsivity under 93 mV bias [103].

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The infrared light-induced negative effect was found in MoS2 photodetector by Wu et al. [105]. Similar phenomenon was also found in plasmonic hot carrier photodetector [106]. The whole device is made from gold. Under illumination, electrons undergo electron-electron scattering and electron-phonon scattering after the damping process of surface plasmon (Figure 4.13(b)). Under this circumstance, the mean free path and the mobility reduced, generating a negative conductance of photodetector device.

4.4 Plasmonic metamaterial and metasurface A plasmonic metamaterial, built by artificial meta-atoms of plasmonic nanostructures or nanowaveguides, has the ability of steering the electromagnetic properties of effective permittivity and permeability [107]. Due to the intrinsic loss of metallic material, the outputs of the three-dimensional metastructures are usually weak, resulting in a low efficiency of the device. A metasurface consisting by a two-dimensional layer of metallic nanostructures was further proposed [108]. By introducing the abrupt phase changes, the stationary phase usually adopted in classical Fermat’s principle can be changed. In this sense, the phase will not accumulate along the light path continuously, so that the actual path of light could be dramatically reduced for certain optical functions [108]. Using spatially varying geometric parameters and subwavelength antenna separation, the metasurfaces create an optical response varied spatially, which (a) → E

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−150 −200 off on off

on off on

off on

Figure 4.13 New mechanism for plasmonic hot-carrier based photodetection. (a) Plasmonic hot carrier mechanism combined with free-carrier mechanism, (b) negative response based on plasmonic hot carrier generation. Reprinted, with permission, from [103,106]

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reshapes the wavefronts at will. In this section, we will reveal the breakthrough in metamaterial and metasurface.

4.4.1 Anomalous reflective and refractive material The early idea of negative refractive index was proposed by Veselago [109], showing that a ‘left-hand’ material has a negative permittivity and a negative permeability simultaneously. In this kind of material, light is routed with opposite phase and group velocities, where anomalous reflection and refraction would be found. The early demonstrations of negative refractive material operated at microwave frequency [110]. In 2005, a negative effective permeability was first exhibited at optical frequencies [111]. Coupling between gold nanodots with geometric size at 10-nm scale realized a strong magnetic response, which was attributed to the antisymmetric plasmon resonance excitation. The calculated permeability ranged from –1 to 3 for the tight packing of gold nanoparticles. Three years later, Zhang et al. exhibited a three-dimensional negative refractive index metamaterial at infrared wavelength with a figure-of-merit of 3.5 [112]. Anomalous refraction was observed on the prism made by the proposed mesh-like multilayer structure. The above negative refractive index strategies usually exist at certain light axes; omnidirectional left-hand electromagnetic response in ultraviolet frequencies was further proposed in year 2013 [113]. With a refractive index about –1 across board angles, perfect imaging was achieved in the far field, just as predicted by Pendry [114]. Based on metasurfaces, Capasso et al. established the generalized laws of reflection and refraction [108]. By considering a plane wave with an incident angle and a refraction light at an angle qt , they proposed a generalized form of l0 df Snell’s refraction law nt sin qt  ni sin qi ¼ 2p dx , where nt and ni represent the effective refractive index of the material at either side of incident interface, l0 represents the wavelength in vacuum while df dx represents the gradient of phase changes. From the formula, we can see that, if there is a constant phase-change gradient along the interface, refraction at arbitrary direction could be achieved. As demonstrated in Figure 4.14, the red line represents the wave front, which means that the light bends with normal incident angle, totally different to the classical optics [108]. The follow-up research also includes broad wavelength range anomalous reflection, higher conversion efficiency [115] as well as nonlinear optical metasurface response [116]. Beside the nano-antenna-based metasurface, the nanoholes can also serve as metasurface element inspired by Babinet’s principle [117,118].

4.4.2 Beam-splitter and polarization controller To split or control beam of different wavelength or polarization is of paramount importance for light processing. Traditional light-splitter devices are based on lenses or diffraction gratings, in which light experiences a continuous phase change; the size of the whole devices is therefore relatively large [119]. A two-dimensional

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Incidence Plane of incidence θi

φr θr

Reflection

dΦ/dx

dΦ/dy

ni Metasurface

dΦ/dr

nt

φt z θt x Transmission

y

Figure 4.14 Illustration of generalized reflective and refractive law. Reprinted, with permission, from [108] hyperbolic metasurface supporting surface plasmon polaritons is designed to achieve a compact on-chip spectrum-splitting device [120]. Single-crystal silver nanostrips were used for the realization of low-loss wavelength-dependent propagation of SPP owing to different spatial dispersion relation curve under different light wavelength (Figure 4.15). It is worth mentioning that diffraction-free propagation of SPP at wavelength 540 nm is another remarkable discovery in this study; the flat dispersion curve in Figure 4.15(b) enables all spatial vector components of SPP to propagate in the same direction. By contrast, at the wavelength of 490 or 640 nm, diffraction of SPP happens. In another recent research, a wavelength-encoded light signal of telecommunication wavelength could be demultiplexed using Fano resonance antenna metasurface, providing a functional link in ultra-compact integrated optical circuits [120]. Control of polarized light is another hot topic in metasurface study. Polarized light splitter is typically based on birefringence in crystals, also suffering from the thickness limitations. In addition, the polarization selectivity propagating of SPPs (only TM wave is permitted) also limit the splitting of polarized light in such

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Figure 4.15 Two-dimensional hyperbolic metasurface. (a) Scanning electron microscopy graph of whole structure, (b) the dispersion relationship of the hyperbolic metasurface and (c) wavelength-dependent refraction. Reprinted, with permission, from [120] configuration, causing information loss of one polarization state. Closely and orderly packaged subwavelength apertures were proposed as polarization-selective metasurfaces [117]. In such metasurfaces, light is coupled to SPPs in the two columns of parallel apertures. The interference of the SPP field components excited by each column gives rise to different propagating directions of right and left circlepolarized light.

4.4.3 Sub-diffractive limit superlens and metalens Under the limitation of diffraction, the resolution limit of an optical system is determined by the formula: h ¼ 0:61l=ðn  sin qÞ, where ðn  sin qÞ is the numerical aperture (NA) of the objective lens. To date, the maximum NA of the objective lens is about 1.7, that means, for a 532-nm laser, that the resolution limit can approach ~190 nm [121]. The information of the finest feature of objects is carried by evanescent wave with a minus spatial wave number, which cannot be received in the far-field region [114]. Pendry proposed the concept of perfect lens in year 2000 [114]. In his view, a slab lens with a refractive index of –1 will magnify the intensity of evanescent wave, projecting a perfect image at another side of the lens. Zhang et al. experimentally fabricated the near-field superlens in 2005, achieving a resolution of

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60 nm under 364-nm illumination [122]. Two years later, a hyperlens with the dispersion line shape of hyperbolic curves was demonstrated, in which the evanescent wave was transformed into propagating wave. An important influential factor is the slope of the hyperbolic dispersion curves [123]. When the slope is designed to approach zero, the transverse wave vector components will propagate along the radial direction at the same phase velocity, creating an image without distortion in the far field. In addition, the hyperlens was used to demagnify the objects, showing potential in high-resolution optical lithography [124]. Recently, Su et al. theoretically designed a real-time tuning of a hyperlens to eliminate chromatic aberration (Figure 4.16). By replacing the titania with an electro-optical material, they achieved an active tuneable hyperlens working at a wavelength ranging from 413 to 459 nm [125]. The above-mentioned superlens suffers from low light-transmission efficiency for the sake of subwavelength resolution. The flat hyperbolic metasurface, supporting diffraction-free propagating of surface electromagnetic wave, may propel the undistorted imaging in two-dimensional flat devices [120]. Provided super-resolution is not required, a metalens based on spatially dispersive nanoantennas has more superiorities than the traditional lens for aberration correction and fabrication process. For example, to eliminate all chromatic aberration over large wavelength region in the macro-lens, a typical strategy was integrating more materials into one lens. For the metalens, one only needs to change the (a)

(b) 15

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Figure 4.16 Real-time tunable hyperlens. (a) Schematic illustration of tunable hyperlens, (b) the dispersion relationship under different external field and (c-f) the electric filed distributions on focal plane of hyperlens under different external field. Reprinted, with permission, from [125]

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shape, size or the separation of the nanostructures (usually made by a single material) to achieve a better control of the wave front. The phase profile of a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi metalens is described by: jðx; y; lÞ ¼ ½2pð x2 þ y2 þ f 2  f Þ 1l where (x, y) is the position relative to the centre (light axis), f is the focal length and l represents the incident wavelength [126]. Antennas with multiple resonances were designed to realize achromatic broadband lenses by engineering the linear phase change (versus wavenumber), the subwavelength separation as well as the antenna orientation [126]. Furthermore, lattice evolution algorithm was introduced to the flat optics, and multiwavelength-operated achromatic lenses were achieved by varying the location and orientation of the preselected elements [127]. Fourier transform and inverse Fourier transform were also studied using an on-chip SPP platform [128].

4.5 Quantum plasmonics The characteristics of plasmonic devices can usually be accurately described by classical electromagnetism. However, when the mode volume of SP is continuously decreasing into nanoscale, new phenomena emerge where classical theory description is inappropriate. For example, the classical electromagnetic theory predicts that the field in nano-gaps should be enhanced with the reducing of gap-size. In reality, the deduction does not accord with experimental observations, especially for tiny gaps below 10 nm [129,130]. Consequently, the concepts of quantum plasmonics are introduced to treat these problems.

4.5.1 Quantum properties of surface plasmon In quantum mechanics, the most basic properties of any quantized particles are that they can exhibit both wave-like and particle-like properties. In other words, it is wave-particle duality [129–131]. The wave-like behaviour means that particles should carry phase and demonstrate the interference, resulting in a sinusoidal field distribution. The particle-like behaviour mainly indicates the statistical properties of particles, such as anti-bunching which shows a dip at zero delay in their secondorder correlation function [132–134]. In order to verify the quantum properties of SP, the wave-particle duality, which is the most elementary quantum mechanics, needs to be investigated. The first evidence of wave-particle duality of SP was addressed by Lukin’s group in 2007. They demonstrated the particle-like behaviour of a single SPP by coupling the emission from an individual quantum dot (QD) to a silver nanowire (Ag NW) [132]. Then, in 2009, Kolesov et al. used a nitrogen-vacancy (NV) centre which is coupled to a silver nanowire to show the wave-particle duality of a single SPP (Figure 4.17(a)) [133]. In their experiment, a single NV centre, as the quantum emitter, can spontaneously emit a single photon which was coupled into silver nanowire at a time. This process ensured that only a single SPP was generated in the nanowire, which was confirmed by the results of the second-order correlation

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Plamons B d1 d2

A

Wire ends

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g2(T)

1.5 1.0 0.5 0.0

−4 −2 0 2 4 Delay T (ns)

Figure 4.17 Probing wave-particle duality of SPPs. (a) Single NV centre coupled to silver nanowire. A single SPP interferes with itself (wave-like, left) and shows sub-Poissonian statistics (particle-like, middle). BS: beam-splitter, d1 and d2 are the distances between the NV centre and the two ends (A and B) of a nanowire, respectively, PA and PB are photodiodes, and Pc is photon correlator. (b) Single SPPs excited in a metallic waveguide by single photon. The inset shows the secondorder quantum coherence, g(2)(t). Reprinted, with permission, from [133,135] function. The self-interference of a single SPP was also observed, which is a strong evidence of wave-like behaviour. Maier’s group went further by exciting single SPP in metallic ridge waveguide using the optical quantum states of parametric down-conversion (Figure 4.17(b)) [135]. Quantum statistical properties of photons emitted from both ends were measured. In this study, they focused on the loss of SPP. Their result shows that the loss caused by SPP can be regarded as a linear and non-correlated Markov environment. It has no impact on the correlation properties of quantum states. Therefore, the transmission loss of SPP can be handled by classical methods. Another issue of concern is whether SPP devices could maintain the coherence of quantum states, which was verified by Altewishcher et al. in 2002 [136]. The quantum polarization entanglement states of two-photon were generated through spontaneous parametric down-conversion (SPDC) in a nonlinear crystal. Then, the entanglement photon pair were irradiated through a metal thin film (MTF) with

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A1

A1

1

L C BBO

P1

IF

& HWP

P2 C

IF

L A2

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Figure 4.18 Transmission of polarization-entangled photons through metallic hole array. The inset shows the fourth-order quantum interference fringes. BBO: b-barium borate nonlinear crystal, C: compensating crystal, HWP: half-wave plate, L: lens, TEL: confocal telescope, A1 and A2: metal grating, P1 and P2: polarizer, IF: interference filter, P1 and P2: single-photon detectors. Reprinted, with permission, from [136] subwavelength hole array (Figure 4.18). The anomalously transmitted photons underwent the transition from photon to SPP and back to photon. Many photons were lost because of the ohmic losses from MTF. The survived photons finally reached the detectors and were found to be highly entangled. Further experiments suggested that the entanglement in other degrees of freedom (time-energy, orbit angle momentum, etc.) could be maintained during the photon-SPP-photon transition as well [137,138]. It seems so weird that the quantum information can be encoded into collection collisions of massive charges and delivered back without being destroyed. Nevertheless, these experiments have confirmed that entanglement between SPPs can be made and applied for quantum information processing, such as SPP-based remote control.

4.5.2 Quantum plasmonic integrated circuits Since SPP can confine light into the nanoscale, the footprints of integrated optical devices based on SPP can be dramatically reduced without the restriction of the

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diffraction limit. At the same time, the fact that plasmonic devices can maintain the coherence of quantum states has already been demonstrated. Therefore, quantum plasmonic integrated circuits (QPICs) could be constructed with not only the characteristics of classical quantum circuits but also a super-small size. Similar to their electronic counterparts, QPICs should integrate multiple functions components, such as quantized SPP generators, modulators and detectors. In an integrated quantum plasmonic circuit, generation of quantized SPP can be done by indirect or direct ways. The indirect method is to couple the external single-photon sources, such as spontaneous parametric down-conversion photon pair, to SPP waveguides [139] by edges, gratings or prisms. An efficient way is to excite the SPP mode through adiabatic coupling between dielectric waveguides and SPP waveguides. In theory, more than 90 per cent of conversion efficiency can be acquired. For direct methods, researches in recent years is focusing on the configuration where a single quantum emitter, including quantum dots and NV colour centres, is placed near metal waveguides [140,141]. The coupling efficiency between quantum emitters and SPP waveguides is superior. Most energy will spontaneously emit and couple into SPP waveguide mode, forming a quantized SP state. Another method is to configure quantum emitters near a plasmonic nanostructure. When frequency matching condition is satisfied, emitters will spontaneously radiate energy into the metal structure and excite the localized quantum SP. If the emitter is adhered to the tip of near-field probe, the excitation position can be precisely controlled. Another potential method is tantamount to fill the area covered by the SPP mode with a nonlinear dielectric material [142]. Spontaneous parametric down-conversion (SPDC) of the SPP mode can directly generate the SPP quantum state. Owing to the very small mode volume of SPP mode, it is expected that this method can achieve higher efficiency than that in the dielectric waveguide. Frequency-doubled SPP has been realized on thin metal film [143], which means the SPDC in the SP circuit will come soon. Manipulation of SPP quantum states can also be achieved by similar strategies as the optical quantum states being controlled in integrated dielectric optical waveguides [144]. For instance, SPP quantum states can be manipulated in an integrated circuit consisting of SPP directional coupler and phase retarder which are both linear manipulation devices. In order to improve their efficiency, a promising method is to introduce nonlinear interactions, including the nonlinear interaction between SPP and SPP, and the interaction between SPP and matters. However, since the nonlinear coefficient of material is low, the nonlinear interaction between SPP and SPP is very weak. Therefore, it is sometimes difficult to achieve this function. Fortunately, the interaction between SPP and matters is very strong, thanks to the smaller mode volume and stronger intensity of SPP. In this section, we mainly introduce the implementation of SPP quantum circuits based on linear scheme. In 2012, Fujii et al. verified that SPP does not change the indistinguishability of photons [145]. With the improvement of micronanofabrication technology, the quantum interference between SPs in integrated SPP waveguides becomes possible. In 2013, Zwiller et al. proposed an integrated gold strip SPP waveguide splitter [146]. Two photons generated by spontaneous

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Vb

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I

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Figure 4.19 Quantum plasmonic integrated circuits. (a) HOM interference of SPP in gold stripe waveguide; (b) electric detection method for direct detecting SPP. Reprinted, with permission, from [146,149] parametric down-conversion were coupled into the gold strip waveguide to excite two coherent SPPs. Quantum interference between the two SPPs was found for the first time by second-order correlation measurement. Finally, 43 per cent interference visibility was obtained, but it was still below the threshold of quantum interference (Figure 4.19(a)). In order to realize the quantum interference of SPPs in the integrated SP circuit, the hybrid SPP waveguides loaded by dielectrics have been used to achieve the double SPP quantum interference of 50 per cent higher than the classical limit [147]. At the same time, Ren’s group introduced the highest interference visibility so far, which is 95.7 per cent [148]. These experiments fully proved that SPPs, similar with photons, were bosons and could be utilized in integrated quantum information processing, such as constructing quantum C-NOT gates and other logic devices based on interference. For the SPP detectors, electrical methods can be used directly. Experiments show that when a metal nanowire waveguide was placed on a germanium field effect transistor, the SPP excited the electron-hole pair in the germanium nanowire, then the current would be detected [149] (Figure 4.19(b)). In order to improve the detection efficiency of SPP quantum information, superconducting detectors can be used on the SPP waveguide. Therefore, the whole QPICs can be realized without conversion from SPP to photons.

4.6 Barriers and perspectives Advances in the described ultra-small antennas, waveguides, light sources, photodetectors and modulators provide more freedom to the integrated optics. At the same time, one should be advised that challenges and opportunities are also huge now. Due

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to the lossy nature of surface plasmon resonance material, the efficiency of those devices is limited. The optical devices fabricated by the nanostructures and waveguides always suffer from relatively low optical efficiency. New materials are needed in order to compensate for the contradiction between confinement and losses. Recent breakthroughs demonstrated that SPP can be supported by two-dimensional materials with just atomic-layer thickness [150], providing new research directions. Another problem is the wavelength covering ability, and plasmonic resonance is always linked to the specific wavelength for specific light properties. For example, the metasurface working at ultraviolet frequency is relatively lacking and the resonance peak tuning range is relatively narrow. More versatile structures and modulating methods still need further study. Self-assembly and nano-imprint technology methods may pave the future direction [30,151]. Nanofabrication and characterization approaches for finer plasmonic structures are also research frontiers, which enable deeper understanding of plasmonic science [2]. In a word, plasmonic nanostructures and waveguides are in the way to reform the integrated optics; nevertheless, disruptive theory and techniques are still highly appreciated to realize widespread practical applications.

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Chapter 5

Crystalline thin films for integrated laser applications Gurvan Brasse1 and Patrice Camy1

Since the end of the 70s, thin films have attracted a growing interest in many fields especially for photonic applications, due to the increasing needs in telecoms, biophotonic, environment, defence, as well as for civil protection. The purpose of this book chapter is to present the main elaboration methods of dielectric crystalline thin films dedicated to laser media or scintillators, by focusing on the liquid phase epitaxy (LPE) method which offers new application perspectives, in a complementary way to those offered by bulk crystals. The LPE technique, which has been widely used for the growth of semiconductor thin films, is a very relevant method for growing dielectric crystalline thin films such as oxides or fluorides with thicknesses lying from few microns to few hundreds of microns. The purpose here is thus to focus on dielectric crystalline thin films, which offer new perspectives and applications. The deposition of thin films has indeed contributed to the functionalization of surfaces by giving them properties such as antireflection, photochromism, electrochromism, photocatalysis, photoluminescence or electroluminescence. More recently, the emergence of integrated optics has opened new perspectives such as the multiplication of active and passive optical functions on a same substrate, by structuring the materials as thin films by ‘top down’ or ‘bottom up’ approaches. This book chapter is based on scientific results of researches carried out at the CIMAP laboratory in Caen (France), but also in other internationally recognized research centres all over the world. After having done an overview of the development of dielectric thin films for optical or optoelectronics applications, a state of the art is drawn up concerning the main processing techniques. Some essential theoretical notions about the concept of epitaxy and the specificity of the process in the liquid phase are then introduced, before highlighting the importance of the experimental approach implemented for the growth through the description of the different preparation stages of crystalline thin films grown by LPE. 1 Centre de recherche sur les Ions, les Mate´riaux et la Photonique (CIMAP), UMR 6252 CEA-CNRSENSICAEN-Normandie Universite´, CAEN, France

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The different issues concerning the growth of crystalline thin films by this method are thus discussed, and the importance of experimental parameters such as the substrates’ nature, their required surface states, the used solvents, as well as the preparation steps of the epitaxial layers such as cleaning, shaping and polishing are described. In addition, the various possibilities for post-processing of the layers, in order to optimize their properties regarding the suited applications, are discussed. To illustrate the purpose, the growth under a controlled atmosphere of fluoride thin films is discussed and illustrated by two concrete examples: rare-earth (RE3þ)doped CaF2 films on CaF2 substrate and RE3þ-doped LiYF4 thin films on LiYF4 substrate. A state of the art of oxides thin films grown by LPE and proposed for photonic applications is also drawn, by considering several examples of silicates, tungstates, garnets and perovskites. Finally, an overview of various photonic applications based on RE-doped dielectric crystalline thin films elaborated by LPE is presented and illustrated by some results reported so far, especially for laser operating from the UV-visible until the middle infrared (MIR) spectral range. This chapter aims to share scientific knowledge in an educational approach with students, technicians, engineers, researchers and teachers who wish to deepen their knowledge on thin films for photonic applications.

5.1 General context 5.1.1 State of the art and overview of the main techniques to produce thin films Since the 70s, many materials have been considered as thin films and, at the same time, various elaboration techniques have been developed. To draw the state of the art of the different synthesized materials in a thin film shape, it is necessary to take an overview of the different technologies implemented for this purpose. So, without developing the case of semiconductors, it is nevertheless essential to mention that the first crystalline epitaxial layers grown by the liquid phase epitaxy (LPE) technique were constituted by Gallium Arsenide (GaAs), Indium Phosphide (InP), Aluminium-Gallium Arsenide (GaAlAs), which are semiconductors intended for the realization of the first laser diodes. The rise of this crystal growth method has then allowed some innovations in photonics, thanks to the elaboration of various semiconductors materials but also of dielectric ones, as presented below. Among the various key existing deposition or growth techniques for the elaboration of dielectric thin films, let us mention: –

The chemical vapour phase deposition (CVD) methods are widely used for the processing of semiconductor thin films, but also for dielectrics. Their principle is to elaborate a material that can be amorphous or crystalline, from the decomposition of gaseous sources in contact with a substrate carried at a suitable temperature. These methods can be classified according to various criteria, such as the pressure for which the growth occurs, the heating mode of

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the substrate, the physical characteristics of the reactants or also the means used to initiate the deposition. As examples, it is possible to mention: the MOCVD (metal organic chemical vapour deposition), PECVD (plasmaenhanced chemical vapour deposition), APCVD (atmospheric pressure chemical vapour deposition), LPCVD (low-pressure chemical vapour deposition), UHVCVD (ultra-high vacuum chemical vapour deposition) and RTCVD techniques (rapid thermal chemical vapour deposition). Many variations of such CVD technologies exist that, associated to the high growth rates up to 10 mmmin–1, make these methods very common and suitable in industry. The PLD (pulsed laser deposition) method is based on the vaporization of a target by using a focused laser beam on it. The plasma, which is formed (the ‘plume’) by this way, is then oriented towards a substrate in order to initiate a crystallization onto this area. This method has led to many achievements such as: films of Er3þ: Y2O3 [1], layers of Nd3þ:Gd3Ga5O12 (or GGG) and Nd3þ:Y3Al5O12 (or Yttrium-Aluminium-Garnet (YAG)) epitaxially grown on YAG substrate for laser applications as waveguides [2], films of Ti3þ: Sapphire on Sapphire substrates (Al2O3) [3]. Laser ablation leads to high crystalline quality thin dielectric layers but remains limited by small dimensions in the order of 1 to 2 cm2, as well as by the low thicknesses of the so-obtained films reached by using this technique (generally below one micrometre). The MBE method (molecular beam epitaxy or molecular jet epitaxy) is a technique that sends a controlled flow of atoms and/or molecules on the surface of a temperature-controlled substrate under an ultra-vacuum. The use of an extremely high vacuum avoids a pollution of the reactive species with possible residual gases. These reactive species are obtained from sources contained in Knudsen cells and evaporated under vacuum after heating. Depending on the chosen sources, complex structures can be synthesized layer by layer. Nevertheless, the MBE technique presents extremely low growth rates in the order of 0.1 to 1 mmh–1, and the important cost of such installations, due to the ultra-high vacuum required, is a limitation to the use of this technology only for products with very high added values. Crystalline layers of very good quality, but with low thickness, of Er3 þ:CaF2 [4] or Nd3þ:LaF3 [5] have been deposited by using this technique. More recently, a variant of the CVD method, which is called ALD (atomic layer deposition), has been developed to grow materials atomic layer by atomic layer; in this manner, it becomes possible to reach monoatomic layers grown onto surfaces with strong aspect ratios. This method is especially well suitable for the deposition of very high-quality crystalline layers with very low thicknesses (107 ) planar resonators integrated in PICs. In Section 6.4, we highlight recent results on integration of bulk microcavities with Q > 109 . Section 6.5 concludes the chapter.

6.2 Overview of coupling techniques Confined modes in ring microcavities were initially observed in crystalline cavity lasers. The lasing was studied in Sm:CaF2 resonators, and presence of the modes was confirmed by the observation of the tangential laser emission from the surface of the sphere [76]. Transient laser operation was utilized to confirm existence of the long-lived modes in a ruby ring of several millimeters in diameter [77]. The transient process was attributed to pulsed laser excitation of WGMs with quality factors (Qs) of 108–109. Experimental studies of the lower-Q modes were continued in both amorphous and liquid microcavities supporting free beam coupling [38,40,78–88]. The nonlinear optical effects such as four-wave mixing and stimulated Raman scattering were observed. The quality factor of the modes participating in the processes was selected to be not very high because of the necessity of coupling with the modes through the radiative channel (free beam coupling) and because of the relatively large linewidth of the lasers used in the experiments. The free beam coupling quality degrades exponentially with the quality factor increase. The observation of the laser emission [77] was a smart tick allowing highQ WGM observation. In this case the optical pumping of the laser can be achieved using low-Q leaky modes. This approach did not tell one how to interrogate the

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passive high-Q modes. As the result, the research of the ultra-high-Q modes ðQ > 107 Þ was frozen for three decades after the first observation of the modes [77]. The existence of the ultra-high-Q WGMs was confirmed using a direct measurements in passive fused silica resonators [42,92] only after an efficient scheme for the coupling with the modes of a microsphere (also valid for other cavity shapes) was developed [90–92]. Coupling to very high-Q modes of open dielectric resonators of any nature is usually achieved via frustrated total internal reflection. The coupling rate depends on the distance between the resonator and the evanescent field coupler as well as on the coupler geometry. This feature allows for a control over the coupling rate. The mode overlap of the resonator and the coupler should be sustained to achieve good coupling efficiency. In addition, phase matching between the resonator and the coupler modes is required. It is important to achieve selective coupling between the modes of interest in multimode systems. The so-called “critical coupling” can be achieved if all the conditions are satisfied. In a critically coupled resonator, all the light fed into the mode either is attenuated in the resonator (single coupler scheme) or transmitted though the resonator without loss (double coupler scheme).

6.2.1 Input-output formalism and critical coupling The notion of critical coupling is fundamental in radio frequency engineering [89,94]. It basically calls for matching the electrical resistance of a device and an external electric line. The principle has been expanded to optical resonators [94,95] and became one of the basic characteristics of the integrated cavity structures. It is an important feature since the internal attenuation of the resonators is independent on the coupling-related loss. The rate of the coupling between a waveguide and a resonator mode matching the rate of the intracavity loss of any nature at the resonance implies the criticality. Critically coupled waveguide and a cavity mode are characterized with 100% energy exchange. Let us explain the criticality using the standard input-output formalism neglecting the attenuation due to resonator imperfections [4]. We consider two input-output configurations shown in Figure 6.1 assuming the complete spatial Ein(t)

E0(t-t0)

T

Eout(t)

E1in(t)

T1 E1out(t) E1 0(t)

E0(t) E2 0(t)

(a)

(b) E2out(t)

T2

E2in(t)

Figure 6.1 (a) A ring resonator with single linear coupler. (b) A ring resonator with two couplers

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matching of the mode and the coupling elements. The input-output relationships [94,95] for configuration in Figure 6.1(a) are pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi (6.1) E0 ðtÞ ¼ i T Ein ðtÞ þ 1  T E0 ðt  t0 Þ; pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi (6.2) Eout ðtÞ ¼ 1  T Ein ðtÞ þ i T E0 ðt  t0 Þ; and input/output relationships for configuration Figure 6.1(b) are pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi E1 0 ðtÞ ¼ i T1 E1 in ðtÞ þ 1  T1 E2 0 ðt  t0 Þ; pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi E1 out ðtÞ ¼ 1  T1 E1 in ðtÞ þ i T1 E2 0 ðt  t0 Þ; pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi E2 0 ðtÞ ¼ i T2 E2 in ðtÞ þ 1  T2 E1 0 ðtÞ; pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi E2 out ðtÞ ¼ 1  T2 E2 in ðtÞ þ i T2 E1 0 ðtÞ:

(6.3) (6.4) (6.5) (6.6)

Here t0 ¼ Ln0 =c is the round trip time, T , T1 , and T2 are the power transmission coefficient of corresponding couplers (usually wavelength-dependent), and Ei 0 (i = 1,2) are the classical amplitudes of the electric fields. The field Ein ðtÞ belongs to a single spatial propagating mode, e.g. a Gaussian beam. The condition of the spatial mode matching is required to ensure energy conservation. For example, from (6.1) and (6.2), we derive jE0 ðtÞj2 þ jEout ðtÞj2 ¼ jEin ðtÞj2 þ jE0 ðt  t0 Þj2 . Since (6.1,6.2) and (6.4–6.6) are linear, they are valid for both classical and quantum cases. To find a solution of Equations (6.1) and (6.2), one can use a lumped approximation for the mode. We assume that (i) the cavity has high-finesse ðT  1Þ; (ii) the intracavity field of the externally pumped mode can be presented e 0 expðiwtÞ, where w is the carrier as a product of slow and fast parts E0 ¼ E e0 frequency of the external nearly resonant pump; and (iii) the slow amplitude E does not change significantly during the round trip time t0 . In p this case, ffiffiffiffiffiffiffiffiffiffiffi ffi e 0 ðtÞ  t0 E e_ 0 ðtÞ, 1  expðiwt0 Þ ’ iðw0  wÞt0 , and e 0 ðt  t0 Þ ’ E 1T ’ E 1  T=2, so that (6.1) and (6.2) can be rewritten as pffiffiffiffi   T T _ e e E0 þ þ iðw0  wÞ E 0 ¼ i Ein eiwt ; (6.7) 2t0 t0 pffiffiffiffi e 0: Eout ¼ Ein þ i T E (6.8) To rewrite the set of equations in a more conventional form, we substitute T=ð2t0 Þ ¼ g0c , where g0c is the half width at the half maximum (HWHM) of the mode determined by the coupling efficiency. Field amplitude Ein belongs to the field propagating in the vacuum and mode matched with the corresponding resonator mode. Expectation value for the field is rffiffiffiffiffiffiffiffiffiffiffiffi 2pPin ijin e ; (6.9) Ein ¼ cn0 A where Pin is the power of the external pump, fin is the phase of the external pump, and A is the effective cross-section area of the pumped mode.

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We present the complex amplitude of the electric field of the running wave as a e 0 ðtÞ, where the dimensionless spatial product of spatial and temporal parts, EðrÞE distribution EðrÞ is normalized to unity max jEðrÞj ¼ 1, and define the mode volume as ð f (6.10) V ¼ jEðrÞj2 dV : V

b ð0Þi ¼ Vn0 I=c (I ¼ cn0 jE e 0 j2 =2p here is the maximal intensity of Since ℏw0 hN the electromagnetic wave within the mode), we can write b ð0Þi ¼ ℏw0 hN

V e 2 n20 f jE 0 j : 2p

Therefore, the amplitude of the electric field inside the resonator is sffiffiffiffiffiffiffiffiffiffiffiffiffiffi e 0 ¼ 2pℏw0 A; E V n20 f

(6.11)

(6.12)

b ð0Þi. where A is the slow amplitude of the field normalized such that jAj2 ¼ hN With these substitutions, we obtain the equation for the normalized field in the mode A_ þ ½g0c þ iðw0  wÞA ¼ F0 ;

(6.13)

Eout 2g ¼ 1 þ i 0c A: Ein F0

(6.14)

where rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2g0c Pin ifin e : F0 ¼ i ℏw0

(6.15)

Equation (6.14) is an ordinary differential equation that can be used for the description of the coupling process with the mode of a resonator. The initial sets (6.1,6.2) and (6.4–6.6) can also be analyzed in terms of spectral amplitudes. It is a convenient approach to find the linear transfer function of the cavity. Let us do it for a cavity that attenuates some light. We rewrite (6.1) in steady state as pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi (6.16) E0 ¼ E0 eiwt0 ea 1  T þ i T Ein ; where a  1 is the (frequency independent) total amplitude absorption of the light in the resonator per round trip. The amplitude of the output pump light Eout can be found from equation pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi (6.17) Eout ¼ iE0 eiwt0 ea T þ Ein 1  T ;

Integration of optical microcavities and it is equal to pffiffiffiffiffiffiffiffiffiffiffiffi 1  T  exp½iwt0 exp½a Eout pffiffiffiffiffiffiffiffiffiffiffiffi : ¼ Ein 1  exp½iwt0 exp½a 1  T

167

(6.18)

We introduce notations g¼

a T ; g ¼ ; wt0 ¼ ðw  w0 Þt0 þ 2pl; 2pl ¼ w0 t0 ; t0 0c 2t0

where w0 is the mode frequency and l is the mode number. In the vicinity of the resonance, we have Eout g  g  iðw0  wÞ : ¼  0c g0c þ g þ iðw0  wÞ Ein

(6.19)

Equation (6.19) shows that all the power is absorbed in the resonator ðAout ¼ 0Þ if g0c ¼ g and w ¼ w0 . This is the condition of the criticality of coupling. In the case of a ring resonator with two couplers (“add-drop” configuration, Figure 6.1(b)), the criticality condition looses its meaning for the transmitted light. It still holds for the reflected light. The critical coupling in the case of the two couplers would mean no reflection and 100% transmission. It is valid only in the case of coupling to a single spatial mode. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi E0 ¼ E0 eiwt0 ea 1  Tc1 1  Tc2 þ i Tc1 Ein ; (6.20) where Tc1  1 and Tc2  1 are the coupling factors for the two couplers. Output fields are described by equations pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi Eout1 ¼ iE0 eiwt0 ea Tc1 þ Ein 1  Tc1 ; (6.21) p ffiffiffiffiffiffi ffi (6.22) Eout2 ¼ iE0 eiwt0 =2 ea=2 Tc2 ; Equation (6.22) depends on the position of the second coupler and the resultant phase of Eout2 can change. The solutions can be approximated by expressions Eout1 g  gc2  g  iðw0  wÞ ; ¼  c1 gc1 þ gc2 þ g þ iðw0  wÞ Ein pffiffiffiffiffiffiffiffiffiffiffiffi 2 gc1 gc2 Eout2 ; ¼ Ein gc1 þ gc2 þ g þ iðw0  wÞ

(6.23) (6.24)

in the vicinity of the resonance. We have taken into account that eiwt0 =2  1 in this case. It is easy to see that the transmission through the resonator is nearly lossless if gc1 ¼ gc2  g. In this case, the reflection goes to zero.

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Using this approach, we can introduce the quality factor for a resonator with a single coupler as Q¼

w0 : 2ðg0c þ gÞ

(6.25)

In general, the quality factor can be defined as Q ¼ w0 =2g0 , where 2g0 ¼ ðdE=dtÞ=E is the energy ring down factor and E is the energy of the light stored in the resonator. Finesse of the resonator can be introduced as F ¼ wFSR =2g0 , where wFSR ¼ 2p=t0 is the free spectral range of the resonator. For a resonator with a single coupler, the finesse is F ¼ 2p=T.

6.2.2 Prism couplers Prism couplers are versatile and are suitable for coupling light to any open dielectric resonator independently on its refractive index. The refractive index of the prism should exceed the effective refractive index of the resonator mode. The flexibility of the method is relaying upon the possibility of selection of the coupling prism material and shape. PIC prism couplers were developed recently [74]. Evanescent field prism couplers were developed to introduce light into optical waveguides [96–99]. Prism-waveguide coupling efficiency exceeding 90% has been demonstrated [100,101]. Prism coupling to microspheres was investigated both theoretically and experimentally in [88,90,91,94,102,103]. The best reported efficiency of prism coupling to microsphere modes is ~80% [94]. A coupling efficiency exceeding 97% was achieved in elliptical lithium niobate resonators [104]. The prism-assisted coupling efficiency of 99% with a spheroidal resonator was reported [105]. Even better coupling efficiency was demonstrated with 1.8-mm lithium niobate resonator interrogated using a diamond coupling prism [106]. The technique of prism coupling is based on three principles. First, the input beam has to be focused inside the prism at an angle that provides phase matching between the evanescent wave of the total internal reflection spot and the resonator mode, respectively. Second, the beam shape is optimized to achieve the spatial modal overlap in the near field. And third, the air gap between the resonator and the prism surfaces is optimized to achieve critical coupling. The loaded quality factor for the prism coupler in the case of the fundamental mode sequence of a microsphere is given by the expression [91]  qffiffiffiffiffiffiffiffiffiffiffiffiffi  pðn2r  1Þl3=2 d qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp p n2r  1 ; (6.26) Qc ¼ l 2 2 2nr np  nr where nr is the refractive index of the resonator, np is the refractive index of the prism, d is the shortest distance from the prism to the resonator, l is the wavelength of the light in the vacuum, and l is the azimuthal number of the mode. While np > nr is expected, it is worth noting that the refractive index of the light confined in the resonator can be smaller than the refractive index of the resonator host

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material. It means that the prism coupler made of the same material as the resonator allows coupling to the modes. The validity of (6.26) was studied for spheroidal resonators [107]. It was confirmed that the equation is still valid but may need a small correction factor for better accuracy (see (6.27) and (6.28), the correction is given by the numerical factor 3.6). For a birefringent resonator, it is reasonable to introduce ordinary, no , and extraordinary, ne , refractive indexes, instead of nr . The corrected analytical formulas for the loaded Q-factors become 3=2

QTM c ¼

3:6pðn2o  1ÞlTM qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; 2no n2p  n2o

QTE c ¼

3:6plTE qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2ne ðn2e  1Þ n2p  n2e

3=2

(6.27)

(6.28)

here lTM and lTE are corresponding azimuthal numbers of the modes. Please note ! ! that the TE modes of a microsphere have ðE?Z Þ and correspond to TM modes in the planar waveguide description that we adopted here. The schematic diagram explaining geometrical mode matching for a prism coupler is shown in Figure 6.2. The collimated light is focused on the surface of the prism. The prism is located in the close proximity of the open dielectric resonator, and the collimated beam is focused on the contact spot between the resonator and the prism. The refractive index of the prism np is larger than the refractive index of the resonator mode nr . The wave vector of the light inside the resonator is kr  nr w=c, where c is the speed of light in vacuum. The evanescent field outside of the resonator has the same longitudinal wave vector. The evanescent field is propagating along the prism surface with the wave vector kz ¼ np w sin f=c, where f is the angle of incidence. The optical spatial modes are phase matched when kr ¼ kz sin f ’ nr =np :

(6.29)

The aperture matching is the second important factor for achieving an efficient coupling. If the apertures are not matched, the light will not enter the resonator. The aperture of a WGM of a generic spheroidal open resonator on a flat prism surface is an ellipse with axes ratio ðr=RÞ1=2 where r is the vertical radius of curvature of the resonator in the vicinity of the contact spot, and R is the horizontal radius of curvature of the resonator next to the contact spot. Aperture matching with a Gaussian beam occurs when rffiffiffi r ; (6.30) cos f ’ R Equations (6.29) and (6.30) are incompatible for the case of a microsphere and a prism with flat faces. The best achieved coupling with a microsphere and an

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Body of the toroid

WGM resonator

2(rl/nr)1/2

l/2nr

2(Rl/nr)1/2 (b)

Plane surface of a coupler

Contact spot

Evanescent field Gaussian beam Body of the coupler

(a)

The size of the contact spot is 2(Rl/nr)1/2

(c)

cos f = (r/R)1/2

Figure 6.2 Explanation of the mode matching between a resonator and a prism coupler. (a) Side view of the resonator and the coupler. (b) Contact spot between the resonator and the coupler is given by the resonator shape. (c) Visualization of the requirement for the incidence angle of the Gaussian beam to achieve the mode matching axio-symmetric Gaussian beam is approximately 80% [94]. This problem can be solved [105] if the resonator has a spheroidal shape such that "  2 # nr r ¼R 1 : (6.31) np Alternatively, a mode with optimal effective refractive index rffiffiffiffiffiffiffiffiffiffiffiffi r nr ¼ np 1  R

(6.32)

can be used. Another possibility is to optimize the spatial mode of the coupling beam with astigmatic optics. An axio-symmetric Gaussian beam can be transformed to an elliptical beam that has perfect overlap with the modes of an arbitrary dielectric microresonator. Intermodal mixing is the third factor limiting the coupling efficiency. This is a generic problem arising, for instance, for waveguide integrated cavities [55,71]. It exists for mode-matched and phase-matched couplers. Modes in multimode resonators overlap and interact with each other. The mode of interest emits into other modes limiting the maximum achievable optical coupling (in the sense of the critical coupling) [108]. To suppress this effect, the number of modes should be reduced by, e.g., shaping of the resonator [169,110,111]. The coupling element should be optimized as well. The coupling element, for instance, is able to induce the mode interaction since it breaks the symmetry of the system. Thin single-mode fiber tapers belong to the least invasive resonator probes, in this sense. To illustrate the impact of the prism coupler on the resonator spectrum, one can measure the shift of the optical spectrum associated with the loading. This type of experiment was performed, and frequency shift comparable with the resonator

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Normalized transmission, dB

0

(a)

–10 –20 –30 –40

–40

–20

0

20

40

Normalized transmission

1.0 0.8 0.6 0.4 0.2 0.0 –1.0 (b)

–0.5 0.0 0.5 Frequency, (MHz)

1.0

Figure 6.3 (a) Demonstration of the tuning of the resonator bandwidth from 100 MHz to 55 kHz. The plot is normalized so that the transmission of the overloaded resonator is considered as unity. The relative transmission of the underloaded resonator drops by 10 dB at 55 kHz. Dispersion-like narrow resonances in the loaded filter arise due to interaction of the pump light with high-Q modes via the loaded mode. These resonances can be removed if the Q-factor of the high-order optical modes is reduced. The resonator was configured so that higher-order modes had negligible effect. (b) Frequency shift of the resonance due to evanescent field coupling. Reprinted, with permission, from [112] bandwidth was measured [112]. Two prism couplers were utilized to obtain a transmission filter function using the resonator. While the loading was increased, the frequency of the mode under study was shifting (Figure 6.3). A special experimental technique was developed to measure the relative frequency shift and separate it from the frequency drift and the other technical effects observed in the system. There exists a common mistake made in the measurement of the coupling efficiency with a prism coupler. A major disadvantage of the coupler is that it supports multiple spatial modes. A perfect contrast for the absorption resonance can be measured even though the coupling is far from being critical. To do it, one can use a small aperture collimator. Changing the position of the collimator that does not collect all the radiation exiting the resonator, it is possible to tune the system to a dark interference fringe created by the light that coupled to the resonator and light that reflected from (or interacting with different modes of) the resonator surface. Checking the output beam profile and ensuring that it is a Gaussian one helps avoiding this mistake.

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6.2.3 Angle-cut fiber couplers In some laboratory experiments, it is desirable both to pump the resonator using a single-mode fiber and to collect the light exiting the resonator to a single-mode fiber. The beam profile of light exiting the coupling prism (and required for a perfect mode matching) is elliptical for the majority of the resonator shapes. It makes it harder to collect the light into a fiber using spherical optics. Direct coupling techniques to the fiber were therefore studied. Initially developed sidepolished fiber couplers [109,113,114] had limited efficiency owing to the residual phase mismatch between the guided wave and the mode. A phase-matched coupling technique was proposed using an angle-polished fiber tip in which the coreguided wave undergoes total internal reflection [114]. Coupling the dielectric microspheres and semiconductor lasers was also studied by means of a similar technique [116,117]. To achieve the coupling, the tip of a single-mode fiber is angle polished. The angle is chosen to fulfill the phase-matching requirement given by (6.29). The light propagating inside the core undergoes total internal reflection at the polished surface and escapes the fiber. The system is equivalent to a prism coupler with the collimating input optics eliminated. The output light is not confined. It is possible to use two angle-polished couplers to realize the input and output coupling. The applicability of this technique is limited by the availability of fibers with high refractive index. The method is not widely used nowadays since the tapered fibers are more versatile for the coupling of a resonator mode and a single-mode fiber. The tapers confine both the input and output light.

6.2.4 Tapered fiber couplers Various fiber optics directional couplers are based on the single-mode fiber tapers [118–120]. A fiber taper is a single-mode bare waveguide of optimized diameter (typically, a few microns for the near-infrared wavelength). A taper is made by stretching a heated fiber to form a filament at least one end of which is optically connected to the fiber. The taper transition transforms the fiber core mode in the untapered fiber section to a cladding mode in the taper waist. The effective phase velocity of light changes in the taper transition section, allowing efficient phase matching with optical waveguides and open microresonators. The coupling is achieved through the evanescent field. Tapered fiber couplers provide the most efficient coupling for open microcavities [49,50,121–127]. The couplers are also used with photonic crystals [128–132] and other micro as well as nano optical fiber structures requiring evanescent field interrogation [133–139]. Unlike prism couplers, the tapers do not introduce parasitic reflections and have limited effect on the cavity modes. The taper is placed within the proximity of the mode localization, allowing simple focusing and alignment of the input beam as well as collecting the output beam. It saves the fundamental mode and filters other waveguide modes. The efficiency of tapered fiber couplers reaches 99.99% for coupling fused silica resonators [124].

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The fiber taper coupling is possible with arbitrary small resonators where the coupling region is comparable with the wavelength [140]. This technique is not optimal with larger resonators since the interaction region is small if compared with the resonator dimensions. As the result the coupling is not selective with respect to the resonator spectrum. To achieve the long enough phase matched interaction region, the phase velocity of the light in the mode and in the taper should coincide. The phase velocity depends on the taper’s diameter and the refractive index. The diameter of the taper gradually decreases towards the tip, and so does the effective refractive index. It is possible to achieve the ultimate phase matching and critical coupling by placing the resonator at a proper point of the adiabatic taper. As the result of the above condition, the fiber tapers are useful for bigger resonators with refractive indexes similar to silica (1.4–1.45), and generally cannot be utilized with higher index glass and crystalline resonators. The effective refractive index of the taper can be changed only between values of refractive index of the air/vacuum and the refractive index of the material the fiber is made of. It is not trivial to make a phase-matched taper when the resonator is made of lithium niobate or diamond, for instance, though the planarized silicon waveguide would likely do the trick.

6.2.5 Planar coupling The planar coupling is the most promising one for the practical packaging of systems containing optical microresonators. Planar waveguides are historically used to couple to microring and microdisk resonators fabricated on the same platform [45,141–147]. Planar coupling to ultra-high-Q microresonators was studied very recently and will be discussed in more detail in what follows. The technology of integration of bulk resonators on a PIC came to the focus of the engineering development two decades ago. An analytical technique for evaluation of the coupling efficiency between a microdisk optical resonator and a straight waveguide was presented in [121,148]. A similar problem was evaluated numerically [149,150]. A few waveguide couplers for bulk resonators were tested experimentally. For example, strip-line pedestal antiresonant reflecting waveguides have been utilized for interrogating microsphere resonators as well as for constructing microphotonic circuits [151–153]. The particular waveguides have strong dispersion since they rely on the resonant nature of reflections from multiple dielectric layers in the cladding. A gold-clad pedestal planar waveguide structure solves this problem and provides wide band coupling [154]. Usefulness of polymer waveguides for planar integration of ultra-high-Q resonators also was demonstrated [73,155].

6.3 Ultra-high-Q PIC microcavities Initial demonstrations of planar microcavities did not produce ultra-high-Q factors. The Q-factor of a standard planar microresonator does not exceed 105 and Q ¼ 106 is considered as a very high one. The reasons are related to the fabrication specific

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material and surface quality limitations leading to the excessive attenuation and scattering of light confined in the waveguides, as well as extrinsic loss mechanisms, such as coupling loss. Recent efforts resulted in improvement of both the understanding and the technology and, as the result, planar resonators with Q-factor reaching 108 were produced. In what follows, we highlight a few breakthrough developments in this area.

6.3.1 High-Q Si PICs Undercut silicon disc microcavities were among the first studied experimentally. These high-purity crystalline silicon microdisks provided tight optical confinement (low bending loss) and demonstrated the linear attenuation of 0.1 cm1. Resonant mode quality factors as high as 5  106 were measured experimentally and the limiting value for the Q-factor ðQ ’ 8:5  106 Þ associated with bulk material absorption was predicted [156]. The undercut microdisk architecture is not truly integrated. It requires a fiber taper for the coupling [157]. It has problems with attachments of active electronic functionalities as well as electrodes. The narrow fused silica post supporting the undercut Si microdisk results in a large thermal resistance from the active microdisk cavity to the Si substrate. It leads to the low threshold thermal bistability. Planar integrated silicon disks (silicon on insulator platform) [157] demonstrated slightly lower Q-factor approaching 3  106 and allow avoiding all the problems associated with the undercutting. A different geometry of a planar integrated Si microcavity was demonstrated in [158]. A wedge-resonator and a waveguide vertically coupled system were created on a silicon chip. The cavity and the waveguide located in different planes in this case. The shallow-angle wedge was realized due to the geometry. The waveguide remained intact allowing one to engineer desirable loading of the microresonator in spite of the relatively low Q-factor of the structure ðQ  8  104 Þ. The breakthrough in the development was achieved with silicon microrings [51]. Silicon ring resonators with internal quality factors of Q ¼ 2  107 , corresponding to record low 2.7 dB/m bend-limited propagation loss were demonstrated. The improvement was achieved due to the reflowing photoresist and oxidationbased smoothing techniques applied to a ridge waveguide. The ridge waveguide substantially reduces sidewall interaction with the fundamental transverse electrical (TE) and transverse magnetic (TM) modes. It was predicted that the propagation loss limit for silicon has not yet been reached in the improved resonators. Very recent measurements with bulk Si microresonators confirmed this prediction and revealed Q ¼ 1:2  109 [159]. It means that even better Si PICs are feasible.

6.3.2 High-Q SiN PICs Silicon nitride Si3 N4 waveguides combine the large bandgap and wide transparency range with complementary metal–oxide–semiconductor (CMOS) fabrication methods and a large effective nonlinearity [168]. Ultra-high-Q Si3 N4 microring resonators with laterally offset planar waveguide directional couplers were among

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the first planar microrings demonstrated at 1060 ðQ ¼ 1:9  106 Þ, 1310 ðQ ¼ 2:8  106 Þ, and 1550 nm ðQ ¼ 7  106 Þ [52]. The record-high integrated waveguide coupled intrinsic quality factor Q ¼ 8  107 at a 9.65-mm bend radius was realized in the improved configuration (Figure 6.4) [55]. This is a very large number for a PIC device that can lead to a significant broadening of PIC applications to low-noise RF photonic oscillators and narrow-line lasers. It was mentioned in the paper that planar Si3 N4 microring resonators with intrinsic Q e 8  108 can become feasible with further improvements of the technology. To fabricate the high-Q resonator, high-quality Si3 N4 was deposited via lowpressure chemical vapor deposition (LPCVD) on a 15 mm fused silica layer on a Si substrate [55]. A very thin (40 nm) film was chosen to lower the confinement factor and decrease sidewall scattering loss at the expense of a higher-bend radius device. Contact lithography defined the microcavity shape and directional couplers. The bus waveguide-to-ring gap was generally >1 mm wide due to the low waveguide confinement and low coupling needed for achievement of the high-quality factor. The shape of the waveguides had to be optimized to realize the high-Q (Figure 6.5). It was shown that the straight waveguide is not always optimal for the coupling with the microring. Finally, the samples were thoroughly annealed before testing, to reduce the roughness of the waveguides. The very-high-Q resonators [55] required relatively large bending radius to support the high-Q factor because of their small optical thickness. Silicon nitride microresonators integrated into the silicon-on-insulator (SOI) platform by depositing Si3 N4 on top of SOI wafers allowed achieving intrinsic-Q factors of 2  107 for much smaller (240 mm) bending radius [53]. Further need for the group velocity dispersion engineering in the resonators called for planar integration of the relatively thick Si3 N4 waveguides. The Si3 N4 material group velocity dispersion (GVD) is normal at around 1500 nm. A highconfinement Si3 N4 waveguide with a height in excess of 700 nm allows achieving

Drop

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Figure 6.4 Infrared camera image of an ultra-high-Q Si3N4 microring resonator with two couplers. The resonator is optically pumped in a resonance near 1550 nm

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Figure 6.5 Ultra-high-Q Si3N4 microring resonator spectra for three different directional coupler designs: (a) 5-mm straight bus waveguide, (b) 3.8mm straight bus waveguide, and (c) 3.8-mm weakly tapered gap waveguide. Reprinted, with permission, from [55] anomalous GVD due to the geometrical contribution [56]. Thick waveguides are impacted by the stress accumulated in the material. The high film stress of Si3 N4 prevents thick (>400 nm) films from being deposited without cracks. This problem was analyzed and a solution was proposed, leading to demonstration of microcavities made of waveguides with cross section of 910 nm tall by 1800 nm wide and having Q ¼ 7  106 at 1550 nm [54]. Microresonators with 1.35 mm thick Si3 N4 waveguides and optical Q-factors of 3.7  106 were fabricated using photonic Damascene process, where due to a stress-control technique based on dense substrate pre-patterning the large waveguide thickness was achieved [56]. Q-factor values reaching 2  107 were reached by further combining the photonic Damascene process with the reflow technique [59]. In yet another development, thick waveguidebased “finger-shaped” Si3 N4 microresonators with intrinsic Qs up to 1:7  107 and a free spectrum range of 24.7 GHz were demonstrated [57]. The PIC Si3 N4 resonators with optimized GVD and high-quality factors became ideal for generation of optical frequency combs [58,60–62] and low-noise RF signals [63].

6.3.3 High-Q fused silica PICs Fused silica microresonators were the first ones allowing quality factors exceeding a billion [42]. The SiO2 resonators were also the first microcavities with Q > 108 demonstrated on a chip [37]. The silica toroid-shaped microresonators were created using a combination of lithography, dry etching, and a selective reflow process. The resonators were undercut and needed a fiber taper coupler. Silica microtoroid resonators with monolithically integrated waveguides were demonstrated but the Q-factor was not as high ðQ 4  106 Þ [161].

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A monolithically integrated SiO2 optical microcavity having a record high-Q factor ðQ > 2:3  108 Þ was demonstrated very recently [64] (Figure 6.6). The materials, process steps, and the use of an in-plane silicon nitride waveguide to send light in and out of the resonator enable full integration of these ultra-high-Q resonators with other photonic devices in a PIC. The silicon nitride waveguide had a thickness of approximately 250 nm. It is initially 3 to 3.5 mm in width at the edge of the wafer and is tapered to about 900 nm near the resonator to achieve phase matching with the resonator optical mode. The microresonator supports the design controls required to realize many device functions previously possible using only bulk microcavities. Efficient generation of the mode locked Kerr frequency comb was achieved in the microcavity.

6.3.4 High-Q lithium niobate PICs Transparent crystals with quadratic nonlinearity, such as lithium niobate and tantalate, are widely used in physics. List of their applications include optical frequency conversion, electro-optical modulation, opto-mechanics, and optical frequency comb generation. Bulk WGM resonators made out of these materials revealed optical quality factors exceeding 109 [163,170]. Prism couplers were utilized to integrate this type of resonators. On-chip undercut microdisks with Q ¼ 1:5  107 observed at around 770 nm were recently created [69]. A fiber taper was utilized to couple light to the resonators. Planar integration of lithium niobate and lithium tantalate waveguides and resonators became possible because of the development of the thin-film LiNbO3on-insulator technology [65]. Hybrid and monolithic integration methods were involved. The hybrid approach utilizes silicon or silicon-nitride PIC structures integrated with thin-film LiNbO3. Only a portion of light is confined in the LiNbO3 film in this case, and the propagation loss is related to both the silicon nitride and LiNbO3. The nonlinearity of LiNbO3 cannot be used to its full capacity in the hybrid integrated structures. The relatively low waveguide loss of 0.3 dB/cm was demonstrated [66,164].

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Silicon Silica resonator

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Figure 6.6 A design of the integrated ultra-high Q SiO2 optical microcavity. Reprinted, with permission, from [64]

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The directly etched LiNbO3 photonic microstructures had relatively high propagation loss till recently, when LiNbO3 micro-waveguides were fabricated. The integrated waveguide propagation loss as low as 2.7 dB/m was achieved through an optimized standard etching process. A nearly critically coupled ultra-high-Q-factor microcavities with loaded Q of 5  106 and intrinsic Q of 107 were demonstrated experimentally (Figures 6.7 and 6.8) [67]. The technology was utilized to create integrated modulators [68] as well as broadband frequency combs [70]. The record Q LiNbO3 microcavities were fabricated using 600-nm thick X-cut LiNbO3 thin films placed on 2 mm of fused silica on silicon substrates [67]. Electron beam lithography was utilized to define patterns in hydrogen silsesquioxane (HSQ) resist with multipass exposure. The patterns were subsequently transferred into the LiNbO3 thin film using a commercial inductively coupled

Figure 6.7 Ultra-high Q-factor LiNbO3 microcavity with a coupling waveguide produced with a direct LiNbO3 thin film etching. Reprinted, with permission, from [67]

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Figure 6.8 Transmission spectra of the planar LiNbO3 microcavity. Reprinted, with permission, from [67]

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plasma reactive ion etching (ICP RIE) tool. Ar plasma was used to etch LiNbO3. The chamber conditions as well as plasma power were tuned to minimize surface re-deposition of removed LiNbO3 and other contaminations present in the chamber.

6.4 Integration of bulk microcavities for PIC applications As one can see from the discussion above, the microcavities integrated in PICs can reach quality factors on the order of 107 108 . Bulk cavities allow achieving much high-quality factors. Single-crystal optical WGM resonators with Q ’ 3  1011 were demonstrated [44]. There is a steady interest in the planar integration of these ultra-high-Q cavities on a PIC without a significant degradation of their quality factors. In this section, we overview results of several recent attempts resulted in demonstration of feasibility of the planar integration of the bulk resonators while achieving quality factors on the order of a billion. Integration of crystalline microcavities with planar waveguides is problematic when their refractive index is smaller then the refractive index of the substrate supporting the waveguide. In this case, the modes of the open resonator can irradiate into the substrate (Figure 6.9). As the result, the integral quality factor of the modes as well as the efficiency of the waveguide coupler degrade significantly.

(a)

(c)

(e)

(b)

(d)

(f)

Figure 6.9 Spatial profile the field intensity for the fundamental and the first dipole WGMs for different height of the protrusion, x0, confining the modes: (a) x0 ¼ 2 mm, (b) x0 ¼ 8 mm, and (c) x0 ¼ 11 mm. The intensity is illustrated by color density. Light escapes to the higher-index substrate from both fundamental and first-order dipole modes if the height of protrusion is small enough. The field leaving the WGM is transferred to a Bessel beam freely propagating in the substrate. Reprinted, with permission, from [165]

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This property was utilized to reduce the spectral density of high-Q modes in a resonator with optimized shape [165]. The refractive index of the resonator can be considered as a small if nSiO2 > nres , since fused silica is a conventional substrate in planar waveguide systems (e.g., SOI). For instance, ultra-high-Q CaF2 WGM resonator cannot be efficiently integrated with a waveguide etched on a SiO2 platform since nCaF2 ¼ 1:426 and nSiO2 ¼ 1:444 at 1550 nm. The waveguide should protrude from the substrate by a distance comparable with the optical wavelength to achieve the coupling and preserve the Q. This is not a simple task since the waveguide must have a rather small cross section to support only a single mode for an efficient coupling. Such a structure would be extremely fragile. Coupling to a multimode waveguide reduces the coupling efficiency since the bulk resonator interacts with many spatial modes simultaneously. This problem was solved with undercut fiber taper discussed in what follows.

6.4.1 Integration of bulk lithium niobate and tantalate resonators on an SOI platform It is possible to integrate a bulk resonator with a waveguide made of the same material as the resonator. This is similar to the planar integration of the LiNbO3 resonators on LiNbO3 platform, discussed in Section 6.3.4. For instance, coupling of a high-Q LiNbO3 resonator to an integrated LiNbO3 pigtailed planar waveguide was demonstrated, and 33% coupling efficiency was realized with a resonator overloaded to Qe107 . The waveguide was made in X-cut lithium niobate substrate by proton exchange and the maximum Q-factor achieved with the resonator/ waveguide structure was 1:3  108 . The coupling performance was limited due to the resonator and the waveguide refractive index mismatch [166]. Another, similar, attempt for planar coupling of a LiNbO3 WGMR characterized with Q ’ 6  107 resulted in 11% coupling efficiency limited because of the multimode nature of the resonator and the waveguide [167]. Heterogeneous integration of the bulk microresonators on silicon PICs is more attractive as it allows direct coupling of the resonators with other planar components. The planar integration of this kind is the easiest for the resonators made with crystals having comparably high refractive index nr . A nearly critical coupling of a planar Si waveguide and a LiTaO3 resonator with loaded Q ’ 5  107 was recently demonstrated to prove this capability [72]. The silicon waveguides, despite their very small mode profile and dimensions, enable efficient phase matching and a strong interaction to the LiTaO3 microresonators having a much larger mode cross section, typically necessary to suppress any nonidealities due to the thermal or nonlinear effects for the RF photonics applications. Efficient interaction of a nanoscale waveguide and the LiTaO3 resonators with diameters in the millimeter range and thicknesses in 100 mm range was demonstrated [72]. The Si waveguides were fabricated on a SOI platform via electron lithography and plasma etching. Positive electron resist (ZEP 520A) was utilized so the Si

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Figure 6.10 Coupling of a metalized lithium tantalate resonator with a Si waveguide. Reprinted, with permission, from [72] waveguides had etched trenches on their sides. The etched waveguides were coated with a 50-nm atomic layer deposition of SiO2. The coupling was achieved by vertically coupling the resonators to the Si waveguides. Figure 6.10 shows photo images of the WGM resonator held by a metal post. A piezo stage holds the metal post, enabling us to precisely control the air gap between the waveguide and the resonator surface. A nearly intrinsic (unloaded) Q of 1:8  108 is measured in the weak coupling regime. The coupling gets stronger and approaches critical coupling as the gap is reduced. In this case, the loaded Q becomes 4:5  107 and the resonance contrast reaches 90%. This nearcritical coupling occurs with a waveguide-resonator gap of 300–350 nm. This value is in close agreement with numerical simulations. It would be reasonable to expect that the critical coupling with Q-factor of 108 should be reached, since the intrinsic Q-factor is 1:8  108 . The discrepancy is explained by the reduction in the intrinsic Q-factor of the resonator from 1:8  108 to 6:8  107 when the waveguide-resonator gap decreases. This degradation is mainly due to the presence of the silicon slabs that are in close proximity to the Si waveguide and can interact with the resonator mode, especially at smaller gaps. Higher-quality factors are expected when these slabs are removed from the Si waveguide.

6.4.2 Integration of bulk calcium fluoride resonators on a polymer platform A viable approach for planar integration of low refractive index crystalline microresonators is to create a low refractive index waveguide substrate [73]. Polymer waveguide platforms are suitable for this purpose. Some optically transparent polymers, such as cyclic transparent optical polymer (CYTOP), have a refractive index much smaller than that of MgF2 and CaF2 resonator host materials. Integration of high-Q fused silica WGM resonators with polymer waveguides was demonstrated previously, and nearly critical vertical coupling was achieved with these resonators achieving loaded Q ’ 106 [155]. Crystalline WGM resonators

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integrated on the polymer platform allow reaching two orders of magnitude better quality factors. Nearly critical coupling of a CaF2 WGM resonator loaded to Q ¼ 108 by a UV15LV polymer waveguide was demonstrated. The Q value was still limited by the parasitic emission of the light from the resonator to the substrate modes matched with the resonator modes due to finite dimensions of the interaction region. We expect that properly designed polymer waveguides with reduced overlap integral between the mode of the microresonator and the substrate will allow efficient integration of resonators characterized with even higher-quality factors. To perform the experiments, a polymer waveguide [162] matched with a CaF2 microresonator was fabricated and tested [73]. A fiber-pigtailed antireflection (AR)-coated aspheric collimator was combined with a properly selected (AR)coated aspheric focusing lens for the waveguide interrogation. The focusing assembly was mounted on a linear translation stage. The polymer waveguide chip was placed at the very corner of actively controlled top plate of MAX311 stage against the focusing assembly. Visible (650 nm) coherent light was used for the ease of alignment. The light was focused at the proximity of the waveguide entrance. The waveguide became visible when the collimated light entered it and was scattered off the waveguide imperfections. The brightness of the glowing waveguide was maximized by proper positioning of the input focusing assembly at the final stage of the pre-alignment procedure. The visible laser was replaced with a 1550-nm fiber pigtailed New Focus laser at the next step. The light exiting the waveguide was collected into a light pipe (multimode waveguide). The light pipe was equipped with a DC10C photodiode connected to a Tektronix oscilloscope. The laser wavelength sweep and the oscilloscope were synchronized with the help of an adjustable saw-tooth signal generator, so the detected trace represented insertion loss of the polymer waveguide under test, superimposed with response of the focusing optics. Alignment was completed when the photodiode signal was maximized by precise re-positioning of the focusing assembly. A CaF2 resonator with 6.05-mm diameter and 0.4-mm thickness was built from a cylindrical preform firmly attached to a metal post via mechanical grinding. The resonator circumference had a frustrated conical shape with rounded bottom edge characterized with radius of curvature of 200 mm. Because of the conical shape the WGM field was pushed to the bottom of the resonator enabling both vertical and planar coupling. The resonator quality was pretested using a BK7 evanescent field prism coupler [105]. The intrinsic bandwidth of the fundamental mode family did not exceed 26 kHz, which corresponds to Q ¼ 7:4  109 . Then the resonator post was attached to a 3D manipulation stage (Nanomax MAX311) and approached the polymer waveguide coupled to 1550-nm light (Figure 6.11). The coupling was noticed when the distance between the resonator surface and the waveguide was less than >3 mm. The resonator mode spectra were measured by scanning the laser frequency. Nearly critical coupling with a mode characterized with Q ’ 108 was demonstrated. The Q factor was expected to be at least an order of magnitude higher. The reason for the

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Figure 6.11 Coupling of a calcium fluorite resonator with a polymer waveguide. Reprinted, with permission, from [73] Q degradation is the interaction of the WGMs with the waveguide substrate. This is somewhat similar effect to one mentioned in Section 6.4.1.

6.4.3 Integration of bulk magnesium fluoride resonators on a SiN platform The highest Q-factor was achieved with bulk MgF2 resonators heterogeneously integrated on Si3N4 on silica SiO2 platform [74]. Fabrication process of the planar couplers utilizes CMOS-compatible fabrication steps including LPCVD of films (SiO2, Si3N4, and a-Si) on 6-inch diameter silicon wafers and dry-etching processes. The integrated resonator Q-factor approaching 109, while keeping 1-dB waveguide insertion loss, was demonstrated in the system. Figure 6.12 presents a conceptual illustration of the integrated package based on a ultra-high-Q resonator and a PIC containing input/output prism-waveguide couplers. The on-chip waveguide coupler utilized the principle of a bulk prism coupler adapted to the low-loss silicon-nitride on silica waveguide with a negative taper beam expander designed to achieve optimal mode matching and phase matching to the lowest-order mode in the ultra-high-Q MgF2 crystalline microresonator. The angle the light was emitted by the coupler was selected to fulfill the phase matching condition at the chip-air interface in order to evanescently excite the WGM inside the MgF2 resonator. The total internal reflection (TIR) condition was automatically satisfied at this reflection angle. The adiabatic negative taper was designed to match profiles of the lowestorder WGM and the waveguide mode. A 200 mm-long adiabatic negative taper at the tip of prism-waveguide coupler expands the optical mode to nearly 10 mm as the waveguide width reduces from 6 mm to 200 nm. Another negatively tapered waveguide was placed symmetrically across from the first negatively tapered waveguide with an optimized lateral shift to collect the light exiting the mode. The effective index of the optical mode out of the tip of the prism-waveguide coupler is close to that of the SiO2 surrounding cladding (1.444) and the effective index of the WGM inside the resonator is estimated to be 1.37. To avoid emission

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e uid veg Wa

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Figure 6.12 Schematic of the integrated MgF2 resonator. Reprinted, with permission, from [74]

Figure 6.13 A semiconductor DFB laser coupled with the integrated MgF2 resonator. Reprinted, with permission, from [74] of the light from the mode to the cladding impacted previous experiments, the waveguide coupler was undercut. The Si3N4 waveguides achieved coupling in of an emission from a commercial semiconductor distributed feedback (DFB) laser and coupling out of the optical wave circulating in the resonator. The DFB laser achieved self-injection locking to the resonator mode with the loaded Q changing from 1:9  109 (100-kHz bandwidth) to 6:4  107 (3-MHz bandwidth) depending on the coupling strength adjusted by the gap between the resonator and the coupler. A packaged module (Figure 6.13) containing the high-Q resonators, the on-chip prism-waveguide coupler, the DFB laser die, a fiber pigtail, and other microcomponents provided a robust platform which generated stable and low-noise optical frequency comb generated at less than a mW power level. An alternative approach to integrate bulk crystalline resonators on a silicon nitride chip was proposed [75]. Quality factors of 108 were demonstrated in SrF2, BaF2, and CaF2 integrated on the platform. The photonic chip combines the benefits of a tapered optical fiber with the benefit of a planar technology and a planar silicon substrate, while preserving the quality factor of the crystalline resonators.

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The on-chip taper coupler was designed as follows [75]. Once coupled on to the chip, the light is highly confined inside a single-mode Si3N4 waveguide, before transitioning to a SiO2 beam section where light is able to evanescently couple to a bulk microresonator, and then re-entering the Si3N4 waveguide. The Si3N4 adiabatically tapers down at the ends of the SiO2 beam in order to smoothly reduce the effective propagation constant and increase the mode-field area in order to overlap with the modes of the beam, as well as reduce reflection at the interfaces. The SiO2 beam has a larger cross section than the Si3N4 waveguide. As the result, it has the capacity to confine numerous higher-order modes. To maximize conversion to the fundamental mode, the Si3N4 waveguide is centrally located in the transverse plain of the SiO2 beam. The undercutting of the silicon substrate beneath the beam is essential to maintaining the light confinement during propagation. To squeeze the vertical confinement of the mode inside the SiO2, so as to maximize the evanescent area interacting with the resonator, the SiO2 layer thickness must be minimized. Under a certain thickness, however, light propagating inside the Si3N4 waveguide begins to leak into the higher-index Si substrate; thus, a balance must be struck in the chosen SiO2 thickness.

6.5 Conclusion In this chapter, we discussed recent advances in planar integration of monolithic optical microcavities of various kinds. Starting from an overview of the major characteristics of the optical microcavities and their couplers, we presented results of the experiments performed around the globe and validating feasibility of a highquality factor microcavity on a chip. The best resonators fabricated directly on a chip have Q-factors of 100 millions. The bulk resonators integrated on a chip heterogeneously allow an order of magnitude higher Q-factors. These resonators can be utilized in lasers, oscillators, optical, and RF photonic filters and other devices notable not only because of their outstanding performance but also because of their small size and low power consumption.

Acknowledgments The author acknowledges stimulating discussion with Dr. Ali Adibi, Dr. John Bowers, Dr. Marko Loncar, Dr. Tobias Kippenberg, Dr. Daryl Spencer, Dr. Kerry Vahala, Dr. Ben Yoo, and Dr. Mian Zhang. This work was done as a private venture and not in the author’s capacity as an employee of the Jet Propulsion Laboratory, California Institute of Technology.

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antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006). [154] I. M. White, J. D. Suter, H. Oveys, et al., “Universal coupling between metal-clad waveguides and optical ring resonators,” Opt. Express 15, 646– 651 (2007). [155] T. Le, A. A. Savchenkov, H. Tazawa, W. H. Steier, and L. Maleki, “Polymer optical waveguide vertically coupled to high-Q whispering gallery resonators,” IEEE Photon. Technol. Lett. 18, 859–861 (2006). [156] M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: Theory and experiment,” Opt. Express 13, 1515–1530 (2005). [157] M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15, 4694–4704 (2007). [158] F. Ramiro-Manzano, N. Prtljaga, L. Pavesi, G. Pucker, and M. Ghulinyan, “A fully integrated high-Q whispering-gallery wedge resonator,” Opt. Express 20, 22934–22942 (2012). [159] A. E. Shitikov, I. A. Bilenko, N. M. Kondratiev, V. E. Lobanov, A. Markosyan, and M. L. Gorodetsky, “Billion Q-factor in silicon WGM resonators,” Optica 5, 1525–1528 (2018). [160] D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, and J. E. Bowers, “Integrated Si3N4/SiO2 ultra high Q ring resonators,” Proc. IEEE IPC 1, 141–142 (2012). [161] X. Zhang and A. M. Armani, “Silica microtoroid resonator sensor with monolithically integrated waveguides,” Opt. Express 21, 23592–23603 (2013). [162] S. M. Garner, S. S. Lee, V. Chuyanov, et al., “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35, 1146–1155 (1999). [163] D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Optics 18, 123002 (2016). [164] L. Chang, Y. Li, N. Volet, L. Wang, J. Peters, and J. E. Bowers, “Thin film wavelength converters for photonic integrated circuits,” Optica 3, 531–535 (2016). [165] F. Ferdous, A. A. Demchenko, S. P. Vyatchanin, A. B. Matsko, and L. Maleki, “Microcavity morphology optimization,” Phys. Rev. A 90, 033826 (2014). [166] G. Nunzi Conti, S. Berneschi, F. Cosi, et al., “Planar coupling to high-Q lithium niobate disk resonators,” Opt. Express 19, 3651–3656 (2011). [167] I. S. Grudinin, A. Kozhanov, and N. Yu, “Waveguide couplers for ferroelectric optical resonators,” arXiv preprint arXiv:1404.6582 (2014). [168] D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOScompatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).

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[169]

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, et al., “Morphologydependent photonic circuit elements,” Opt. Lett. 31, 1313–1315 (2006). L. Maleki and A. B. Matsko, “Lithium niobate whispering gallery resonators: Applications and fundamental studies,” Chapter 13 in “Ferroelectric Crystals for Photonic Applications: Including Nanoscale Fabrication and Characterization Techniques (Springer Series in Materials Science),” edited by P. Ferraro, S. Grilli, and P. D. Natale, (Springer, 2008).

[170]

Note added to the proofs: A SiN resonator with Q-factor 0.26 billion was demonstrated very recently. W. Jin and Q.-F. Yang, L. Chang, et al., “Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high-Q microresonators,” arXiv: 2009.07390 (2020).

Chapter 7

Electric and magnetic sensors based on whispering gallery mode spherical resonators Tindaro Ioppolo1

The field of integrated optics has been rapidly expanding since its establishment in 1970 due to the availability of high-quality optical materials and the development of optical fibers. Light is guided and confined near the surface of dielectric structures with typical cross-section size of the order of several wavelengths. This chapter describes the development of sensors that are based on the shift of the optical modes of spherical micro cavities. These optical modes are commonly referend as whispering gallery mode (WGM) and are observed when light is confined near the surface of the resonator via total internal reflection. The chapter mainly focuses on electric and magnetic field tuning of polymer spherical resonators; however, these studies show the potentials for a new class of ultrasensitive optical devices. Tethered and untethered configurations of these sensors are also described. In recent years, several applications of the WGM (also referred to as the morphology-dependent resonances or MDR) have been proposed. Some of these include those in, micro-cavity laser technology [1–4], spectroscopy [5–7] and optical communications (switching [8] and filtering [9–11]). Several sensor concepts have also been proposed exploiting the WGM shifts of microspheres for biological applications [12,13], trace gas detection [14], impurity detection in liquids [15] as well as mechanical sensing including force [16,17], pressure [18], temperature [19], wall shear stress [20,21], electric field [22–24], magnetic field [25,26], acceleration [27] and displacement [28].

7.1 Sensor concept A simplified description of the WGM phenomenon can be obtained using geometric optics as shown in Figure 7.1. Light coupled into the microsphere, for example using a tapered section of an optical fiber, circumnavigates the interior surface of the sphere through total internal reflection as long as the index of 1 College of Engineering and Computing Sciences New York Institute of Technology, Old Westbury, New York, USA

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Micro-resonator

Figure 7.1 Ray optics description of the WGM in a circular path refraction of the optical resonator is greater than the index of refraction of the surrounding medium. An optical resonance is excited when the optical path length of the light travelling along the sphere surface is a multiple integer of the wavelength of the light, that is 2pRn ¼ ll, where R is the radius of the resonator, l is an integer, l is the wavelength and n is the index of refraction of the resonator. The above relationship is valid as long as the radius of the resonator is greater than the wavelength of the light and the index of refraction of the surrounding medium is not changing. If the morphology of the resonator such as the size and the index of refraction of the sphere are perturbed, the resonance condition leads to a relationship between the optical mode shift and the changes in the morphology of the resonator as follows: DR Dn Dl þ ¼ R n l

(7.1)

where DR is the strain effect and Dn is the stress effect. The above relationship relates the optical mode shift with the change in the radius and the index of refraction of the resonators. One of the most important parameters that makes this sensor concept unique is the high optical quality factor defined as Q ¼ l=dl (dl is the linewidth of the optical resonance) and related to the measurement resolution of the device. Optical quality factor of the order of 109 was demonstrated using silica spherical resonators [29]. Typical values of the optical quality factor using spherical polymer resonator are of the order of 107.

7.1.1 Tethered sensors In this configuration, the optical modes are excited coupling light from a tuneable laser (with nominal power of a few mW) into the sphere using a tapered section of a single-mode optical fiber [30,31] as shown in Figure 7.2. The optical fiber, which carries light from the tunable laser, serves as an input/output port for the microsphere. When the laser light is introduced into the microsphere through the tapered section of the optical fiber, the sphere’s WGMs are observed

Electric and magnetic sensors based on WGM spherical resonators

Transmission spectrum

micro-resonator

δλ

To photodiode

From laser

199

λ

Tapered fiber

Figure 7.2 A schematic of the WGM sensor and its output

Emission spectrum

From pulsed laser Doped micro-resonator

To spectrometer Emitted light

δλ

λ

Figure 7.3 A schematic of the untethered WGM sensor and its output as sharp dips in the transmission spectrum at the end of the fiber, as illustrated in Figure 7.2.

7.1.2 Untethered sensors In this configuration, the optical modes are excited remotely without the need of an optical fiber as input-output port. The polymer spherical resonator is usually doped with a dye and it is excited remotely using a pulsed laser, as shown in Figure 7.3. The light emitted from the dye couples with the WGMs of the resonator. If the emitted light is introduced into the entrance slit of a spectrometer, sharp peaks are observed in the emitted light, as shown in Figure 7.3. The fact that the optical modes are excited and monitored remotely allows for remote sensing. This design is useful were optical fibers could interfere with the dynamics of the system under investigation. Experiments have been carried out as a proof of concept for temperature [32] and wall pressure measurements [33] using dome-shaped optical resonators. The above concept could be applied to other sensors, e.g. of electric and magnetic fields.

7.2

Stress and strain tuning of an optical spherical resonator

When an elastic spherical resonator is subjected to external forces (surface forces and body forces), it experiences an elastic deformation leading to a shift of its

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Optical fiber

WGM

R r

φ

Figure 7.4 A spherical coordinate system of a coupled WGM sensor optical resonances. Here we report the stress effect and strain effect that are caused by external forces acting on a linear elastic spherical resonator [16,17]. The elastic deformation of a linear elastic solid is governed by the Navier equation as follows: !

! 1 F rr  u þ ¼ 0 r uþ 1  2n G

2

!

(7.2)

!

where u is the vector displacement of a point within the sphere, n is the Poisson ! ratio, G is the shear modulus and F is the body force. A solution of the above equation can be written as superposition of the homogenous (no body forces) and the particular solutions (including the body forces). The homogeneous solution can be written in spherical coordinate systems (see Figure 7.4) as [34,35]: ur ¼ uJ ¼

X

 An ðn þ 1Þðn  2 þ 4nÞrnþ1 þ Bn nrn1 Pn ðcos JÞ

(7.3)

X  dPn ðcos JÞ An ðn þ 1Þðn þ 5  4nÞrnþ1 þ Bn nrn1 dJ

where ur and uJ are the radial and the polar components of the vector displacement. Pn s represent the Legendre polynomials, and An and Bn are constants that are determined by imposing the boundary condition.

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The normal and shear components of the stresses can be found using the stressdisplacement equation and can be expressed as [34,35]: X    An ðn þ 1Þ n2  n  2  2n rn þ Bn nðn  1Þrn2 Pn ðcos JÞ sr;r ¼ 2G P 2 n2 ½An ðn þ 1Þðn2 þ 4n þ 2 þ 2nÞrn þ B Pn ðcos JÞþ sJ;J ¼ 2G nn r dP ð cos J Þ n ½An ðn þ 5  4nÞrn þ Bn rn2 cotðJÞ dJ (7.4) P n n2 sj;j ¼ 2G ½An ðn þ 1Þðn  2  2n  4nnÞr þ Bn nr  Pn ðcos JÞþ dP ð cos J Þ n ½An ðn þ 5  4nÞrn þ Bn rn2 cotðJÞ dJ X   dPn ðcos JÞ  sr;J ¼ 2G An n2 þ 2n  1 þ 2n rn þ Bn ðn  1Þrn2 dJ The particular solution to the Navier equation can be derived in a general analytical form if the body forces acting on the sphere can be represented as a conservative field. In this case, the body force can be related to a potential function Y as F ¼ rY. Thus, a particular solution to the Navier equation can be written as [34,35]: u p ¼ rj

(7.5)

where the function j is a solution of the following Poisson equation r2 j ¼

1  2n Y 2ð1  nÞG

(7.6)

If, further the function Y can be expressed as a combination of harmonic functions Y ¼ Vn Rn Pn ðCosJÞ, then the radial and polar components of the displacement are given as follows: ur ¼

ð1  2nÞðn þ 2Þ Vn Rnþ1 Pn ðcos JÞ 4ð1  nÞð2n þ 3ÞG

(7.7)

The components of the stress are, respectively: sRR ¼

srJ ¼

Vn ½ð4n þ 6Þn þ ðn þ 2Þðn þ 1Þð1  2nÞRn Pn ðcos JÞ 2ð1  nÞð2n þ 3Þ (7.8) ð1 þ 2nÞðn þ 1Þ dPn ðcos JÞ Vn Rn 2ð1  nÞð2n þ 3Þ dJ

The above solution (particular solution) and the homogeneous solution are combined together to satisfy the boundary conditions for a given external problem.

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The strain effect on the optical mode shift that is induced by an elastic perturbation of the resonator morphology (no body force) can be written as: DR ur ¼ ðr ! R; J ! p=2Þ R R P ½An ðn þ 1Þðn  2 þ 4nÞRnþ1 þ Bn nRn1 Pn ð0Þ ¼ R

(7.9)

The stress effect on the optical mode shift can be calculated using the Neumann-Maxwell equation since it provides a relationship between the principal component of the stress and the refractive index as follows:   nr ¼ n0r þ C1 srr þ C2 sJJ þ sjj   nJ ¼ n0J þ C1 sJJ þ C2 srr þ sjj (7.10) nj ¼ n0j þ C1 sjj þ C2 ðsJJ þ srr Þ Here nr , nJ and nj are the refractive indices in the direction of the three principal stresses and n0r , n0J and n0j are the refractive indices for the unstressed material. The coefficients C1 and C2 are the elasto-optical constants of the dielectric material. The materials investigated in these studies are polydimethylsiloxane (PDMS) and poly(methyl methacrylate) (PMMA), and for both materials C1¼C2. In addition, if the shear stress acting on the sphere surface is zero, the strain effect can be simplified as follows:   Dn nr  n0r nJ  n0J nj  n0j C srr þ sJJ þ sjj ¼ (7.11) ¼ ¼ ¼ n n n0r n0J n0j Therefore, the optical mode shift due to an elastic deformation of the sphere can be written by combining (7.9) and (7.11) as follows: P ½An ðn þ 1Þðn  2 þ 4nÞRnþ1 þ Bn nRn1 Pn ð0Þ Dl ¼ R l   C srr þ sJJ þ sjj þ (7.12) n The stress effect, however, is negligible compared to the strain effect as reported in [16]. Therefore, for the application presented in this chapter, it will not further discussed.

7.3 Electric field induced WGMs In these studies, a dielectric sphere of radius R and dielectric permeability e1 are considered [22–24]. The sphere is surrounded by a fluid of dielectric permeability e2 immersed in a uniform electric field with strength E0 , as shown in Figure 7.5.

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E0

Optical fiber

R

WGM r ϑ

φ ε1

ε2

Figure 7.5 A coupled WGM sensor in an electric field The external electric field induces forces on the dielectric material that can be divided into a body force and a surface force. The body force arises due to the nonuniformity of the dielectric permeability of the material and due to the non-uniform distribution of the electric field. The relationship between the body force and the properties of the medium can be written as follows: 1 1 f ¼  E2 r  ða1 þ a2 ÞrE2 2 4

(7.13)

where a1 and a2 are functions of the properties of the material. The parameter a1 expresses a change in the inductive capacity for a strain that is parallel to the electric field, while a2 expresses a change in the inductive capacity for a strain that is normal to the electric field. The surface forces arise from discontinuities in the dielectric permeability and can be written as: h h i i a2  a1  a2  a1  Fs ¼ e þ E E n þ eþ E E n 2 2 2 1 h e þ a i he þ a i 2 2 E2 n  E2 n  (7.14) 2 2 2 1 Since, in these studies, the dielectric permeability of the sphere is uniform and also the distribution of the electric field within the sphere is uniform, the body force term acting on the sphere is zero. On the other hand, at the interface between the

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sphere and the surrounding medium, there are surface forces acting on the sphere. The surface force is obtained from (7.14) and reduces to the following expression: (  )   9 ðb1  b2 Þe22 þ ða2  b2 Þe21 þ ðb2  a1 Þe22 cos2 ðJÞ Pr1 ¼ E02 (7.15) ðe1  22 Þ2 with

a2 ¼ e2 and h a1 ¼ e1 þ ða2  a1 Þ=2, i b1 ¼ ðe1 þ a2 Þ=2, 2 b2 ¼ e0 2ðe2 =e0 Þ  2ðe2 =e0 Þ  2 =6. Note that the last two expressions for a and b are derived using the Clausius-Mossotti relationship. The stress and strain distributions within the sphere are given by (7.3) and (7.4), respectively, where the coefficients of the series expansion are determined by satisfying the boundary conditions at the sphere surface, that are: sr;r ðRÞ ¼ Pr1 ;sr;J ðRÞ ¼ 0

(7.16)

The relative change in the optical path length of the microsphere at J¼p/2 can be written as: "  #

2 ( DR 3e2 ð1  2nÞ e1 2 ðJ ¼ p=2Þ ¼ E0 ða2  b2 Þ  a1 þ 3b1  2b2 R 6Gð5n þ 7Þ e2 e1 þ 2e2 "  #) ð4n  7Þ e1 2  þ ða2  b2 Þ þ a1 ; b2 3Gð5n þ 7Þ e2 (7.17)

Equation (7.17) shows that the strain effect on the optical mode shift is a quadratic function of the strength of the applied external electric field and a function of the electric and elastic properties of the microsphere’s material. Again, as reported in [16], the stress effect is negligible and therefore is not reported here. Experiments were carried out to study the effect of electric field on the optical modes of the spherical resonators. A resonator made of PDMS 60:1 (60 parts of polymer base; 1 part of curing agent) and diameter of 900 mm was placed between two metallic plates that were connected to a DC power supply, as shown in Figure 7.6. The electric field was changed by changing the voltage applied to the electrodes. Figure 7.7 shows the transmission spectrum with zero electric field and with an electric field of 50 KV/m. As shown in Figure 7.7, when the electric field is turned on, the WGM experiences a blue shift indicating that the sphere is elongating along the direction of the electric field. Figure 7.8 shows the shift as a function of the external applied electric field, along with the analytical results for different experiments. Test 1 represents the measurement that was taken by introducing the sphere between the two metallic plates and then turning on the electric field. For this first measurement, there is a good agreement between the measurements and the analytical results. Tests 2, 3 and 4 are measurements that were taken by first exposing the sphere to a fixed external electric field of 200 kV/m for a period of time of 2 min for test 2, 2 h for

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Plates

Microsphere

Power supply

Figure 7.6 An experimental setup for static electric field measurements, using a PDMS microsphere placed between two electrodes 0.59

E0=50 kV/m

Δλ= 1.9 prn

E0=0V/m

Signal (arb. units)

0.57 0.55 0.53 0.51 0.49 1.312495

1.3125

1.312505

1.31251

1.312515

1.31252

λ.μm

Figure 7.7 Transmission spectra trough the sphere-coupled fiber. Reprinted, with permission, from [24] test 3 and 4 h for test 4. The results showed that the optical shift becomes stronger and stronger after exposing the sphere for a long period to a fixed electric field. This effect is mainly due to the alignment of the dipoles in PDMS along the direction of the electric field. Thus, a surface charge is established along the surface of the sphere inducing an increase of the electrostatic pressure acting on the sphere.

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–15

Analysis

–20

test1

–25 test4

–30 –35

test3

–40

test2

–45

test5

–50 0

100

200

300

E,kV/m

Figure 7.8 Experimental results. Reprinted, with permission, from [23] 0 E0=0.75 MV/m E0=1MV/m

(ΔR/R) × 103

–5

–10

–15

–20

0

2

4

6

8

10

12

14

t, hrs

Figure 7.9 The effect of poling duration on sphere deformation; 60:1 PDMS microsphere with a 700-mm diameter. Reprinted, with permission, from [24] Further experiments were carried out to study the time evolution of the WGM shift for a fixed value of the applied external electric field. Figure 7.9 shows the WGM shift over a period of 14 h and for a sphere made of PDMS 60:1. As shown in Figure 7.9, the WGM shift increases with time but reaches an asymptotic value after nearly 6 h. In addition, the WGM shift increases with the strength of the applied external electric field. Figure 7.10 shows the time evolution of the WGM shift for a sphere made of Super Soft Plastic by M-F Manufacturing Company. In this case, the saturation of the WGM shift is achieved

Electric and magnetic sensors based on WGM spherical resonators 0

2

4

6

207

8

0

WGM shift, pm

–2 –4 –6 –8 –10 –12 –14 –16 Time, (s)

Figure 7.10 The effect of poling duration on sphere deformation; Super Soft Plastic by M-F Manufacturing Company microsphere with a 1141mm diameter with 0.11-MV/m poling electric field. Reprinted, with permission, from [28] 5 tp = 5 min

4

(ΔR/R) × 106

3 2

tp = 3 min

1 0 tp = 0 min

–1 –2 –3

0

200

400

600 E0, kV/m

800

1,000

1,200

Figure 7.11 Polarity reversal test for a 10:1 PDMS microsphere at varying poling duration tp. Reprinted, with permission, from [24] after a few seconds. Figure 7.11 shows the effect of switching the direction of the external electric field. In this experiment, the sphere made of PDMS 10:1 was first poled for 2 h and then the electric field was turned off and its direction reversed. A baseline measurement (with no poling) was also carried out for comparison. As shown in Figure 7.11, the WGM shifts reverse their directions, reach a maximum value and then start to decrease. A further analysis was carried out to study this effect by imposing to the previous model a surface charge density distribution s0 , on the surface of the spherical resonator. The addition of uniform surface charge on the spherical resonator led to

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a new expression for the pressure acting on the surface of the sphere as follows: (  )   9 ðb1  b2 Þe22 þ ða2  b2 Þe21 þ ðb2  a1 Þe22 cos2 ðJÞ Pr ¼ E02 ðe1 þ 22 Þ2 ( ) 6½ðb2  b1 Þ2 þ ð2a2 e1 þ a1 2  b2 ð2e1 þ 2 ÞÞcos2 ðJÞ s0 E0 þ ðe1 þ 22 Þ2 ( ) ½b1  b2  ða1  4a2 þ 3b2 Þcos2 ðJÞ 2 s0 þ ðe1 þ 22 Þ2 (7.18) If this pressure term is introduced into the boundary condition, given by (7.16), the corresponding WGM shift can be written as: " #   Dl 18a2 e21 nð2þnÞþ18a1 e22 nð2þnÞ9b1 e22 ð7þ9nþ10n2 Þþb2 2e21 nð2þnÞ þe22 ð7þ9nþ10n2 Þ 2 ¼ E0 l 2ðe1 þ22 Þ2 Gð1þnÞð7þ5nÞ " # 6ð2a2 e1 þa1 2 Þnð2þnÞþ3b1 2 ð7þ9nþ10n2 Þþ3b2 ð4e1 nð2þnÞþ2 ð7þ5nþ8n2 ÞÞ s0 E 0  2ðe1 22 Þ2 Gð1þnÞð7þ5nÞ " # s2 ½2ða1 4a2 Þnð2þnÞþb1 ð7þ9n10n2 Þþb2 ð7þ21nþ16n2 Þ  0 2ðe1 22 Þ2 Gð1þnÞð7þ5nÞ (7.19)

Equation (7.19) shows that the WGM shift is a function of three terms. The first term is due to the electrostrictive effect, the second term is a linear term and the last term is a constant term that arises from the surface charge density. Figure 7.12 shows the WGM shift for two values of the shear modulus and surface charge density of s0 ¼ 3:3x106 C=m2 . The surface charge is obtained for a poling electric field of E0 ¼ 0 V/m (no poling) and E0 ¼ 1 MV/m using the 1 0.5 0 (ΔR/R) × 106

–0.5 –1 –1.5

V 0 C/m2; G=333 kPa

–2

V 0 C/m2; G=250 kPa

–2.5

V –3.3×10 –6C/m2; G=333 kPa

–3

V –3.3×10 –6C/m2; G=250 kPa

–3.5 0

1000

500

1500

E0, kV/m

Figure 7.12 Relative deformation of a 10:1 PDMS sphere calculated from (7.19). Reprinted, with permission, from [24]

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E0 following expression s0 ¼ ðe1  e2 Þ 2e3e22þe . For this calculation, the values of 1 e1 ¼ 2:8e0 , e2 ¼ e0 , a1 ¼ ðe2  1:8e0 Þ and a2 ¼ ðe2  e0 Þ were used. As shown in Figure 7.12, the analysis captures well the trend observed in the experiments (see Figure 7.11). The above concept has been used for the development of photonic electric field sensors as well as non-contact displacement sensors. Electric field resolutions of the order of a few V/m were reported using a solid sphere that was coated with a liquid PDMS layer [22]. Using the same concept, a non-contact displacement sensor was developed with resolution of few hundreds of nanometres, using a sphere made of Super Soft Plastic by F-M Manufacturing Company. The electric field generated by the two plates was 0.56 MV/m [28].

7.4 Magnetic field induced WGM In these studies, a polymer sphere doped with magnetic polarizable particles is immersed in a uniform static magnetic field H0 [25,26]. Since the equation describing the magnetic field can be obtained by replacing the inductive capacity with the magnetic permeability, the above analysis can be extended to a sphere that has a relative magnetic permeability mr, surrounded by a fluid that has a magnetic permeability m0. Figure 7.13 shows the configuration used for the analysis and the experiments.

H0

Optical fiber

R

WGM

r

φ μr

μ0

Figure 7.13 A coupled WGM sensor in a uniform static magnetic field

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The magnetic pressure acting on the surface of the sphere surface can be written as: p¼

 b1  b2 2 m0 ðmr  1Þ  2 b2 H þ ðmr  1ÞH 2 Cos2 J þ H Cos2 J þ H 2 2 2 2

(7.20)

where H is the magnetic field within the sphere. The coefficients b1 ¼ @m=@eii and b2 ¼ @m=@ekk are the magnetostrictive coefficients where eii and ekk are the normal components of the strain. Again, since the sphere has a uniform magnetic permeability, the magnetic field within the sphere is uniform and therefore the body force acting within the sphere is also zero. Equation (7.20) can be simplified for nearly incompressible materials as follows:

b1  b2 3B20 2 P2 (7.21) p ¼ ðmr  1Þ þ m0 m 0 ðm r þ 2 Þ2 where P2 ¼ ð3cos2 J  1Þ=2 and B0 ¼ m0 H0 is the external inductive magnetic field. The optical shift on a plane that is normal to the imposed external magnetic field is obtained following the same procedure discussed in Section 7.3 as:

Dl DR 7  4n b1  b2 3B20 2 ¼ ¼ ðm r  1 Þ þ (7.22) l R 4Gð7 þ 5nÞ m0 m0 ðmr þ 2Þ2 Here G and n are the shear modulus and the Poisson ratio of the doped polymer, respectively. Similar to the electric field relationship presented above, the induced WGM shift is a quadratic function of the applied external magnetic field and also a function of the elastic and magnetic properties of the doped polymer material. Experiments were carried out by placing a spherical doped resonator in a uniform magnetic field. For these experiments, the microsphere was made of PDMS 60:1 that was doped with magnetic polarizable particles (MQP-S-11-9, Magnequench). The volume fraction of the particles was approximately 30%. The sphere used in the experiment had a 400-mm radius and was coated with a thin layer of pure PDMS 60:1 with a 5-mm thickness. This outside shell served as a waveguide for the propagation of the WGM. Figure 7.14 shows a photograph of the doped resonator. The sphere was placed in a uniform magnetic field that was generated using a solenoid as shown in Figure 7.15. The inductive magnetic field was measured using a Gauss  meter. The shear  modulus of the doped polymer was calculated as G ¼ G0 1 þ 2:5x þ 14:1x2 ; where G0 is the shear modulus of the pure polymer and x is the volume fraction of particles. Figure 7.16 shows the transmission spectrum of the observed WGM shift with no field and with a field of 4 mT. The observed quality factor was 2  106. Figure 7.17 shows the experimental results along with the analytical prediction. As

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Figure 7.14 The photograph of a PDMS microsphere (D 900 mm) doped with magnetic polarizable particles. The figure also shows the silica stem used to hold in place the microsphere

Power supply

Gauss metre

MR-PDMS microsphere

MR-PDMS microsphere

Optical fiber

Solenoid Solenoid

Figure 7.15 The photograph and schematic of the experimental setup for magnetic field measurements

Intensity (ar.Units)

1.02

B0=4mT

B0=0

0.97 0.92 0.87 0.82 1.31288

1.31289

1.3129

1.31291

1.31292

Laser wavelength, mm

Figure 7.16 The transmission spectrum of WGM with and without applied external magnetic field. Q ¼ 2  106. Reprinted, with permission, from [25] shown in Figure 7.17, the experimental data agrees reasonably well with the analytical results. From this data, it was possible to estimate a resolution of ~1 mT provided that a quality factor of 107 is achieved. Studies were also carried out to study the effect of harmonic magnetic field on the doped microspheres.

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0 0

5

10

15

20

–20

Δλ, pm

–40 –60 –80 –100

μr=1.22 μr=1.15 Experiment

–120

Figure 7.17 Experimental and analytical results with a 400-mm radius doped sphere. Reprinted, with permission, from [25]

7.5 Conclusions The study reported here shows that PDMS polymer resonators can be tuned using an external electric field. The studies also show the potential for high-resolution electric field sensors and non-contact displacement sensors. The sensitivity of the microsphere to an applied external electric field can be improved if the microsphere is poled in an external electric field. In addition, if the polymer microsphere is doped with magnetic polarizable particle, it can be tuned using an external magnetic field, and could potentially be used as a magnetic field sensor. The data reported here show a sensor resolution of the order of  mT using a microresonator with optical quality factor of 107. This resolution could be improved using softer polymers and magnetic polarizable particles with larger magnetic permeability.

References [1] Risti´c, D., Berneschi, S., Camerini, M., et al. ‘Photoluminescence and lasing in whispering gallery mode glass microspherical resonators’. J. Lumin. 2016; vol. 170, pp. 755–760. [2] Cai M., Painter O., and Vahala K.J. ‘Fiber-coupled microsphere laser’. Opt. Lett. 2000; vol. 25, pp. 1430–1432. [3] Nunzi Conti G., Chiasera A., Ghisa L., et al. ‘Spectroscopic and lasing properties of Er3þ-doped glass microspheres’. J. Non-Cryst. Solids 2006; vol. 352, pp. 2360–2363. [4] Ioppolo T., and Manzo M. ‘Lasing from a dome shaped optical resonator’. J. Laser Phy.2014; vol. 24, 115803.

Electric and magnetic sensors based on WGM spherical resonators [5] [6] [7]

[8] [9] [10] [11] [12] [13] [14] [15]

[16] [17] [18] [19] [20]

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Palma G., Falconi C., Nazabal V., et al. ‘Modeling of whispering gallery modes for rare earth spectroscopic characterization’. IEEE Photon. Technol. Lett.2015; vol. 27, pp. 1861–1863. von Klitzing W. ‘Tunable whispering modes for spectroscopy and CQED experiments’. New J. Phys.2001; vol. 3, pp. 14.1–14.14. von Klitzing W., Long R., Ilchenko V.S., Hare J., and Lefevre-Seguin V., ‘Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy’. Opt. Lett. 2001; vol. 26, pp. 166–168. Tapalian H.C., Laine J.P., and Lane P.A., ‘Thermooptical switches using coated microsphere resonators’. IEEE Photon. Technol. Lett. 2002; vol. 14, pp. 1118–1120. Absil P.P., Hryniewicz J.V., Little B.E., Wilson R.A., Joneckis L.G., and Ho P.-T. ‘Compact microring notch filters’. IEEE Photon. Technol. Lett. 2000; vol. 12, pp. 398–400. Rabiei P., Steier W.H., Zhang C., and Dalton L.R. ‘Polymer microring filters and modulators’. J. Lightwave Technol. 2002; vol. 20, pp. 1968–1975. Little B.E., Chu S.T., and Haus H.A. ‘Microring resonator channel dropping filters’. J. Lightwave Technol.1997; vol. 15, pp. 998–1000. Vollmer F., Brown D., Libchaber A., Khoshsima M., Teraoka I., and Arnold S., ‘Protein detection by optical shift of a resonant microcavity’. Appl. Phys. Lett. 2002; vol. 80, 4057–4059. Arnold S., Khoshsima M., Teraoka I., Holler S., and Vollmer F. ‘Shift of whispering gallery modes in microspheres by protein adsorption’. Opt. Lett.2003; vol. 28, pp. 272–274. Rosenberger A.T., and Rezac J.P. ‘Whispering-gallery mode evanescentwave microsensor for trace- gas detection’. Proc. SPIE 2001; vol. 4265, pp. 102–112. Ioppolo T., Das N., and Otugen M.V. ‘Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new raytracing analysis and sensor experiment’. J. Appl. Phy.2010; vol. 107, 103105. ¨ tu¨gen M.V. ‘High-resolution force sensor Ioppolo T., Ayaz, U.K., and O based on morphology dependent optical resonances of polymeric spheres’. J. Appl. Phy.2009; vol. 105, 013535. ¨ tu¨gen M.V., and Sheverev V.A. Ioppolo T., Kozhevnikov M., Stepaniuk P., O ‘A micro-optical force sensor concept based on whispering gallery mode resonator’. J. Appl. Opt.2008; vol. 47, pp. 3009–3014. ¨ tu¨gen, M.V. ‘Pressure tuning of whispering gallery mode Ioppolo T, and O resonators’. J. Opt. Soc. Am. B 2007; vol. 24, pp. 2721–2726. ¨ tu¨gen M.V. ‘Temperature measurements using a Guan G., Arnold S., and O micro-optical sensor based on whispering gallery modes’. AIAA J.2006; vol. 44, pp. 2385–2389. ¨ tu¨gen M.V., and Sheverev, V. ‘A micro-optical Ioppolo T., Ayaz U.K., O wall shear stress sensor concept based on whispering gallery mode

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Integrated optics Volume 2: Characterization, devices, and applications resonators’. 46th AIAA Aerospace Sciences Meeting and Exhibit, 8–11 January 2008. ¨ tu¨gen M.V. ‘Direct measurement of wall shear Ayaz U.K., Ioppolo T., and O stress in a separating and reattaching flow with a photonic sensor’. Meas. Sci. Technol. 2013; vol. 24, 124001. ¨ tu¨gen M.V., Christensen M., and MacFarlane D. Ahmed A., Ioppolo T., O ‘Photonic electric field sensor based on polymeric micro-spheres’. J. Poly. Sci. B 2014; vol. 52, pp. 276–279. ¨ tu¨gen M.V. ‘Tuning of whispering gallery Ioppolo T., Ayaz U.K., and O modes of spherical resonators using an external electric field’. Opt. Express 2009; vol. 17, pp. 16465–16479. ¨ tu¨gen M.V. ‘Electric field-induced deforIoppolo T., Stubblefield J., and O mation of polydimethylsiloxane polymers’. J. Appl. Phys. 2012; vol. 112, 053301.044906. ¨ tu¨gen M.V. ‘Magneto-rheological polydimethylsiloxane Ioppolo T., and O micro-optical resonator’. Opt. Lett.2010; vol. 35, pp. 2037–2039. Rubino E., and Ioppolo T. ‘Dynamical behavior of magnetic polarizable polymer microsphere using whispering gallery mode’. J. Poly. Sci. B 2018; vol. 56, 598. ¨ tu¨gen M.V., Fourguette D., and Larocque L. ‘Effect of Ioppolo T., O acceleration on the morphology dependent optical resonances of spherical resonators’. J. Opt. Soc. Am. B. 2011; vol. 28, pp. 225–227. Rubino E., and Ioppolo T. ‘Electrostrictive optical resonators for noncontact displacement measurement’. Applied Opt.2017; vol. 56, 229. Gorodetsky M.L., Savchenkov A.A., and Ilchenko V.S. ‘Ultimate Q of optical microsphere resonators’. Opt. Lett.1996; vol. 21, pp. 453–455. Knight J.C., Cheung G., Jacques F., and Birks, T.A. ‘Phase-matched excitation of whispering gallery mode resonances using a fiber taper’. Opt. Lett. 1997; vol. 22, pp. 1129–1131. Serpengu¨zel, A., Arnold S., Griffel G., and Lock J.A. ‘Enhanced coupling to microsphere resonances with optical fibers’. J. Opt. Soc. Am. B. 1997; vol. 14, pp. 790–795. Ioppolo T., and Manzo M. ‘Dome shaped whispering gallery mode laser for remote wall temperature sensing’. Appl. Opt.2014; vol. 53, pp. 5065–5069. Manzo M., and Ioppolo T. ‘Untethered photonic sensor for wall pressure measurement’. Opt. Lett.2015; vol. 40, pp. 2257–2260. Love A.E.H. Treatise on the Mathematical Theory of Elasticity. Cambridge: Cambridge University Press; 4th edition, 1926. Hetnarski H., and Ignaczak J. Mathematical Theory of Elasticity. New York: Taylor and Francis, 2004.

Chapter 8

Nonlinear integrated optics in proton-exchanged lithium niobate waveguides and applications to classical and quantum optics Marc De Micheli1 and Pascal Baldi1

8.1 Introduction From the theoretical point of view, nonlinear integrated optics is not a new field. A lot was predicted by Nicolas Bloembergen and his colleagues, who after the discovery of lasers in 1960, decided to proceed the following way: ‘We took a standard textbook on optics and for each section we asked ourselves what would happen if the intensity was to become very high. We were almost certain that we were bound to encounter an entirely new type of physics within that domain’. [1]. This allowed them to publish a famous paper [2] in which they established the two conservation laws that govern nonlinear optics: the energy conservation and the phase (momentum) conservation. Since then, the field has been continuously developing. All the fundamentals of nonlinear optics can be found in the fourth edition of the book by Robert W. Boyd [3], which presents the origin of nonlinearity and explains why non-centro-symmetry of the material is mandatory in order to obtain nonlinear coefficients of even orders. In this chapter, we will concentrate on the second-order nonlinear interactions, coupling three waves in processes that are known as second harmonic generation (SHG), sum/difference frequency generation (SFG/DFG) or spontaneous parametric down conversion (SPDC). In these cases, the conservation laws can be written as:
energy conservation: w1 þ w2 ¼ w3

(8.1)


phaseðor momentumÞconservation: k1 þ k2 ¼ k3

(8.2)

The second condition also being known as the ‘phase-matching condition’. As already mentioned, to observe nonlinear effects, the intensity must be very high. In a waveguide, very high intensities can be easily reached, even with modest 1 Universite´ Nice-Sophia Antipolis, INstitut de PHYsique de NIce – INPHYNI – UMR 7010 CNRS, Parc Valrose, France

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incident power, and maintained over long propagation distances. Therefore, the first particularity of the guided wave configuration is that it is a configuration in which nonlinear effects can hardly be ignored. This can be a limitation such as in optical telecommunications where the nonlinear effects limit the power that can be injected in the fibres and therefore the number of channels per fibre and the distance between the repeaters. But this is clearly an advantage if you are interested in nonlinear effects to create new sources or manipulate the optical signal. This is presented in Figure 8.1, which shows how the bulk and the guided wave configurations compare. In the bulk configuration, the section S of the beam and the useful length of the crystal L (the length were the power density remains high) are correlated as they both depend on the focusing. In a waveguide, as soon as the power is injected in the waveguide of section S, it remains confined and the length of interaction L is only limited by the propagation losses. 2 As the conversion efficiency is given by h / PLS , the freedom to play independently with L and S in the waveguide case makes it possible to achieve conversion efficiencies that are several orders of magnitude higher than in the bulk configuration. This is obviously an advantage as these effects can be used to produce new sources such as: UV sources using SHG, tuneable IR sources using DFG (optical parametric oscillator, OPO), correlated photon pair sources or squeezed light sources using SPDC. Another particularity of nonlinear integrated optics is that, for a given direction of propagation, the waveguide can offer several modes depending on the index profile of the waveguides. This introduces new possibilities to satisfy the second conservation law (8.2), which can now be written with the wave vector of the different modes: (8.3)


momentum conservation between modes : i1 þ j2 ¼ k3

Bulk S

L nonlinear crystal Waveguide

waveguide

S

L

Figure 8.1 Comparison of the bulk and the guided wave configuration

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i (resp  j, k) being the mode number of the mode at the frequency w1 (resp  w2, w3) involved in the nonlinear interaction. This condition can be represented by a phase-matching diagram (Figure 8.2). This conservation law requires a way to compensate for the dispersion, which is present in every optical material, in order to have a constructive effect all along the interaction path. In the bulk configuration, this constructive configuration is usually obtained by using the birefringence of the material and turning the crystal to adjust the propagation direction and obtain phase matching. In the following paragraphs, we will see in more detail how the modal dispersion present in any waveguide can replace or be combined with the birefringence to fulfil the phase-matching condition. Another way to satisfy the phase-matching condition is to introduce a periodicity in the nonlinear material. This was already studied by Bloembergen et al. and, in this case, the phase conservation condition becomes: (8.4)

k1 þ k2 ¼ k3  K

The associated phase-matching diagram is represented in Figure 8.3. The periodicity K can either affect the index of the material or the nonlinear coefficient involved in the interaction. These cases are known as quasi-phasematched (QPM) cases. Similarly to birefringence phase matching, quasi phase matching can also be used in waveguides and combined with modal dispersion to find other phase-matching possibilities. Therefore, the confinement in waveguides makes it possible to observe efficient nonlinear effects with low pump power, and the use of the waveguide dispersion can enlarge the phase-matching possibilities, but it would be wrong to conclude that nonlinear interactions are much easier in waveguides. Indeed, the constraints are carried over to the choice of the material and to the waveguidefabrication process, which have to provide: ●

● ●

good mechanical properties, including the possibility to cut and polish the waveguide input and output facets, high nonlinear c2 coefficients, low-loss waveguides with a precisely controlled index profile,

β1

β2

β3

Figure 8.2 Phase-matching diagram

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β1

K

β3

Figure 8.3 Quasi phase-matching diagram

●

● ●

no or minor modifications of the nonlinear coefficient during the waveguidefabrication process, a precise manipulation of the sign of the nonlinear coefficient and optionally, the possibility to combine these technologies.

Some of these constraints are common constraints in integrated optics and they already explain why several chapters of this book focus on a given material or a family of materials: glass, polymers, lithium niobate, liquid crystals and so on. The extra requirements, specific to nonlinear optics, dramatically reduce the number of usable materials in nonlinear integrated optics and explain why the field is governed by material and technical issues. In this chapter, we will concentrate on the results obtained in proton-exchanged (PE) lithium niobate (LiNbO3) waveguides.

8.2 Proton exchange in LiNbO3 8.2.1 The first discoveries: High dne, low loss In 1982, the first paper describing the PE process in lithium niobate [4] generated a great interest in the integrated optics community [5,6], as it made it possible to produce low-loss waveguides with a high-index contrast. This resembled a Holy Grail for this community dreaming of achieving highly confining waveguides and developing compact devices based on sharp bends and highly efficient electro-optic and nonlinear sections. Besides this strong interest, PE proved to be very easy to implement (simply dropping the crystal in hot water is sufficient to obtain an index increase) but much more difficult to control. We observed strange behaviour in the mode spectrum [7], other authors reported instabilities [8]. Aging of the waveguides was carefully studied [9], and many attempts were made to reduce the losses [10], obtain waveguides in optical damage resistant material [11] or try to stabilise the index profile with annealing [12]. In order to find a way through these difficulties, we started studying the correlation between the crystallographic and optical properties [13] of the waveguides, which revealed that behind apparently similar index profiles it was possible to have very different crystallographic qualities and therefore different

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stabilities, propagation losses, and electro-optic and nonlinear properties. Even though knowledge of the impact of the PE process on the material properties was still in its infancy, many groups attempted to use it to develop nonlinear devices.

8.2.2 Combination with birefringence phase matching In the early eighties, the only way to produce waveguides in LiNbO3 was metal indiffusion using temperatures above 1000  C [14], and the best results were obtained with titanium indiffusion [15,16]. This process can be used to fabricate graded index waveguides guiding both polarisations, with a small index increase (< 2.10–2) and low propagation losses. They were successfully used in nonlinear optics [17,18], but with a limited phase-matching range. As soon as the PE process was identified as an interesting way to fabricate waveguides in LiNbO3, it was established that the PE process increased the extraordinary index (dne ¼ 0.1) and decreased the ordinary one (dno ¼ 0.04), that the modified layer could be up to 10-mm thick, and that it was possible to superimpose the Ti:indiffusion and the PE process [19]. When the PE parameters are chosen such that the exchange layer is very deep, it is possible to consider that the PE process modifies the substrate index values while the Ti:indiffusion creates the waveguide (Figure 8.4). As we established that it was possible to control the index modification due to the PE process by annealing or by changing the acidity of the bath [20], we proposed to use the PE process to modify the substrate birefringence in order to increase the phase-matching possibilities using TIPE waveguides [21–23]–. The TIPE configuration was also proposed for many other applications [24–26]–, but despite the many efforts made to improve the quality of these waveguides [27], no really practical devices have been fabricated.

8.2.3 Cerenkov configuration Thanks to their high-index contrast and their step index profile, the PE waveguides support rather low-loss radiation modes, which can be used to satisfy the phasematching condition. In this case, the phase-matching condition becomes: 1 þ 2 ¼ k3 cos ðqÞ

(8.5)

where q is the radiation angle in the substrate and k3 the propagation vector of the wave radiated in the substrate. The corresponding phase-matching diagram is plotted in Figure 8.5. This configuration, known as the Cerenkov configuration, has been extensively studied in the case of SHG in planar waveguides, and has produced interesting results [28,29]. But these interesting results have never been transferred to channel waveguides as the difficulty to collect the harmonic radiated in a half-cone in the substrate was not compensated by the fact that the phase-matching condition is automatically satisfied as the angle q can freely adjust.

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b)

0.1

0. 0

5

y (μm)

5

y (μm)

∆no

0.

.05

Figure 8.4 Index profile of the TIPE waveguide. The measurement of the ordinary and the extraordinary modes supported by these waveguides makes it possible to plot both index profiles. They show that the dn created by both processes is added and that the PE process creates a positive dne ¼ 0.1 and a negative dno ¼ –0.04 @0.633nm. As the PE process can modify the crystal over a depth greater than 10 mm, it can be treated as a modification of the substrate index, the waveguide being created by the Ti:indiffusion. Reprinted, with permission, from [19]
(1982) Elsevier

Nonlinear integrated optics in PE LiNbO3 waveguides and applications β1

221

β2

θ

k3

Figure 8.5 Cerenkov phase-matching diagram

8.2.4 Destruction of the c2 and strain-induced losses in channel waveguides But there are two other reasons that explain why the first nonlinear devices using PE waveguides were not completely successful. First, researchers discovered that in certain circumstances, the PE process was reducing or completely destroying the nonlinear coefficients of the crystal [30,31]. But to fully understand the problem, it was necessary to have a clear picture of the crystalline structure of the PE layer as a function of the fabrication parameters. As can be seen in Figure 8.6, the HxLi1-xNbO3 layer can be in several crystallographic phases (where dne varies linearly with the strain e33) depending on the chosen fabrication parameters and the final substitution ratio x [32,33]. Further measurements, that will be described in Section 8.3.3, have shown that the a phase is the only one to present unmodified nonlinear coefficients. Most of the successful devices produced up to now have a waveguide in this crystallographic phase. The second problem encountered with PE waveguides with a high index increase is that, due to the important strains induced by cell parameter mismatch between the exchanged layer and the substrate, the channel waveguides present polarisation-conversion processes. Since, in PE waveguides, the extraordinary polarisation is the only one that is guided, and, since in LiNbO3, the birefringence is negative, the ordinary part of the mode easily couples with ordinary radiation modes, and thus induces high propagation losses. A detailed study of this effect is provided in a number of papers [34–37]. Despite the high interest the PE process initially attracted for its capacity to fabricate highly confining waveguides, during the nineties, interest and research efforts were transferred to waveguides remaining in the a phase and therefore presenting an index increase of the order of a few 10–2. This was obtained either by the APE process, which consists in annealing the waveguide to redistribute the protons after creating a thin PE layer, or the SPE process, which consists in using a proton-poor source for the exchange. This tendency was also reinforced by the need to prepare waveguides in periodically poled lithium niobate (PPLN) crystals, which required waveguide-fabrication processes soft enough not to disturb the periodic organisation of the domains.

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δne

APE

0.2

PE

β4 0.15 β3

0.1

κ2

β2

β1

κ1 0.05

Direct Exchange Exchange + annealing α

ε33 . 103

0 0

1

2

3

4

5

6

Figure 8.6 Relation between the extraordinary index increase and the cell expansion for crystals exchanged following different recipes. This figure shows several regions were the dne varies linearly with the strain. They are identified as crystallographic phases. The PE region corresponds to bi phases that can be obtained using pure benzoic acid or acid with a small amount of lithium benzoate. ki phases can be obtained only by annealing (annealed proton exchange, APE). The a phase is the phase of the congruent crystal. It can be obtained using the soft proton exchange (SPE) process (with an amount of lithium benzoate greater than a threshold) or by strong annealing. In this phase, the nonlinear properties are maintained; while in the other phases, they can be slightly or dramatically reduced

8.3 Periodic poling 8.3.1 Surface domains: Titanium diffusion and heat treatment Nowadays, we benefit from high-quality bulk PPLN crystal; but in the late 1980s, the available poling techniques were only able to produce shallow periodic domains just under the surface of the crystal. One of these techniques consists in using Ti:indiffusion, which makes the Zþ domains flip into Z– [38–41]. When the Ti film is periodically patterned before diffusion, one obtains periodic domains extending 1 or 2 mm under the surface and presenting a triangular or trapezoidal shape (Figure 8.7).

Nonlinear integrated optics in PE LiNbO3 waveguides and applications Initial position of the Ti films

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Inverted area

Proton Exchanged area

Figure 8.7 Cross section of periodic domains obtained by TI:indiffusion on the Zþ face of an LN crystal This organisation is far from ideal, but it can be efficiently used with a waveguide produced by a technique other than Ti:indiffusion. SPE and APE processes are quite indicated in this case and have both been used [42–45]. The same kind of shallow periodic domains under the surface can also be obtained by using a periodic pattern of silicon oxide on the positive c-face of LiNbO3 in combination with a heat treatment. This causes a periodic out-diffusion of LiO2 and domain reversal in the surface layer [46].

8.3.2 E-Field poling In the early nineties, a new method appeared for fabricating a periodic domain structure with ideal laminar domains in LiNbO3. It consists in applying a strong external field through a wafer. At room temperature, 21 kV/mm are necessary to reach domain switching, and a periodic electrode has to be applied to the surface of the crystal to obtain periodic domains. This electrode can be liquid or metallic, and this technique can be used to fabricate periodic domains with periods larger than 10 mm on wafers that are a few hundred microns thick [47,48]. The quality of the domains obtained was immediately confirmed by very good nonlinear conversion efficiencies in a bulk SHG experiment. A lot of effort was put into improving the control of the domains produced and increasing the thickness of the wafers used, as well as the length of the devices produced. Confirmations came rapidly, and were achieved using a QPM optical parametric oscillator and a 5.2-mm-long, 0.5-mm-thick LiNbO3 crystal, periodically poled with a period of 31 mm, pumped by a 1.064-mm Q-switched Nd:YAG laser, and temperature-tuned over the wavelength range 1.66–2.95 mm [49]. Figure 8.8 shows the scheme of a typical setup used to periodically pole 0.5-mm-thick 3’ LiNbO3 wafers. Some of these setups present optical windows that allow domain formation to be observed in real time with the help of a microscope and a fast camera. These observations served as a basis for the discovery of the different scenarios of sideways domain wall motion and were used to prove that each of these scenarios can be selected by choosing the degree of deviation between the applied field and the minimum poling field. These mechanisms were modelled taking into account the surface and bulk charge motion, which is induced by the application of the external field and which causes screening fields that prevent the

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LiCl

Dielectric mask

Figure 8.8 Typical scheme of an E-field poling setup used to pole LiNbO3 or LiTaO3 wafers up to 3’. Some setups present optical windows that allow domain formation to be observed in real time with the help of a microscope and a fast camera polarisation reversal from taking place [50]. These studies have also shown that when the poling parameters are chosen far from equilibrium, one can observe the loss of wall shape stability and the formation of nano-domains. These nanodomains have raised a lot of interest as they can be used to produce high-capacity optical memories [51] and they are actively studied [52]. These nano-domains can also affect the performances of nonlinear devices, as will be presented in Section 8.3.4. Most of the studies cited above concerned congruent LiNbO3 and LiTaO3 crystals and they focused on the ferroelectric properties of these crystals. But some studies focused on nonlinear optical applications, such as frequency doubling, with the aim of creating blue and green powerful sources, which require PPLN crystals with short poling periods (6–7 mm) and MgO doping to minimise photorefractive sensitivity. Some interesting results were obtained in congruent crystals, employing a 50-mm-long first-order PPLN sample to generate continuous wave (cw) powers of 2.7 W [53], in the green, and 60 mW [54], in the blue. But although these results

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were obtained using high-temperature (200  C) phase matching, power instabilities and thermal lens effects could not be completely suppressed, as well as green- or blue-induced infrared absorption. The motivation to fabricate periodically poled MgO-doped lithium niobate (PPMgOLN) was then quite strong; but, as it was observed that the poling scenario depends on the mobility of the surface and bulk charges, which is modified by MgO doping, specific poling conditions have to be determined for precise domain engineering in MgO:LiNbO3. These were reported for X-, Y- and Z-cut wafers [55]. Other groups may have found different recipes, but nowadays all the available commercial crystals for SHG in the visible range are PPMgOLN [56]. To conclude this study of poling, the specific case of poling previously PE crystals needs to be discussed. This will be presented in Section 8.3.4, which presents all the different issues faced when combining periodic poling and PE.

8.3.3 The different PE processes and their impact on the nonlinearity of the crystal Before discussing the impact of PE on PPLN crystals, it is important to know the impact of the PE process on the lithium niobate crystal itself as a function of the chosen PE parameters. We have already mentioned the existence of different crystallographic phases in PE layers, but we need to describe the process in a greater detail. Using a wide range of fabrication parameters and crystal orientations, we were able to identify up to seven crystallographic phases in HxLi1-xNbO3 layers. The exchanges were carried out on optical grade X- and Z-cut LiNbO3 using, as proton sources, melts and solutions of different acidity such as: NH4H2PO4, KHSO4, benzoic acid with and without lithium benzoate, stearic acid, melts of K2SO4-Na2SO4-ZnSO4-KHSO4, and solutions of LiCl and KHSO4 in glycerine. Some of the samples were then annealed between 320 and 400  C, in order to obtain waveguides with a surface index increase ranging between 0.01 and 0.15. The planar waveguides obtained were then characterised using a standard prism coupling setup in order to measure the mode effective indices at 633 nm. The extraordinary refractive index profiles were reconstructed using the IWKB technique [57]. On the same samples taken from different crystallographic planes, researchers recorded rocking curves that were used to reconstruct the surface layer structure [58]. This work resulted in the crystallographic phase diagram shown in Figure 8.6. In this diagram, the phase transitions are characterised by a discontinuity in the relation between the index variation (dne) and the deformations e33 along the axis 3 (optic axis). However, some transitions such as the b1-b2 transition in Z-cut LiNbO3 are not easily observed in this diagram, but further investigations, such as the measurement of the deformation e23 in order to determine shearing in the planes perpendicular to the surface, reveal the discontinuity. Moreover, this diagram shows that in each crystalline phase there is a linear dependence between the index increase (dne) and the deformations (e33), that we assume proportional to the proton concentration, but that the slope changes

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dramatically from one phase to the other. On this basis, we were able to show how this diagram can be used to understand the PE process on LiNbO3 and explains the optical properties of the different waveguides obtained with different exchange and annealing conditions [32].

8.3.3.1

Direct exchange

The a and b phases are obtained by direct exchange using melts of different acidity. When the acidity is varied, using a mixture such as lithium benzoate (L.B.) in benzoic acid (B.A.), a b phase is obtained with highly acidic melts, (b3 and b4 phases require an even more acidic bath such as pyrophosphoric acid) while the a phase is obtained for lithium benzoate concentration r ¼ mL:B: =ðmB:A: þ mL:B: Þ in the melt, higher than a certain threshold that depends on the temperature (Figure 8.9).

8.3.3.2

Annealing

The effect of annealing on the index profile can be rather complicated, leading sometimes to an increase and sometimes to a decrease of the dne. But this complicated behaviour can be easily understood by considering the phase diagram and the fact that an annealing always causes a reduction of the proton concentration and

δne 102 1

T = 250° C

0,5

T = 300° C

0

1

2

3

4

5

6

ρ

Figure 8.9 Extraordinary index increase of PE waveguides as a function of the L.B. concentration in the melt. Reprinted, with permission, from [59]
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thus of the strain e’33. However, during the annealing, the HxLi1-xNbO3 layer may either evolve in a given phase or experience one or several phase transitions. The effect of annealing on the index profile can then be very complicated but perfectly understood if we know the exact phase of the original layer. For example, for an initial exchange leading to the b1 phase, index variation (dne) and depth will increase during annealing due to an evolution in the b1 phase followed by a transition to the b2 or k2 phase [32]. Continuing the annealing will lead to a decrease of dne and an increase of the depth, which corresponds to the evolution through the k2, k1 and a phases. Annealing is the only way to obtain layers in the k phases. Up to now, it has not attracted a lot of interest since waveguides on LiNbO3 in these phases exhibit very high propagation losses due to a poor crystallographic quality or a disturbed interface between the substrate and the exchanged layer.

8.3.3.3 IR absorption Another important feature of PE layers can be studied with IR absorption. After the exchange, the layers produced on X-cut wafers show a strong absorption band near 3 mm, which is due to the vibration of the OH bonds [37]. Depending on the fabrication process, the spectra show a sharp polarised peak alone (s ¼ 3510 cm-1) or followed by a non-polarised broad absorption band (s ¼ 3280 cm-1) (Figure 8.10), which tends to disappear when the acidity of the melt is reduced or during annealing. The precise correlation between the IR absorption spectra and the phase diagram remains to be determined. However, we have noticed [60] that the nonpolarised absorption corresponds to the presence of interstitial protons that do not contribute to the index increase, while the polarised peak corresponds to protons in a substitution site that contribute to the index increase. In the case of waveguides in the a phase, the absorption is considerably weaker (this phase corresponds to a very low proton concentration) and at a slightly different frequency (s ¼ 3490 cm
1). Though they are still rather qualitative, these observations of the IR spectra are very important as they reveal the presence of different kinds of phonons that will modify the properties of the crystal or of the dopants introduced in the crystal.

8.3.3.4 Nonlinear optical properties of PE lithium niobate waveguides Studies of the effects of PE on the nonlinear properties of the crystal have led to some controversy. Everybody agrees that the nonlinearity is strongly reduced in HxLi1-xNbO3 layers with high-proton concentrations, but some authors claim that it is possible to restore the nonlinearity after certain heat treatments [61,62], while others have observed the opposite behaviour [63]. In order to clarify this situation, we have investigated the influence of PE on the second-order optical nonlinearity [64] using reflected SHG measurements on the polished waveguide end face [65]. This study allows us to show that it is possible to produce waveguides that do not present a reduction of the nonlinear coefficient, using the one-step PE process we have call SPE. Moreover, these results, combined with those previously published,

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2 % L.B

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Figure 8.10 Infrared absorption spectra of the OH bonds created in PE waveguides fabricated at 250  C and with different melts. The sharp polarised peak at s ¼ 3510 cm-1 corresponds to protons in Liþ sites, while the broad absorption band around s ¼ 3280 cm-1 corresponds to interstitial protons randomly distributed in the crystal. Reprinted, with permission, from [59]
(1999) Springer tend to indicate that the possibility of restoring nonlinearity by annealing depends on the crystallographic phase in which the initial waveguide is prepared. For the SPE waveguides whose index profile is provided in Figure 8.11, we used a low-acidity melt and an exchange duration of 70 h to reach the a phase directly. The registered nonlinear signal is identically continuous from the surface to the bulk. Furthermore, we did not observe any difference between the waveguide and the bulk regions as regards the reflected beam quality. This indicates that this kind of exchange, using a low-acidity melt, completely preserves the nonlinear optical properties of the material. For the PE waveguide [32] prepared in the b2 phase, using a bath containing 1% of lithium benzoate and an exchange duration of 5 h at 300  C, the result is completely different. Monitoring the SH reflected beam (2w) going from the bulk to the waveguide, we observed that the signal practically disappears when the exchanged region is reached. The reflected SH signal measured in the exchanged region is less than 5% of the value registered for the bulk region. This indicates that, in this case, the guide nonlinear coefficient is only 20% of the bulk value. At the interface between the exchanged layer and the substrate, the nonlinear signal increases while the quality of the reflected beam is severely degraded.

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Figure 8.11 Reflected infrared and SH signals obtained on a SPE waveguide (3% BL, 300  C, 70 h). Reprinted, with permission, from [59]
(1999) Springer This phenomenon was also observed with a much higher intensity on APE waveguides. Indeed, on our sample, which was annealed in several steps of 1- or 2-h heating at 330 and 350  C, the SH signal, which was strongly reduced after the initial PE, appears to be two orders of magnitude higher in the exchanged layer than in the substrate (Figure 8.13). In this case also, the increase is accompanied by a strong degradation of the quality of the SH reflected beam. Examination of the edge of the sample under an optical microscope indicates that the quality of the end face is equivalent to that of the SPE samples. These results suggest that the strong diffusion is due to the poor crystallographic quality of the exchanged layer or of its interface with the substrate. Despite these difficulties, this sample suggests that nonlinearity is at least restored in the initially exchanged layer. There is no evidence of a linear region at the surface as the fundamental and the second harmonic signals increase simultaneously. This could be due to the fact that the initial PE waveguide was achieved in the b2 phase and not in the b1 phase, which is used by most other authors [66,67] using a pure benzoic melt around 200  C. In Section 8.3.4, we will extend our analysis of PE to its effects on the periodic domain structure in periodically poled material.

8.3.4 PE and periodic poling 8.3.4.1 PE in PPLN crystals In this section, we will investigate how the different PE processes affect the domain structure in PPLN crystals using a selective chemical etching technique. We will show that it is possible to produce a waveguide in PPLN without partially erasing the domain structure, by using a highly diluted melt [68] for the exchange process.

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Figure 8.12 Reflected infrared and SH signals obtained on a PE waveguide (1% L.B., 300  C, 5 H). The pictures on the right correspond to the reflected SH spot at different positions identified by a number. Reprinted, with permission, from [59]
(1999) Springer

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Figure 8.13 Reflected infrared and SH signals obtained on an APE waveguide. The annealing consists in several steps of 1- to 2-h heating at 330 and 350  C. The SH spot corresponding to the position #3 is not represented but is identical to the spot #2 in Figure 8.12. Reprinted, with permission, from [59]
(1999) Springer For our study, PE and SPE planar waveguides were prepared in the same conditions as those used for the nonlinear measurements. The APE waveguide was exchanged for 25 min with r ¼ 1% and annealed at 350  C for 6 h to reach the a phase.

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Figure 8.14 Schematic of the periodically poled samples where the PE surface was polished at a small angle. Reprinted, with permission, from [59]
(1999) Springer The samples were polished at a wedge angle q of approximately 0.3 to allow observation from the top of both the exchanged and the unexchanged regions (Figure 8.14). A chemical solution of HF (40%) and HNO3 (65%), in the proportions of 1:2, was used to reveal the domains [69]. This mixture etches the Zoriented domains much faster than the Zþ and after 10 min of etching, the structure was clearly visible through an optical microscope. Photographs taken on each waveguide are shown in Figures 8.15 to 8.17. On PE waveguides, after 10 min of etching, domains were visible in the region of the sample where the exchanged layer had been completely polished off, while the initial surface layer presented no periodic structure (Figure 8.15). On APE waveguides, chemical etching reveals a picture similar to that observed on PE waveguides (Figure 8.16). This indicates that the standard annealing process we used on this sample does not allow any regrowth of the domains through the exchanged region. Nevertheless, this experiment is not precise enough to determine whether the periodic structure disappeared in the entire guiding region or only in part of it. On SPE waveguides, the picture taken after 10 min of chemical etching and reported in Figure 8.17 shows that even though the domain structure is far from being perfectly periodic (important progress has been made since), it is present in both the substrate and the exchanged region. This fabrication technique which induces no crystallographic phase transition makes it possible to prepare SPE waveguides in PPLN without erasing the domain structure [70]. Nevertheless, more recent studies, using very short HF etching to reveal the domains, have shown that in the Zþ part of the structure, the SPE process

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Figure 8.15 Top surface of periodically poled sample where the PE waveguide was polished away at a small angle. Chemical etching reveals that the exchanged layer shows no periodic structure. The black line on the left of all pictures is a scratch on the surface of the sample that reveals the part of the sample that was not polished. Reprinted, with permission, from [64]
(1997) OSA sometimes induces the formation of surface nano-domains [71]. This explains the poor nonlinear performance observed in certain channel waveguides produced by SPE in PPLN crystals. The study was performed using complementary methods of domain visualisation: piezoelectric force microscopy (Figure 8.18) and confocal Raman microscopy, which have confirmed the existence of needle-like nanodomains, which can be responsible for the degradation of the nonlinear response of certain waveguides created in PPLN crystals.

8.3.4.2

E-field poling of PE samples

In addition to the fabrication of waveguides in PPLN crystals, which is the most widely used approach to fabricate devices, we have also studied the influence of the different PE layers on the poling process. From the material point of view, this study is very rich and has shown the important role played by the substitution ration and the thickness of the layer, at least. The presence of a PE layer increases the threshold field (the minimum field necessary to obtain poling), modifies the domain wall kinetics and can induce the formation of irregularly shaped domain walls (Figure 8.19) [72–74]. As the PE process modifies the composition of the surface layer, the screening mechanism is affected. Depending on the excess applied field (difference between the applied field and the threshold field), one can observe domains with very different shapes. Classical isolated hexagonal domains form in a low excess field

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Figure 8.16 Top surface of periodically poled sample where the APE waveguide was polished away at a small angle. Chemical etching reveals that the exchanged layer shows no periodic structure. Reprinted, with permission, from [64]
(1997) OSA (Figure 8.20). In a moderate excess field (~1 kV/mm), one can observe wide anisotropic domain boundaries or oriented domain rays depending on the thickness of the PE layer (Figures 8.21 and 8.22). With a high excess field (>2 kV/mm) and thick PE layers, the nucleation starts with stars that develop over time into a web structure (Figure 8.23) [75]. Increasing the precision of the domain observation also revealed that, in front of the moving domain walls, one can observe the formation of broad domain boundaries with nano-domain structures and that the width of these bands depends on the applied field [76]. A review of the effects is presented in [77], but the process is not controlled enough to allow to use the PE to pattern the domain structure and produce efficient devices, as was repeatedly proposed.

8.3.5 Components After providing a detailed description of periodic poling, PE processes and the different ways they can be combined, we will see how c2-based interactions between guided waves have been used to produce a large number of components in classical and quantum optics. In this paragraph, we will focus on the classical devices, which include two families of components: sources at new frequencies and all the optical information-processing devices used for ultra-fast telecommunications.

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Figure 8.17 Top surface of periodically poled sample where the SPE waveguide was polished away at a small angle. Chemical etching reveals a domain structure that is far from being perfectly periodic but is unaffected by this exchange. Reprinted, with permission, from [64]
(1997) OSA

8.3.5.1

SHG

At a time when no laser diodes were available at short wavelengths, since the first successful announcement dates back to 1991 [78], nonlinear optics was a clear way to obtain blue and green sources from the available lasers emitting at 800 nm or 1 mm. APE and SPE waveguides were quite attractive, as they allowed devices to be efficient at low pump power using the d33 nonlinear coefficient [79,80]. These waveguides were also attractive as they presented lower photorefractive sensitivity than Ti:indiffused waveguides that could not compete at these short wavelengths. Since quasi phase matching allowed cascading processes, it was also possible to create red, green and blue in a single PPLN waveguide section mixing SHG and SFG processes [81]. In order to further improve the efficiency of these frequency doublers, several groups worked on the reverse PE process that makes it possible to create embedded waveguides where the overlap between the interacting modes is optimised [82]. Despite all these efforts, no practical device had been produced because the photorefractive sensitivity was still too high to produce stable components. In the meantime, semiconductor laser diodes started to appear. A lot of effort was then put into adapting the poling process to MgO-doped material to produce the bulk source emitting powers that could not be achieved by laser diodes [83,84] but were necessary for laser displays and laser projection. PPMgOLN frequency doublers are

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Figure 8.18 (a) PFM view of the surface at the interface between the Zþ and Z
areas. (b) A scheme of the interface cross-section showing the shape of the surface nano-domains appearing in the Zþ area now commercial devices and this effort also benefited to the integrated optics community, which adapted the waveguide-fabrication processes to the MgO-doped material [85,86].

8.3.5.2 Parametric fluorescence Besides the effort to create new visible sources, the integrated optics community also paid close attention to the new sources created in one or several of the

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Figure 8.19 First observation of the modification of the domain shape in the presence of a PE layer on both faces of the LiNbO3 wafer. The schemes under the pictures represent the section of the wafer telecommunication bands based on spontaneous parametric down conversion (SPDC) or difference frequency generation (DFG). Components working in this wavelength range are easier to fabricate since the PPLN sections require longer periods (~15 mm), the tolerances on the waveguide dimensions are higher, and the photorefractive sensitivity and the residual absorption are far smaller. This more than compensates for smaller nonlinear coefficients in that wavelength range. In the early 1990s, we observed SPDC in APE waveguides using a CW Ti: sapphire laser that was starting to be commercially available, and noticed that it was possible to generate a signal between 1.2 and 2.4 mm [87,88] by tuning the pump wavelength between 0.76 and 0.84 mm (Figure 8.24). These observations were made at room temperature using a pump power ranging between 1 and 15 mW, allowing us to obtain up to 10–14 W of fluorescence. This was a record value [89] even though the periodic domains used, obtained by Ti:indiffusion, were far from perfect (Figure 8.7). Since then, the improvements described in Section 8.3 have been introduced in the fabrication of these devices, such as waveguides with optimised overlap [90]. The conversion efficiency is now around 10–9 W for 2-cm-long samples. These observations were the basis for the fabrication of single photon sources that will be described in Section 8.4, namely single photon pair generators.

8.3.5.3

DFG and amplification

Another way to use these waveguides is to launch both the pump and the signal at the input and to use the idler created by DFG or the amplified signal at the output. The first configuration was extensively studied to implement optical wavelength conversion in telecommunication networks. Indeed, wavelength conversion addresses a number of key issues in WDM networks including transparency, wavelength routing and network capacity [91]. DFG is a quite attractive means to

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Y

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Figure 8.20 Domain shape obtained applying a low excess field on a 500-mmthick LiNbO3 wafer with a 3.4-mm-thick PE layer obtain wavelength conversion, as it offers quite a large conversion bandwidth (~100 nm) without adding excess noise. Since the early work demonstrating an efficiency of 40%/Wcm2 over a 30-nm bandwidth [92], much progress has been accomplished and multiple wavelength conversions have also been reported in PPLN waveguides [93,94]. One of the major experimental difficulties of these frequency converters is that the waveguides are multimode at the pump wavelength. To reach the published efficiencies, one has to optimise the injection in the pump mode that interacts efficiently with the signal and idler modes. This requires a very precise alignment setup and an active adjustment. Taking advantage of the efficiency of nonlinear conversion, a solution was proposed to solve this problem using a cascade of nonlinear interactions: SHG followed by DFG [95]. In this case, the pump is injected at the frequency wp and converted to 2 wp through SHG. The harmonic at 2 wp is then mixed with the signal at frequency wp-dw to create the idler at wpþdw, which carries the same information as the input signal at wp-dw. The advantage of

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Figure 8.21 Domain shape obtained applying a 1.2-kV/mm excess field on a 500-mm-thick LiNbO3 wafer with a 3.4-mm-thick PE layer. The domain boundary becomes broad and anisotropic this configuration (Figure 8.25) is that the waveguide is single mode at all the frequencies that have to be injected in it, which dramatically simplifies the coupling. This configuration was precisely modelled [96], experimentally demonstrated [97,98] and became the standard configuration scheme [99] for this kind of application. There are many other ways to use DFG in optical telecommunication, such as parametric amplification [100,101], modulation or multiplexing/demultiplexing [102]. Several reviews have been published on all-optical signal-processing technologies and their applications for telecommunication [103,104]. They mention that wavelength conversion at key network nodes is a fundamental functionality that can allow for better use of network resources. Devices based on three-wave interactions in PE periodically poled lithium niobate waveguides, which exhibit suitable properties with respect to nonlinear mixing efficiency, propagation loss and ease of fabrication, are good candidates for that purpose. They have to compete with components based on semiconductor optical amplifiers or four-wave mixing in silicon waveguides or fibres. But all these technologies are still at the stage of enabling technologies and are not really implemented in the field. DFG can also be used to generate some signal in the THz wavelength range by mixing two waves with similar wavelength [105]. Over the years, this process has been improved [106] even though LiNbO3 is absorbent at the THz frequencies. This has been taken into account in the modelling of THz generation in LiNbO3

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Figure 8.22 Evolution with time of the linear domain observed with an applied excess voltage of 1.4 kV/mm on a 500-mm-thick LiNbO3 wafer with a 4.6-mm-thick PE layer. Pictures are taken 11.5, 13.1 and 15.0 s after the first domain appears structures in order to optimise the waveguide length [107]. Nevertheless, it seems that other materials such as potassium titanyl phosphate (KTP) could be more suitable for this purpose [108].

8.4 Single photon pair generators Since the beginning of the twenty-first century, quantum photonics has been developing very rapidly. This is due to major fundamental research achievements that have shown that photons were very good vectors to carry quantum information, and was also due to the availability of guided wave tools that can create, propagate, manipulate and measure the photons in quantum states. These tools are particularly interesting because they allowed quantum information processing to leave the labs and be implemented in commercial telecommunication systems [109]. Since the signal in a quantum protocol cannot be amplified, the components designed for quantum information processing need to be very low-loss, when including internal losses and coupling losses with the fibres used for transportation. This puts a strong pressure on the design of the integrated circuits that are necessary to generate, manipulate and measure the single photon pairs and squeezed states. Many papers have shown that nonlinear optics is mandatory to generate the photon pairs and the squeezed states. In this sub-section, we will describe the

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Figure 8.23 Evolution with time from the star domains to the web structure observed with an applied excess voltage of 2.4 kV/mm on a 500-mmthick LiNbO3 wafer with a 4.6-mm-thick PE layer. Pictures are taken 5.19, 5.45 and 5.66 s after the first domain appears efforts made to develop the sources needed in the integrated optic format, and, in the next one, we will discuss their combination with directional couplers to produce quantum photonic integrated circuits (QPICs). To produce the first source of integrated entangled photon pairs, we used the SPE process to fabricate waveguides in PPLN. Launching 1 mW at 657 nm in these waveguides, we obtained 2.10–6 photons pairs per incident pump photon (Figure 8.26), which represents an efficiency four orders of magnitude higher than what was obtained with bulk sources [110]. This result showed that it was possible to build all the pigtailed systems and to design circuits integrating the pair generator with the functionalities needed to process quantum information, essentially directional couplers. This concept was developed in more detail in [111]. The entangled photon pair generators can also be used to create heralded single photon sources [112]. Indeed, single photon sources are essential for fundamental experiments as well as for certain quantum cryptographic key distribution protocols, but no perfect on-demand single photon state source exists. Heralded single photon sources (Figure 8.27) cannot produce single photons on demand, but they indicate when a photon is emitted, which is a great advantage as it reduces the noise due to the detectors used at that [113] and therefore improves the performance of the quantum system under test.

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Λ = 20 μm Λ = 21 μm λi

2.0 Λ = 18 μm

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0.82

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Figure 8.24 First signal and idler waves observed at the output of an APE PPLN waveguide and their evolution as a function of the pump wavelength. The dots are the measured wavelength and the lines represent the numerical predictions. Reprinted, with permission, from [88]
(1995) IEEE

2ωp – ωp + δω ωp + δω

ωp – δω 2ωp ωp

Figure 8.25 Sketch of the frequency shifter based on the cascade of SHG and DFG

8.5 Quantum photonics integrated circuits on PPLN The interest of QPICs is that they allow the integration of several functionalities on the same chip, which reduces coupling losses with input and output fibres. The difficulty to produce them comes from the fact that they are essentially composed of nonlinear sections and directional couplers, which both provide a functionality that is very sensitive to waveguide parameters. The quasi phase matching, and therefore the wavelengths of the emitted signal and idler photons, are very sensitive to the effective index of the modes as well as the coupling ratio of the directional couplers. To fabricate these QPICs with a reasonable yield one has to control the

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Figure 8.26 Experimental setup used to characterise the first integrated version of a single photon pair generator. F: filter to block the pump. To get phase matching at degeneracy (ls ¼ li), the sample was heated up to 102  C. The signal and idler photons were measured with germanium APDs and both the single counts and the coincidences were collected to evaluate the quality of the entanglement

Laser

Filter

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1550 nm 1310 nm WDM

Germanium APD

Single-mode telecom optical fibre

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Figure 8.27 Scheme of a heralded single photon source. It is composed of a photon pair generator working out of degeneracy. The WDM coupler separates the two photons of the pair. The short wavelength is sent to a detector that generates an electrical signal heralding the presence of the single photon in the fibre domain structure and the index profile with a much greater precision than when fabricating components supporting only one functionality, and then build the subsystem associating the devices that operate at the right wavelengths. Temperature and electro-optic tuning cannot compensate for all the imperfections.

8.5.1 Quantum relay The first QPIC we fabricated was a quantum relay (Figure 8.28). It is ideally composed of a photon-pair creation zone, two adjustable 50/50 couplers, and

Nonlinear integrated optics in PE LiNbO3 waveguides and applications

&

D1

D2 C2

A B

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al ign ms λ u t @ an Qu o Bob t

C

C1 l igna ms @λ u t n e Quam Alic fro ulsed 2 P @ λ/ r lase

Figure 8.28 Scheme of a quantum relay QPIC composed of a photon-pair creation zone, two adjustable 50/50 couplers, and segmented tapered waveguides at all input/output ports segmented tapered waveguides [114] at all input/output ports to maximise the mode overlap between the fibres and the waveguides at the wavelength of operation. The waveguiding structures, obtained using the SPE process, enable light propagation with low losses and a very high conversion efficiency in a 1-cm-long PPLN zone. The two electro-optically tuned directional couplers C1 and C2 consist of waveguides integrated close to each other over mm-long distances above which electrodes are deposited. The curved sections for approaching and separating the waveguides are 1-cm long to minimise curvature losses. The fabrication details and the performances of the QPIC we produced are listed in [115]. With this non-ideal chip, presenting rather high overall losses (propagation losses ~0.4 dB/cm and segmented couplers not implemented), the achievable quantum communication distance could possibly be augmented by a factor of 1.4, whereas an optimised device could lead to a factor of 1.8. These results, however, are good enough to show the applicability of an integrated optical technology on lithium niobate for quantum information processing and applications.

8.5.2 Squeezed states Another QPIC we produced more recently using SPE waveguides on PPLN is a chip that generates and detects squeezed states of light. On this circuit, the propagation losses at l ¼ 1.56 mm are as low as 0.04 dB/cm, and at the operating temperature of 104  C, the PPLN section stands up to 40 mW at 780 nm without showing any mode hoping. The directional coupler is not electro-optically adjusted and the ideal 50/50 ratio was obtained by producing several (17) devices with a slightly different coupling length. The amplitude of variation of the coupling length was calculated on the basis of our usual waveguide parameter fluctuations. This

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11 μm

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InGaAs photodiodes

Homodyne detection

3 cm 5 cm

Figure 8.29 Schematic of our photonic chip on lithium niobate. The chip includes an SPDC stage, consisting of a periodically poled waveguide (with poling period L ¼ 16.3 mm) to generate squeezing at 1560.44 nm, and an integrated directional coupler detecting the interferometric part of the homodyne squeezing. The whole chip length is 5 cm. All waveguides are obtained by SPE [28] and have a width of 6 mm. The 127-mm spacing between the input (output) waveguides is compatible with off-the-shelf fibre arrays. The homodyne photodiodes are outside the chip and are bulk commercial components illustrates the progress achieved since the first quantum relay was created. The fabrication details and the performances of this squeezed-state QPIC, which demonstrated 2 dB of squeezing, are listed in [116]. The manufacturing yield and the quality of these QPICs could be further improved by using broadband adiabatic couplers, as we have demonstrated [117], by incorporating segmented couplers at the fibre input and output and by using antireflection coating to avoid the residual cavity effect that is useful for device characterisation [118] but introduces performance instabilities (Figure 8.29).

8.6 Further improvements To further improve the performances of PPLN-based nonlinear PICs, one should work on increasing the power confinement in order to increase nonlinear efficiency and on reducing the photorefractive sensibility in order to improve device stability. An increase of the acceptable pump power and the operating wavelength range could also be useful in sensors.

8.6.1 Power-resistant materials The photorefractive effect can be reduced using MgO-doped LiNbO3 crystals. Therefore, we have started to adapt the SPE process to these crystals [119]; in this preliminary work, we have shown that, contrarily to other waveguide-fabrication techniques, the SPE process makes it possible to fabricate waveguides in MgO:

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LiNbO3 without reducing its nonlinear coefficient and without erasing the effect of MgO doping on photorefractive damage. As the SPE parameters in MgO:LiNbO3 are quite identical to those used in congruent LiNbO3, it is reasonable to think that we will be able to fabricate good waveguides in PPMgOLN, but this remains to be demonstrated. Another option will be to use LiTaO3 crystals, which are interesting because of their transparency in the blue; but in this case, the confinement and the nonlinear coefficient would be reduced, which explains why we would prefer the PPMgOLN approach.

8.6.2 Highly confining waveguides 8.6.2.1 High-index soft proton-exchanged (HISoPE) waveguides Nonlinear efficiency can be increased by working on the confinement mode. Recently, we discovered that, contrarily to the first conclusion we drew from the crystallographic phase diagram presented in Figure 8.6, it is possible to have PE waveguides in LiNbO3 showing at the same time a strong index increase (dne  0.1 @ l ¼ 0.633 nm) and preserved nonlinear coefficients. We named these waveguides ‘high-index soft proton-exchanged’ (HISoPE) waveguides [120]. Other studies show that electro-optic properties are also preserved in these waveguides [121]. To obtain these waveguides, one has to use a lithium benzoatebenzoic acid melt with a lithium benzoate content r just smaller than the threshold value discussed in Section 8.3.3 and Figure 8.9 [122], or one can create a high vacuum in the PE cell [123]. These waveguides are very interesting, but before they can be used in efficient devices, we still need to reduce the losses observed in the channel waveguides. Indeed, these waveguides present high strains and stresses and therefore hybrid modes (modes with both TE and TM polarisations), which are very lossy since, in Z-cut substrates, the ordinary polarised TE component easily couples with radiation modes, as we demonstrated [37].

8.6.2.2 Thin-film lithium niobate Another option to increase the confinement is to use thin-film LiNbO3 or lithium niobate on insulator (LNOI), which are commercially available, to create waveguides that exhibit reasonable losses and benefit from a very strong vertical confinement. The lateral confinement can be obtained either by dicing [124–126], etching [127], strip loading the LiNbO3 film [128] or by using the APE process [129–131]. They have already shown excellent normalised nonlinear conversion efficiencies [128,132–134], but most of the time those figures are far from the calculated theoretical values and are obtained on very short waveguides since the homogeneity of commercially available substrates is far from sufficient to guarantee phase matching on a distance greater than a few mm [135]. Obviously, despite the great potential shown by LNOI, a lot of work must still to be done to use it to fabricate PICs integrating several functionalities with a reasonable yield.

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8.7 Today’s issues 8.7.1 Control of the domains To produce PICs with a reasonable yield, fabrication processes need to be well controlled. Our choice is therefore to use well-known technologies such as the SPE process in PPLN and try to solve the remaining problem that can be described as follows. When fabricating the waveguides in PPLN, it may happen that 20 to 50 mmdeep needle-like nano-domains [70] form in the Zþ section of the crystals, partially destroying the periodical organisation of the polarisation along the waveguide. Therefore, it would be interesting to be able to create the periodic inversion of the domains after the waveguide fabrication on the Z- face of the crystal.

8.7.1.1

E-beam poling of PE samples

Very recently, we tested a new combination of PE and periodic poling using e-beam writing to produce the domains. This technique has been tested in the past [136–139] without clear success, but recently it was reported that the use of a resist layer on the irradiated surface was a good way to improve domain structure quality [140,141]. Indeed, the high number of electrons trapped in the resist are located in a limited volume over the LiNbO3 surface and form an effective electrode. This technique is interesting for nonlinear optics as it can be used to pole MgOdoped LiNbO3 crystals or to pole the crystal after waveguide fabrication by SPE [142], as shown in Figure 8.30(a). The difficulty of the process is to produce a long PPLN grating, which requires moving the sample in the chamber of the scanning

10 μm (a)

10 μm (b)

Figure 8.30 AFM image of an SPE waveguide (vertical, underlined by the dashed line) going through the periodical domain structure (horizontal): dark – initial state, white – written domain. (a) Inside one segment of writing and (b) illustration of the stitching error between two written segments when the nonlinear grating is obtained by concatenation of several PPLN sections

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electron microscope (SEM) and can cause some stitching errors (Figure 8.30(b)). Nevertheless, the nonlinear results obtained with these waveguides [143] are excellent except for stitching errors. We have studied the impact of these errors in detail [144], and they can be dramatically reduced using a SEM with interferential control of the translation table; thus, this technique should allow the fabrication of highly controlled domain structures of useful size.

8.7.2 Insensitive phase-matching configurations 8.7.2.1 Experimental observation of insensitive phase-matching configurations As already mentioned several times in this chapter, the QPICs are difficult to fabricate with a reasonable yield because the features that need to be implemented are very sensitive to fabrication tolerances. With technologies available today, it is impossible to reduce further these fabrication tolerances; therefore, it would be interesting to design devices that are less sensitive to these tolerances. We very recently established that in SPE waveguides in PPLN, phase-matching configurations insensitive to waveguide width can be found when combining quasi phase matching and modal phase matching (MPM). We have demonstrated numerically that this property extends to other waveguide parameters and that it is due to the particular index profile of the SPE waveguides. We have also shown that this insensitive design can be extended to other material combinations as long as they present similar index profiles. The idea of using modal dispersion to compensate for material dispersion is not new and was envisioned and tested several times [145,146]. Some authors noticed that it was a way to obtain noncritical phase-matching conditions [147,148]. Nevertheless, as soon as the quasi phase-matching techniques became available, the community focused on the optimisation of devices using the first-order mode for all interacting wavelengths. This choice was motivated by the fact that in this case it is easier to optimise the overlap between the interacting modes and to couple the light in and out of the nonlinear waveguide. Nevertheless, in this configuration, the phase matching in optical waveguides is so critical that any non-homogeneity becomes problematic [149] and that the fabrication tolerances limit application possibilities [150]. Using SPE waveguides in PPLN and combining quasi phase matching and MPM, phase-matching conditions can be obtained that associate a-TM00 mode for the fundamental and a-TM10 mode for the harmonic and are insensitive to the waveguide width (Figure 8.31) [151].

8.7.2.2 Numerical studies of the phase mismatch By introducing in simulation programs a very precise description of the index profile of the SPE waveguides used, it is possible to calculate the poling period L necessary to compensate for the phase mismatch Db between the TM00 mode at l and any of the TMij modes (i and j being the number of zeros of the field along the depth and width axes, respectively) supported by these waveguides at l/2 as a function of different waveguide parameters. In Figure 8.32, we present the result as

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P2ω

TM01

Λ = 16.4 μm

(a.u.) 20

Width 5 μm Width 6 μm Width 7 μm

TM10 @ λ/2

15

Width 8 μm

10 TM00 @ λ/2

TM00

5 TM20 0

1,460

1,480

TM00 @ λ

1,500

1,520

1,540

λ (nm)

Figure 8.31 Phase-matching spectra of an SPE waveguide produced in PPLN using different modal configurations for L ¼ 16.4 mm. This curve shows that the combination of the TM00-TM01 gives a phasematching insensitive to the waveguide width when it varies in the 5 to 8 mm range

Wavelength 1.45 μm Λ (μm)

TM01 TM01

16.0 TM30

TM20

15.5 TM20

TM00

15.0 TM10 14.5 TM00 4

5

6

7

8

9 μm

Figure 8.32 Numerically calculated phase-matching period compensating for the phase mismatch Db between TM00 mode at l and TMij modes at l/2 as a function of the waveguide width. In this figure, the colours represent the sequence number of the modes by decreasing the effective indices. Pictures on the right represent the field profile of the harmonic modes that were observed experimentally

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Wavelength 1.55 μm TM10 19

Λ, μm

TM03 18

17

TM01

16

TM00

0.6

0.8

1.0

1.2

b, μm

Figure 8.33 Numerically calculated phase-matching period compensating for the phase mismatch Db between TM00 mode at l and TMij modes at l/2 as a function of the waveguide depth

a function of the width, and we can see that L varies more or less with the width of the waveguide, whatever mode is chosen for the harmonic frequency, except when the harmonic is carried by the TM10 mode. In this case and in this range of width, the waveguide index profile is such that the TM00 mode at l and the TM10 mode at l/2 have the same variation with respect to the waveguide width, and therefore the quantity L remains unchanged. This corresponds to an insensitive phase-matching configuration, which is quite remarkable as the phase matching is preserved whatever the waveguide width chosen in a range that extends from 5 to 8 mm at least. Numerically, similar curves can be plotted presenting L as a function of the waveguide depth or of the index increase (Figures 8.33 and 8.34), and one can observe that for the TM00 mode at l and the TM01 mode at l/2 the phase mismatch in SPE waveguides does not vary significantly with any of the waveguide parameters. This indicates that this phase-matching configuration can have an insensitive design that is very interesting for producing PICs. To see whether this insensitive phase-matching configuration can be extended to other types of waveguides, we introduced values in our calculations, which are typical of waveguides that can be obtained by varying (by steps or continuously) the Ga content in a stack of AlGaN layers epitaxially grown on an AlN substrate. In this case and for l ¼ 1.5 mm, the maximum index difference dn can be as high as 0.226 and the width and the depth of the waveguide have to be chosen accordingly to keep the waveguide single mode at the fundamental frequency. In these waveguides, the modal dispersion is strong enough to compensate for the material dispersion without using quasi phase matching. The interaction between the TM00 mode at l and the TM01 mode at l/2 is again insensitive to the variation of the

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Integrated optics Volume 2: Characterization, devices, and applications Wavelength 1.55 μm 19 TM10 TM03

Λ, μm

18

17 TM02 16 TM01 15

TM00 0.03

0.04

0.05

0.06

0.07

0.08

δn0

Figure 8.34 Numerically calculated phase-matching period compensating for the phase mismatch Db between TM00 mode at l and TMij modes at l/2 as a function of waveguide index increase dn0 waveguide width (Figure 8.34) as soon as the dependence on the depth (y) of the index profile is a function of the type: g ðyÞ ¼ e
ðy=bÞ

a

(8.6)

This is a similar shape to that of the SPE waveguides, the only difference being the value of a. In SPE waveguides, the insensitive configuration is obtained for a ¼ 0.6, while for AlGaN waveguides the minimum sensitivity is obtained for a ¼ 0.4. This is shown in Figure 8.35, where we plotted the amplitude of the variation of Dneff when the width of the waveguide varies between 0.5 and 1 mm as a function of the parameter a of the shape of the index profile along the depth.

8.8 Conclusion In this chapter, we examined the poling and the PE processes in LiNbO3. We also discussed the different ways of combining these processes and showed that SPE on PPLN is the best compromise available today to achieve c2-based PICs. To improve their performance, we intend to implement tapers at the fibre input and output, use e-beam poling after waveguide fabrication by SPE to have a better control of the domain shape, and use MgO-doped LiNbO3 substrates to reduce power-induced instabilities. Besides, the best way to increase the fabrication yield of nonlinear PICs is certainly to work on the design and to create devices more tolerant or insensitive to fabrication imperfections.

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Variation of ∆neff

0.003

0.002

0.001

0.1

0.2

0.3

0.4

0.5

0.6 α

0.7

0.8

0.9

1.0

1.1

Figure 8.35 Amplitude of the variation of Dneff as a function of the parameter a of the shape of the index profile along the depth. The variation of Dneff is equal to Dneff max – Dneff min when the waveguide width varies between 0.5 and 1 mm A lot more can be done with nonlinear components using a combination of several phase-matching protocols such as MPM and quasi phase matching in SPE waveguides. At some point, this will come into conflict with the need for maximum confinement in order to pack more functionalities on the chip, because quite probably the higher the confinement, the more sensitive the devices will be. Other approaches, such as using the LNOI platform, are certainly appealing, but they must demonstrate controlled and low-loss functionalities before they can be used to produce PICs and especially QPICs. Even if it does not seem as appealing, and is more a question of technology than science, a PIQ designed nowadays must have low and even extremely low losses, which means that no amplifier should be integrated on the chip to compensate for losses. Indeed, a higher degree of integration cannot be achieved at the expense of higher chip power consumption.

Acknowledgments Pascal Baldi is immensely indebted to Marc De Micheli for having introduced and guided him in the world of research since his PhD thesis. When Marc suddenly passed away in July 2019, this chapter was not complete and, at the request of the editors, Pascal finished it in tribute to Marc. In quote are the acknowledgments Marc planned, with which Pascal associates himself: ‘I deeply thank all those who have contributed to this work, starting with my former supervisor, Dan Ostrowsky, who introduced me to the field and my former colleagues, Alain Aze´ma, Jean Botineau, Andre´ Leycuras and Michel Papuchon.

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I also thank my present colleagues, Pierre Aschie´ri, Carlos Montes, Florent Doutre, Tommaso Lunghi, Herve´ Tronche, Se´bastien Tanzilli, Olivier Alibart, Virginia D’Auria, as well as my usual foreign collaborators, Youri Korkishko, Vladimir Fedorov, Serguiey Kostritskii, Vladimir Shur, Paolo Bassi and Fredrik Laurell. Finally I want to mention all the students who have contributed at some point: Jean Philippe Barety, Ming Jun Li, Qing He, Kacem El Hadi, Sufen Chen, Florence Armani, Katia Gallo, Ire`ne Aboud, Pierre Aumont, Loı¨c Chanvillard, Guillaume Bertocchi, Anthony Martin, Florian Kaiser, Davide Castaldini, Sorin Tascu, Oleksandr Stepanenko, Emmanuel Quillier, Michael Dolbilov, Maxim Neradovskiy, Dmitri Chezganov, Xin Hua and Franc¸ois Mondain’. This work was conducted within the framework of the OPTIMAL project under a grant from the European Union by means of the Fond Europe´en de de´veloppement re´gional (FEDER). We also acknowledge the financial support from the European Community through the ERA-SPOT project WASPS, the COST P2 (1997–2001), the European ICT-2009.8.0 FET QUANTIP project (grant agreement 244026) and the Marie Curie program for the PICQUE project (2012), from the Agence Nationale de la Recherche through the projects phoXcry (ANR09-NANO-004-03), e-QUANET (ANR-09-BLAN-0333-01), DFB-OPO (ANR-14CE26-0036-01), INQCA (ANR-14-CE26-0038), from Re´gion PACA through the projects PHOQUINT (2012) and SNATCH (2018), from Universite´ Coˆte d’Azur through the project PEANUTS and from CNRS.

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A. Boes, B. Corcoran, L. Chang, J. Bowers, and A. Mitchell, ‘Status and potential of lithium niobate on insulator (LNOI) for photonic integrated circuits’, Laser Photon. Rev., 12 (4), 1700256, (April 2018), https://doi.org/ 10.1002/lpor.201700256. P.W. Haycock, and P.D. Townsend, ‘A method of poling LiNbO3 and LiTaO3 below Tc’, Appl. Phys. Lett., 48, 698, (1986), https://doi.org/ 10.1063/1.96747. R.W. Keys, A. Loni, R.M. De la Rue, et al., ‘Fabrication of domain reversed gratings for SHG in LiNbO3 by electron beam bombardment’, Electron. Lett., 26,188–190, (1990), https://doi.org/10.1049/el:19900127. M. Yamada, and K.P. Kishima, ‘Fabrication of periodically reversed domain structure for SHG in LiNbO3 by direct electron beam lithography at room temperature’, Electron. Lett., 27, 828–829, (1991), https://doi.org/ 10.1049/el:19910519. H. Ito, C. Takyu, and H. Inaba, ‘Fabrication of periodic domain grating in LiNbO3 by electron beam writing for application of nonlinear optical processes’, Elect. Lett., 27 (14), 1221–1222, (1991), https://doi.org/10.1049/ el:19910766. Y. Glickman, E. Winebrand, A. Ariea, and G. Rosenman, ‘Electron-beaminduced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion’, Appl. Phys. Lett., 88, 011103, (2006), https://doi.org/10.1063/ 1.2159089. D.S. Chezganov, M.M. Smirnov, D.K. Kuznetsov, and V.Y. Shur, ‘Electron beam domain patterning of MgO-doped lithium niobate crystals covered by resist layer’, Ferroelectrics, 476 (1), 117–126, (2015), https:// doi.org/10.1080/00150193.2015.998909. D.S. Chezganov, E.O. Vlasov, M.M. Neradovskiy, et al., ‘Periodic domain patterning by electron beam of proton exchanged waveguides in lithium niobate’, Appl. Phys. Lett., 108, 192903, (2016), http://dx.doi.org/10.1063/ 1.4949360. M. Neradovskiy, D. Chezganov, L. Gimadeeva, et al., ‘Highly efficient nonlinear waveguides in LiNbO3 fabricated by a combination of Soft Proton Exchange (SPE) and E-beam writing’, ECIO, 18–20 May 2016, Warsaw, paper O-15, http://www.ecio-conference.org/wp-content/uploads/ 2016/06/ECIO-o-15.pdf. M. Neradovskiy, E. Neradovskaia, D. Chezganov, et al., ‘Second harmonic generation in periodically poled lithium niobate waveguides with stitching errors’, J. Opt. Soc. Am. B, 35, 331–336, (2018), doi.org/10.1364/ JOSAB.35.000331. W. Sohler, and H. Suche, ‘Second-harmonic generation in Ti-diffused LiNbO3 optical waveguides with 25% conversion efficiency’, Appl. Phys. Lett., 33 (6), 518, (1978). A. Azema, J. Botineau, M. de Micheli, and D. Ostrowsky, ‘Efficient SHG with clad Ti:LiNbO3’, J. Quant. Elect., 17 (12), 2486–2488, (1981).

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W.K. Burns, and R.A. Andrews, ‘Noncritical phase matching in optical waveguides’, Appl. Phys. Lett., 22 (143), 1994, (1973). M.L. Bortz, S.J. Field, M.M. Fejer, et al., ‘Noncritical quasi-phase-matched second harmonic generation in an annealed proton-exchanged LiNbO3 waveguide’, Trans. Quant. Elect., 30 (12), 2953–2960, (1994), https://doi. org/10.1109/3.362710. E.J. Lim, S. Matsumoto, and M.M. Fejer, ‘Noncritical phase matching for guided-wave frequency conversion’, Appl. Phys. Lett. 57, 2294, (1990), https://doi.org/10.1063/1.104166. M. Santandrea, M. Stefszky, V. Ansari, and C. Silberhorn, ‘Fabrication limits of waveguides in nonlinear crystals and their impact on quantum optics applications’, New J. Phys., 21, 033038, (2019), https://doi.org/ 10.1088/1367-2630/aaff13. M. Neradovskiy, H. Tronche, X. Hua, et al., ‘Phase-matching insensitive to waveguide parameters variations in c2 based nonlinear integrated optics devices’, OSA, 15–19, (July 2019), Hawaii, USA, paper NM3B.6.

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Chapter 9

Next-generation long-wavelength infrared detector arrays: competing technologies and modeling challenges Marco Vallone1, Alberto Tibaldi1,2, Francesco Bertazzi1,2, Andrea Palmieri1, Matteo G.C. Alasio1, Stefan Hanna3, Detlef Eich3, Alexander Sieck3, Heinrich Figgemeier3, Giovanni Ghione1 and Michele Goano1,2

9.1 Introduction Infrared (IR) radiation covers a broad portion of the electromagnetic spectrum spanning a wavelength range from 1.0 to 30 mm and beyond, hence between visible light and microwaves. A large part of the IR spectrum does not reach the Earth’s ground, because the radiation is blocked by the atmospheric CO2 and H2O. The remaining portions of the spectrum are often called “transmission windows” and define the IR bands that can be used for ground-based IR imaging systems, see Figure 9.1: “near-infrared” (NIR, l ¼ 0:8  1 mm), “short-wave infrared” (SWIR, l ¼ 1  3 mm), “mid-wave infrared” (MWIR, l ¼ 3  5 mm), “long-wave infrared” (LWIR, l ¼ 8  14 mm), and “very long-wave infrared” (VLWIR, l ¼ 14  30 mm, not shown in Figure 9.1). IR imaging is widely used for both military and civilian applications. Military applications include target acquisition, surveillance, night-vision, and tracking to guide defense interceptor seekers. Civilian applications include thermography, short-range wireless communication, spectroscopy, weather forecasting, and IR astronomy [1,2]. An IR detector can sense the energy emitted directly from objects in a scene, which is why they are widely employed for night-vision systems. However, the appearance of an imaged object is mainly determined by its temperature and emissivity. As an object gets hotter, it radiates more energy and appears brighter to 1 Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy 2 IEIIT-CNR, Corso Duca degli Abruzzi 24, Torino, Italy 3 AIM Infrarot-Module GmbH, Theresienstraße 2, Heilbronn, Germany

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Figure 9.1 Atmospheric transmittance of electromagnetic radiation vs. wavelength. Reprinted, with permission, from [1] a IR imaging system. Instead, emissivity is determined by the imaged object’s material. For example, a cloth has generally lower emissivity than the human skin, which will appear brighter when imaged by a IR focal plane arrays (FPAs) detector, even when they have exactly the same temperature. The choice of the IR sub-bands to be employed in the imaging process depends strongly on the type of atmospheric obscurants interposed between the target and the imager. For example, since smoke particle size ð 0:5 mmÞ is much smaller that typical MWIR or (still better) LWIR wavelength, MWIR and LWIR radiations are less scattered by smoke than NIR or SWIR radiations, which then are better suited to image a scene through smoke. Other applications may require to compare the same scene, when imaged in two or three bands at the same time, in order to detect the temperature of the imaged object. This is of crucial importance in several military applications, in order to identify a possible threat. Modern IR detection and imaging techniques were first investigated during the Second World War, aiming to obtain true images of the scene in IR bands. First, a simple row of detectors were employed: an image was generated by scanning the scene across the strip using, as a rule, a mechanical scanner (first-generation detectors). In 1959, Lawson and co-workers [3] triggered the development of variable bandgap HgxCdxTe alloys, providing an unprecedented degree of freedom in IR detector design: in this II-VI pseudo-binary semiconductor alloy, the G point direct bandgap can be tuned from that of the semimetal HgTe (0.3 eV) to that of CdTe (1.5 eV) simply by varying the mole fraction x of the Cd in the composition. Since the eighties, new photodetectors started to exploit the photovoltaic effect in semiconductors (Figure 9.2). Here, the photons with energy greater than the energy gap, incident on the front surface of the device, generate electron-hole

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Figure 9.2 p  n junction photodiode: (a) structure of abrupt junction, (b) energy band diagram, (c) electric field, and (d) current-voltage characteristics for the illuminated and not illuminated photodiode. Reprinted, with permission, from [4, Ch. 9] CRC Press pairs in the material on both sides of the junction. The carriers generated within a diffusion length from the junction reach the space-charge region by diffusion. Then electron-hole pairs are separated by the strong electric field; minority carriers are readily accelerated to become majority carriers on the other side. By this way, a photocurrent is generated, shifting the current-voltage characteristic in the direction of reverse current (see Figure 9.2(d)). Photovoltaic detector arrays are usually illuminated from the back side with photons passing through a transparent detector array substrate, often a CdZnTe layer transparent in IR bands, on which a few microns of HgCdTe (the absorber) are epitaxially grown. The Cd molar fraction of the HgCdTe layer is chosen conveniently, in order to obtain an energy gap suitable for SWIR, MWIR, or LWIR bands. Still during the eighties, new detectors built as two-dimensional (2D) N  N matrices of pixels – called FPAs – started to be developed (second-generation detectors, see Figure 9.3(a-c)), operating in a given wavelength band, normally MWIR or LWIR. At present, most imaging systems can be regarded as composed of an objective with diameter D and focal length F able to image a scene on a focal plane, and a FPA detector like in consumer-grade digital cameras. As a practical concept, each pixel can be regarded as a single detector, capable to convert radiation into an electrical signal. In the last decades, IR imaging systems evolved to advanced detectors [5] with multicolor capabilities (third-generation detectors, see Figure 9.3(d-e)). These systems gather data at the same time in separate IR spectral bands in order to discriminate both absolute temperature and unique signatures of objects in the scene. By providing this new dimension of contrast, multiband detection also enables advanced color-processing algorithms to further improve sensitivity above that of single-color devices. Such multispectral detection allows for rapid and

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Figure 9.3 First (a) and second (b) FPAs generation. Adapted and reprinted, with permission, from [6] AIP Publishing. In panel (c), the typical architecture of a HgCdTe-based FPAs with hybridized to a readout integrated circuit (ROIC). Adapted and reprinted, with permission, from [1]. (d) Schematic of a third-generation dual-band MWIR / LWIR detector pixel; (e) its experimental normalized spectral response spectrum at about 60 K. The cutoff wavelengths of the two bands were 5.4 mm, for the MWIR, and 9.1 mm, for the LWIR band. Adapted and reprinted, with permission, from [7] efficient understanding of the scene in a variety of ways. In particular, two-color IR FPAs can be especially beneficial for threat-warning military applications. By using two IR wavebands, spurious information, such as background clutter and sun glint, may be subtracted from an IR image, leaving only the objects of interest. Multispectral IR FPAs can also play many important roles in the Earth and planetary remote sensing, astronomy, etc. For these reasons, the effective signal-tonoise ratio of two-color IR FPAs greatly exceeds that of single color IR FPAs for specific applications. Most of the radiation emitted in the human environment lies in the MWIR/ LWIR bands, which are also known as thermal bands. In this context, optical imaging tools for MWIR and LWIR are commonly referred to as “long-wavelength IR” detection systems. Examples of applications of such instruments include pollution monitoring, gas sensing, and spectroscopy based on detecting the chemical species that absorb MWIR and LWIR radiation. Another relevant application involves astronomy, which require very large format, high-sensitivity, and resolution sensors for both space- or ground-based MWIR and LWIR imaging systems [8,9] (e.g. the wide field IR camera on the Hubble Space Telescope is equipped with a 4096  4096 format charge-coupled-device FPA, with 15 mm-wide pixels [10]). This clarifies why the increasing demand of advanced IR imaging systems for civilian, scientific, and military applications has promoted significant efforts toward the development of large format, high-sensitivity photodetectors especially

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for MWIR and LWIR bands (although in the present days SWIR and VLWIR have an increasing importance). Aiming to minimize the cost of production, the most relevant requirements for next-generation IR detectors are ● ● ● ● ●

FPA size pixel pitch broadband operation high operating temperature (HOT) operation light coupling capability In order to avoid over-extending the scope of the chapter and the consequent risk of lessening its usefulness, its focus will be limited a few important points: * the increasing demand for large FPAs which offer high-quality imaging and improved spatial resolution at competitive cost of production * the necessity to reduce dark current toward the room temperature operability or at least to achieve detectors with reduced cooling requirements

Even if it will not be described in detail in this chapter, it is worth to mention the possible alternative to HgCdTe-based IR detection and imaging technology offered by the nearly lattice-matched InAs/GaSb/AlSb material system, also known ° family [11–14]. The possibility of realizing type-II broken-gap hetas the 6.1A erostructures and of controlling the energy gap through adjustment of the layer composition and thickness have led to the development of new device concepts and architectures with potentially suppressed Auger generation rates, and consequently lower dark currents and higher operating temperature. Among the proposed architectures [15] are double heterostructures and unipolar-barrier structures such as graded-gap M-, W-structures, nBn, pMp, and pBn detectors, superlattice absorbers surrounded by electron- and hole-blocking unipolar barriers, also known as complementary barrier detectors (CBIRD), pBiBn designs, and interband cascade IR photodetectors (ICIPs) [16]. Besides technological advances in detector material growth and processing, readout circuit design, large FPA hybridization, and packaging, further performance improvements of FPAs are possible by integration of photonic functions in FPA detectors (integrated optics). Even if not addressed in this chapter, they include the integration of micro- and nano-structured surfaces (photonic crystals) or photontrapping structures, aimed at increasing the detector quantum efficiency and possibly helpful to reduce the dark current [17,18] (useful reviews on these arguments can be found in [1,6,18,19]). Optical components based on metasurfaces (arrays of metalenses) have the potential of being monolithically integrated with IR FPAs to increase their operating temperature and sensitivity [20]. In the MWIR, several transparent conducting oxides (TCOs), such as indium tin oxide (ITO), are characterized by a negative real permittivity ðe < 0Þ, allowing to fabricate active plasmonic periodic nanostructures on the illuminated face of FPAs, where the resulting plasmonic resonance wavelength can be tuned by changing the carrier concentration [21].

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9.2 Lower cost, large FPAs with subwavelength pixel pitch Just like for dynamic random access memories (DRAMs) integrated circuits (ICs), the growth rate of the number of pixels on an IR array (the FPA size or format) has been growing exponentially for 30 years, in accordance with Moore’s Law, with a doubling time of approximately 18 months [18]. As shown in Figure 9.4(a), astronomical applications may require large format, highly sensitive IR arrays with size greater than 100 megapixels. However, the request of large format FPAs is deeply connected with the pixel pitch, hence with the number of pixels per unit area. Before 2000, the typical pixel pitch of IR-FPA detectors ranged between 20 and 40 mm without strong incentives toward its reduction, since at that times research was focused on understanding the detector and material physics [22–26], on the development of high-quality, low dark current, and high-sensitivity detectors [4,27–29], on multi-color detector architectures [7,30,31], and on getting larger format FPAs [9,18]. Recently, cost and performance considerations have driven a significant effort to reduce the pixel pitch, an achievement made possible (see Figure 9.4(b)), thanks to continuous and substantial technological advancements. Recent studies indicate as an important technological milestone the development of IR HgCdTe-based FPAs with sub-wavelength pixel pitch, with the advantage of reducing their volume, lowering their weight, and, potentially, cutting their costs. First, when a FPA standard format is selected for production, a smaller pitch corresponds to smaller chips, allowing to fabricate more chips per wafer [32]. Second, under some constraints [33,34], the reduction of the pixel pitch provides better image quality and improved image resolution, very important features for both military and civilian purposes [6,9]. The present technologies enabled the production of high-quality IR-FPA detectors with pixel size of the order of 10–15 mm [35–37], and high-performance

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FPAs with pixel dimensions approaching the wavelength scale (Nyquist limit) are under intense investigation [9,32,38,39]. Consider an imaging system composed by a camera objective with focal ratio F ¼ f =D (where f and D are its focal length and aperture diameter, respectively) and a detector, consisting of a FPA with square pixels of pitch d. Its operation ranges between two extremes [9,32,38,39]: the diffraction-limited case, if the optical frequency is half the sampling frequency (Nyquist criterion), and the opticslimited case, if the Airy disk diameter produced by the lens is equal to d. The two cases are respectively described by the conditions [34]
Fl 2 ðdiffraction-limited systemÞ ð9:1aÞ ¼ 0:41 ðoptics-limited systemÞ: ð9:1bÞ d If the optical system is limited by diffraction according to the Nyquist criterion (9.1a), further reduction of d is not beneficial in order to maximize the image resolution. On the other hand, when the detector size d equals the diameter of the Airy’s disk (optics-limited system), the condition (9.1b) follows, and there is no advantage in increasing d beyond this value. Equation (9.1a) also shows that an optical system with focal ratio F ¼ 1 and pixel pitch d ¼ 5 mm exhibits performance identical to a more conventional F ¼ 4 system with d ¼ 20 mm detectors, with the advantage of an overall smaller volume, lower weight, and potentially cheaper imaging sensor. Therefore, a diffraction-limited optical system with F ¼ 1 and d ¼ l=2 appears as an optimal choice [9,38]. However, since detectors operate over a given l-band and not at a single wavelength, some trade-offs must be accepted, and as reference values, several groups recommend d ¼ 5  6 mm for LWIR and d ¼ 2  3 mm for MWIR [9,32,38,39]. When such technologically challenging target values for d are considered, it is important to keep under control the inter-pixel crosstalk [17], which includes a number of separate phenomena that may be occurring in the detector or read-out integrated circuit (ROIC) simultaneously. In this chapter, the following definition is adopted: excluding the ROIC, the inter-pixel crosstalk can be defined as the electrical response of a FPA pixel when an IR beam illuminates another pixel of the array. Nevertheless, more precise definitions of inter-pixel crosstalk components will be given in Section 9.2.2. Mesa-type structures [40–43] or microlenses [44,45] may be helpful to attenuate some of the possible sources of inter-pixel crosstalk. Diffusive inter-pixel crosstalk, which is caused by the diffusion of photogenerated carriers in the quasineutral region of a pixel [17,34,46], can be prevented, in mesa-type structures, by etching deep trenches between pixels. This is not possible in planar structure, which are widely adopted for large format HgCdTe FPAs. This choice simplifies the technological process (no etching steps), leading to higher-quality devices [47]. Nevertheless, planar arrays may be subjected to diffusive inter-pixel crosstalk, that limits the benefits of pitch reduction because of the typically large diffusion length

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of minority carriers. Indeed, for high-quality LWIR detectors, it is of the order of several tens of microns at typical operating temperatures [34]. In order to study and minimize the detrimental effects of inter-pixel crosstalk, realistic, multiphysics, three-dimensional (3D) electromagnetic (optical), and electric simulations are a crucial step for the development of state-of-the-art detectors. Inter-pixel crosstalk can be realistically simulated by illuminating a subarray (e.g. 5  5) with a Gaussian beam focused on its central pixel, and calculating the photogenerated carrier density Gopt by a full-wave electromagnetic simulation based, e.g. on the finite-difference time-domain (FDTD) method. The outline of the method is reported in Sections 9.2.1 and 9.2.2, along with more precise definitions of inter-pixel crosstalk and an example of calculation.

9.2.1 Comprehensive electromagnetic and electrical simulations The propagation of electromagnetic waves in any medium is completely described by the solution of Maxwell’s equations by means of full-wave numerical schemes. A common practice in FPA detectors is to adopt the FDTD, which is used to discretize and solve Maxwell’s equations on a cubic grid known as the Yee grid [48–50]. The absorbed photon density Aopt (number of absorbed photons of wavelength l per unit volume and time) can be evaluated as the divergence of the time! averaged Poynting vector hS i [45,51–53] !

Aopt ¼ 

!

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!

where hn is the photon energy, E its electric field vector, and s is the electrical conductivity, calculated from the material complex refractive index b n ¼ n þ ik as  2 al e ¼ n2  k2 ¼ n2  4p (9.3) na s¼ m0 c where m0 is the vacuum magnetic permeability, c is the speed of light in vacuum, and a ¼ 4pk=l is the absorption coefficient. The optical generation rate distribution Gopt ðlÞ into the pixel due to interband optical absorption is given by Gopt ðlÞ ¼ hAopt ðlÞ, where the quantum yield h, defined as the fraction of absorbed photons which are converted to photogenerated electron-hole pairs, is usually assumed to be unitary. When the electromagnetic solution is known, the carrier photogeneration rate distribution Gopt ensuing from the illumination enters as source term in the continuity equation of a drift-diffusion equations set. The array can be discretized with an appropriate meshing tool which generates a denser grid in regions where gradients of current density, electric field, free charge density, and material composition are present. Electric contacts are usually treated as ohmic with zero resistance, where charge neutrality and equilibrium are assumed, applying ideal

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Neumann boundary conditions to the outer boundaries of the array. After having appropriately translated the electrical properties of all the FPA array materials (HgCdTe, CdTe, eventual oxide layers, etc.) into the software material library required by the adopted simulation tool, the drift-diffusion equations can be solved by the finite-box method, interpolating on the electric mesh the values of Aopt calculated on the Yee’s grid. As anticipated, Gopt enters the continuity equations for the electron and hole current densities Jn;p (where Rn;p  Gn;p is the net recombination rate in absence of carrier photogeneration) @n @t ! ! @p r  J p ¼ qðRp  Gp  Gopt Þ þ q ; @t !

!

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(9.4)

whereas the Poisson equation, to be self-consistently solved with (9.4), current density (9.5) !

!

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(9.5)

and Fermi distributions, is written as [54,55] !

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(9.6)

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where Nphot;i is the photon flux through its illuminated face, treated as a simulation parameter. If the illuminating beam is monochromatic, repeating the whole (electromagnetic and electric) simulation for an ensemble of N discrete wavelengths ln , the obtained Iph;i and QEi will be spectral quantities.

9.2.2 Small pixels and inter-pixel crosstalk in planar FPAs As an example of calculation, Figure 9.5(a-c) reports the Gopt distribution, simulated by FDTD by illuminating a planar LWIR 5  5 uniform composition HgCdTe pixel sub-array, cooled at 77 K and sketched in Figure 9.5(d) and (e), with a monochromatic Gaussian beam centered on its central pixel. The geometry, doping

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Figure 9.5 2D distribution of Gopt , for a planar LWIR detector with pixel pitch d ¼ 5 mm, when illuminated with a monochromatic Gaussian beam (l ¼ 2; 5; 9:5 mm) (panels (a), (b), and (c), respectively). The detector scheme is sketched in panels (d) and (e). Adapted and reprinted, with permission, from [34] profiles, and all the details of the computational method are described in [34]: in short, the pixels have p-on-n polarity and are identified by a d  d  tabs cell, where tabs ¼ 2 mm is the HgCdTe thickness along the vertical growth direction. The array has a 100% fill factor without any trench between pixels, and three cases were examinated, considering d ¼ 3; 5; 10 mm. The Gaussian beam were obtained by an optical system with F ¼ 1 and numerical aperture NA ¼ 0:447, focusing the beam on the central pixel. It is worth stressing that the tail of a beam focused by an optical system unavoidably illuminates also the nearest neighboring (NNs) and corner neighboring (CNs) pixels around the central pixel (CP) of the miniarray (see their definitions in Figure 9.5(d)). This is one of the components of the inter-pixel crosstalk, the optical crosstalk. Starting from a set of Gopt ðln Þ calculated for an ensemble of N discrete ln , and following [46], the inter-pixel optical crosstalk can be quantified as the ratio between carriers photogenerated in the i-th pixel (with volume Vi ) and those photogenerated in the whole array (with volume W): Ð V Gopt ðx; y; zÞ dx dy dz : (9.8) Oi ¼ Ð i W Gopt ðx; y; zÞ dx dy dz It is also important to realize that, even if we illuminate only the central pixel, the photogenerated carriers diffuse in all directions, and a non-negligible photocurrent contribution Iph;i is always present also in each i-th neighboring pixel. In

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particular, for the considered material, the minority carriers diffusion length Ldiff is much greater than the pixel pitch (Ldiff  150 mm at 77 K, and the overall lifetime is around 0:3 ms), so that carrier diffusion is very effective. According to [46], the ratio between the photocurrent in the i-th pixel and the photocurrent in the entire array Iph;i Ti ¼ X Iph;n

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(where the sum is done over all the pixels in the array) may be regarded as the total crosstalk, since it depends on both electrical (carrier diffusion related) and optical (beam tail related) effects. Figure 9.6 reports the simulated spectral QEi (left column) and crosstalks Oi and Ti (right column) for the three considered values of pixel pitch, d ¼ 3; 5; 10 mm, for the CP, NNs, and CNs. Considering the central pixel only, it can be noticed that both OCP and TCP (red solid lines and stars) tend to 1 for decreasing l, and increase with d for all wavelengths, as follows from simple geometrical reasons. Regarding NNs and CNs, both optical and electrical crosstalks concur in determining Ti , although not in a simple additive way, due to the nonlinearity of drift-diffusion equations. The contribution of optical crosstalk becomes progressively less relevant when l decreases below d, because the beam radius becomes smaller. On the contrary, when l > d, the total crosstalk is dominated by the optical contribution (Ti  Oi , both for NNs and CNs). This means that, thanks to the small absorber thickness ðtabs ¼ 2 mmÞ, in the spectral interval l ¼ 5  9 mm even a pixel pitch as narrow as 3 mm could allow a total crosstalk Ti  0:1, a value typical of present standard devices [56,57]. Even smaller values of Ti could be obtained by reducing the electrical crosstalk with non-planar FPAs, like in [1, Chapter 7] and [56,58]. In summary, numerical simulation employing Gaussian beam illumination and appropriate definitions for crosstalk can be regarded as a valuable tool for crosstalk investigation.

9.2.3 Modeling photoresponse for non-monochromatic illumination Generally, the lens of an IR camera focuses a scene containing all the wavelengths in a given spectral window ½lmin ; lmax , with a spectral power distribution that, at least for thermal sources (e.g. buildings, human bodies, rocket and airplane engines, exhaust gases, etc.), may be well approximated by a Planck’s distribution with blackbody temperature TB . Traditional detector arrays are typically designed for narrow-band illumination, due to inadequate absorption and charge-collection efficiency when photons with very different wavelengths illuminate the FPA. Detector designs overcoming these issues are based on photon-trapping microstructures [17,18,59,60], type-II strained-layer superlattice (SLS) architectures [1,18,61], multispectral adaptive FPAs [6,62], quantum well IR photodetectors (QWIP) [18], etc. As detectors become increasingly complex, more design

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Figure 9.6 Simulated spectral QE and inter-pixel crosstalk contributions Oi (lines) and Ti (symbols), under Gaussian illumination centered on the central pixel, for d ¼ 3; 5; 10 mm. Adapted and reprinted, with permission, from [34]

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variations need to be considered, requesting rapid and efficient simulations without sacrificing the accuracy. For this purpose, it is important to develop modeling methods conceived for efficient simulations of the photoresponse of FPAs illuminated by non-monochromatic, broadband optical sources. A possible approach consists in performing a single broadband FDTD optical simulation, using a very narrow time domain Gaussian pulse fðtÞ as an input, with spatial Gaussian shape. If we discretize it, a discrete Fourier transform (DFT) gives  2 t fðtÞ ¼ sin ð2pn0 tÞexp  2 ; t ¼ nDt t M 1 X Fðni Þ ¼ fðnDtÞcos ði2pni nDtÞ;

(9.10)

n¼0

where M is the number of time steps needed to obtain convergence, n0 is the central frequency of the pulse, t is the temporal pulse width, and Dt is the time step. Typically t  l=ð2cÞ, whereas the choice of Dt depends on the size of the spatial optical mesh, and must fulfill the Courant condition [50, Sec. C.3.2]. For a uniform optical mesh, a spatial step in the order of l=ð10 nÞ is oftenpan ffiffiffi appropriate choice, and the Courant condition is fulfilled for Dt  l=ð10 n c 3Þ or smaller. M depends on the chosen tolerance and therefore is not explicitly set. During the simulation, the fðnDtÞ values are !stored and employed to calculate ! Fðni Þ. If the j’s represent the vectors’ E and H components, Fðni Þ can be used to obtain the rates Ai;opt through (9.2) at all the frequencies fni g with a single FDTD simulation. The N rates Ai;opt can be then normalized and summed according to the spectral density of the considered optical source (generally, this should be done by an automatic script integrated in the optical simulator), obtaining the aggregated rates Aagg and Gagg ¼ hAagg (see Ref. [63] for details on the method). Following this approach, the effects of the spectral distribution of the IR source (e.g. its blackbody temperature TB , if it is a thermal source), or the effect of detector geometrical parameters can be assessed, employing Gagg as the source term of electrical, drift-diffusion based, 3D simulations. Electrical simulations allow to define a useful figure of merit [63], i.e. the ratio Ci between the photocurrent Iph collected by the electrical contact of the i-th pixel and by the miniarray’s central pixel CP, Ci ¼

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(9.11)

that can be regarded as a possible definition of the inter-pixel crosstalk. An example of results can be seen in Figure 9.7, where the effect of the optical source blackbody temperature TB and the absorber thickness tabs were assessed for the same LWIR detector shown in Figure 9.5(d) and (e).

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9.3 HOT HgCdTe detectors: Technologies and modeling approaches Minimizing the dark current and the noise mechanisms limiting the performance of photodetectors is a fundamental purpose [23]. For these purposes, the first solution is to operate at low temperature, usually around 77 K, in order to reduce the high carrier generation-recombination (GR) rate inherent in all narrow bandgap detectors. However, the required cryogenic cooling of HgCdTe IR detectors is very expensive, and, in the last 15 years, huge efforts have been invested to develop detectors with reduced cooling requirements, known as HOT detectors [64–67].

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Considering a detector based on a very general photodiode scheme, the dark current depends on intrinsic mechanisms (only related to the material properties), and defect-related mechanisms that depend on bulk and/or surface defects. The first group of mechanisms are: ●

●

the Auger and radiative GR in the n- and p-doped regions, generating the ensuing diffusion current, the band-to-band tunneling (BTBT),

whereas the most important defect-related mechanisms include ●

● ●

Shockley-Read-Hall (SRH) GR mechanisms in the depletion region, generating a diffusion current as well, trap-assisted tunneling, and surface GR processes.

The most important parameter that affects the details of images captured by a FPA is the noise equivalent temperature difference (NETD). This is not strictly related to pixel’s geometry and ensuing optical resolution, since it is defined as the temperature difference which would produce a signal equal to the average noise of a FPA [4,6]. A FPA with good NETD performance is more suitable for detecting slight differences in temperature between objects, which provides more details and more accurate images, with a higher ability to detect smaller objects at greater distances in all weather conditions, an important requirement in many civilian and military applications.

9.3.1 Defects- and tunneling-related dark current The NETD is heavily affected by the dark current, which is dominated at low temperatures by the diffusion component, while at high temperatures by defectrelated components. At increasing operating temperature a growth of the electrically active defects density occurs, leading to a significant increase of the dark current. Therefore, any approach aiming at reducing one of the dark-current components (acting on the related GR-mechanism) is helpful in increasing the maximum temperature at which a FPA can operate. Reducing or eliminating defect-related GR-mechanisms, the FPA would result Auger-limited, i.e. characterized only by dark-current contributions that cannot be eliminated just by an improvement of the material quality (e.g. reducing the impact of SRH mechanism, related to defects density, especially to Hg-vacancies [68]). Modeling can be very helpful in understanding the contributions of GRmechanisms to dark current. For example, in [68], the dark currents of two sets of MWIR detectors with n-on-p architecture were analyzed. In Figure 9.8, the 3D structure of a single-pixel, as modeled in [68], is shown. The difference between the two sets was only the adopted doping technique [7,29]: one set was Hg-vacancy p-doped through a standard technology (acceptor concentration NA ¼ 2  1016 cm3 ), while for the other set Au was used as acceptor ðNA ¼ 5  1015 cm3 Þ and the number of Hg vacancies was kept low.

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Figure 9.8 3D structure of the MWIR single-pixel photodetectors modeled in [68], with its 2D cross-section at the device center. Adapted and reprinted, with permission, from [68]

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The dark-current contributions for these detectors were simulated in the driftdiffusion approximation, and in Figure 9.9 experimental and simulated dark-current densities versus reverse bias are reported. 3D simulations included the GR contributions of Auger, SRH, radiative, BTBT, and impact ionization GR-mechanisms, for the described two variants of doping.

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Regarding BTBT, simulations adopted a less idealized case respect to the classical work by Kane [69], adapting a model proposed in [70,71], according to which the BTBT generation rate is given by   B D1 Dþ1 2 RBTBT ¼ A d E exp  pffiffiffiffi (9.12) d E where E is the electric field, and the A and B coefficients are [72,73] qffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi p me Eg3 q2 2me : A ¼  3 2 pffiffiffiffiffi ; B ¼ pffiffiffi 4p ℏ Eg 2 2 qℏ

(9.13)

The BTBT rate depends on the parameters D (a fitting parameter) and pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d  2qni L=e, where Eg is the bandgap, me is the electron’s mass, e is the average dielectric constant, L is the total device length, ni the intrinsic carrier density, and q and ℏ the electron charge and the reduced Planck’s constant, respectively. Impact ionization (II) is customarily included in device simulations by means of a semiempirical post-processing involving a bias voltage V dependent gain factor MðV Þ that multiplies the dark-current density Jdark ðV Þ simulated taking into account all other generation mechanisms, Jdark;II ðV Þ ¼ MðV ÞJdark ðV Þ:

(9.14)

The advantage of this approximate approach is to avoid the very intensive computations involved by a self-consistent inclusion of II in the DD model, e.g. through the Okuto-Crowell formulation [74]. The gain factor MðV Þ have the form [75,76]    Vth M ðV Þ ¼ exp aV exp  (9.15) V which depends on the two fitting parameters, a and Vth . Modeling revealed to be very useful (a) to understand the importance of reducing vacancy density in order to reduce SRH contribution to dark current, and (b) to ascribe the rapid increase of dark current in Figure 9.9(a) to the impact ionization, instead of BTBT or trap-assisted-tunneling as initially suspected. An extensive discussion on these points and on the adopted models for BTBT and II can be found in [68]. There are several methods to reduce defects-related contributions to dark current, which can belong to two classes. One approach is based on improving growth and post-growth processing techniques, or to optimize the choice of dopants (as in the discussed example), in order to reduce the defect density. The other strategy consists of developing new detector device architectures that are less sensitive to the presence of defects. Some specific approaches are the adoption of high-quality passivation, reduction of dislocations, adoption of thin absorber to reduce the material volume when possible, and barrier detectors [77–79].

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Figure 9.10 Schematic energy band diagram of an ideal nBn detector under illumination and low reverse bias. Adapted and reprinted, with permission, from [6] Among the possible approaches, the unipolar nBn barrier detectors, whose schematic is shown in Figure 9.10, is particularly interesting. It consists in a thin wide bandgap layer (represented by the “B”) sandwiched between a n-doped narrow bandgap absorber (whose thickness should be comparable to the absorption length of light in the device, typically several microns) and a thin n-doped narrow bandgap contact region, used to drive the device to reverse bias operation. The important point is to have almost zero valence band offset so that there is no hole barrier present throughout the heterostructure, while a large conduction band offset (electron barrier) is kept. This barrier schematic allows photogenerated minority carrier (holes) to flow to the contact with ease, even at very low bias. Instead, the majority carrier dark current and the (possible) surface current are blocked by the large energy barrier in the conduction band. Since there is no high-field depletion region present in the device structure (where SRH GR-processes are very effective), the nBn detector can effectively suppress and reduce dark-current contributions associated with SRH processes and tunneling mechanisms [6].

9.3.2 Auger-suppressed and fully carrier-depleted detectors In p-doped absorbers, the Auger-7 rate is dominant over Auger-1 [23,80], but its lifetime is much longer than the latter. Therefore, the n-on-p architecture (a low-pdoped absorber sandwiched between a CdTe substrate and a high n-doped contact region), which was developed in the early days and used for decades, should be preferable. However, this is not what generally happens.

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Figure 9.11 Schematic structures for (a) DLHJ, (b) DLPH, and (c) Pþ nPþ HgCdTe detectors with p-on-n. Adapted and reprinted, with permission, from [6] Detectors based on n-on-p architectures are fabricated by growing a p-type HgCdTe layer using Hg vacancies as acceptors, and obtaining the np-junction by ion implantation. In fact, using Hg vacancies in the active layer degrades the minority carriers lifetime, as they increase the SRH GR rate. As a result, the detector exhibits higher dark current than for the case of extrinsic p-type doping. Actually, as discussed in Section 9.3.1, possible attempt to reduce the SRH contribution is to avoid Hg vacancies, employing other dopants as acceptors. Another approach is to adopt p-on-n architectures, which enable different strategies aimed at reducing the dominant Auger-1 mechanism (that has shorter lifetime than Auger-7) in the n-absorber, leading to the so-called Auger-suppressed detectors. This is the approach adopted starting from mid-eighties [6] and now widely implemented. The reduction of the Auger contribution to dark current can be obtained extending the concept of the p-on-n architecture to double layer heterojunction (DLHJ), double-layer planar heterostructures (DLPH), non-equilibrium Pþ nPþ or also Pþ N  n N  N architectures [81], see Figure 9.11. The idea is to exploit low doping levels in the absorber and peculiar band energy profiles to obtain fully carriers depleted absorber at moderate reverse bias voltage. Let us describe this in more detail. Depleted photodetectors operate under a particular condition: the space charge region should occupy a significant fraction of the detector, i.e. a fraction larger than the quasi-neutral regions. The outcome is a substantial reduction of Auger-1 transitions in the n-doped regions, and the ideal situation would be a detector without quasi-neutral regions. In order to understand the trends of carrier generations with doping and band energy profiles, absorber thickness, pixel size, etc., it is not possible to pursue a unique and straightforward modeling approach. For example, the analyses in [81] were conducted by a combined one-dimensional (1D) analytical model, and 2D numerical simulations within the drift-diffusion approximation, each other reciprocally validating their own results. The approach of carrier depletion may be helpful also in reducing considerably the inter-pixel diffusive crosstalk in dense FPAs, as already argued in quite old works [83,84]. This issue is particularly complex, and also in this case combined – numerical and analytical – methods of analysis may reveal their strength.

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As an example, [82] investigated the FPA shown and described in Figure 9.5 by means of 3D numerical simulations, performed by commercial codes that solved the optical problem with the standard full-wave FDTD method and the electrical problem with the finite-box method within the drift-diffusion approximation (see a brief description in Section 9.2.1). The authors calculated the diffusive inter-pixel crosstalk that takes place when a realistic, non-monochromatic (blackbody) Gaussian beam is focused on the miniarray’s CP, for a few values of absorber and carrier depletion region thicknesses. The diffusive contribution to crosstalk DNNs originates from carriers photogenerated in the illuminated pixel that diffuse laterally to the neighboring ones, and it is defined as the ratio DNNs ¼

Idiff ;NNs ; Iph;CP

(9.16)

where Idiff ;NNs is the current that carriers, photogenerated in the CP and diffused laterally in neighboring pixels, produce in NNs, and Iph;CP is the photocurrent collected by the CP. In parallel an approximate, closed-form model, aimed at better understanding the effects of diffusion on crosstalk was developed. The model avoids to solve the carrier diffusion problem, and it is based instead on a probabilistic description that complements a much more tractable 1D diffusion model. All the details of the closed-form model can be found in [82]. In this way, it was possible to obtain compact expressions for diffusive crosstalk, suitable to develop design rules to keep diffusive crosstalk under control, acting on pixel pitch, absorber thickness, extension and depth of the absorber depleted region. The crucial step was the validation of the closed-form model against the results of 3D numerical simulations for several values of parameters, whose results are shown in Figure 9.12(a). After this validation step, the model was employed to obtain several trends of DNNs with respect to FPA pixel pitch and absorber thickness. An example of the results that can be obtained is reported in Figure 9.12(b).

9.3.3 Compositionally graded HgCdTe detectors The approach of carrier-depleting the HgCdTe absorber layer by using appropriate composition and doping profiles [6,81,85,86] has received attention as a method of reducing the dark current, and the adoption of Hg1xCdxTe absorbers with finetuned compositional grading is becoming a standard option also in order to optimize the quantum efficiency (QE) and to reduce the inter-pixel crosstalk due to carrier diffusion [87,88]. For example, [89] considers a detector, whose scheme is shown in Figure 9.13, where the absorber layer was given a graded composition, varying the Cd mole fraction from x ¼ 0:21 to x ¼ 0:19, from its lower to its upper interface, in order to maintain a constant peak wavelength at the temperature of operation. In addition, in order to increase realism, two 0:5 mm thick transition regions with linear compositional grading connect the low-Eg absorber layer (where Eg is the bandgap) to two high-Eg regions, important to obtain HOT operation. Thus, the capability to numerically predict the performance of FPA IR

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Figure 9.13 A p  i  n photodiode with compositional grading: (a) reverse bias approximate energy band diagram, (b) its architecture, (c) the calculated energy band diagram at equilibrium. Adapted and reprinted, with permission, from [89] C The Optical Society detectors with realistic state-of-the-art composition profiles is a present need and an essential step toward their development. Most commercial 3D device simulators allow to handle the electrical modeling of photodetectors, even if compositionally graded. Conversely, the full-wave calculation of Gopt may require the development of particular techniques. In fact, the

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solution of the electromagnetic problem for detectors with arbitrary composition profile may not be straightforward, since not all simulators manage a compositional grading, requiring to define the detector geometry as a stack of layers each with uniform optical properties. For planar structures, one possible method is to sample the profile, converting it to a staircase, thus discretizing the detector itself into a large stack of layers, each with uniform values for the real and imaginary parts of the HgCdTe refractive index n and k. Details of the method with hints for its implementation are described in [90]: in short, a Tcl [91] script builds the device geometry, discretizing the compositionally graded layers into N sublayers, building N look-up tables ðlm ; nm ; km Þi , for values lm 2 ½1; 20 mm, separated by 0:1 mm. In the end, N material libraries will be produced, allowing the FDTD algorithm to deal with N uniform-composition regions. In Figure 9.14(a), 3D overall view of a single pixel shows the discretization into N ¼ 10 sublayers of the low-Eg absorber region and the two transition regions. In Figure 9.14 (b) and (c), the real and imaginary parts of the complex refractive index n and k, calculated for T ¼ 140 K and l ¼ 9 mm, are shown for a small portion of a vertical 2D cutplane (the dashed portion shown in panel (a)). In Figure 9.14(d) and (e) n and k are shown along a vertical 1D cutline at center pixel: panel (d) is centered across the low-Eg absorber region, and panel (e) across one of the two transition regions. The importance of simulating Aopt ðlÞ keeping into account the compositional grading of the detector’s absorber depends on the steepness of the grading. If the composition gradient is very low, often an average of composition across the detector is an acceptable approximation. For example, for the structure in [89], the Cd mole fraction x varies linearly in the absorber in the interval x 2 ½0:19; 0:21, and the use of an averaged composition is an acceptable approximation. This can be observed in Figure 9.15(a), where the calculated QEðlÞ is shown, comparing FDTD spectra obtained with the described discretization scheme with N ¼ 10 (stars), or averaging the n and k in each graded region (circles). As a counterexample, Figure 9.15(b) shows the corresponding simulation for a variant of the absorber for which the compositional grading is still linear, but steeper, varying in the interval x 2 ½0:19; 0:25. It reveals that as soon as moderately steeper profiles are considered, the approximation loses precision, enforcing the necessity of accurate FDTD simulations to obtain reliable modeling results. Figure 9.15(a) and (b) also shows the spectra obtained with the ray tracing, a method based on classical optics and absorption Beer’s law [92]. This method is not a valid alternative: since the interfaces with metallizations are highly reflecting in the considered IR bands, large metallization contacts lead to substantial absorption enhancement close to cutoff wavelength, due to spatial resonances and cavity effects [33]. Since ray tracing does not address interference, it often underestimates the cutoff wavelength, as well evident in the cited figures. Regarding the choice of the discretization parameter N for the FDTD electromagnetic simulation, its value has generally a small impact on the computational cost of the simulation. Consequently, it is recommended to choose a value large enough to sample the absorption coefficient profile aðzÞ properly, in order to get an accurate estimate of the detector’s cutoff wavelength.

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Figure 9.14 (a) 3D overall view of a single pixel, showing the discretization into sublayers of the low-Eg absorber region and the two transition regions. In panels (b) and (c), the real and imaginary parts of the complex refractive index n and k, calculated for T ¼ 140 K and l ¼ 9 mm, are shown for a small portion of a vertical 2D cutplane. In panels (d) and (e) n and k are shown along a vertical 1D cutline at center pixel: panel (d) is centered across the low-Eg absorber region, and panel (e) across one of the two transition regions. Adapted and reprinted, with permission, from [90]

9.4 Conclusions IR FPAs have come a long way since the first photovoltaic 2D arrays were produced in the 1980s. Today they provide nearly ideal background-limited performance that will enable much of the space science over the next decades. The unique properties of HgCdTe, combined with appropriate detector design, make it easy to

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Figure 9.15 Calculated QE spectra: comparing FDTD spectrum obtained with the described discretization scheme, with N ¼ 10 (stars), or averaging the n and k in each graded region (circles). Dashed line, spectrum obtained with the ray tracing method. Panels (a) and (b) refer respectively to the Cd profiles when in the absorber the Cd profile varies linearly in x 2 ½0:19; 0:21 or in the x 2 ½0:19; 0:25 intervals. Adapted and reprinted, with permission, from [90] predict its ongoing leading role in the IR imaging. Nevertheless, Sb-based superlattice fabrication processing is based on standard III-V technology, implying lower costs of mass production and constituting a relatively new alternative for an IR material system in LWIR and VLWIR bands. HOT and fully-depleted (Augersuppressed) detectors, barrier detectors, multi-bands FPAs, and subwavelength operation are among the key ingredients to obtain IR FPAs with superior performance. In addition, advances in metamaterials and photonic crystal structures let us glimpse new approaches to device design methodologies, improving light coupling with the detector active region and promising several new ways to integrate photonic functions for the enhancement of IR detector performance.

References [1] Dhar NK, Dat R, and Sood AK. Advances in infrared detector array technology. In: Pyshkin SL, Ballato JM, editors. Optoelectron. Adv Mater Dev. Rijeka, Croatia: IntechOpen; 2013. pp. 149–190. [2] Bhan RK, and Dhar V. Recent infrared detector technologies, applications, trends and development of HgCdTe based cooled infrared focal plane arrays and their characterization. Opto-Electron Rev. 2019;27(2):174–193. [3] Lawson WD, Nielsen S, Putley EH, et al. Preparation and properties of HgTe and mixed crystals of HgTe-CdTe. J Phys Chem Solids. 1959;9(3):325–329. [4] Rogalski A. Infrared Detectors. 2nd ed. Boca Raton, FL: CRC Press; 2011.

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Integrated optics Volume 2: Characterization, devices, and applications Zhang S, Soibel A, Keo SA, et al. Solid-immersion metalenses for infrared focal plane arrays. Appl Phys Lett. 2018;113:111104. Vanamala N, Santiago KC, and Das NC. Enhanced MWIR absorption of HgCdTe (MCT) via plasmonic metal oxide nanostructures. AIP Adv. 2019;9:025113. Kinch MA, Brau MJ, and Simmons A. Recombination mechanisms in 8–14–m HgCdTe. J Appl Phys. 1973;44(4):1649–1663. Kinch MA. Fundamental physics of infrared detector materials. J Electron Mater. 2000;29(6):809–817. Kinch MA. Fundamentals of Infrared Detector Materials. Bellingham, WA: SPIE; 2007. Bertazzi F, Moresco M, Penna M, et al. Full-band Monte Carlo simulation of HgCdTe APDs. J Electron Mater. 2010;39(7):912–917. Bertazzi F, Goano M, and Bellotti E. Calculation of Auger lifetime in HgCdTe. J Electron Mater. 2011;40(8):1663–1667. Tennant WE, Lee D, Zandian M, et al. MBE HgCdTe technology: A very general solution to IR detection, described by “Rule 07”, a very convenient heuristic. J Electron Mater. 2008;37(9):1406–1410. Kinch MA. HgCdTe: Recent trends in the ultimate IR semiconductor. J Electron Mater. 2010;39(7):1043–1052. Wollrab R, Schirmacher W, Schallenberg T, et al. Recent progress in the development of hot MWIR detectors. In: 6th International Symposium on Optronics in Defence and Security (OPTRO 2014). Paris; 2014. Coussa RA, Gallagher AM, Kosai K, et al. Spectral crosstalk by radiative recombination in sequential-mode, dual mid-wavelength infrared band HgCdTe detectors. J Electron Mater. 2004;33(6):517–525. Sood AK, Egerton JE, Puri YR, et al. Design and development of multicolor MWIR/LWIR and LWIR/VLWIR detector arrays. J Electron Mater. 2005;34 (6):909–912. Holst GC, and Driggers RG. Small detectors in infrared system design. Opt Eng. 2012;51(9):096401. Vallone M, Goano M, Bertazzi F, et al. Comparing FDTD and ray tracing models in the numerical simulation of HgCdTe LWIR photodetectors. J Electron Mater. 2016;45(9):4524–4531. Vallone M, Goano M, Bertazzi F, et al. Simulation of small-pitch HgCdTe photodetectors. J Electron Mater. 2017;46(9):5458–5470. Strong RL, Kinch MA, and Armstrong JM. Performance of 12-mm- to 15mm-pitch MWIR and LWIR HgCdTe FPAs at elevated temperatures. J Electron Mater. 2013;42(11):3103–3107. Reibel Y, Pe´re´-Laperne N, Augey T, et al. Getting small: New 10 mm pixel pitch cooled infrared products. In: Infrared Technology and Applications XL. vol. 9070, Proceedings of the SPIE; 2014. p. 907034. Reibel Y, Pe´re´-Laperne N, Augey LRT, et al. Update on 10 mm pixel pitch MCT-based focal plane array with enhanced functionalities. In: Infrared

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Integrated optics Volume 2: Characterization, devices, and applications Sze SM. Physics of Semiconductor Devices. 2nd ed. New York: John Wiley & Sons; 1981. Selberherr S. Analysis and Simulation of Semiconductor Devices. Wien: Springer-Verlag; 1984. Wehner JGA, Smith EPG, Radford W, et al. Crosstalk modeling of small-pitch two-color HgCdTe photodetectors. J Electron Mater. 2012;41(10):2925–2927. Armstrong JM, Skokan MR, Kinch MA, et al. HDVIP five-micron pitch HgCdTe focal plane arrays. In: Infrared Technology and Applications XL. vol. 9070, Proceedings of the SPIE; 2014. p. 907033. Knowles P, Hipwood L, Shorrocks N, et al. Status of IR detectors for high operating temperature produced by MOVPE growth of MCT on GaAs substrates. In: Electro-Optical and Infrared Systems: Technology and Applications IX. vol. 8541, Proceedings of the SPIE; 2012. p. 854108. Wehner JGA, Smith EPG, Venzor GM, et al. HgCdTe photon trapping structure for broadband mid-wavelength infrared absorption. J Electron Mater. 2011;40(8):1840–1846. Schuster J, and Bellotti E. Analysis of optical and electrical crosstalk in small pitch photon trapping HgCdTe pixel arrays. Appl Phys Lett. 2012;101 (26):261118. Rogalski A, Martyniuk P, and Kopytko M. Type-II superlattice photodetectors versus HgCdTe photodiodes. Progress Quantum Electron. 2019; p. 100228. Rogalski A, Antoszewski J, and Faraone L. Third-generation infrared photodetector arrays. J Appl Phys. 2009;105(9):091101. Vallone M, Palmieri A, Calciati M, et al. Non-monochromatic 3D optical simulation of HgCdTe focal plane arrays. J Electron Mater. 2018;47 (10):5742–5751. Ashley T, and Elliott CT. Model for minority carrier lifetimes in doped HgCdTe. Electron Lett. 1985;21(10):451–452. Elliott CT. Non-equilibrium modes of operation of narrow-gap semiconductor devices. Semiconductor Sci Tech. 1990;5(35):S30. Martyniuk P, and Rogalski A. HOT infrared photodetectors. Opto-Electron Rev. 2013;21(2):239–257. Wang P, Xia H, Li Q, et al. Sensing infrared photons at room temperature: From bulk materials to atomic layers. SMALL. 2019;15(46):1904396. Vallone M, Mandurrino M, Goano M, et al. Numerical modeling of SRH and tunneling mechanisms in high-operating-temperature MWIR HgCdTe photodetectors. J Electron Mater. 2015;44(9):3056–3063. Kane EO. Theory of tunneling. J Appl Phys. 1961;32(1):83–89. Verhulst AS, Leonelli D, Rooyackers R, et al. Drain voltage dependent analytical model of tunnel field-effect transistors. J Appl Phys. 2011;110 (2):024510. Ahmed K, Elahi MMM, and Islam MS. A compact analytical model of bandto-band tunneling in a nanoscale p-i-n diode. In: 2012 International Conference on Informatics, Electronics and Vision (ICIEV); 2012.

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[72] Adar R. Spatial integration of direct band-to-band tunneling currents in general device structures. IEEE Trans Electron Devices. 1992 April;39 (4):976–981. [73] Jo´z´wikowski K, Kopytko M, Rogalski A, et al. Enhanced numerical analysis of current-voltage characteristics of long wavelength infrared n-on-p HgCdTe photodiodes. J Appl Phys. 2010;108(7):074519. [74] Okuto Y, and Crowell CR. Energy-conservation considerations in the characterization of impact ionization in semiconductors. Phys Rev B. 1972 Oct;6 (8):3076–3081. [75] Elliott CT, Gordon NT, Hall RS, et al. Reverse breakdown in long wavelength lateral collection CdxHg1xTe diodes. J Vac Sci Technol A. 1990;8 (2):1251–1253. [76] Rothman J, Mollard L, Gouˆt S, et al. History-dependent impact ionization theory applied to HgCdTe e-APDs. J Electron Mater. 2011;40(8):1757– 1768. [77] Maimon S, and Wicks GW. nBn detector, an infrared detector with reduced dark current and higher operating temperature. Appl Phys Lett. 2006;89 (15):151109. [78] Itsuno AM, Phillips JD, and Velicu S. Predicted performance improvement of Auger-suppressed HgCdTe photodiodes and p-n heterojunction detectors. IEEE Trans Electron Devices. 2011;58(2):501–507. [79] Itsuno AM, Phillips JD, and Velicu S. Mid-wave infrared HgCdTe nBn photodetector. Appl Phys Lett. 2012;100(16):161102. [80] Kinch MA, Aqariden F, Chandra D, et al. Minority carrier lifetime in pHgCdTe. J Electron Mater. 2005;34(6):880–884. [81] Schuster J, Tennant WE, Bellotti E, et al. Analysis of the Auger recombination rate in PþNnNN HgCdTe detectors for HOT applications. In: Infrared Technology and Applications XLII. vol. 9819, Proceedings of the SPIE; 2016. p. 98191F. [82] Vallone M, Goano M, Bertazzi F, et al. Diffusive-probabilistic model for inter-pixel crosstalk in HgCdTe focal plane arrays. IEEE J Electron Devices Soc. 2018;6(1):664–673. [83] Kamins TI, and Fong GT. Photosensing arrays with improved spatial resolution. IEEE Trans Electron Devices. 1978;25(2):154–159. [84] Dhar V, Bhan RK, and Ashokan R. Effect of built-in electric field on crosstalk in focal plane arrays using HgCdTe epilayers. Infrared Phys Tech. 1998;39(6):353–367. [85] Martyniuk P, Gawron W, Pawluczyk J, et al. Dark current suppression in HOT LWIR HgCdTe heterostructures operating in non-equilibrium mode. J Infrared Millim Waves. 2015;34:385–390. [86] Schuster J, DeWames RE, and Wijewarnasurya PS. Dark currents in a fullydepleted LWIR HgCdTe P-on-n heterojunction: Analytical and numerical simulations. J Electron Mater. 2017;46(11):6295–6305. [87] Vallone M, Goano M, Bertazzi F, et al. Reducing inter-pixel crosstalk in HgCdTe detectors. Opt Quantum Electron. 2020;52(1):25.

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Integrated optics Volume 2: Characterization, devices, and applications Vallone M, Goano M, Bertazzi F, et al. Constraints and performance tradeoffs in Auger-suppressed HgCdTe focal plane arrays. Appl Opt. 2020;59. Rogalski A, Kopytko M, and Martyniuk P. Performance prediction of p-i-n HgCdTe long-wavelength infrared HOT photodiodes. Appl Opt. 2018;57 (18):D11–D18. Vallone M, Goano M, Bertazzi F, et al. FDTD simulation of compositionally graded HgCdTe photodetectors. Infrared Phys Tech. 2019;97:203–209. Ousterhout J, and Jones K. Tcl and Tk toolkit. Addison-Wesley Professional; 2010. Spencer GH, and Murty MVRK. General ray-tracing procedure. J Opt Soc Amer. 1962 ;52(6):672–676.

Chapter 10

Arrayed waveguide gratings for telecom and spectroscopic applications Dana Seyringer1

In the initial phase of integrated optics, one of the largest commercial successes were the applications in the field of telecommunications. The main problem to be solved was the fact that the conventional electric data transfer, where only one electric signal can be transferred per cable, was no longer capable of handling the exponentially growing required bandwidth. It was therefore imperative to switch to optical technologies. However, at first, it was not clear how optical technologies could be used for telecom applications. The original idea was to make the classical optics smaller and use them as micro-electro-mechanical systems (MEMS). Despite some challenges in the production, this approach promised a shorter time to market than the alternative integrated optics, which would require the development of entirely new concepts to replace the classical electric data transfer. Nevertheless, the big advantage of integrated optics was the promise that, in the long run, the solutions could be integrated onto a chip by simply applying the well-established complementary metal-oxide-semiconductor (CMOS)-technology, which would bring down the component costs considerably faster. Nowadays, optics and photonics are widely regarded as one of the most important key technologies, having an impact on nearly all areas of our life and covering a wide range of applications in science and industry. However, new fields of applications require integrated optical solutions, pushing photonics towards increased miniaturization. As a result, photonics integrated circuits (PICs) are gradually replacing discrete optical components to allow multiple functionalities on a single chip. With the telecom market as its initial application, the target for integrated optics was clear, but the approaches that could be used to replace the classical solutions had still to be developed. The main advantage of using optical data transfer is the possibility to send several optical signals simultaneously in one glass fibre without them interfering with one another. Therefore, one of the first major challenges was how to bring these signals into one fibre and then separate them at the receiving end of the transmission. 1

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A very obvious way was to use cascaded Mach-Zehnder Interferometer (MZI) to separate wavelengths serially, whereby individual elements are used to multiplex (or demultiplex) wavelengths on a one-by-one basis [1]. The main disadvantage of this approach is that the MZI based demultiplexers become considerably larger which, particularly for the high-channel-count applications, eliminates integration onto a chip. To reduce the size of the demultiplexers, the MZIs were replaced by ring resonators [1]. Their advantage was the compactness compared to MZIs, but it was still a cascaded approach, which is not suitable for high-channel-count applications. Thin film filters (TFF) and fibre Bragg gratings (FBG) were the first of those used in wavelength division multiplexing (WDM) systems when channel counts were low [2–5]. Although they use different physical mechanisms, they both still function by filtering wavelengths serially. TFFs use a concatenated set of individual interference filters, each of which has multiple dielectric coatings that pass a single wavelength and reflect all the others (Figure 10.1-TFF). TFFs work well for low-channel-counts but have limitations at higher channel counts (typically greater than 16) due to size and accumulated insertion losses.

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FBGs rely on a grating formed in the fibre core, which reflects a single wavelength but transmits all other wavelengths (Figure 10.1-FBG). Each FBG is designed with a different grating period L to multiplex or demultiplex a single wavelength in the system. The reflected wavelength is demultiplexed from the system fibre using an optical circulator. As is the case for TFFs, the serial process restricts the practical channel count due to size, accumulated insertion losses and the cost of individual piece parts. In contrast to TFFs and FBGs, arrayed waveguide gratings (AWG) and freespace diffraction gratings (FSDG) use a parallel approach that is more conducive to high-channel-count applications [6–8]. The AWGs are superior to other filters, in that they offer low loss and high channel count and can be mass produced. As the name says, the core element of an AWG is an array of waveguides of different lengths, which produce a constant phase shift from one waveguide to the next. In the output coupler, the various frequencies, used as the transmitting channels, interfere constructively at different focal points at the end of the coupler and consequently are coupled into different waveguides (Figure 10.1-AWG). The main advantage of this approach is that the spectral separation of optical signals is done in parallel and not in a sequential manner and therefore AWGs can achieve much higher integration densities than the other approaches. FSDGs work on a principle similar to that of the AWGs. The gratings are termed free-space gratings because the phase difference between diffracted beams is generated in free space, rather than in dispersion media such as waveguides. The basic elements of a FSDG are the input and output fibres, micro-optics array, collimating lenses and a finely ruled or etched diffraction grating, which serves as the dispersion engine to separate wavelengths into individual output fibres (Figure 10.1-FSDG). When a polychromatic light beam impinges on a diffraction grating, each wavelength is diffracted and directed to a different point in space. A fibre is placed at the focal points of each wavelength. In order to focus the different wavelengths, a lens system or a concave diffraction grating may be used.

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The AWGs are the most promising devices for filters or multi/demultiplexers in WDM systems because of their low insertion loss, high stability and low cost. AWGs were proposed and first reported in 1988 by Smit [9]. The first devices operating at short wavelengths were reported by Vellekoop and Smit [10–13], while Takahashi et al. reported the first devices operating in the long wavelength window [14,15]. Dragone extended the concept from 1
N demultiplexers to N
N devices, the so-called wavelength routers [16,17], which play an important role in multi-wavelength network applications. AWGs are known by several different names: the optical phased arrays (PHASARs), phased-array waveguide gratings (PAWGs) or waveguide-grating routers (WGRs). The acronym AWG, introduced by Takahashi [14], is the most frequently used name today.

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10.1.1 AWG principle An AWG multiplexer/demultiplexer is a planar waveguide device with both imaging and dispersive properties. It consists of input/output waveguides, the number of which usually equals the number of transmitting channels, an array of waveguides (also called phased array, PA) and two star-couplers (also called free propagation region, FPR) as shown in Figure 10.2. The waveguides in the phased array are spaced at regular intervals with a constant path-length increment DL from one to the next and join the star couplers at each end. AWGs can function both as multiplexers and as demultiplexers. An example of the operating principle of an AWG configured for spectral demultiplexing can be seen in Figure 10.2. In this configuration, the input star coupler is an expanding free-propagation region where the light beam becomes divergent, while the output star coupler functions as a focusing free-propagation region where each spectrally separated light beam is focused at one well-defined point on the focal line. Operation of the AWG demultiplexer can be explained as follows: one of the input waveguides (usually the waveguide positioned at the centre of the object plane of the input star coupler) carries an optical signal consisting of multiple wavelengths, l1 – ln into the coupler. Once in the coupler, the light beam is no longer confined laterally and expands. The array waveguides capture this diverging light, which then propagates towards the input aperture of the output star coupler. The length of array waveguides is selected so that the optical path length difference between adjacent waveguides, DL equals an integer multiple of the central wavelength, lc of the demultiplexer. For this wavelength, the fields in the individual arrayed waveguides will arrive at the input aperture of the output coupler with equal phase, and the field distribution at the output aperture of the input coupler will be reproduced at the input aperture of the output coupler. In the output star coupler, the light beam interferes constructively and converges at one single focal point on the focal line. In

Array of waveguides (phased array, PA) Output array aperture Input coupler aperture Output star coupler (FPR)

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λc Focal line

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Figure 10.2 Principle of an AWG optical demultiplexer

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this way, for the central wavelength lc, the input field at the object plane of the input star coupler is transferred to the centre of the image plane of the output star coupler. If the wavelength is shifted to lc  Dl (i.e. l1, l2, . . . .), there will be a phase change in the individual PA waveguides that increases linearly from the lower to the upper channel. As a result, the phase front at the input aperture of the output star coupler will be slightly tilted, causing the beam to be focused on a different position of the focal line in the image plane (Figure 10.3 left). By placing the waveguides in the correct positions, the field for each wavelength can be coupled into the respective output waveguide [18,19]. As a result, Figure 10.3 (right) shows the simulated spectral response (transmission characteristics) of AWG separating four optical signals.

10.1.2 Different types of AWGs Various AWGs are available on the market today, and their optical characteristics depend largely on the optical properties of the waveguide materials used. AWGs can be fabricated on various material platforms such as silica-on-silicon (SoS)buried waveguides [20–24], silicon-on-insulator (SOI) ridge waveguides [25], SOI nanowires [26,27], buried InP/InGaAsP ridge waveguides [28–31], polymer waveguides [32–34] or Si3N4 waveguides [35–37]. In terms of material, they can all be divided into two main groups, the so-called low-index contrast and highindex contrast AWGs.

10.1.2.1 Low-index contrast AWGs

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Phase front

Low-index contrast AWGs (SoS-based waveguide devices) were introduced to the market in 1994 [38]. They are considered an attractive dense wavelength division multiplexing (DWDM) solution because they represent a compact means of offering higher-channel-count technology, have good performance characteristics and can be more cost-effective per channel than other methods. Compared to other technologies, they may also offer quicker design cycle time, a uniform product and

–15 –20 –25 –30 –35 –40 –45

Array waveguides

Output waveguides

λ1

–50 1,546

1,547

1,548

1,549

1,550

1,551

1,552

Wavelength (nm)

Figure 10.3 Focusing the wavelengths on different positions of the focal line with four demultiplexed wavelengths (left). The result is called an AWG spectral response (right)

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the potential for easier scalability due to large commercial volumes [39]. A further advantage of low-index contrast AWGs is that they can be included in a more complex management system, such as optical add drop multiplexers (OADMs) [40] or with variable optical amplifiers (VOAs) [41,42]. With the recent development and growth of the fibre-to-the-x (FTTx) market, the AWGs have also been used for coarse wavelength division multiplexing (CWDM) applications, where a much lower number of transmitting optical signals is required [43]. In next-generation access networks (NGAN), AWGs have been found to be highly suitable as optical coders/encoders that can generate and process optical codes directly in the optical domain [44]. A comprehensive overview of AWGs and their applications can be found in [45]. For the most part, the low-index-contrast AWGs use SiO2-buried rectangular waveguides, usually with a cross section of (6
6) mm2 and a low refractive index contrast between the core (waveguide) and the cladding, Dn ~ 0.011 (refractive index of the core nc ~ 1.456, and refractive index of the cladding ncl ~ 1.445, as shown in Figure 10.4 upper row left). This parameter is also often expressed in percent as Dn ~ 0.75% from (nc – ncl)
100/nc. Low-index contrast AWGs still hold a large share of the AWG market because of their many advantages. Firstly, their modal field matches well with that of single-mode optical fibres (SMF), making it relatively easy to couple them to fibres (Figure 10.4 lower row left). Secondly, they combine low propagation loss (40 channels) leads to a rapid increase of the AWG size, and this, in turn, causes the deterioration of

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Measurement 0

|Lu = 0.4 dB|

IL = –5.1 dB

–15

BX = –36 dB

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BX = –21.4 dB

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Design 1a

IL = –8.2 dB

–15

–25 –30

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–45 –50 0.844

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850.5

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–20

BX = –22 dB

–10

Insertion loss (dB)

Design 1b

Insertion loss (dB)

850.0

IL = –7.9 dB

0

IL = –4.3 dB

–10

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–25

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852.0

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IL = –2 dB

0

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–5 BX = –32 dB

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Design 1c

Insertion loss (dB)

–10 –10 –15 –20 –25 –30

–45 –50

0.848

0.850

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Wavelength (μm)

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0.852

0.854

–35 845.0

845.5

846.0

846.5

847.0

847.5

Wavelength (μm)

Figure 10.19 Simulated/measured spectral responses of four 8-channel, 100-GHz Si3N4-based AWGs optical performance such as higher insertion loss and in particular higher channel crosstalk. Figure 10.21 also shows the simulated spectral response of 80-channel, 50-GHz AWG applying the same design parameters as in 40-channel, 50-GHz AWG design, i.e. dd ¼ 1.2 mm, dx ¼ 3.5 mm (Design 3a). From the characteristics

323

Design 2b

0 –2 –4 –6 –8 –10 –12 –14 –16 –18 –20 –22 –24 –26 –28 –30 –32 –34 –36 –38 –40 837.0

837.5

838.0

838.5

839.0

Insertion loss (dB)

Design 2a

Insertion loss (dB)

Arrayed waveguide gratings for telecom and spectroscopic applications 0 –2 –4 –6 –8 –10 –12 –14 –16 –18 –20 –22 –24 –26 –28 –30 –32 –34 –36 –38 –40

839.5

837.0

837.5

837.5

838.0

838.5

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839.0

839.5

Insertion loss (dB)

0 –2 –4 –6 –8 –10 –12 –14 –16 –18 –20 –22 –24 –26 –28 –30 –32 –34 –36 –38 –40 837.0

838.0

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839.5

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Design 2d

Design 2c

Insertion loss (dB)

Wavelength (nm) 0 –2 –4 –6 –8 –10 –12 –14 –16 –18 –20 –22 –24 –26 –28 –30 –32 –34 –36 –38 –40 837.0

837.5

838.0

838.5

839.0

839.5

840.

Wavelength (nm)

Figure 10.20 Simulated spectra of four designed 20-channel, 50-GHz Si3N4based AWGs is evident that the optical signals of 80-channel, 50-GHz AWG are much wider compared to 40-channel, 50-GHz AWG (defined through the bandwidth, B@5dB, and B@20dB, i.e., a width of optical signal, measured at a 5 dB, and 20 dB drop from transmission peak). The widening of the optical signal causes the increase in insertion loss IL by nearly 1 dB and particularly much higher adjacent channel crosstalk, AX and background crosstalk BX compared to 40-channel, 50-GHz AWG. The reason for such strong widening of the optical signals is a coupling in the phased array in the 80-channel, 50-GHz AWG (one of the mechanisms causing a high channel crosstalk). Increasing the number of output waveguides (parameter Num), the number of waveguides in the phased array (parameter Na) also increases and the optical path length difference between waveguides (parameter dL) decreases. As a result, the PA waveguides are placed closer to each other causing a coupling between them. This can be avoided by positioning arrayed waveguides further from each other (increasing parameter dd). Figure 10.22 shows the simulated spectral response of the same 80-channel, 50GHz AWG but with different parameter, dd ¼ 1.75 mm (Design 3b) and dd ¼ 2.2 mm (Design 3c). Both spectra feature the shape of optical signals similar to the signal shape of 40-channel, 50-GHz AWG. Such a high separation avoids the coupling in the phased array leading to a strong improvement of AWG optical properties. The proposed 80-channel, 50-GHz AWG designs were fabricated, and Figure 10.23 shows the detailed view of three measured optical signals in the

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Integrated optics Volume 2: Characterization, devices, and applications 40-channel, 50-GHz AWG

80-channel, 50-GHz AWG (Design 3c)

0

0

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Insertion loss (dB)

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BX = –38 dB

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852

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833

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835

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AX = –23.8 dB

839

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843

AX = –11.8 dB B@–5dB

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838

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837

Wavelength (nm)

850.7 850.8 850.9 851.0

851.1 851.2 851.3 851.4 851.5

Wavelength (nm)

–50 838.0 838.1

838.2

838.3

838.4

838.5

838.6 838.7

838.8

838.9

839.0

Wavelength (nm)

Figure 10.21 Simulated spectral response of Si3N4-based 40-channel and 80-channel, 50-GHz AWGs with calculated background crosstalk, BX and detailed view of the adjacent channel crosstalk, AX in the middle of the spectrum

middle of each spectrum, together with the calculated performance parameters. Similar to the simulations, these parameters describe very well the response of the optical properties to the design parameters. Particularly, the width of the optical signals from Design 3b and Design 3c is nearly the same and much narrower than the width of optical signals in Design 3a. The lowest insertion loss was reached in Design 3b (dd ¼ 1.75 mm), IL ¼ –6.7 dB. Design 3a, although having dd ¼ 1.2 mm, features the highest losses caused by widening of the optical signals (IL ¼ –10.3 dB). The worst adjacent channel crosstalk was measured between the channels in Design 3a, where PA waveguides were positioned the closest to each other causing the coupling in the array (AX ¼ –6.8 dB). The lowest adjacent channel crosstalk was achieved in the Design 3c, where the biggest separation was applied between PA waveguides (AX ¼ –9.41 dB). Background crosstalk BX also confirms the improvement of the channel isolation with increased parameter dd.

10.4.2.4

256-channel, 42-GHz AWG-spectrometer for SD-OCT

To design 256-channel, 42-GHz (¼ 0.1 nm) AWG–spectrometer, the following design parameters were used: dx ¼ 3.5 mm and dd ¼ 2.2 mm. Figure 10.24 (left)

Arrayed waveguide gratings for telecom and spectroscopic applications 80-channel, 50-GHz AWG (Design 3b)

80-channel, 50-GHz AWG (Design 3c)

0

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Wavelength (nm) AX = –33.5 dB

0

AX = –22 dB

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Insertion loss (dB)

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–40

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844.7

844.8

844.9

845.0

845.1

845.2

845.3

845.4

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Figure 10.22 Simulated spectral response of Si3N4-based 80-channel, 50-GHz AWGs (Design 3b, 3c) with calculated background crosstalk, BX and detailed view of the adjacent channel crosstalk, AX in the middle of the spectrum

shows the AWG layout of this design in a window of 20 mm
20 mm. The size of the structure reached 13 mm
14 mm. Figure 10.24 (right) plots the simulated spectrum of the first 16 channels with the calculated performance parameters [98]. The AWG was fabricated using standard CMOS processes [99]. Figure 10.25 shows the mask layout and the final chip comprising the various AWGs and additional test structures. Figure 10.26 presents the whole measured spectrum. Figure 10.27 shows the detailed view of the first 20 channels with the highest losses and the highest channel crosstalk (left), and 22 channels to the right of the centre wavelength with lowest losses and lowest channel crosstalk in the spectrum (right). The 256-channel, 42-GHz AWG was integrated in a standard fibre-based OCT system and tested by performing first OCT measurements [100]. Interference signals were coupled into the AWG and the individual wavelengths were projected onto a commercial CCD camera. Standard OCT processing including background subtraction, wavelength resampling and dispersion compensation followed by fast Fourier transformation (FFT) were performed. Figure 10.28 (upper row) shows an in vitro mouse ear, 10
averaged. Figure 10.28 (lower row) shows a tomogram of

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–5

AX = –6.8 dB

–10

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829.0

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IL = –6.7 dB AX = –8.89 dB

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–5 80-channel, 50-GHz AWG (Design 3b)

830.5

–10 BX = –23.9 dB –15 –20 –25 –30 –35 853.5

854.0 854.5 Wavelength (nm)

855.0

0

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80-channel, 50-GHz AWG (Design 3c)

–5

IL = –8.3 dB AX = –9.41 dB

–10 –15 BX = –25 dB –20 –25 –30 –35 865.0

865.5

866.0 866.5 Wavelength (nm)

867.0

Figure 10.23 Measured spectral responses of 80-channel, 50-GHz AWG: Design 3a, dd ¼ 1.2 mm; Design 3b, dd ¼ 1.75 mm and Design 3c, dd ¼ 2.2 mm

Arrayed waveguide gratings for telecom and spectroscopic applications 0

IL = −4.87 dB

−5

327

AX = 17.63 dB

Insertion loss (dB)

−10 −15 −20 −25

BX = −49.3 dB

−30 −35 −40 −45 −50 0.8430

0.8435

0.8440

0.8445

0.8450

0.8455

Wavelength (μm)

Figure 10.24 Layout of 256-channel, 42-GHz AWG (left); detailed view of the simulated spectrum consisting of the first 16 channels with calculated AWG performance parameters (right)

OCT - Engine (MMI) DC/MMI Test MMI-A Test (Group 1) MMI-A Test (Group 2) Integrated OCT Signal

Design 256-42 GHz-D2

Design 256-42 GHz-D1

1 cm AWG_Layout_3A OCT - Engine (DC)

Figure 10.25 Mask layout with two different 256-channel, 42-GHz AWGs (left); fabricated chip (right) an in vivo fingertip, 10
averaged. These results show that in vivo imaging using an AWG for OCT application is sensitive enough for imaging scattering tissue. Further steps will be taken to acquire in vivo ophthalmic tomograms.

10.5

Conclusion

In the past years, the AWGs have proven to be superior to other filter approaches in that they provide reasonably good performance, allowing a high channel count

Normalized AWG Transmission (dB)

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−10 −15 −20 −25 −30 820

822

824

826

828

830 832 834 Wavelength (nm)

836

838

840

842

844

Figure 10.26 Measured spectral response of 256-channel, 42-GHz AWGspectrometer

IL = −9.865 dB

BX = −25 dB

−5

−10

AX = 7.6 dB

IL = −6.384 dB

−5

AX = 12.276 dB

−10

−15

−15

−20

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−25 −30 820.0

0 Normalized AWG Transmission (dB)

Normalized AWG Transmission (dB)

0

−25

820.5

821.0 Wavelength (nm)

821.5

822.0

−30 835.0

835.5 836.0 Wavelength (nm)

836.5

837.0

Figure 10.27 Detailed view of the first 20 channels with the highest losses and the highest channel crosstalk (left); 22 channels to the right of the centre wavelength with lowest losses and lowest channel crosstalk in the spectrum (right) and a compact footprint. The low-index contrast AWGs have particularly found application as filters and multi/demultiplexers in WDM systems, because of their low insertion loss, low channel crosstalk, high stability and low cost. However, the low refractive index contrast causes a great bending radius of the waveguides used in the AWG structures. As a result, the silica-based AWGs are usually very large, which limits the integration density of such components on a single chip. Unlike the low-index contrast AWGs, with the high-index contrast AWGs the waveguide’s size decreases proportionally to the increasing refractive index

Arrayed waveguide gratings for telecom and spectroscopic applications

329

250 μm

250 μm

Figure 10.28 OCT tomograms using an AWG as grating for spectral domain OCT: in vitro mouse ear imaged, 10
averaged (upper row) and in vivo fingertip, 10
averaged (lower row)

contrast, which makes it possible to use a far smaller bending radius of the waveguides, leading to a significant reduction in the AWG size. However, as was demonstrated in this chapter, when applying the same design, the performance parameters deteriorate significantly with the increasing number of output waveguides (transmitting channels) and therefore it was necessary to develop new AWG design procedures. The small chip size and proven reliability in telecommunication applications have allowed access to new markets in the medical and pharmaceutical sphere, where AWGs can be used as highly sensitive spectrometers. The fact that they can be integrated on a chip enables the realization of robust and cost-effective mobile devices. Since AWGs have proven their utilization in applications, such as the OCT, they are likely to be used in many other markets in the future where high integration and reliable performance are required.

Acknowledgements My sincere thanks go to my project colleagues, particularly to Elisabet Rank and Wolfgang Drexler from Medical University of Vienna; Alejandro Maese-Novo, Moritz Eggeling, Paul Muellner and Rainer Hainberger from AIT Austrian Institute of Technology GmbH; Martin Sagmeister, Marko Vlaskovic, Jochen Kraft, Guenther Koppitsch and Gerald Meinhardt from AMS AG; Horst Zimmermann from TU Wien; and Lenka Gajdosova from Vorarlberg University of Applied Sciences. The development of AWG-spectrometer was carried out in the framework of the project COHESION, no. 848588, funded by the Austrian Research Promotion Agency (FFG).

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[44] Broeke R.G., Cao J., Ji C., et al. ‘Optical-CDMA in InP’. IEEE J. Sel. Top. Quantum Electron. 2007, vol. 13(5), pp. 1497–1507. [45] Cincotti G. ‘Optical signal processing using AWGs’. 2014 The European Conference on Optical Communication (ECOC); Cannes, France, Sep 2014. (IEEE) pp. Tu 4.6.1. [46] Reed G.T., and Knights A.P. Silicon photonics: An introduction. Chichester: John Wiley & Sons, Ltd; 2004. [47] Pavesi L., and Lockwood D.J. (eds.) Silicon photonics. Berlin: Springer; 2004. [48] Deng Y., Liu Y., and Gao D. ‘Low crosstalk arrayed waveguide grating with cascaded waveguide grating filter’. J. Phy.: Conf. Series. 2011, vol. 276(1). [49] Lee K.K., Lim D.R., Luan H.-C., Agarwal A., Foresi J., and Kimerling L.C. ‘Effect of size and roughness on light transmission in a Si/SiO2 waveguide: experiments and model’. Appl. Phys. Lett. 2000, vol. 77(11), pp. 1617–1619. [50] Doerr C.R., Chen L., Buhl L.L., and Chen Y.-K. ‘8-channel SiO2/Si3N4/Si/ Ge CWDM receiver’. IEEE Photon. Technol. Lett. 2011, vol. 23(17), pp. 1201–1203. [51] Doerr C.R., Chen L., Chen Y.-K., and Buhl L.L. ‘Wide bandwidth silicon nitride grating coupler’. IEEE Photon. Technol. Lett. 2010, vol. 22(19), pp. 1461–1463. [52] Seyringer D., Gajdosova L., Burtscher, C., Kuzma, A., Chovan, J., and Uherek, F. ‘Design of low loss silicon nitride 8-channel AWG’. AIP Conference Proceedings; Sˇtrbske´ Pleso, High Tatras, Slovakia, June 2018 (College Park, Maryland, USA: American Institute of Physics; 2019), pp. 020042-1–020042-5. [53] Cheben P. ‘Wavelength dispersive planar waveguide devices: echelle and arrayed waveguide gratings’ in Calvo M.L., Lakshminarayanan V. (eds.). Optical waveguides: From theory to applied technologies. London: CRC Press; 2007. Chapter 5. [54] Kong S.-H., Correira J.H., de Graaf G., Bartek M., and Wolffenbuttel R.F. ‘Integrated silicon microspectrometers’. IEEE Instru. Measur. Mag. 2001, vol. 4(3), pp. 34–38. [55] Bradshaw J.T., Mendes S.B., and Saavedra S.S. ‘Planar integrated optical waveguide spectroscopy’. Anal. Chem. 2005, vol. 77(1), pp. 29–36. [56] van Dam C. ‘InP-based polarization independent wavelength demultiplexers’. PhD. thesis, Delft Univ of Technol., Delft, The Netherlands, 1997. [57] Apollo Photonics, Inc.: http://www.apollophoton.com [58] Optiwave: http://www.optiwave.com [59] Seyringer D. Arrayed waveguide gratings. SPIE Spotlights – New e-book series. Bellingham, Washington, USA: SPIE Press; 2016. [60] Fontaine N.K., Scott R.P., and Yoo S.J.B. ‘Dynamic optical arbitrary waveform generation and detection in InP photonic integrated circuits for Tb/s optical communications’. Opt. Commun. 2011, vol. 284(15), pp. 3693– 3705.

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Integrated optics Volume 2: Characterization, devices, and applications Chu Y., Zheng X., Zhang H., Liu X., and Guo Y. ‘The impact of phase errors on arrayed waveguide gratings’. IEEE J. Sel. Top. Quantum Electron. 2002, vol. 8(6), pp. 1122–1129. Ismail N., Sun F., Sengo G., et al. ‘Improved arrayed-waveguide-grating layout avoiding systematic phase errors’. Opt. Exp. 2011, vol. 19(9), pp. 8781–8794. Seyringer D. ‘Design and simulation of 128-channel 10 GHz AWG for ultradense wavelength division multiplexing’. 2012 14th International Conference on Transparent Optical Networks (ICTON); Coventry, UK, July 2012 (IEEE, 2012). Seyringer D., Bielik M., and Kytka M. ‘Introduction of a new software tool to design arrayed waveguide gratings’. Proceedings of the 17th International Conference on Applied Physics of Condensed Matter; Novy Smokovec, High Tatras, Slovakia, June 2011. pp. 122–125. Seyringer D., and Bielik M. ‘AWG-Parameters: new software tool to design arrayed waveguide gratings’. Proc. SPIE 8627, Integrated Optics: Devices, Materials, and Technologies XVII; San Francisco, CA, USA, Mar 2013. Seyringer D., Schmid P., Bielik M., Uherek F., Chovan J., and Kuzma A. ‘Design, simulation, evaluation, and technological verification of arrayed waveguide gratings’. Opt. Eng. 2014, vol. 53(7), p. 071803. R-Soft: http://optics.synopsys.com/rsoft Photon Design: https://www.photond.com Seyringer D., and Schmid P. ‘A new software tool is developed to evaluate the measured/simulated transmission characteristics of optical multilexers/ demultiplexers’. Proc. SPIE 8167, Optical Design and Engineering IV; Marseille, France, Sep 2011. Seyringer D., and Hodzic E. ‘Calculation of accurate channel spacing of an AWG optical demultiplexer applying proportional method’. Proc. SPIE 9520, Integrated Photonics: Materials, Devices, and Applications III; Barcelona, Spain, May 2015. Martens D., Ramirez-Priego P., Murib M.S., et al. ‘A low-cost integrated biosensing platform based on SiN nanophotonics for biomarker detection in urine’. Anal. Meth. 2018, vol. 10(25), pp. 3066–3073. Tyler N.A., Fowler D., Malhouitre S., et al. ‘SiN integrated optical phased arrays for two-dimensional beam steering at a single near-infrared wavelength.’ Opt. Exp. 2019, vol. 27(4), pp. 5851–5858. Akca B.I., and Doerr C.R. ‘Interleaved silicon nitride AWG spectrometers’. IEEE Photon. Technol. Lett. 2019, vol. 31(1), pp. 90–93. Fercher A.F., Drexler W., Hitzenberger C.K., and Lasser T. ‘Optical coherence tomography - principles and applications’ Rep. Prog. Phy. 2003, vol. 66(2). https://www.thorlabs.com, “Optical Coherence Tomography Tutorial”. http://wasatchphotonics.com/oct-tutorial. Leitgeb R., Drexler W., Unterhuber A., et al. ‘Ultrahigh resolution Fourier domain optical coherence tomography’. Opt. Exp. 2004, vol. 12(10), pp. 2156–2165.

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[78] Tsai C.-C., Lin, Y.-S., Chen, T.-H., et al. ‘Ultrahigh resolution optical coherence tomography via Ce3þ:YAG double-clad crystal fiber source’. Conference on Lasers and Electro-Optics; San Jose, CA, USA, May 2010, pp. CThT3. [79] Fercher A. F. ‘Ophthalmic interferometry, in optics in medicine, biology and environmental research.’ Selected Contributions to the First International Conference on Optics Within Life Sciences (OWLS I); Garmisch-Partenkirchen, Germany, Aug 1990 (Amsterdam, Elsevier, 1991), pp. 221–228. [80] Tanno N., Ichikawa T., and Saeki A. Lightwave Reflection Measurement. Japanese Patent # 2010042, 1990 (Japanese Language). [81] Chiba S., and Tanno N. ‘Backscattering optical heterodyne tomography’. Prepared for the 14th Laser Sensing Symposium, 1991 (Japanese language). [82] Huang D., Swanson E.A., Lin C.P., et al. ‘Optical coherence tomography’. Sci. 1991 vol. 254(5035), pp. 1178–1181. [83] Fercher A.F., Hitzenberger C.K., Drexler W., Kamp G., and Sattmann H. ‘In vivo optical coherence tomography’. Am. J. Ophthalmol. 1993, vol. 116(1), pp. 113–114. [84] Swanson E.A., Izatt J.A., Hee M.R., et al. ‘In vivo retinal imaging by optical coherence tomography’. Opt. Lett. 1993, vol. 18(21), pp. 1864–1866. [85] Zysk A.M., Nguyen F.T., Oldenburg A.L., Marks D.L., and Boppart S.A. ‘Optical coherence tomography: a review of clinical development from bench to bedside’. J. Biomed. Optics. 2007, vol. 12(5), p. 051403. [86] Gora M., Karnowski K., Szkulmowski M., et al. ‘Ultra high-speed swept source OCT imaging of the anterior segment of human eye at 200 kHz with adjustable imaging range’. Opt. Exp. 2009, vol. 17(17), pp. 14880–14894. [87] Srinivasan V.J., Adler D.C., Chen Y., et al. ‘Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head’. Invest. Ophthalmol. Vis. Sci. 2008, vol. 49(11), pp. 5103– 5110. [88] Fujimoto J., and Swanson E. ‘The development, commercialization, and impact of optical coherence tomography’. Invest. Ophthalmol. Vis. Sci. 2016, vol. 57(9), pp. OCT1–OCT13. [89] Stifter D. ‘Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography’. Appl. Phys. B. 2007, vol. 88(3), pp. 337–357. [90] Swager A.F., Faber D.J., de Bruin D.M., et al. ‘Quantitative attenuation analysis for identification of early Barrett’s neoplasia in volumetric laser endomicroscopy’. J. Biomed. Opt. 2017, vol. 22(8), p. 86001. [91] Cossmann M., and Welzel J. ‘Evaluation of the atrophogenic potential of different glucocorticoids using optical coherence tomography, 20-MHz ultrasound and profilometry; a doubleblind, placebo-controlled trial’. Br. J. Dermatol. 2006, vol. 155(4), pp. 700–706. [92] Nguyen V.D., Akca B.I., Wo¨rhoff K., et al. ‘Spectral domain optical coherence tomography imaging with an integrated optics spectrometer’. Opt. Lett. 2011, vol. 36(7), p. 1293.

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Akca B.I., Nguyen V.D, Kalkman J., et al. ‘Toward spectral-domain optical coherence tomography on a chip’. IEEE J. Sel. Top. Quantum Elect. 2012, vol. 18(3), pp. 1223–1233. [94] van Leeuwen T.G., Akca I.B., Angelou N., et al. ‘On-chip Mach-Zehnder interferometer for OCT systems’. Adv. Opt. Technol. 2018, vol. 7(1-2), pp. 103–106. [95] Seyringer D., Burtscher C., Partel S., et al. ‘Design and simulation of Si3N4 based arrayed waveguide gratings applying AWG-parameters tool’. 2016 18th International Conference on Transparent Optical Networks (ICTON); Trento, Italy, Jul 2016 (IEEE), pp. 1–5. [96] Seyringer D., Burtscher C., Partel S., et al. ‘Design and simulation of 20-channel, 50-GHz Si3N4-based arrayed waveguide grating applying AWG-parameters tool’. Proc. SPIE 10106, Integrated Optics: Devices, Materials, and Technologies XXI; San Francisco, CA, USA, Feb 2017 (SPIE). [97] Seyringer D., Maese-Novo A., Muellner P., et al. ‘Design and optimization of high-channel Si3N4 based AWGs for medical applications’. Proceedings of the 6th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2018); Funchal, Madeira, Portugal, Jan 2018 (SCITEPRESS, 2018), pp. 213–220. [98] Seyringer D., Sagmeister M., Maese-Novo A., et al. ‘Compact and highresolution 256-channel silicon nitride based AWG-spectrometer for OCT on a chip’. 2019 21st International Conference on Transparent Optical Networks (ICTON); Angers, France, Sep 2019. [99] Sagmeister M., Koppitsch G., Muellner P., et al. ‘Monolithically integrated, CMOS-compatible SiN photonics for sensing applications’. MDPI Proceedings; Graz, Austria, Sep 2018, vol. 2 (13), p. 1023. [100] Rank E.A., Nevlacsil S., Muellner P., et al. ‘Spectral domain and swept source optical coherence tomography on a photonic integrated circuit at 840nm for ophthalmic application’. Proc. of Optical Coherence Imaging Techniques and Imaging in Scattering Media III; Munich, Germany, Jun 2019.

Chapter 11

Integrated quantum photonics Devin H. Smith1, Paolo L. Mennea1 and James C. Gates1

Acronyms CW FHD FWM KDP KTP LN NV PHC PP QD QKD SFG SiV SNSPD SoI SPDC

11.1

Continuous wave flame hydrolysis deposition Four-wave mixing Potassium dihydrogen phosphate Potassium titanyl phosphate Lithium niobate Nitrogen-vacancy Photonic crystal Periodically poled, e.g. PPLN or PPKTP Quantum dot Quantum key distribution Sum-frequency generation Silicon-vacancy Superconducting nanowire single-photon detector Silicon-on-insulator Spontaneous parametric down-conversion

Introduction

Photons will play an essential role in the future technologies that harness quantum phenomena. While many quantum systems exist, photons are easy to control and noise-resistant, driving interest in their use. Entanglement, the very idea that made Einstein nervous about quantum mechanics [1], is incredibly useful; applications of quantum photonics include secure communications, simulation of complex systems and potentially universal quantum computation. Additionally, photonics is key to enabling the emerging field of quantum technologies in which light is often used to 1

Optoelectronics Research Centre, University of Southampton, Southampton, UK

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control and manipulate quantum systems such as cold atoms or single ions. This chapter will only be concerned with quantum photonics: systems where the photons themselves act as carriers of quantum information. Quantum photonics suffers from many of the same problems and constraints as the classical photonics addressed in previous chapters, only more so. The aim is still to make, manipulate, and detect light, only in minute quantities: typically, a single photon is used as the information carrier in quantum photonics. For reasons of fundamental physics amplifiers cannot be used, leaving a total loss budget for the system efficiency of ~3 dB. This leaves two fundamental problems for consideration: 1. 2.

Making a ‘quantum state of light’ Reducing loss in the rest of the system to very low levels

These issues raise two key questions: what is a quantum state of light, and what comprises the rest of the system? In the case of integrated quantum photonics, a quantum state of light typically begins with a single photon or something that can approximate one, which we shall discuss in Section 11.3. This is then turned into a larger ‘entangled’ state of many single photons in the rest of the system in order to accomplish something useful, which requires good couplers, phase modulators and detectors; ideally, the detectors and modulators are fast enough that some of the photons can be detected and such measurements used to change subsequent parts of the quantum operation via the modulators, so-called feed-forward. In practice a few more components are often required: filters to separate signals and, more severely, bright pump lasers from the single photons; and chip-to-chip or chip-to-fibre interconnects. At present, most quantum photonics has not achieved monolithic integration: whilst this is the goal, shown in Figure 11.1(b), the present case more closely resembles Figure 11.1(a): discrete sources, circuits and detectors connected via fibre and, often, bulk optics. Of course, ‘quantum’ being an active area of research for nearly every possible technology, our survey will inevitably omit some topic areas, for which we apologise. We hope to cover the most promising and prominent approaches to the problems.

11.2 Applications Whilst the focus of this chapter is on the technological challenges and developments in designing quantum photonics, a brief explanation of the goals and applications of the field is useful in providing context for the technical problems. The field of ‘quantum science/engineering’ has grown dramatically in the last few years. Initially, the two drivers of the field were quantum key distribution (QKD) and quantum computing, though more recently a large number of other applications have been explored, including metrology and communication. QKD dates back to 1984 [2] in its simplest form, and consists of sending single photons (or very weak laser pulses) between two parties to distribute an encryption key. Done correctly, the resulting key is provably secret even over a lossy channel

Integrated quantum photonics Couplers, Modulators Sources

Circuitry (a)

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Fibre interconnect

Detectors Cryostat

Everything Cryostat

(b)

Figure 11.1 Cartoon highlighting the key elements of integrated quantum photonic systems; in practice, the sources, circuitry and detectors are typically on separate devices interconnected via optical fibre, as in (a). In the ideal case, all components are present in a single device, (b), with the detectors necessitating operation at cryogenic temperatures and with some errors – up to about 10% – in the resulting measurements. However, signals still degrade over distances and so naı¨ve schemes only work over distances of a few hundred kilometres via fibre or air. As quantum signal amplification is forbidden by the so-called ‘no-cloning principle’, a different solution is required. The most obvious one is to go via satellite in outer space to reduce atmospheric losses, which in principle can extend the reach of QKD significantly; this carries substantial engineering challenges. The more relevant solution to this book is the ‘quantum repeater’, the best quantum-compatible answer to the amplification problem. This is a device that takes two quantum signals and transfers entanglement between them. Set up along a chain this can in principle allow QKD over arbitrary distances by only transmitting the quantum data between the end stations, using the entanglement generated by the repeaters as a precondition of the transmission. A repeater, however, is not a trivial thing to design. In fact, none have yet been made that really deserve the name: an all-photonic quantum repeater requires approximately a million single photons to transmit one photon worth of information assuming a 95% source efficiency including coupling to fibre [3]. Intermediate devices do exist and would help, but are still on a large enough scale that a chipbased solution would be useful; such a chip must interact with long-haul communications efficiently. The other major application can, in principle, be implemented all on chip: quantum computers. A quantum computer is a device that exploits quantum entanglement between the qubits (quantum bits) in the computer to speed up algorithms. The most famous such speedup is Shor’s algorithm [4], which allows for the factoring of a large number exponentially faster via the quantum Fourier

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transform; this algorithm breaks nearly all cryptosystems currently in use. Photons are a suitable object to act as a qubit [5], but the requirements to make a useful photonic quantum computer are significant but surmountable [6]: the total loss in the system must be 1/2 or less (including source and detector efficiencies), other errors must be minimal (< 0:1% per operation), and the total number of distinct photonic modes needed is millions or even billions of distinct, controllable modes. Again, there are intermediate way-points available with ten or a hundred modes, but the sheer scale of the problem is one reason that free-space quantum optics researchers consider moving on-chip: fabrication is repeatable in a way that bulk optics is not. Demonstrations so far, particularly on-chip, have been at the scale of one to four photons and up to about ten modes. The problem of scaling up once the individual devices have been improved is one to look forward to, but at present research remains necessary to improve individual device performance.

11.3 Quantum states of light In order for interesting quantum phenomena to occur, a non-classical state of light must be used: in practice, this typically means Fock states, i.e. states of a definite photon number. In most protocols, this means states of either zero or one photon being present in a particular time step and waveguide. Other states can be used, in the so-called ‘continuous variable’ regimes, but they are generally much more vulnerable to errors due to loss than single-photon-based schemes. Once the decision is made to use single photons as the information carrier, several schema exist for representing information with that single photon–analogous to the different keying schemes in telecommunications. For many practical engineering considerations, the choice of scheme is a detail compared to the overall problem, but the more common of these are as follows: Path Polarisation Time-bin Frequency On-off

A photon is in one of several (often two) waveguides, labelled 0, 1, 2, etc. This is the most common scheme in integrated devices. Horizontal (0) and vertical (1) polarisation represents a qubit. This has been the most common scheme in bulk optics, but birefringence makes it difficult in integrated optics. Each clock cycle is divided into several time-bins, with a photon in one of the bins representing 0, 1, 2. . . . Different spectral bins are used. It is difficult to get different photons to interact using this scheme. A photon is either present (1) or absent (0) in each waveguide. This scheme, whilst obvious, is incredibly sensitive to loss and thus impractical.

The generation of a single photon seems, on the face of it, a simple problem. Unfortunately, it turns out not to be in practice. The most obvious solution to the problem is to use a single emitter – an atom, quantum dot or similar – to emit into a

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mode of interest. Typically, a cavity is required to ensure that a reasonable fraction of the light is collected; this complicates greatly the fabrication process, as the cavity must be longitudinally aligned to the light emitter on a sub-wavelength scale. As a consequence, most high-efficiency integrated true single-photon sources emit vertically into free space, from whence the light is collected into a fibre. Fortunately, a single-photon source can be emulated using nonlinear optics and a detector. Either the cð2Þ process of spontaneous parametric down-conversion (SPDC) or the cð3Þ spontaneous four-wave mixing (SFWM) can be used, depending on the material. In brief, SPDC is the inverse process of sum-frequency generation: an input pump photon spontaneously decays into two daughter photons whilst following the typical phase matching conditions of momentum and energy conservation. In a typical experiment, this happens with probability about 1 in 109 or so for each photon that passes through the nonlinear medium. If the phase-matching is chosen carefully, the two daughter photons can be separated either by wavelength or polarisation. In two-photon experiments such as many present-day proof-ofprinciple experiments, these two photons are then used as two separate photons, though this approach does not scale to larger photon counts. To scale up to largescale experiments one of the two photons must be detected, ‘heralding’ the presence of the other. A switching network must then be used to move the photons into the input ports of the device that is actually of interest, as each individual light source must succeed with low probability or accidental emission of multiphoton states can occur, which is very problematic. The two schemes above, using a ‘true’ photon source or a ‘heralded’ photon from a photon-pair source, both remain viable paths to success; it is not clear at this time if one or the other will eventually come to dominate the field. We will thus discuss both in the following sections.

11.3.1 ‘True’ single-photon sources In the abstract, creating a single-emitter photon source is easy: you take something with clean energy levels, put one of them in a cavity and collect the output light. There are a variety of emitters one can use for such a scheme, including any of the multiple things named ‘quantum dots’ and any of a number of dopant atoms or ions in a solid. These emitters can then be driven either optically or electrically into a ‘ready’ state, from which their decay back to a lower energy level emits the photon of interest. The optical mode of the emission is typically not compatible with other optics, integrated or otherwise. This leads to the second component of most such schemes, an optical cavity. The Q-factor of this cavity is typically chosen carefully to optimise between repetition rate and Purcell enhancement of the emission into the cavity mode. Care must also be taken to ensure that the emitted photon is spectrally pure; most true single-photon sources are cooled to cryogenic temperatures to enhance emission into the zero phonon line. Ideally multiple sources would be spectrally identical, allowing the photons generated therefrom to interfere, but doing so with quantum dot sources in particular has proved challenging in practice.

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As there is only a single emitter present, the two-photon probability in a single clock cycle can be zero if the excitation of the emitter is done carefully; as emission of multiple photons from a particular source is a particularly problematic error for quantum computers this is a major advantage of the true single-photon source over heralded sources.

11.3.1.1

Semiconductor quantum dots

Unfortunately for this discussion, a ‘quantum dot’ can be any of a number of things, depending on context. The term ‘quantum dot’ simply implies that the energy levels of something are discretised in the dot: in semiconductors, this is typically both the electron and hole energy levels, achieved through containing a small region of a smaller-bandgap material in a larger-bandgap material. Photon emission is typically generated from the recombination of an electron-hole pair, or exciton, trapped in the dot. We will discuss methods for generating a trapped exciton below. A key advantage of quantum dots is the ability to be electrically driven [7]. The most common type of quantum dots used as single-photon sources is III–V eptaxial self-assembled quantum dots. The most studied materials are InAs or InGaAs in a GaAs matrix. A detailed description of the process is available elsewhere [8]; the concise description is that a very thin layer of lower-bandgap semiconductor is deposited in such a way that surface tension causes the layer to form very small, typically lens-shaped, droplets on the surface. Another layer of the substrate semiconductor is then put down overtop of the quantum dots, freezing them in place. Self-assembled quantum dots typically have good, but variable, optical properties; the self-assembling nature leads to variability in both positioning and spectrum. Several groups [9] have attempted to position the dots deterministically with varying levels of success, but in doing so invariably have worse optical properties. The random location of the dots leads to a problem for integrability, as does the need to form them in an epitaxial layer: without enhancement due to confinement, the great majority of the light from the dot will be lost. The quantum dot sources with the current best efficiency in the world [10], are formed by finding a ‘good’ dot with a confocal microscope and then forming a vertically emitting cavity around them, with the potential for spectral tunability and entangled photon emission using electrodes to tune the dot electrically or magnetically. This approach is the most promising, but results in a photon coupled to free space. Other groups have attempted to form a cavity in-plane, notably by placing a photonic crystal (PhC) cavity around the dot. As far as we are aware, this is still being done at random: many PhC cavities are created in a sample, and then tested to see which ones (at random) contain a dot at the right wavelength. This process has a yield of less than 1%, which is enough for testing, but will need to be improved for applications. For more information about this area we refer the reader to an excellent review [11] that discusses the interfacing of quantum dots to photonic crystal structures. There are also attempts to use epitaxial quantum dot layers grown in nanowires in heterogenous systems. A nanowire (in this context) is a high aspect ratio bit of

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semiconductor; grown correctly, it can contain the self-assembled quantum dots described above or so-called 1-dimensional ‘quantum wells’. The high aspect ratio allows the nanowire to act as an optical waveguide in the length dimension. After culling the nanowires for suitable candidates – remember that the process here is random – a particular nanowire can be integrated into other optical systems in a few ways. The easiest to explain here is that they can be placed on a tapered waveguide of another material and ‘adiabatic coupling’ can occur between the nanowire and the taper with fairly high efficiency (exceeding 90% [12]) if done correctly.

11.3.1.2 Atomic-scale emitters In this section all the other integrable ‘true’ single-photon emitters will be considered. Whilst quantum dots contain hundreds to millions of atoms, the emitters considered here are formed either of a single isolated (perhaps ionized) atom, or few-atom ‘colour centres’ that form in crystalline materials. Many early experiments in quantum optics, such as those of Aspect [13] that won the Nobel prize, were performed with photons emitted from an isolated rare earth ion in a vacuum trap. This idea remains relevant to the present day, as quantum computing using ion traps is an active area of research and the crossconnects between them are optical; it is not, however, integrated and thus not relevant to this book. In principle, a single atom or ion, correctly located in a cavity formed in a solid, would be a suitable single-photon emitter. Unfortunately, creating such a device has proven to be challenging. The most common emitter in use is actually from defect centres in diamond, most notably the so-called nitrogen-vacancy (NV) centre [14], which consists of a nitrogen atom adjacent to a vacancy defect in the diamond. Initially, these NV centres were either found naturally or created by bulk doping [15], though modern techniques [16] have shown that they can be created in situ with high reliability via femtosecond laser diffusion of defects. The emitted light must then be captured, a non-trivial engineering problem in diamond photonics. Unfortunately, NV centres have some intrinsic properties that limit their ultimate usefulness. In particular, even at zero temperature, they have a fairly high ‘branching factor’ into modes other than the desired zero-phonon line, leading to limit on the efficiency of the source. This has led to study of a variety of other diamond colour centres, mostly of the form (Atom)-(Vacancy) for your choice of atom. The most studied is the silicon-vacancy (SiV) centre, which in theory has some superior properties to the NV centre. In principle the whole system can then be integrated in diamond, or using a similar technique to the nanowires mentioned above, the emitted light can be coupled into a waveguide by adiabatic coupling. As the remainder of integrated photonics in diamond is less developed this approach has been pursued by a variety of groups. Two more ‘true’ single-photon sources need to be mentioned: dyes and nanotubes. Some so-called ‘dye’ molecules, most famous in optics for use in dye lasers, can be contained in a host crystal which can be deposited on a waveguide [17] or contained in a polymer waveguide with reasonable efficiency. As dye

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molecules have more degrees of freedom than atomic species, the properties can be tailored somewhat. A nanotube – equivalent to a sheet of graphene rolled into a cylinder – can also act as a single emitter due to its small size and simple structure; placed on the surface of an engineered waveguide the light generated can be transferred into photonic circuitry [18].

11.3.2 Heralded photon sources An alternative plan to the ‘true’ single-photon source is to use something more familiar to many in the integrated photonics space: nonlinear optics. Depending on the material of interest it is likely that one or more nonlinear optical processes are available to make quantum light available via nonlinear optics: in cð2Þ media spontaneous parametric down-conversion (SPDC) is possible, whilst in cð3Þ media one of several spontaneous four-wave mixing (SFWM) processes can work. For explanatory purposes, we shall begin with SPDC. Whilst the name refers to parametric down-conversion, an explanation in terms of sum-frequency generation is likely easier to follow for most. Quantum mechanics asserts that all processes are reversible, albeit with low probability: SPDC is the time-reversed version of sumfrequency generation (SFG). In SFG, two photons convert into a single photon of higher energy (lower wavelength) subject to the ‘phase-matching conditions’ – conservation of energy and momentum: (11.1)

w1 þ w2 ¼ w0 !

!

!

!

(11.2)

k1 þ k2 ¼ k0 þ G !

where w is the (angular) frequency and k the momentum of the respective beam, ! and G is the grating vector for quasi-phase-matched crystals. In integrated photonics, it is not uncommon to modulate cð2Þ via periodic poling, and, in this formulation, periodic poling turns up as a momentum vector; typically in integrated optics all the fields are copropagating, turning a vector equation into a scalar one. In a strictly classical formulation of nonlinear optics, this process is not reversible: if you input field 0 into the system, nothing happens. However, a semiclassical calculation shows that the reverse process does occur, and with probabilities given by the exact same constraints as the SFG process has. With a low probability – about 1 in 109 – a single photon from field 0 will split into a photon pair in fields 1 and 2; as a typical laser pulse has many photons, it is not difficult to generate photon pairs by this method. One possible problem is that the probability to generate more than one photon is not that low – in fact, reducing the pump power is often necessary to prevent higher-order processes generating four or six photons from occurring. The ideal number is less than 0.1 photon pairs per pulse to provide a reasonable tradeoff between generating too many and too few photons. The reader will note that this is much less than the total loss figures quoted earlier in this chapter of 1/3 loss; fortunately, we can use the paired nature of the photons to solve the problem using heralding. That is, the time correlation of the photons is used to know when one

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photon has been generated by watching for the other half of the pair; upon detecting the herald the existence and location of the ‘heralded single photon’ is known. One must then build a multiplexed version of these sources to ensure that the known photon output is present in the output port: this can be done either spatially or temporally. In either case, upon detecting the herald photon for a particular output, the single-photon output must be switched into the output of interest – more on this problem in Section 11.4. In practice, spontaneous four-wave mixing is generally a similar process to SPDC, i.e. degenerate SFWM, except that the field 0 typically loses two photons to generate the daughter photons: this brings the three wavelengths much closer together, which can cause issues with other noise sources such as Raman scattering. The pump in both cases will ideally be filtered out of the waveguide; for SFWM, this can prove challenging. Non-degenerate SFWM schemes, with two distinct pump beams, can also be used to simplify phase-matching or filtering at the cost of increased operational complexity and stability requirements. It is not uncommon to want 100 to 170 dB of suppression of the pump light with respect to the single photons, with single-photon insertion loss minimised. This is a nontrivial engineering problem, and many current experiments leave the pump co-propagating with the quantum signal through the experiment, with filtering done off-chip just before detection. The scaling of SFWM is quadratic in the pump power, whist SPDC, being a one-photon process, is linear in the pump power – in practice this allows lower pump power to be used in SPDC sources. Many clever schemes exist for generating photons on-chip in various entangled states, which we are not going to cover here. Let the reader be assured that if a particular encoding scheme or entangled state will solve their problem then a device can be fabricated that will promote that scheme; the particulars ultimately take a backseat to the fundamental limitations of the devices.

11.3.2.1 High-contrast cð3Þ crystals

The first integrated SFWM sources were demonstrated in silicon over a decade ago [19], whilst silicon nitride has also been shown to act as a good-quality SFWM source [20]. Two major designs exist: A (relatively) long waveguide, often formed into a spiral for compactness, with the phase-matching engineered geometrically; or an onchip ring/racetrack resonator with Q-factor engineered to to control the wavelength of the daughter photons. The latter approach tends to produce a comb of single-photon lines which must be discriminated spectrally; this is a requirement that, with care, might be a useful feature or at least not harmful. The resonator-based approach also reduces the pump power required due to field enhancement; for the highest-Q resonators ð 106 107 Þ, the pump can be as small as 0.1 mW for optimal operation. In general, the silicon sources are more mature at this time, being used in many demonstrations; the silicon-nitride-based sources may have more future upside as the intristic loss and noise in SiN should be superior.

11.3.2.2 Silica The first waveguided sources of quantum light were made by four-wave mixing in long lengths of optical fibre: whilst not integrated per se, this represented the first

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step towards integrated sources. More recently, on-chip SFWM sources have been developed in a variety of on-chip silica waveguides: UV-laser written [21], femtosecond-laser written [22] and etched waveguides. Because of the relatively low index contrast on silica relatively more pump power is required, and ringresonator based integrated sources are not possible. One key advantage of some silica-based integrated sources is their interoperability with fibre: this allows standard telecommunications parts to be used as well as allowing long-haul quantum communications. It is also possible to make the sources in fibre, but that lies outside the scope of this chapter.

11.3.2.3

cð2Þ crystals

In bulk quantum optics, the use of various crystals for SPDC dates back many years – and some of those crystals support both waveguide formation and periodic poling, allowing on-chip deployment. Lithium niobate (LN) and potassium titanyl phosphate (KTP) are both being investigated for use on-chip, and in both media the challenges are reversed with respect to other, more traditional, integrated media such as silica glass and silicon: modulators and photon sources are easy to make, and all the other components (including the waveguide itself) are more challenging. Periodically-poled lithium niobate (PPLN) waveguides for SPDC were first demonstrated in 2001 using proton-exchange waveguides [23]. In general, PPLN waveguides will have a much higher nonlinear efficiency than any other process discussed here, and the engineering of PPLN for nonlinear optics is extremely well understood, allowing any particular wavelengths of interest to be used. There may be problems with the purity (quality) of photons from PPLN due to the dispersion characteristics of the crystal, leading to unintended entanglement between the photons generated; for this reason and others, some research has been done on using PPKTP waveguides as well. PPKTP has, due to group-velocity matching, optimally pure single photon generation in the C band [24]. In the abstract, these two media are of a kind, with similar properties; of course, the engineering challenges to create a system prove to be different in practice.

11.4 Low-loss components The other major difference between conventional and quantum photonics is the lack of amplifiers in the quantum regime. For reasons of fundamental physics, amplification of quantum signals is impossible; moreover, many quantum protocols only tolerate small amounts of loss. For instance, any photonic quantum computer must have less than 1/3 loss per photon total. This leads to the overwhelming concern in the quantum photonic community towards loss, reducing loss and paths to low-loss components. Often, these are not the headline results – improving the loss in a waveguide does not yield high-impact publications, but it does improve the state of the art.

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Other than the photon sources, there are roughly five components in an optical system: waveguides, couplers, phase modulators, detectors and interconnects. This is a fairly arbitrary division of the field into devices, but provides a useful framework for considering the advantages and disadvantages of different materials and fabrication techniques. The figure of merit that is most useful to evaluate the performance of quantum photonic devices is not the physical density of the components but the density compared to their loss – that is to say, the number of components you can combine before too many of the photons are lost. A measure of this value, the functional complexity Cf , is defined as [25]  2 10 Cf ¼ ; aLd lnð10Þ where a is the transmission per unit length in decibels (including bends, couplers and phase-shifters) and Ld is the unit device length. The bend radius used to connect components together must be chosen to minimise losses; but assuming optimal design, the waveguide propagation and bend losses set the scale of the problem for the rest of the components. For instance, silicon provides very small device footprint due to its high refractive index and well-understood fabrication techniques, but current devices also have very high propagation loss. This means that the functional complexity remains modest (less than 100 [26]). At the other end of the scale, silica has extremely large footprints, but commensurately lower loss, leading to a demonstrated functional complexity of hundreds of elements and a theoretical optimum nearer 5  104 . It should also be noted that many applications (including heralded single-photon sources) require delay-lines to provide time to act on quantum measurements, which can be problematic in lossier materials. Most interesting quantum photonic devices are multimode, i.e. distinguishable by path, mode profile, frequency or otherwise. In most quantum photonics the modes are the modes of distinct, single-mode waveguides of the same polarisation, but other encoding schemes are possible, as described in Section 11.3. This design implies that waveguide couplers are essential; crossovers are also useful but not necessarily required. Depending on application, dichroic couplers for use as filters may also be useful – all of these devices carry over directly from classical photonics with care taken to minimise loss. We mention it here simply because that care is often time-consuming and is problematic for some systems. We now approach the more difficult devices – fast modulators and fast, efficient single-photon detectors. The electro-optic modulator, made from LN or potassium dihydrogen phosphate (KDP) for instance, is an extremely common tool in classical photonics for its speed and ease of manufacture. This leads to much research on methods for integrating said modulators into a larger system without introducing excess loss – either through hybrid systems with interconnects or building the entire system in active media. The alternative is to build modulators some other way. The current workhorse is the thermo-optic phase shifter, that is, a heater placed on top of a particular waveguide

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to change the optical phase via the index of refraction. This suffers from two major flaws: first, it is slow – typically switching in milliseconds – and thus impractical for dynamic applications; and second, it requires significant temperature change, making it cryogenically incompatible. The remaining options are all in the early stages of research or have potential problems: in many ways, designing a low-loss, high-speed modulator is the key problem for the field at this point. We will mention in the material sections below any promising candidates for a good modulator; however, it is to be noted that there are not any obvious solutions at the present time. Prior to 2005 [27], the key problem for the field was designing high-efficiency photon detectors, preferably fast, and preferably that could discriminate between different photon numbers. The best available detectors at the time, silicon-based single-photon avalanche diodes (SPADs), had limited efficiency, and particularly for the integrated optics case only work below the band-edge of silicon. The way forward was not clear: in the telecommunications band, the best available detectors were III–V (usually InGaAs) SPADs, which are inefficient and noisy, and other alternatives were all but unobtainable. Fortunately, two related developments in superconducting detectors mostly solved the problem: the superconducting nanowire single-photon detector (SNSPD)* [28] and the transition edge sensor (TES) [27]. The transition edge sensor consists of a small film of a superconducting material, typically tungsten, held below the transition temperature and current biased: upon being hit by light, the film’s conductivity changes strongly and proportionally to the signal, permitting photon number resolution;† unfortunately, the TES is quite slow, with kHz repetition rates and response times, limiting application to experiments where feed-forward is not necessary. The SNSPD is easier to explain: a small meandering wire of superconductor is placed in the light beam, again current-biased; when one or more photons is absorbed, some portion of the wire goes ‘normal’, leading to a large, rapid change in resistance. SNSPDs, if carefully engineered, can have near-unit efficiency both absorbing light and converting the absorption into an output. For technical reasons, SNSPDs have weaker requirements on the cryogenic systems, typically operating at the few kelvin level whilst TESs operate in the hundreds of millikelvin. SNSPDs have, as a result, become commercially available from a variety of suppliers, with a closed-cycle fridge suitable for their operation available for a reasonable price. Both TESs and SNSPDs have been shown to work on a variety of integrated platforms: they consist of a thin film, which can simply be fabricated on the surface of a suitably designed waveguide. However, the remainder of the system then needs to be able to operate at cryogenic temperatures without shedding more heat than can be dissipated by the fridge. This proves to be a substantial constraint in practice, leading to the makeshift solution of fibre-connected detectors off-chip. This

*

Some sources omit ‘nanowire’, calling them SSPDs. The TES is a smaller version of the superconducting detectors used bolometrically as the standard for power measurement.

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necessitates out-coupling from the chip, and increases lag in the system, but is currently the primary method in use. The final part needed for an integrated quantum optical system is interconnects: if loss is a major concern and noise also problematic, shielding the detectors from the pump laser (for instance) often requires that multiple chips are used and interconnected. Hybridising between substrates can also allow one to take advantage of, for instance, the electro-optic properties of LN. Chip coupling losses to fibre or chip-to-chip vary between systems from a major advantage to a major problem.

11.5

Material platforms

We will now review the major contenders as a material for quantum optics, which are unsuprisingly the major materials in use in classical optics: silica, silicon, and silicon nitride, III–V materials and LN. Table 11.1 presents an overview of the current status of prominent material platforms.

11.5.1 Silica The extremely low material losses of high-purity silica that have made it so successful for long distance telecommunications also make it an obvious choice for this highly loss-sensitive application; several different techniques for waveguide formation have been used in quantum optics. Other glasses also form waveguides, but the additional losses mean that only silicate glasses have been used in quantum photonics. The low refractive-index contrast typical of silica waveguides is both a benefit and a hindrance; the resulting large mode-sizes permit direct butt-coupling to standard optical fibre with excellent efficiency, but the resulting bend radii on-chip lead to limited device densities. The key advantage of a fibre-matched mode is that it relaxes the stringent requirement that all components – the sources, modulators and crucially the cryogenic detectors – be present on a single chip with compatible fabrication processes and operating conditions. ‘Free’ coupling on and off chip is then available, for instance to a set of fibre-coupled superconducting detectors. Several fabrication approaches have seen use for silica quantum devices, divided into the traditional combination of photolithographic definition and etching, and laser inscription techniques, itself subdivided into femtosecond writing and direct-UV writing. Laser inscription has the advantage of being maskless, making it highly suited to rapid prototyping and low-volume production; as a result, these software-defined techniques are common in quantum photonics research. The direct-UV writing technique produces channel waveguides via photobleaching of an absorption in the UV with a focused CW laser spot, which leads to a local refractive index increase on the order of 103. This requires photosensitive glass layers, typically silica-on-silicon with a germanosilicate core layer produced via flame hydrolysis deposition (FHD). This approach also enables inscription of first-order Bragg gratings via two-beam interference, which have been used both to

30 [29] 180 [31] 75 [26] 860 [25] 20 2 [37] –

Bulk optics Silica Si SiN (TriPleX) LiNbO3 GaAs Diamond 0 0.2 2.0 8 dB cm1) and fabrication yields are low. Ridge waveguides are more efficient with losses of ~1 dB cm1 [52]. Modulators in III–V materials are relatively simple to realise, and use the electro-optic effect as in LN. The high electro-optic effect (0.2 V cm for GaAs) allows p phase shifts [53] with relatively short electrodes (7 mm) and small drive voltages and thus permits higher-density devices than LN [54]. However, it should be noted that the typical losses for active waveguides is higher than passive, typically (2 to 3 dB cm1). As loss is not a key concern for the telecommunications industry, where gain is ubiquitous, the technology challenge of loss will need to be addressed by the quantum photonics community. III–V compounds have not had the same investment as silicon technologies and thus improvements in materials and fabrication techniques may significantly improve losses in the future.

11.5.6 Hybrid systems Combining several material platforms into a single system – are of course possible. Most GaAs-based sources used are coupled to a different medium for use, for instance [55]. The two major drivers of integrated hybridisation are sources, where attempts are made to move the emitted photon efficiently (often through adiabatic mode transfer) to the rest of the system, and modulators, with research being done into integrating LN modulators with devices otherwise made of another material

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[56]. The source hybridisation research is particularly promising, as it allows the useful features of true single-photon sources to be integrated with reasonable yield into a system.

11.6

Conclusion

Researchers in quantum optics, accustomed to working in bulk, are gradually accepting the advantages of integration. Unfortunately, at present, the technology is insufficiently developed to bring the latest experiments on-chip, and the people that historically have been working in quantum optics are not fabricators of integrated photonics. The field of integrated quantum photonics thus brings together two groups of people: the quantum scientists on the one hand, and the fabricators on the other. In some cases, people have come across the divide, and in others close collaborations exist between two separate groups of researchers; both approaches have led to significant advances in the state of the art over the last few years. Many papers have been published on the topic, though most of those are proofs-of-concept for various proposals rather than serious technical development of the platform looking forward; obtaining technical specifications for the various components reported in the literature proved surprisingly difficult. At present the future of integrated quantum photonics is not clear: whilst applications exist in quantum communications, they are not nearly as expansive and interesting as the more general and larger-scale applications in quantum computing, simulation or metrology. These applications might be superseded by work in other fields: whilst there is a race between technologies inside quantum photonics for supremacy, the same is true on a larger scale for the race for scalable quantum computers. The race between the different technologies in quantum photonics also has no clear winner at present – silica has distinct advantages in fibre compatibility, silicon in mature manufacturing technologies, and silicon nitride and LN seem to have future upside that has not yet been realised. III–V materials host quantum dots, but losses are high. Diamond hosts true single-photon sources, but almost all other integrated optical mechanisms are yet to be developed. In principle, the ultimate solution might be a combination of materials. Advancement requires a few things: fast modulation, whole-system integration, and filtering on-chip on a massive scale if optical pumps are used. All of these things either need to be cryocompatible, or new detectors are required. The future is ahead of us. Many, many people are working towards solving the numerous problems. We hope that this chapter has introduced the state of play, but play is ongoing and progress is rapid.

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Chapter 12

The optical reservoir computer: a new approach to a programmable integrated optics system based on an artificial neural network Sendy Phang1, Phillip D. Sewell1, Ana Vukovic1 and Trevor M. Benson1

12.1

Introduction

It is now around 50 years since Stewart Miller first introduced the term integrated optics. His original paper [1] proposed a miniature form of laser beam circuitry and indicated routes towards achieving the fabrication of small waveguides (suggesting in his paper that channel widths in the 2–5 mm range may be achievable), integrated lasers, phase modulators, couplers and frequency-selective filters. Interestingly, Miller’s original paper specified laser wavelengths as being 0.4 to 10þ mm. Accompanying papers [2–4] described techniques for the analysis of the proposed integrated laser circuitry. In the intervening period, the terms photonics and photonic integrated circuits (PICs) have come into widespread use. Photonics is ‘the technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon’ [5]. Optoelectronics refers more specifically to devices or circuits that encompass both electrical and optical functions. The rapid development of reliable components for optical communications systems drove much of the early research into integrated optics. The present-day photonics has a vast range of scientific and technological applications, including telecommunications, information processing, materials processing, biological and chemical sensing, medical diagnostics and therapy, display technology and optical computing. The field of integrated optics (photonics) research is now very broad, covering active and passive photonic devices fabricated on many materials platforms including compound semiconductors, silicon and other group IV elements, dielectrics and polymers [6]. New materials, such as graphene and other advanced 2D materials, epsilon near-zero materials and phase-change materials, have emerged. Improvements in nanofabrication technology, including lithography and advanced 1 George Green Institute for Electromagnetics Research, Faculty of Engineering, University of Nottingham, Nottingham, UK

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etching techniques, allow the fabrication of sophisticated nanostructured waveguide devices; these include photonic crystals, subwavelength-structured (meta) materials with engineered optical properties and plasmonic structures. However, as discussed, for example, by Smit et al. for InP-based photonics [7] and Lim et al. [8] and Dumon et al. for silicon photonics [9], the commercialisation of integrated photonic solutions has driven the development of a set of standard foundry-level photonic building blocks which can be brought together to realise a variety of circuits and systems. This approach has enabled the processing of multi-project wafers through which a small customer can benefit from the low-costs associated with large volume processing using a variety of materials platforms [10]. In parallel to these remarkable technological developments, improved computational power has enabled significant advances in the simulation of photonics devices and systems. Present-day techniques must typically provide accurate vector results, or at least a reliable error estimate, for multi-scale problems potentially incorporating non-trivial materials properties and arbitrary geometries. The design of an individual component within an integrated optical circuit may be undertaken to satisfy specified performance requirements; for example, operation over a certain optical bandwidth, reduced propagation or insertion loss, or low reflectivity. In a traditional approach to integrated optics design, a designer may use a favoured simulation package to try out different geometric parameters or material values to garner information on the behaviour of a certain type of device. Plotting the data obtained from multiple simulations provides a useful means for establishing behavioural trends, so allowing optimal device parameters to be found [11,12]. This systematic approach is useful if the particular problem has only a few variable design parameters, but quickly becomes limited as the number of variables grows, or if there is a complex performance interdependency between design variables. The shift towards foundry-level processing moves the design process towards the integration of a number of basic functional building-blocks in order to obtain a desired functionality [7,10]. An alternative approach to integrated optics design is component synthesis where a computer creates designs that meet user-defined requirements or constraints. Whilst existing designs can be refined in this manner, the synthesis approach has the ability to produce new designs that are unconstrained by perceived knowledge, or former solutions. Such a component synthesis approach generally utilises the ability of global optimisation techniques to search a multidimensional variable space. A genetic algorithm (GA) is one such global optimisation approach. First introduced by Holland [13], GAs are based around the theory of evolution through natural selection and mutation starting from some randomly generated population of possible solutions; much of the terminology of GA research has been retained from this biological background. The automated optimisation provided by genetic algorithms finds applications in multiple fields [14–17]. In electromagnetics, GAs have been applied, for example, in the design of antennas and antenna arrays, frequency selective surfaces and grating filters [16]. Here, the goal is usually to find the best solution to a particular problem with a fitness function connecting the GA to the physical problem in hand.

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Section 12.2 provides a non-exhaustive review of some typical applications of genetic algorithms in integrated optics (photonics) design, as a sub-set of inversedesign [18–20] or bio-inspired [21] optimisation schemes to optimise structures based on functional performance criteria specified through a fitness function (figure of merit). Section 12.3 will explore another artificial neural network in the form of a reservoir computer (RC) and discuss how a reservoir computer might be implemented using the building blocks and concepts of integrated optics (photonics). Some concluding remarks complete the chapter.

12.2

Some applications of genetic algorithms in integrated optics design

In a simple evolutionary GA given by Goldberg [22], the basic processes are reproduction, cross-over (mating) and mutation (random perturbation) performed on a binary coded string of data that represents the solution domain. The performance of each member of an initial, randomly generated, population is evaluated using a fitness function. The fitness function quantifies how well the user-defined requirements of a problem are fulfilled by an individual solution. By mimicking natural selection, those genomes from a population that more closely fit the fitness function are given a larger chance of being preserved for a future generation in a selection process. Selection creates a new population for the next generation (iteration) of the GA. This creation of generations continues until convergence or until some other completion criteria, such as reaching a maximum number of generations or when there is no further improvement to the best solution found, are met. The processes of selection, recombination and mutation can cause a significant change to the makeup of a population from one generation to the next. To avoid the best solution from one generation being lost in this process, elitism can be introduced to preserve the best solutions from one population (generation) to the next [23,24]. The global optimisation of photonic components using such an approach clearly requires the simulation of many trial designs, a large percentage of which may later be discarded. The performance of each trial design is assessed using simulation, with electromagnetic frequency domain solvers or circuit-based techniques [25] being well suited to this task. Our earlier studies on component synthesis [26] identified (i) the need for a trade-off between calculation error and runtime and (ii) that it may not always be possible to exactly meet a given design specification requiring the definition of the overall fitness function to include some weighting of these. In [27], we showed how, by ensuring the adequate control of solver accuracy, a hierarchy of simulation techniques used within a single GA improves the efficiency of the optimisation process for rib waveguide designs. Two rib waveguide designs were successfully studied; these respectively targeted minimal birefringence and the effective optical coupling of a photonic integrated circuit (rib waveguide) to an optical fibre. Defects in membrane photonic crystals have led to the development of compact optical components [28]. The operation of these components is based on the

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photonic bandgap (PBG) created by the coherent interaction of light scattered from objects (say holes) located at the vertices of a fixed periodic lattice. Many groups have applied optimisation techniques to refine some of these structures. Examples include the reliable design of a fibre-to-photonic-crystal-waveguide spot-size converter [29], a micro-to-nano waveguide-coupler [20], bends [30,31] and power dividers or splitters [31–33]. As briefly noted in the introduction, this is just one of a diverse range of photonics devices that are based on using and processing light on the nano (sub-wavelength) scale. Obtaining various functionalities through arrays of scattering centres whose position is not constrained by the layout of a formal photonic crystal lattice has also been considered, a concept referred to as an optical application specific integrated circuits or OASICs [34]. Strategies for global optimisation in photonics design were considered in the OASIC context in [35]. Two familiar but important issues that arise in the context of the global optimisation of photonic components were discussed. These are (i) the need for fast simulation tools and means for assessing individual particular designs and (ii) the strategies that a designer can adopt to control the size of the problem design space to reduce runtimes without compromising the convergence of the global optimisation tool. A review of topological optimisation (i.e. optimisation of the spatial placement or distribution of materials) within the context of nano-photonics was given in [36]. This review covered the basics behind topological optimisation covering applications ranging from photonic crystal design to surface plasmon devices and future challenges in the field of nonlinear optics. Recently, optimisation techniques have led to the enhancement of the detection sensitivity of a gold nano-structure based surface plasmon resonance biosensor; the ‘microgenetic’ algorithm was used in conjunction with three-dimensional finite difference time domain (FDTD) electromagnetic simulations [37]. Molesky et al. [18] highlight some background work on using inverse design in this field of nano-photonics, before discussing specific emerging inverse design applications and challenges arising from nonlinear optical interactions in micro- and nano-scale resonators and in the fields of topological photonics [38] and metasurfaces.

12.3 Functional integrated optics powered by a reservoir computer 12.3.1 Introduction to an algorithmic reservoir computer The historical overview of integrated optics provided in Sections 12.1 and 12.2 showed that traditional parameter sweeping and stochastic evolutionary algorithm-based optimisation methods have been used to achieve desired functionalities in optical components and circuits. In this section, we overview a relatively recent artificial neural-network (ANN) concept called the reservoir computer (RC), also known as an echo-state network (ESN) [39], and show that integrated optics is a promising exploratory ground for a physical implementation of an ANN.

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Initially the RC approach is proposed as an alternative to a traditional ANN based on the recurrent neural-network (RNN) [39,40]. Figure 12.1(a) shows the schematic of the architecture of an RNN scheme, and Figure 12.1(b) shows the schematic of the architecture of an RC scheme. Both approaches are comprised of three main parts, namely an input channel or channels, a neuron kernel and an output channel or channels. It is a feed-forward network with a feedback loop in the synaptic connection pathways providing a time-dependent function between its (a)

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Figure 12.1 Schematic illustration of (a) the recurrent neural network (RNN) and (b) the reservoir computer (RC) scheme. The green-dashed lines illustrate direct input to read-out connection. The red solid-lines illustrate the signal flow diagram and the updating process during the training regime of both approaches

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input and the output. In principle, the fundamental difference between the RNN and the RC occurs during the training phase. Figure 12.1 shows the flow of signals during the normal operations (in black) and the training phase (in red) for both schemes. Throughout this chapter, the vector symbols u, x and y, respectively, denote the RC input signals, neuron activation states and RC output signal(s). The red-coloured signal flow diagrams only occur during the training phase, although it is stressed that in principle both systems may have a continual training phase during their lifetime. As signified by Figure 12.1(a), the RNN works by finding appropriate weighting elements of the input, systems kernel and read-out weights during its training from known input-target examples. Such a training approach puts a limit on the degrees of freedom the neuron kernel may have. Although in principle the RNN exhibits a dynamic internal memory, which allows temporal signal correlation operation, RNNs have not been widely adopted in practice due to their slow convergence in training which often reaches sub-optimal solutions [40,41]. Unlike the RNN, the RC offers a different view of an ANN by embracing randomness. In the RC approach, a distinction is made between the systems kernel and the read-out layer. That is, in the RC approach, the training phase finds the optimum read-out weights only whilst retaining the characteristic of the RCs kernel as a randomly interconnected recurrent neural network; thus, typical RC implementations permit a high degree of freedom in the complicated topology of the neuron kernel, see Figure 12.1(b) [40]. Consequently, the RC offers a more straightforward and flexible implementation than traditional RNN approaches; it offers better scalability than the RNN to handle parallel computing [40]. Not only does an RC provide an alternative line of attack, its performance has been shown to be comparable and better in some applications than other ANN approaches [41,42]. In the RC framework, the neuron kernel is activated by Nu time-varying input signals which are represented as the column vector uðetÞ 2 RNu 1 . The neuronactivation state x is updated using a typical ANN neuron equation, which mimics a biological neural network [39],   (12.1) xðetÞ ¼ ð1  aÞxðet  1Þ þ a f ðWin uðetÞ þ Wkernel xðet  1ÞÞ ; et  0 where a 2 ð0; 1 is a leaking constant, Win 2 RNx Nu is the weight of the input channel and Wkernel 2 RNx Nx is the weight of the neuron kernel, which provides the connection matrix for the interconnected neurons. Note that in this chapter we have the following notation convention, et for a dimensionless unit time-step, t for a real-time parameter, RLM for a real-valued matrix with L rows and M columns, and 0LM for a zero matrix of size ðL  MÞ. Here, Nu , Nx and Ny denote the number of input, neuron and output ports, respectively. The neuron-activation function f ðÞ describes the type of the neuron; different functions such as linear nodes, threshold logic gates, hyperbolic tangent, saturating linear, etc., have been used in the literature with different levels of performance [43]. Although it has been reported that a linear function provides the best memory capacity [42], and that an asymmetric saturating function outperformed a

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hyperbolic tangent function in the classification task [41], there is no clear rule for deciding upon a suitable neuron-activation function f [44]. In the following step, the neuron-activation states become the inputs to the read-out layer whose output yðetÞ 2 RNy 1 is given by yðetÞ ¼ Wout ½uðetÞ; xðetÞ; yðet  1Þ

(12.2)

where ½;  is a column vector concatenate operation and Wout 2 RNy ðNu þNx þNy Þ is the read-out layer weighting. Note that in (12.2), we have allowed a direct connection from the input, the green dashed-line in Figure 12.1. A training regime, using a known pair of inputs and target-output, is required by the RC to obtain the optimum read-out layer in order to perform a certain targeted task. For completeness, a step-by-step training algorithm is summarised in Algorithm 1. For details of the training regime shown here, we refer the reader to [39]. Algorithm 1 Algorithm to find optimum read-out layer weights during the training regime. 1: Given uðetÞ and ytraining ðetÞ 2: Initialise Win and Wkernel 3: X ¼ 0ðNu þNx þNy ÞðNu þNx þNy Þ 4: Y ¼ 0Ny ðNu þNx þNy Þ 5: Wout ¼ 0Ny ðNu þNx þNy Þ 6: for all et do 7: Calculate xðetÞ using (12.1) 8: p ¼ ½uðetÞ; xðetÞ; yðet  1Þ 9: X X þ ppT 10: Y Y þ ½yðetÞpT 11: end for YðX  gIÞ1 12: By regression Wout out 13: return W

12.3.2 An optical reservoir computer as a temporal signal discriminator Sub-section 12.3.1 introduced the principle of a ‘computer’-based reservoir computer. It was shown that the RC makes a distinction between the neuron kernel and a read-out layer; optimisation is performed only to obtain the appropriate read-out weights while keeping the neuron kernel unchanged. In this section, we exploit this merit to implement a photonic hardware implementation of the RC, which we hitherto refer to as an optical reservoir computer (ORC). The optical implementation of a reservoir computer has been gaining in popularity in recent years following the introduction of RC concept. As mentioned

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in Sub-section 12.3.1, the unique optimisation approach in the RC allows a physical implementation of ANN to be more feasible compared to the traditional RNN approach. Optics-based implementations of physical RCs have been reported by using different topologies, including chains of semiconductor optical amplifiers (SOAs), non-linear delay-coupled photonic systems, chains of micro-ring resonators and quarter-billiard cavities, for applications such as pattern, speech and bit pattern recognition [41,45–52]. In the remainder of this section, we propose an example which uses an ORC as a programmable optical signal information–processing device for a sensing application. The ORC, here, employs a D-shaped integrated optics cavity as the neuron kernel to perform temporal signal filtering, targeting bio-chemical spectral ‘fingerprint’ recognition. The operation wavelength of the proposed ORC is in the mid-infrared (MIR) region. The MIR part of the electromagnetic spectrum contains the rich spectroscopic absorption peaks or fingerprints of bio-chemical molecules [53]. It thus offers an exciting area for real-time molecular sensing in areas such as medicine, healthcare, environmental monitoring and security [53]. In particular, the application of MIR radiation in hyperspectral spectrometry shows strong potential for medical diagnostics [54]. To perform in-vivo diagnosis in real-time, one requires a fast signal-processing device because it has been estimated, for example, that cancer cells contain approximately 100 significant bio-molecular signatures. With the rapid development of MIR photonics [55–59], an integrated optics solution based on an ORC is an attractive route towards providing this diagnostic tool. For this reason, we propose, and further explore, a diagnostic approach based on an ORC system that is performed directly on temporal signals, instead of the indirect spectral finger-printing as in [60]. Before we describe the temporal-signal diagnostic approach used, we shall for clarity first describe the sensing element and our implementation of a physical neuron kernel. To obtain the training dataset, we use a time-domain simulation based on the FDTD method [61]; simulations are performed in two-dimensions with principal out-of-plane electric field polarisation, i.e. TM-polarised in a conventional two-dimensional problem sense. Figure 12.2 depicts the sensor and the D-shaped optical cavity which serves as our photonic neuron kernel. The sensor part is assumed, for concept illustration purposes, to be a photonic crystal (PhC) based Mach-Zehnder interferometer (MZI) with a reference of normal sample embedded within some of the air holes on one channel and a test (either normal or contaminated) sample on the other channel, see Figure 12.3(b) and (c). Although here we have used an MZI as our sensor element, in principle one can use any type of sensor available. The D-shaped cavity is a chopped-circle structure with a radius of 50 mm with an input port connected to the sensor and seven output ports. In detail, both structures are implemented within a triangular lattice of an air-hole PhC on a silicon material base whose refractive index is taken to be n ¼ 3:5. For 2.5–2.7 mm operation, we use a lattice constant of r ¼ 0:48a, where the lattice constant a ¼ 1.3 mm and r is the radius of the air hole, noting that the PhC has full TM band-gap region from 2.42 to 2.93 mm.

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Figure 12.2 (a) A simple illustrative sensing element based on a photonic crystal waveguide, the red-coloured holes are for the material sample and (b) an integrated optical sensing element and physical neural kernel based on D-shaped cavity. The PhC base has a lattice constant a ¼ 1:3 mm and r ¼ 0:624 mm is the radius of the air holes For the demonstration, the reference/test sample is represented as a common multi-pole Lorentz-type material [62], e ¼ e1 þ

Np X

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 w2  2idp w

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Figure 12.3 (a) and (c) The real part and (b) and (d) the imaginary part of refractive index of the normal and contaminated samples for several realisations. (e) A typical difference between the refractive index of the normal and the contaminated samples. In (a)–(d), the unperturbed refractive index (blue lines) is included for reference Table 12.1 Material parameters used for the architecture of both schemes and normal and the contaminated samples Parameters

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1.69 ½30; 0:03; 0:03; 0:03  103 ½3:1; 2:53; 2:59; 2:67 mm ½15:2; 0:93; 0:91; 0:88 THz

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through a small random perturbation of the samples dielectric property, which is described as l0p

xl0p ;

where

x 2 U½1; 5  104 

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where U½m; s  denotes a uniform random number with a mean of m and which is bounded between m  s. Several of the material realisations are displayed in Figure 12.3. We now describe our temporal signal diagnostic approach. The ORC system is intended to give an indication of the presence of a contaminant whose fingerprint is, in this example, at l0;c ¼ 2:63 mmm. In this approach, we perform two kinds of simulations: (i) of only a single sensing channel of the MZI without the D-cavity and (ii) of the integrated sensing element and the D-cavity. From these simulations, the time domain out-of-plane electric fields Ez are recorded at the output ports; for clarity, and consistency with the previous section, they are denoted using the same notation and are included in Figure 12.2. It is noted that we performed a Hilbert transformation on all real-valued time-domain results from the FDTD simulations to recover the imaginary part of the signal, thus reintroducing the notion of phase to the temporal signal. Having said that, here, we have used a complex-valued Ridge regression in the read-out training-phase [47]. From the first kind of simulation, we construct the read-out target signal ytarget . The output signal of each MZI channel n;c ui ðetÞ is collected, where the index i denotes different normal (n) or contaminated (c) samples. The target signal is then constructed by taking different combinations of normal-normal and normalcontaminated samples, yðet Þ ¼ BfVi;j ðetÞg;

Vi;j ¼n;c ui ðetÞ  nui ðetÞ

(12.5)

where the (time-domain) signature signal, Vi;j , is the difference in the time-domain signals between the normal and contaminated samples and Bfg denotes a bandpass filter operation. The band-pass filter has been designed to allow signals within the contaminant’s fingerprint spectral region to pass, i.e. of 2.63 mm wavelength. In other words, the read-out layer is designed to calculate and perform temporal signal filtering in the spectral region of the contaminant fingerprint. From the second simulation, i.e. of the full-sensor system including the Dcavity, the kernel output signals n;c xi13 ðetÞ are collected. These signals are reserved as inputs to the read-out layer as training input signals to obtain the layer’s weight values.

12.3.3 Chaotic cavity as a reservoir computer kernel In Sub-section 12.3.2, we described the proposed ORC to process the optical signal output of the sensing element, and how the ORC is designed to perform a complex time-domain signal filtering calculation which is the basis of the proposed temporal signal diagnostic approach. Here, we justify the basis of using the D-shaped cavity as our ORC kernel.

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Figure 12.4 (a) and (b) Eigenfunction at 2.7 mm and the phase relation for the 2.5–2.7 mm operation of the D-cavity, respectively; (c) typical D-cavity output xðtÞ The eigenfunction of the D-cavity at 2.7 mm, see Figure 12.4(a), shows that the electric field reverberates and forms a chaotic nodal pattern in the cavity and strongly decays evanescently into the PhC background. The k-space relation for the D-cavity for the 2.5–2.7 mm operation is depicted in Figure 12.4(b) and confirms the existence of the entire permissible k-space, i.e. kx2 þ ky2 ¼ ðw0 n=c0 Þ2 . It indicates that the interference occurring in the cavity originates from a wave which propagates in all directions, therefore confirming that the D-cavity operates chaotically, as conjectured by Berry [64,65]. Figure 12.4(a) and (b) exemplifies that the D-cavity is a suitable candidate for the physical implementation of a neuron kernel; it exhibits the required complex chaotic wave-dynamics and the fading memory properties. The complex chaotic wave-dynamic is obtained by using such a complex structure. Operation with chaotic dynamics is highly sensitive to a small input signal variation, thus has very good separation property [52]. This separation property is the key in Kernel-type methods [66] as it allows the projection of a low-dimensional input space into a higher-dimensional space. That is, the chaotic neuron kernel represents inputs which are only separable by a complicated non-linear low-dimensional surface as a linear hyperplane in the high-dimensional space [67]. In our ORC implementation context, the chaotic dynamics of the D-cavity allows the projections of the simple input signal coming from the sensing elements, which have a restricted range of waveguide k-space, to the entire permissible k-space of a chaotic system. Furthermore, the optical-size of the D-cavity, which is approximately 50l0 , produces well-separated echoes providing a fading memory property to the ORC kernel. We remind the reader that other physical structures exhibiting these qualities could also be used, examples of which were provided earlier in this chapter. A typical (temporal signal) output of the D-cavity xðtÞ, in Figure 12.4(c), exhibits a signal profile that is commonly found in a reverberating system; it decays exponentially and exhibits a chaotic non-periodic beating pattern, clarified in the inset to the figure, with a long reverberation time reaching almost 100 ps.

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Figure 12.4(c) is obtained by using an incident signal of a Gaussian-modulated sinusoidal pulse centred at f0 ¼ 115:3 THz with a FWHM 0.1 ps duration, i.e. a bandwidth of l ¼ 2:5 to 2.7 mm.

12.3.4 ORC training and validation Previously, it was shown that the D-cavity has a chaotic wave-dynamic and is a suitable candidate for an optical reservoir kernel. Here, we demonstrate the application of the ORC to perform a discrimination task for the proposed bio-chemical sensing application. In order to emulate the typical spiking behaviour in a neural network, we use a chain of Gaussian wave-packages as the incident signal. Each Gaussian wave-package has the same bandwidth as the one used in Figure 12.4(c), but is now sequentially generated with a periodicity of 1 ps. Inspecting (12.2), it can be inferred that the output of the ORC may depend on the kernel’s input signal, the kernel’s output signal and the delayed output signal fed back to the read-out layer. Here in our ORC implementation, we deliberately only consider the input contribution of the kernels output signal and the delayed output signal. We now consider a practical context for the training phase. The weight of the read-out layer Wout is calculated, using the algorithm provided in Algorithm 1. Figure 12.5 shows the relation between kernel output signals xi ðtÞ and their weightings to produce the output signal yðtÞ. We noted that phase information of the training input signal is essential as an ORC functions with coherent light; an estimation approach to resolve this challenge is provided in [47]. In Figure 12.5, we have considered specifically an ORC for the sensing application with a single output. The training optimises the weightings of both kernel output signal and delayed fed back output signal which can be physically realised by a series of signal attenuators, phase delays and a single photo-amplifier at the end of the summing structure. Figure 12.6 shows a typical target output, see (12.5) for the notation, which is used during the training regime of the ORC. It also presents the time-domain

x1

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Figure 12.5 Read-out layer system setup which depends only the neuron activation states and the delayed feedback output signal

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Figure 12.6 (a) and (d) Signature signal V between normal-normal and normalcontaminated samples; (b) and (e) filtered signals BfVg; (c) and (f) normalised spectra of the unfiltered and filtered signals behaviour and the spectrum of the difference between the reference and the test channel signal and the filtered signal BfVg. Subplots (a-c) are for the case when both the reference and the test channels contain normal samples and subplots (d-f) are for the case when the test channel contains a contaminated sample. In general, the signature signal contains several dominant wavelengths, see Figure 12.6(c) and (f); this is due to the random perturbation of the samples chemical fingerprint. The filtering process only passes the signal at the contaminant fingerprint wavelength and thus eliminates the irrelevant signal spectrum-components. In our demonstration, we have generated a database of 65 combinations of normal-normal and normal-contaminated samples by performing simulations of the structure given in Figure 12.2(b). The D-cavity output signals are recorded and become the input of the regression method during the training session. Figure 12.7 (a) and (b) shows the teacher signals and Figure 12.7(c) and (d) the actual read-out signal output obtained after the 65 training sessions. There is a distinct amplitude difference between the normal-normal and normal-contaminated case, of almost 10 times. To provide a quantitative measure of ‘closeness’ between the actual and the training signal, we use the commonly used error figure of Normalised Mean Square Error (NMSE) which is defined by, NMSE ¼

hðyactual  ytarget Þ2 i hy2target i

(12.6)

where, hi is the assembled averaging operation. Using (12.6), the ORC systems shown in Figure 12.7 have NMSE errors of less than 2%. To show how the read-out weight converges as the training session progress, Figure 12.8 shows the normalised norm of the difference of the weight between

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1 yactual (t)

yactual (t)

(c)

375

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–1

–1

–2

–2 0

50 100 Time / ps

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Figure 12.7 A typical comparison between the (a) and (b) teacher signals and the (c) and (d) actual output signal yactual for the case of (a) and (c) normal-normal and (b) and (d) normal-contaminated sample 0

||Wiout||

log10

||Wi+1out – Wiout||

–1

–2

–3 0

20

40

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Figure 12.8 Convergence of read-out weight as function of training epochs

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current and nearest-past training sessions on a log-linear scale. The linear trend-line exemplifies the exponential convergence of the read-out weight as the training session progresses. Thus, a more accurate and consistent weight can be obtained by performing more training. Although here we have ended the training after 65 sessions due to the demanding simulation condition, the convergence of the read-out weight is approaching 0.1%.

12.4 Conclusions This chapter has briefly reviewed some developments in the field of integrated optics since Miller first introduced this concept, noting some approaches to optimise structures based on functional performance criteria. An ORC was then proposed which offers a new heuristic approach to process optical information by using a state-of-the-art data-driven machine learning method that is entirely performed optically. This brings the prospect of an in-vivo diagnostic tool one step closer by allowing temporal light signal discrimination in real time.

References [1] Miller SE. Integrated optics: An introduction. Bell System Technical Journal. 1969;48(7):2059–2069. [2] Marcatili EA. Dielectric rectangular waveguide and directional coupler for integrated optics. Bell System Technical Journal. 1969;48(7):2071–2102. [3] Marcatili E. Bends in optical dielectric guides. Bell System Technical Journal. 1969;48(7):2103–2132. [4] Goell J. A circular-harmonic computer analysis of rectangular dielectric waveguides. Bell System Technical Journal. 1969;48(7):2133–2160. [5] What is Photonics? 2017. Available from: http://www.op-tec.org/what-isphotonics. [6] Thyle´n L, and Wosinski L. Integrated photonics in the 21st century. Photonics Research. 2014;2(2):75–81. [7] Smit M, Leijtens X, Bente E, et al. A generic foundry model for InP-based photonic ICs. In: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2012 and the National Fiber Optic Engineers Conference. IEEE; 2012. pp. 1–3. [8] Lim AEJ, Song J, Fang Q, et al. Review of silicon photonics foundry efforts. IEEE Journal of Selected Topics in Quantum Electronics. 2014;20(4):405– 416. [9] Dumon P, Bogaerts W, Baets R, et al. Towards foundry approach for silicon photonics: Silicon photonics platform ePIXfab. Electronics Letters. 2009;45 (12):581–582. [10] VLC Photonics. 2017. Available from: https://www.vlcphotonics.com/. [11] DellOlio F, and Passaro VM. Optical sensing by optimized silicon slot waveguides. Optics Express. 2007;15(8):4977–4993.

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[12] Rahman B, Obayya S, Somasiri N, et al. Design and characterization of compact single-section passive polarization rotator. Journal of Lightwave Technology. 2001;19(4):512. [13] Holland JH. Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann Arbor; 1975. [14] Karr C, and Freeman LM. Industrial applications of genetic algorithms. vol. 5. CRC Press; 1998. [15] Sigmund BM, Topology Optimization-Theory, Methods and applications. Springer; 2003. [16] Rahmat-Samii Y, and Michielssen E. Electromagnetic optimization by genetic algorithms. Microwave Journal. 1999;42(11):232–232. [17] Wang C, Yu S, Chen W, et al. Highly efficient light-trapping structure design inspired by natural evolution. Scientific Reports. 2013;3:1025. [18] Molesky S, Lin Z, Piggott AY, et al. Inverse design in nanophotonics. Nature Photonics. 2018;12(11):659. [19] Piggott AY, Lu J, Babinec TM, et al. Inverse design and implementation of a wavelength demultiplexing grating coupler. Scientific Reports. 2014;4:7210. [20] Piggott AY, Lu J, Lagoudakis KG, et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics. 2015;9(6):374–377. [21] Silva-Santos CH, Goncalves MS, and Herna´ndez-Figueroa HE. Designing novel photonic devices by bio-inspired computing. IEEE Photonics Technology Letters. 2010;22(15). [22] Goldberg DE, and Holland JH. Genetic algorithms and machine learning. Machine Learning. 1988;3(2):95–99. [23] De Jong KA. Analysis of the behavior of a class of genetic adaptive systems. University of Michigan; 1975. [24] Styan C. Synthesis and optimisation in optoelectronics. University of Nottingham; 2005. [25] Melati D, Morichetti F, Soares FM, et al. Building block based design of photonic integrated circuits for generic photonic foundries. In: 2012 14th International Conference on Transparent Optical Networks (ICTON). IEEE; 2012. pp. 1–4. [26] Sewell P, Vukovic A, and Benson T. Component synthesis in optoelectronics modelling. Microwave and Optical Technology Letters. 2002;33 (5):325–327. [27] Styan C, Vukovic A, Sewell P, et al. An adaptive synthesis tool for rib waveguide design. Journal of Lightwave Technology. 2004;22(12):2793– 2800. [28] Sibilia C, Benson TM, Marciniak M, et al. Photonic crystals: Physics and technology. Springer; 2008. [29] Sanchis L, Ha°kansson A, Lo´pez-Zano´n D, et al. Integrated optical devices design by genetic algorithm. Applied Physics Letters. 2004;84(22):4460– 4462.

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[46] Vandoorne K, Mechet P, Van Vaerenbergh T, et al. Experimental demonstration of reservoir computing on a silicon photonics chip. Nature Communications. 2014;5:3541. [47] Katumba A, Freiberger M, Laporte F, et al. Neuromorphic computing based on silicon photonics and reservoir computing. IEEE Journal of Selected Topics in Quantum Electronics. 2018;24(6):1–10. [48] Duport F, Schneider B, Smerieri A, et al. All-optical reservoir computing. Optics Express. 2012;20(20):22783–22795. [49] Paquot Y, Duport F, Smerieri A, et al. Optoelectronic reservoir computing. Scientific Reports. 2012;2:287. [50] Vandoorne K, Dambre J, Verstraeten D, et al. Parallel reservoir computing using optical amplifiers. IEEE Transactions on Neural Networks. 2011;22 (9):1469–1481. [51] Mesaritakis C, Papataxiarhis V, and Syvridis D. Micro ring resonators as building blocks for an all-optical high-speed reservoir-computing bitpattern-recognition system. Journal of the Optical Society of America B. 2013;30(11):3048–3055. [52] Appeltant L, Soriano MC, Van der Sande G, et al. Information processing using a single dynamical node as complex system. Nature Communications. 2011;2:468. [53] Seddon AB. A prospective for new mid-infrared medical endoscopy using chalcogenide glasses. International Journal of Applied Glass Science. 2011;2 (3):177–191. [54] Petersen CR, Prtljaga N, Farries M, et al. Mid-infrared multispectral tissue imaging using a chalcogenide fiber supercontinuum source. Optics Letters. 2018;43(5):999–1002. [55] Soref R. Mid-infrared photonics in silicon and germanium. Nature Photonics. 2010;4(8):495. [56] Roelkens G, Dave U, Gassenq A, et al. Silicon-based heterogeneous photonic integrated circuits for the mid-infrared. Optical Materials Express. 2013;3(9):1523–1536. [57] Brun M, Labeye P, Grand G, et al. Low loss SiGe graded index waveguides for mid-IR applications. Optics Express. 2014;22(1):508–518. [58] Li W, Anantha P, Lee KH, et al. Spiral waveguides on germanium-onsilicon nitride platform for mid-IR sensing applications. IEEE Photonics Journal. 2018;10(3):1–7. [59] Seddon A, Pan W, Furniss D, et al. Fine embossing of chalcogenide glasses– a new fabrication route for photonic integrated circuits. Journal of NonCrystalline Solids. 2006;352(23–25):2515–2520. [60] Ellis DI, and Goodacre R. Metabolic fingerprinting in disease diagnosis: Biomedical applications of infrared and Raman spectroscopy. Analyst. 2006;131(8):875–885. [61] Lumerical F. Solution, FDTD Solutions 6.5. http://www lumerical com/tcadproducts/fdtd.

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Index

absorbing coefficient 92–3 adiabatic coupling 116, 343 adiabatic negative taper 183 ALD (atomic layer deposition) 131 algorithmic reservoir computer 364–7 Aluminium-Gallium Arsenide (GaAlAs) 130 angle-cut fiber couplers 172 anomalous reflective and refractive material 109 anti-Stokes process 72–3 APCVD (atmospheric pressure chemical vapour deposition) 131 arrayed waveguide gratings (AWG) 295, 297 design 302 channel crosstalk 305–6 dispersion 302–3 focusing effect 302 free spectral range (FSR) 303 insertion loss 305 insertion loss uniformity 305 performance parameters 303–6 design parameters 306–7 high-index contrast AWGs 301–2 low-index contrast AWGs 299–301 principle 298–9 for spectroscopic applications 316 optical coherence tomography (OCT) 317–19 for spectral domain OCT (SD-OCT) system 319–27 for telecom applications 307–16 artificial neural-network (ANN) approaches 364–6, 368

atomic force microscopy (AFM) 24, 49, 246 atomic-scale emitters 343–4 attenuated total reflectance (ATR) 16 Babinet’s principle 109 band-to-band tunneling (BTBT) 279–81 beam-splitter and polarization controller 109–11 Bose–Einstein distribution function 79 boson peak (BP) 66, 74–80 Bragg diffraction 74 Bragg reflections 40, 43 Brillouin scattering 72, 78, 80 Brillouin spectroscopy 74 Bruggeman’s theory 55 Cauchy model 7 Cerenkov configuration 219–21 channel plasmon polariton (CPP) waveguides 99–101 channel waveguides, strain-induced losses in 221–2 chaotic cavity 371–3 chemical vapour deposition (CVD) process 130–1, 311 Chi-squared Error 8 Clausius-Mossotti relationship 204 coarse wavelength division multiplexing (CWDM) applications 300 coherent anti-Stokes Raman scattering (CARS) 18 complementary metal-oxidesemiconductor (CMOS)technology 104, 106, 174, 295

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computed tomography (CT) 46–7 Coulomb force 94 Courant condition 277 critical coupling 164, 167–8, 170, 173, 180–2 crystalline epitaxial thin films 133, 147–8 crystalline thin films for integrated laser applications 129 liquid phase epitaxy method, thin film growth by 132–4 photonic application of RE-doped crystalline thin films grown by liquid phase epitaxy middle infrared (MIR), laser emission in 151–3 saturable absorbers, crystalline thin films for 154 thin-disk configuration, laser oscillator in 153–4 visible domain, laser emission in 149–50 waveguide configuration, laser oscillator in 148–9 single crystalline thin films growth by liquid phase epitaxy fluorides epitaxial thin films 135–43 oxide epitaxial thin films 143–6 shaping of the LPE grown crystalline thin films 146–8 state of the art and main techniques to produce thin films 130–2 crystal truncation rods (CTR) 41–2 cyclic transparent optical polymer (CYTOP) 181 Czochralski method 145–6 Debye model 76 dense wavelength division multiplexing (DWDM) 299, 308, 315 dielectric function model 7 dielectric-loaded SPP (DLSPP) waveguide 99, 101

dielectric single crystalline thin films 133 difference frequency generation (DFG) 216, 236–9, 241 discrete Fourier transform (DFT) 277 distributed feedback (DFB) laser 184 DLSPPW 101 double layer heterojunction (DLHJ) 283 double-layer planar heterostructures (DLPH) 283 Drude model 7–8, 67 echo-state network (ESN) 364 e-field poling 223–5, 232–3 electric and magnetic sensors 197 electric field induced WGMs 202–9 magnetic field induced WGM 209–12 stress and strain tuning of optical spherical resonator 199–202 tethered sensors 198–9 untethered sensors 199 electric field induced WGMs 202–9 electron transport 106–7 ellipsometry 3, 55 applications 8–10 data analysis 6–8 theory 4–5 types of 5–6 energy-dispersive X-ray (EDX) 55 energy loss 98 evanescent field prism couplers 168, 182 extended X-ray absorption fine structure (EXAFS) 37, 48–51, 57 external quantum efficiency (EQE) 106–7 extinction coefficient 92–3 Fabry–Pe´rot (FP) interferometer 78 Fabry-Pe´rot (FP) style microresonators 161–2 Fabry-Pe´rot (FP) resonance 101

Index Fano-dip 93 fast Fourier transformation (FFT) 69, 325 Fermat’s principle 108 Fermi cutoff position 54 fibre Bragg gratings (FBG) 296–7 fibre-to-the-x (FTTx) market 300 finesse 162, 165, 168 finite-difference time-domain (FDTD) method 272, 284, 286, 364 flame hydrolysis deposition (FHD) 349 fluorescence spectroscopy 10 apparatus 11 data analysis 11–12 fluorescence lifetimes 12–13 quenching 13–14 fluorides epitaxial thin films chemical precursors, preparation of 136–7 fluorides, difficulties related to the growth of 135 homoepitaxy of RE3+ CaF2/CaF2 137–40 LiYF4/LiYF4 140–3 liquid phase epitaxy experimental setup under controlled atmosphere 135–6 fluorinating agent 136 fluorophores 10–14 focused ion beam (FIB) etching 147 Fourier domain OCT (FD-OCT) systems 317–18 Fourier transform 71–2 Fourier transform infrared-attenuated total reflectance (FTIR-ATR) 14 Fourier transform infrared-photo acoustic spectroscopy (FTIR-PAS) 14 Fourier transform infrared spectroscopy (FTIR) 14 apparatus 15–16 applications 18 data analysis 16–17

383

-extended ellipsometric spectra 6 theory 14–15 Franz-Keldysh effect 102 free-space diffraction gratings (FSDG) 297 full width at half maximum (FWHM) 44, 50–1, 54, 373 functional complexity 347, 353 functional integrated optics powered by reservoir computer algorithmic reservoir computer 364–7 chaotic cavity as a reservoir computer kernel 371–3 optical reservoir computer (ORC) as temporal signal discriminator 367–71 training and validation 373–6 fused silica microresonators 176 Gallium Arsenide (GaAs) 130 Gaussian beam 169–70, 272–5, 284 genetic algorithm (GA) 362 applications in integrated optics design 363–4 ‘goodness of fit’ 7 graphene-based photodetectors 107 group velocity dispersion (GVD) 175–6 harmonic oscillator model 15 heralded photon sources 344–6 heteroepitaxy 132–3, 146 High-energy surface X-ray Diffraction (HESXRD) 42 high-index contrast AWGs 301–2, 328 high-index soft proton-exchanged (HISoPE) waveguides 245 high operating temperature (HOT) HgCdTe detectors 278 auger-suppressed and fully carrierdepleted detectors 282–4 compositionally graded HgCdTe detectors 284–7 defects- and tunneling-related dark current 279–82

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holographic notch filters (HNFs) 74–5 hybrid plasmon polariton (HPP) waveguide 101–2 hydrofluoric acid (HF) 146 hydrogen silses-quioxane (HSQ) 178 hyper-Raman spectroscopy 18 Indium Phosphide (InP) 130 inelastic neutron scattering (INS) 77, 79 infrared light-induced negative effect 108 infrared spectroscopy 14, 16, 18, 78, 80, 302, 317 input-output formalism and critical coupling 164–8 integrated quantum photonics 337 applications 338–40 low-loss components 346–9 material platforms 349 hybrid systems 354–5 lithium niobate 353 silica 349–51 silicon nitride 352–3 silicon-on-insulator 352 III–V semiconductors 354 quantum states of light 340 heralded photon sources 344–6 ‘true’ single-photon sources 341–4 integrated spectroscopy using THz TDS and LF Raman scattering 65 boson peak investigation 75–80 light-scattering spectroscopy 71–5 terahertz light and excitations in THz region 66–7 terahertz time-domain spectroscopy 67–71 internal quantum efficiency (IQE) 106–7 IWKB technique 225 Kerr effect 102 Kerr frequency 177

Knudsen cells 131 light-scattering spectroscopy 71–5 liquid crystals 45 liquid phase epitaxy (LPE) method 129–30, 134–5 growth of single crystalline thin films by fluorides epitaxial thin films 135–43 oxide epitaxial thin films 143–6 shaping of the LPE grown crystalline thin films 146–8 photonic application of RE-doped crystalline thin films grown by middle infrared (MIR), laser emission in 151–3 saturable absorbers, crystalline thin films for 154 thin-disk configuration, laser oscillator in 153–4 visible domain, laser emission in 149–50 waveguide configuration, laser oscillator in 148–9 shaping of LPE grown crystalline thin films crystalline epitaxial thin films, microstructuration of 147–8 solvent removing, polishing and shaping 146–7 thin film growth by 132–4 lithium niobate (LN) 103, 218, 346–7, 353 lithium niobate on insulator (LNOI) 245, 251 lithium niobate resonator 168, 177, 180 localized surface plasmon (LSP) 91 localized surface plasmon resonance (LSPR) 93 long-range surface plasmon polariton (LRSPP) waveguide 99–100 low-index contrast AWGs 299–301, 308, 328

Index low-pressure chemical vapor deposition (LPCVD) 131, 175, 183 low temperature GaAs (LT-GaAs) 68 luminescence 10 Mach-Zehnder (MZ) EO modulator 104 Mach-Zehnder Interferometer (MZI) 296, 368, 371 magnetic field induced WGM 209–12 MBE method 131 membrane photonic crystals 363 metal-insulator interface 101 metal-insulator-metal (MIM) SPP waveguides 101, 103 metal thin film (MTF) 114–15 microdisks 162, 174 microtoroids 162 middle infrared (MIR), laser emission in 151–3 mixture model (MM) 55 MOCVD (metal organic chemical vapour deposition) 131 modal phase matching (MPM) 247, 251 morphology-dependent resonances (MDR) 197 Mueller matrix 5–6 MWIR detector 279–80 MWIR/LWIR bands 268, 269 nano-mechanical methods 94, 96 Navier equation 201 next-generation access networks (NGAN) 300 next-generation long-wavelength infrared detector arrays 265 high operating temperature (HOT) HgCdTe detectors 278 auger-suppressed and fully carrier-depleted detectors 282–4 compositionally graded HgCdTe detectors 284–7

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defects- and tunneling-related dark current 279–82 lower cost, large FPAs with subwavelength pixel pitch 270 comprehensive electromagnetic and electrical simulations 272–3 modeling photoresponse for nonmonochromatic illumination 275–8 small pixels and inter-pixel crosstalk in planar FPAs 273–5 nitrogen-vacancy (NV) centre 113, 343 noise equivalent temperature difference (NETD) 279 nonlinear integrated optics 216–18 nonlinear optical (NLO) materials 102–4 Normalised Mean Square Error (NMSE) 374 open ring microcavities 162–3 optical add drop multiplexers (OADMs) 300 optical application specific integrated circuits (OASICs) 364 optical characterization techniques 3 ellipsometry 3 analysis of the data 6–8 applications 8–10 theory 4–5 types of 5–6 fluorescence spectroscopy 10 apparatus 11 data analysis 11–12 fluorescence lifetimes 12–13 fluorescence quenching 13–14 Fourier transform infrared spectroscopy (FTIR) 14 apparatus 15–16 applications 18 data analysis 16–17 theory 14–15 optical waveguide characterization 22

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geometrical characterization 24 optical loss measurement 24–5 refractive index measurements 22–4 Raman spectrometry 18 apparatus 20 applications 21–2 data analysis 20–1 theory 19–20 optical coherence tomography (OCT) 317–19 optically pumped semiconductor lasers (OPSL) 149 optical microcavities, integration of 161 bulk calcium fluoride resonators integration on polymer platform 181–3 bulk lithium niobate and tantalate resonators integration on SOI platform 180–1 bulk magnesium fluoride resonators integration on SiN platform 183–5 coupling techniques 163 angle-cut fiber couplers 172 input-output formalism and critical coupling 164–8 planar coupling 173 prism couplers 168–71 tapered fiber couplers 172–3 ultra-high-Q PIC microcavities 173 high-Q fused silica PICs 176–7 high-Q lithium niobate PICs 177–9 high-Q SiN PICs 174–6 high-Q Si PICs 174 optical modulators 102 optical reservoir computer (ORC) 361, 367 functional integrated optics powered by reservoir computer algorithmic reservoir computer 364–7

chaotic cavity as a reservoir computer kernel 371–3 optical reservoir computer as a temporal signal discriminator 367–71 genetic algorithms’ applications in integrated optics design 363–4 as a temporal signal discriminator 367–71 training and validation 373–6 optical spherical resonator, stress and strain tuning of 199–202 optoelectronics 129, 361 oxide epitaxial thin films garnet thin films 144–5 perovskites thin films 145–6 silicate thin films 145 tungstate thin films 143–4 pair distribution function (PDF) 41 Pechini method 43 PECVD (plasma-enhanced chemical vapour deposition) 131 periodically poled lithium niobate (PPLN) 221–2, 224–5, 229, 231–2, 234, 236–7, 240–1, 243–4, 246–8, 250, 346 periodic poling components 233 difference frequency generation (DFG) and amplification 236–9 parametric fluorescence 235–6 second harmonic generation (SHG) 234–5 different PE processes and their impact on the nonlinearity of the crystal 225 annealing 226–7 direct exchange 226 IR absorption 227 nonlinear optical properties of PE lithium niobate waveguides 227–9 e-field poling 223–5

Index proton-exchanged (PE) and periodic poling e-field poling of PE samples 232–3 PE in PPLN crystals 229–32 surface domains 222–3 phased-array waveguide gratings (PAWGs) 297 phase-matching conditions 73, 215, 217, 219, 247, 344 phosphorescence 10 photoconductive antennas 68–9 photoelastic modulator (PME) 6 photonic bandgap (PBG) 39, 364 photonic crystals (PC) 39, 46–7, 342, 362–4, 368 application of XRD to 39–41 microcavities 161 photonic integrated circuits (PICs) 162, 295, 319, 361 photonics defined 361 integrated quantum: see integrated quantum photonics membrane photonic crystals 363 quantum photonic integrated circuits (QPICs) 240–4 photovoltaic detector arrays 267 planar coupling 173, 180, 182 Planck’s constant 281 plasma etching 147, 180 plasmonic-enhanced photodetectors 97 plasmonic heating 98 plasmonic hot-carrier-based photodetector 105 general physical process in 105–8 plasmonic metamaterial and metasurface 108 anomalous reflective and refractive material 109 beam-splitter and polarization controller 109–11 sub-diffractive limit superlens and metalens 111–13 plasmonic modulators 102–5

387

plasmonic nanostructures 92 applications based on 97–8 scattering, absorption and extinction of 92–4 plasmonic resonance, active tuning of 94–6 plasmonics 91–2 plasmonic waveguide circuits for subwavelength light transmission 98–102 PLD (pulsed laser deposition) method 131 Pockels effect 102 Poisson equation 201, 273 poly(methyl methacrylate) (PMMA) 202 polydimethylsiloxane (PDMS) 202, 205 potassium dihydrogen phosphate (KDP) 347 potassium titanyl phosphate (KTP) 239, 346 Poynting vector 93, 272 PPKTP waveguides 346 prism couplers 168–71, 177 proton-exchanged (PE) and periodic poling e-field poling of PE samples 232–3 PE in PPLN crystals 229–32 proton exchange in LiNbO3 215 birefringence phase matching, combination with 219 Cerenkov configuration 219–21 control of the domains 246 e-beam poling of PE samples 246–7 first discoveries 218–19 highly confining waveguides high-index soft proton-exchanged (HISoPE) waveguides 245 thin-film lithium niobate 245 insensitive phase-matching configurations

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insensitive phase-matching configurations 247 phase mismatch, numerical studies of 247–50 periodic poling components 233–9 different PE processes and their impact on nonlinearity of crystal 225–9 e-field poling 223–5 PE and periodic poling 229–33 surface domains 222–3 power-resistant materials 244–5 quantum photonics integrated circuits (QPICs) on PPLN 241 quantum relay 242–3 squeezed states 243–4 single photon pair generators 239–41 strain-induced losses in channel waveguides 221–2 Q-factor 162–3, 173–4, 176, 178, 180–1, 183, 185, 341, 345 quantum cascade laser (QCL) 65 quantum computing 338 quantum dot (QD) 113, 341–2 quantum efficiency (QE) 273, 284 quantum key distribution (QKD) 338–9 quantum photonic integrated circuits (QPICs) 116–17, 240 on periodically poled lithium niobate (PPLN) 241 quantum relay 242–3 squeezed states 243–4 quantum plasmonics 113 integrated circuits 115–17 quantum properties of surface plasmon 113–15 quantum states of light 340 heralded photon sources 344–6 ‘true’ single-photon sources 341 atomic-scale emitters 343–4

semiconductor quantum dots 342–3 quasi-phase-matched (QPM) cases 217 quencher 13 Raman effect 18 Raman enhancement factor 97 Raman intensity spectrum 78–9 Raman polarizability tensor 72 Raman scattering 19, 72, 75, 77–9, 97, 163 Raman spectra 20–2, 44–5, 75 Raman spectrometry 18, 65, 74–80 apparatus 20 applications 21–2 data analysis 20–1 geometrical characterization 24 optical loss measurement 24–5 optical waveguide characterization 22 refractive index measurements 22–4 theory 19–20 Raman susceptibility 76, 79 random bonding model (RBM) 55 Rayleigh scattering 18–19, 72 reactive ion etching (RIE) 147 recurrent neural-network (RNN) 365 reservoir computer (RC) 363–4 rotating compensator ellipsometer (RCE) 5 RTCVD (rapid thermal chemical vapour deposition) techniques 131 saturable absorbers, crystalline thin films for 154 scanning electron microscopy (SEM) 24, 40 scanning near-field optical microscopy (SNOM) 98–9 scattering coefficient 92–3 Scherrer equation 38–9 Schottky contact 106

Index second harmonic generation (SHG) 215, 234–5 Sellmeier model 7 semiconductor optical amplifiers (SOAs) 238, 368 semiconductor quantum dots 342–3 semi-insulating GaAs (SI-GaAs) 68 Shockey-junction devices 106 silica 17, 49–50, 345–6, 349–51 silica-on-silicon (SoS) -based 64-channel, 50-GHz AWG 315–16 -based 8-channel, 100-GHz AWG 308 design 308–10 design verification 311–15 evaluation of simulated results 310–11 fabrication 311 simulation 310 silicon nitride 174, 317, 345, 352–3 silicon nitride microresonators 175 silicon-on-insulator (SOI) 100, 175, 352 silicon-vacancy (SiV) centre 343 silicon waveguides 104, 180, 238, 352 single crystalline thin films growth by liquid phase epitaxy fluorides epitaxial thin films difficulties related to the growth of fluorides 135 homoepitaxy of RE3+ 137–43 liquid phase epitaxy experimental setup under a controlled atmosphere 135–6 preparation of the chemical precursors 136–7 oxide epitaxial thin films 143 garnet thin films 144–5 perovskites thin films 145–6 silicate thin films 145 tungstate thin films 143–4 shaping of the LPE grown crystalline thin films

389

microstructuration of crystalline epitaxial thin films 147–8 solvent removing, polishing and shaping 146–7 single-photon avalanche diodes (SPADs) 348 size-strain plot (SSP) 43 small-angle X-ray scattering (SAXS) 37, 40 soft proton exchange (SPE) 223, 227–8 sol-gel method 131 solid-state Fabry-Perot microcavities 161 spectral domain OCT (SD-OCT) system, AWG-spectrometer for 319 minimum separation, determining between output waveguides 321 between phased array waveguides 320–1 optimizing channel crosstalk in high-channel-count AWGs 321–4 256-channel, 42-GHz AWGspectrometer for SD-OCT 324–7 spontaneous four-wave mixing (SFWM) processes 341, 344–5 spontaneous parametric downconversion (SPDC) 114, 116, 215–16, 236, 244, 341, 344–6, 353–4 static quenching 13–14 Stern–Volmer quenching constant 13 Stokes process 72–3 strain–size plot (SSP) method 45 stress and strain tuning of optical spherical resonator 199–202 structural and surface-characterization techniques 35 X-ray absorption near-edge structure (XANES) 37, 48–50

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Integrated Optics Volume 2: Characterization, devices, and applications

X-ray-based analytical techniques and X-ray diffraction 37–9 X-ray diffraction (XRD) application to detect material strain and stresses 43–6 to nanostructures 41–3 to photonic crystals 39–41 X-ray photoelectron spectroscopy applied to optical materials 52–6 X-rays and computed tomography 46–8 extended X-ray absorption fine structure (EXAFS) 48–51 sub-diffractive limit superlens and metalens 111–13 subwavelength light transmission, plasmonic waveguide circuits for 98–102 sum/difference frequency generation (SFG/DFG) 215 sum-frequency generation (SFG) 341, 344 superconducting nanowire single-photon detector (SNSPD) 348, 352–3 surface domains 222–3 surface-enhanced Raman scattering (SERS) 97 surface plasmon polaritons (SPPs) 91, 98–9, 110–11, 113–16 surface plasmons (SPs) 91 quantum properties of 113–15 surface-sensitive X-ray diffraction (SXRD) 41 swept source OCT (SS-OCT) 318 symmetry-breaking nanostructures 93 tapered fiber couplers 172–3 telecom applications, AWGs for 307 silica-on-silicon (SoS)-based 64-channel, 50-GHz AWG 315–16 silica-on-silicon (SoS)-based 8-channel, 100-GHz AWG 308

design 308–10 design verification 311–15 evaluation of simulated results 310–11 fabrication 311 simulation 310 terahertz-gap 66 terahertz light and excitations in THz region 66–7 terahertz time-domain spectroscopy (THz-TDS) 66–71 tethered sensors 198–9 thin-disk configuration, laser oscillator in 153–4 thin film filters (TFF) 296–7 thin film growth by liquid phase epitaxy method 132–4 thin-film lithium niobate 245 III–V semiconductors 354 time-domain OCT depth scans (TD-OCT) 317–18 time-of-flight elastic recoil detection analysis (TOF-ERDA) 55 titanium diffusion and heat treatment 222–3 Tochigi Nikon Corporation 67, 78 total internal reflection (TIR) condition 172, 183 transition edge sensor (TES) 348 transmission electron microscopy (TEM) 49 transmission windows 265 TSSG-SC (top seeded solution growth - slow cooling) method 143 UHVCVD (ultra-high vacuum chemical vapour deposition) 131 ultra-high-Q PIC microcavities 173 high-Q fused silica PICs 176–7 high-Q lithium niobate PICs 177–9 high-Q SiN PICs 174–6 high-Q Si PICs 174 uniform deformation (UD) 43 uniform deformation energy density (UDED) 43

Index uniform deformation stress (UDS) 43 universal artifact peak 79 untethered sensors 199 vacuum ultraviolet (VUV) 6 variable optical amplifiers (VOAs) 300 very high-density wavelength division multiplexing (VHDWDM) 308 very-high-Q resonators 175 visible domain, laser emission in 149–50 Warren–Averbach method 45 waveguide configuration, laser oscillator in 148–9 waveguide-grating routers (WGRs) 297 wavelength division multiplexing (WDM) systems 296, 301 whispering gallery mode (WGM) 161, 163 electric field induced 202–9 magnetic field induced 209–12 wide-angle X-ray scattering (WAXS) 37 Wiener–Khinchin theorem 72 Williamson–Hall plots 43, 45

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X-ray absorption near-edge structure (XANES) 37, 48–50 X-ray absorption spectroscopy (XAS) 37, 48 X-ray-based analytical techniques and X-ray diffraction 37–9 X-ray diffraction (XRD) application 37 to detect material strain and stresses 43–6 to nanostructures 41–3 to photonic crystals 39–41 X-ray fluorescence (XRF) analysis 37 X-ray microscopy 37, 46 X-ray photoelectron spectroscopy (XPS) 52, 55 applied to optical materials 52–6 X-rays 35, 37–8, 43 and computed tomography 46–8 extended X-ray absorption fine structure (EXAFS) 37, 48–51 YLF substrates 140–2