High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications [1 ed.] 9781624170447, 9781607410096

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

Lasers and Electro-Optics Research and Technology Series

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HIGH-POWER AND FEMTOSECOND LASERS: PROPERTIES, MATERIALS AND APPLICATIONS

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High-Power and Femtosecond Lasers: Properties, Materials and Applications Paul-Henri Barret and Michael Palmer (Editors) 2009. ISBN: 978-1-60741-009-6

High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

Lasers and Electro-Optics Research and Technology Series

HIGH-POWER AND FEMTOSECOND LASERS: PROPERTIES, MATERIALS AND APPLICATIONS

PAUL-HENRI BARRET Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

AND

MICHAEL PALMER EDITORS

Nova Science Publishers, Inc. New York

High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

Copyright © 2009 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA High power and femtosecond lasers : properties, materials, and applications / editors, Paul-Henri Barret and Michael Palmer. p. cm. Includes bibliographical references and index. ISBN 978-1-62417-044-7 (eBook) 1. High power lasers--Industrial applications. 2. Femtoseconds lasers--Industrial applications. 3. Laser pulses, Ultrashort. I. Barret, Paul-Henri. II. Palmer, Michael, 1962TA1695.5.H54 2009 621.36'6--dc22 2009002422

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CONTENTS Preface

vii

Research and Review Studies

xv

Chapter 1

Recent Progress of High Peak Power Solid State Lasers Yung-Sheng Huang, Jung-Sheng Huang and Fang-Ling Chang

Chapter 2

Laser Annealing of Composite Materials with Metal Nanoparticles Andrey L. Stepanov

27

Chapter 3

Single Crystal Photo-Elastic Modulators F. Bammer

71

Chapter 4

Diffractive Microoptics for Technological IR-Lasers V. S. Pavelyev, V. A. Soifer, V. I. Konov, V. V. Kononenko and A. V. Volkov

Chapter 5

Micro- and Nanoscale Heat Transfer in Femtosecond Laser Processing of Metals Yuwen Zhang, D. Y. Tzou and J. K. Chen

159

High Power Femtosecond Laser Machining of Metals in Ambient Medium S. R. Vatsya, Chengde Li and S. K. Nikumb

207

Femtolasers-Mediated Multiphoton Excitation Imaging of Bulk Ocular Tissues Bao-Gui Wang and Karl-Jürgen Halbhuber

231

Optical Properties of Rare Earth Ions Induced by Femtosecond Laser Lixin Yu and Zhongxin Liu

279

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Ytterbium Doped Materials for Femtosecond Lasers Pierre-Olivier Petit, Philippe Goldner, Bruno Viana, Justine Boudeile, Frédéric Druon, Dimitris N. Papadopoulos, Marc Hanna and Patrick Georges

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1

125

315

vi

Contents

Chapter 10

Ultrafast Dynamics of Porphyrins in Higher Excited State Dae Won Cho, Mamoru Fujitsuka and Tetsuro Majima

Chapter 11

Femtosecond Excited-State Ultrafast Dynamics of Complex Molecular Systems: Semiclassical Dynamics Simulations Guang-Jiu Zhao, Yu-Hui Li and Ke-Li Han

369

High Intensity Laser-Matter Interactions: Measurements of Ion and Neutral Emission and Applications A. Daskalova and W. Husinsky

393

Improved Thermal Model and its Application in High-Power Laser Ablation of Target Ranran Fang, Duanming Zhang, Hua Wei and Zhihua Li

415

Chapter 12

Chapter 13

Short Communications Dynamics of Excitons Confined in Semiconductor Thin Films Osamu Kojima and Toshiro Isu High Power Long Pulse Width QCW Laser Diode Bars for Optical Pumping of Yb-Er Glass Solid State Lasers N. I. Katsavets, V. A. Buchenkov and A. L. Ter-Martirosyan

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Index

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335

439 441

455 463

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PREFACE There has been a remarkable upsurge in the importance of high power lasers in the past decade. This book presents an overall survey of recent advances in high peak power solid lasers and reviews recent results in the interaction of high power laser pulses with various dielectric materials containing metal nanoparticles. This book also presents the basics as well as the theory of a single crystal photo-elastic modulator and a consideration of modern approaches to the synthesis of diffractive optical elements for technological IR-laser beams focusing. During ultrafast laser interaction with metal, the electrons and lattices are not in equilibrium. This book presents various two-temperature models that can be used to describe the nonequilibrium heat transfer as well as the results of techniques in high power femtosecond laser machining of metals. This book presents an overview of the current state of the art in the field of femtosecond technology with a special emphasis on the research of highintensity laser-matter interactions. An investigation of non-linear excitation imaging technique including two-photon autofluorescence and second harmonic generated signal imaging is presented to investigate the microstructures of whole-mount corneal, retinal, and scleral tissues in their native environment. Finally, included is a review of recent semiclassical excited-state dynamics simulation results of some complex molecular systems and a report of the dynamics of confined excitons when several exciton states are excited. Chapter 1 - There has been a remarkable upsurge in the importance of lasers, especially in high power lasers, on optics in both pure science and in technology in recent years. Besides, by considering the development of the high power lasers with their rapidly growing list of applications, the obvious needs for an introduction to this newest field is the primary reason for this paper. In this article, the authors present an overall survey of recent advances in high peak power solid state lasers (SSLs). The contents include: Reviewing how the Degnan’s thermal Boltzman factor affects the inversion population which is resulted from the non-uniform temperature distribution in the laser crystal. The Auger effect (or so- called energy transfer up-conversion (ETU) effect) in the laser crystal could result in thermal loading which is a function of pulse repetition frequency (PRF). So the theoretical calculation on the thermo-optic effect and thermal focusing length are discussed to explain the experimental results of SSLs. An introduction to the spatial-time dependence laser model of rate equations for the active (A-O switch) and passive (Cr 4+ :YAG saturable absorber and semiconductor GaAs saturable absorber) Q-switched SSLs is presented.

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In the second part of this paper, the authors study the E-M transverse modes of laser output, especially in the generation of high order transverse modes, and calculate the threshold pump power. In order to obtain a high peak power and single mode laser pulse output, one can use simultaneously the Q-switching and mode locking technique. In this article, the authors talk about its newest development in the past few years. In the third part of this article, the authors talk about the non-linear optical device which utilizes the intense radiation field of the nonlinear optical response of an optical media (i.e. KTP or KDP, QPM, and PPLN nonlinear crystals) to generate a new frequency emission from UV to far Infrared band. Thus, the frequency conversion is a useful technique for extending the utility of high power SSLs. The authors talk especially about the development of pulsed optical parametric oscillation (OPO) in SSLs. The discussion materials are based on some researcher’s recent works. Finally, the OPO tunable source may have impacts on the development of high power SSLs and important applications in some areas such as gravity detection, atmospheric detection, DNA detection, global remote sensing…etc.. But the authors skip this special issue in this article. Chapter 2 - Recent results on the interaction of high power laser pulses with various dielectric materials containing metal nanoparticles are reviewed. Original results together with new publications are observed. In general, the excimer laser pulse modification of silver and copper nanoparticles synthesized by ion implantation in silicate glasses and sapphire are considered. One of features of composite samples prepared by the low energy ion implantation is the growth of metal particles with a wide size distribution in the thin depth from the irradiated substrate surface. Pulsed laser irradiation makes it possible to modify such composite layer, improving the uniformity in the size distribution of the nanoparticles. Changes induced by pulsed laser exposure suggest there are both reductions in average size of the metal nanoparticles, and some long-range dissolution of metal atoms in the matrix. Experimental data on laser modification are explained by photofragmentation and melting of the nanoparticles in the dielectric matrix. Combination of ion implantation and laser annealing is promising technology for fabrication of novel composite optical materials. Chapter 4 - Wide use of infrared (IR) lasers in technological applications (metal cutting and hardening, laser evaporation, laser bending and etc.) have stimulated a research in the field of synthesis of IR-range diffractive microoptical focusing elements, which could retain their functionality under continuous irradiation with high power. Successive fulfillment of this requirement is stipulated both by selection of an appropriate substrate material and by development of technologies for creation a diffractive microrelief on a substrate as well as numerical methods for microrelief optimization taking into account possible technological constraints. The present chapter contains a consideration of modern approaches to the synthesis of diffractive optical elements (DOE) for technological IR-laser beams focusing. Experimental results of produced elements investigation described also. Different ways, from geometrical optics approximation to stochastic optimization, are used for calculation of a diffractive microrelief of IR-range optical elements that focus an illuminating beam into a pre-given 2-dimensional area. Near-IR DOE synthesis on sapphire substrates by plasmochemical etching method is considered. Several diamond focusing DOEs for operating at CO2-laser wavelength (λ=10.6 μm) are produced and presented. The nanosecond UV-laser ablation and plasmochemical lithographic etching technologies for DOE synthesis on CVD diamond plates are discussed.

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ix

Being a perspective optical material, CVD diamond has a high refractive index (n=2.4), resulted in relative high losses by Fresnel reflection. The present chapter includes consideration of a realization of antireflecting structures on a diamond film surface by UVlaser ablation. The advent of silica and silver-halide IR-range optical fibers for technological applications has set tasks of optimization methods development and of forming diffractive microreliefs on optical fiber surface for waveguide beam controlling. The present chapter includes the results of experimental investigation of diffractive microrelief and antireflecting structures that are realized on an end-face of IR-fiber. Chapter 5 - Ultrafast laser material processing has received significant attention due to a growing need for the fabrication of miniaturized devices at micro- and nanoscales. The traditional phenomenological laws, such as Fourier’s law of heat conduction, are challenged in the microscale regime and a hyperbolic or dual phase lag model should be employed. During ultrafast laser interaction with metal, the electrons and lattices are not in equilibrium. Various two-temperature models that can be used to describe the nonequilibrium heat transfer are presented. A semi-classical two-step heating model to investigate thermal transport in metals caused by ultrashort laser heating is also presented. The main difference between the semiclassical and the phenomenological twotemperature models is that the former includes the effects of electron drifting, which could result in significantly different electron and lattice temperature response from the latter for higher-intensity and shorter-pulse laser heating. Under higher laser fluence and/or short pulse, the lattice temperature can exceed the melting point and melting takes place. The liquid phase will be resolidified when the lattice is cooled by conducting heat away. Ultrafast melting and resolidification of the thin gold film and microparticles were investigated. At even shorter pulse width, femtosecond laser heating on metals produces a blasting force from hot electrons in the sub-picosecond domain, which exerts on the metal lattices along with the non-equilibrium heat flow. The author’s work that employs the parabolic two-step heating model to study the effect of the hot-electron blast in multi-layered thin metal films is also presented. Chapter 6 - High power ultra-short-pulse lasers offer significant advantages over their long-pulse counterparts for material processing. Since the duration of the pulse is too short to establish the temperature equilibrium between the electron and lattice subsystems, little melt is produced during processing. Ablation is caused by direct removal of the material. Consequently, the machined surface features conform closely to the intensity profile of the laser beam. The original laser beam suffers significant distortions during propagation through a medium such as air. Intensities enhanced further by the self-focusing of the beam are sufficiently high to cause an optical breakdown of the media, generating plasma. Scattering effects of plasma deform the laser beam profile. Distortion to the optical beam profile can be reduced by conducting femtosecond laser machining in vacuum or the gaseous media less immune to ionization, which restricts its application in the production environment. Removal of material also generates a plasma plume with the additional scattering effects. For certain energy range, the competing self-focusing and gas plasma plume supplemented with the material plasma can combine to cause plasma filamentation and the distortion causing scattering effects balance out yielding an adequately shaped beam profile. Filament of hot plasma also acts as an energy source with similar properties. The energy at which filamentation occurs can be determined by calculating the optical beam profile, which can be

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controlled experimentally thereby yielding a cleaner fabricated surface. Due to significant differences in the processes involved, this type of conformity is less pronounced in case of the dielectrics compared to the metallic materials. This article presents the results on the applications of such techniques in high power femtosecond laser machining of metals. Some discussion on non-metallic materials is also included. Chapter 7 - Currently, femtosecond lasers (femtolasers) are being extensively employed in diverse research and application fields. Femtolasers-mediated multiphoton excitation laser scanning microscopy is one of the most exciting recent developments in biomedical imaging and becomes more and more an inspiring imaging technique in the intact bulk tissue examinations. In this chapter, the non-linear excitation imaging technique including twophoton autofluorescence (2PF) and second harmonic generated signal imaging (SHG) was employed to investigate the microstructures of whole-mount corneal, retinal, and scleral tissues in their native environment. In details, image acquisition was based on intense ultrafast femtosecond near-infrared (NIR) laser pulses, which were emitted from a modelocked solid-state Ti: sapphire system. By integrating high-numerical aperture diffractionlimited objectives, multiphoton microscopy/tomography of ocular tissues was performed at a high light irradiance order of MW-GW/cm2, where two or more photons were simultaneously absorbed by endogenous molecules located in the thick tissues. As a result, the cellular and fibrous components of intact scleral and corneal tissues were selectively displayed with the assistance of the in-tandem detection of 2PF and SHG procedures. Any exogenous dye was not used. High-resolution optical images of keratocytes in cornea, fibroblasts, mature elastic fibers and blood capillaries in sclerae as well as of the retina radial Müller glial cells, ganglion cells, bipolar cells, photoreceptors, and retina pigment epithelial (RPE) cells were acquired. Furthermore, this promising technique has been proved to be an indispensable tool in assisting femtolasers intratissue surgery, especially for in situ assessing the obtained microsurgical effects. Most remarkably, the activated keratocytes, also named myofibroblasts during wound repair, were in vivo detected using the multiphoton excitation imaging in the treated animals twenty-four hours after the intrastromal surgery. In this chapter, RESULTS is divided into five areas of interest: (1) corneal multiphoton imaging; (2) scleral multiphoton imaging; (3) retinal multiphoton imaging; (4) uses of multiphoton excitation imaging in intrastromal laser surgery; (5) uses of multiphoton microscopy in detecting activated stromal cells after surgical laser treatment. Data show that the in-tandem combination of 2PF and SHG imaging allows for in situ co-localization imaging of various microstructural components in the whole-mount ocular tissues. Qualitative and quantitative assessment of microstructures was obtained. The selective displaying merits of tissue components only with the excitation of different wavelengths is the most exciting development for bulk tissue imaging, which allows to selectively studying of three-dimensional (3-D) architecture of cellular microstructures and extracellular matrix arrangement at a substantial depth. Using the laser power within threshold value, the bulk tissues can be imaged numerous times without visible photodisruption. Intrinsic emission multiphoton microscopy/tomography is consequently confirmed to be an efficient and sensitive non-invasive imaging approach, featured with high contrast and subcellular spatial resolution. The non-linear optical imaging yields vivid insights into biological specimens that may ultimately find its clinical application in optical pathological diagnostics. The authors believe that this promising technique will also find more applications in the biological and medical basic research in the near future. Potentially, based on its capability of intrinsic fluorescence imaging, the 2PF of cytoplasmatic

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Preface

xi

NAD(P)H would have a use in studying the dynamics of the mitochondrial bioenergetics and further utility in conducting nanomedical investigations in this organelle. Chapter 8 - Ultrafast titanium-sapphire tunable femtosecond (fs) laser can produce fs and provide high-density to be used as excitation resource, it is ideal tool to study the optical properties of materials. Rare earth (RE) compounds have many potential and practical applications in display device, upconverson laser, fluorescent probe, optical communications and fiber optic amplifiers, etc. The upconversion luminescence (UCL) and fluorescent changes of RE ions in transparent hosts and complex induced by fs laser have aroused a large amount of interests. In this review, the authors systematically reported the progresses of UCL of RE ions (such as Eu3+, Tb3+, Ce3+ and Dy3+, etc) in glass, crystallized hosts, and complexes, including luminescent characteristic, upconversion mechanisms and electronic transition processes. The changes of optical properties of RE ions by fs laser irradiation can achieve valence manipulation of RE ions and microfabrication. Thus in this review the authors also intensively reported the progresses of this topic, including persistent spectral hole burning, structural changes, dynamic processes etc. Chapter 9 - At the end of the last century, three important technological breakthroughs took place in ultra-short laser pulse generation field. In 1985, Strickland and Mourou first demonstrated Chirped Pulsed Amplification [1]. Then Moulton, in 1986, developed a new laser, based on aluminium oxide doped by titanium ions (Ti3+:Al2O3), called Ti:Sapphire [2]. Finally, Spence, Kean and Sibbert carried out the first phase mode-locking (“magicmodelocking”) in Ti:Sapphire also called Kerr Lens Mode-locking [3]. Since this moment, all required elements have been demonstrated to build reliable and efficient ultra-short pulses laser chain. Chapter 10 - It is well known that in the natural photosynthesis system excitation energy captured by the light-harvesting complex is transferred to the reaction center after an energy migration process [1]. In the natural system, higher excitation energy generating the higher excited states of dyes such as chlorophylls and carotenes is also utilized, despite its very short lifetime [2]. Inspired by the natural system, artificial energy transfer systems, in which energy transfer of higher excited-state energy is realized, have been demonstrated by various researchers [3]. On the other hand, for most molecules, no excited singlet states (S2, S3…states) have been observed to emit light upon excitation, the same being true for triplet states (T2, T3…states). This is summarized in Kasha’s rule: The emitting electronic level of a given multiplicity is the lowest excited level of that multiplicity [4]. Chapter 11 - In past years, the femtosecond lasers have been widely used to study the time-dependent phenomena in the fields of physics, chemistry, biology, and material sciences. At the same time, more and more experimental techniques and theoretical methods are developed to investigate the ultrafast dynamics in the electronic excited states of complex molecular systems. Nowadays, the time-resolved ultrafast spectroscopy, excited-state quantum chemical calculations, and excited-state dynamics simulations have been versatile tools for the study of the electronic excited-state ultrafast dynamics of complex molecular systems. In this chapter, the authors have reviewed their recent semiclassical excited-state dynamics simulations results of some complex molecular systems. The detailed changes for molecular conformations and electronic structures in the femtosecond excited-state ultrafast dynamics of Tetraphenylethylene (TPE) and 9,9’-bianthryl (BA) molecules are dynamically simulated. Moreover, the dynamics simulations results are compared with the femtosecond time-resolved spectroscopic results.

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Chapter 12 - This chapter represents an overview of the current state of the art in the field of femtosecond technology with a special emphasis put on the research on high-intensity laser-matter interactions. Ultrashort pulse laser ablation provides a promising approach for processing of almost any kind of material. However, this method has been investigated mainly by research on solid materials such as metals, semiconductors, etc. Studies on large biological molecules are still only slightly covered. Following a brief description of the fundamentals of femtosecond laser technology, an introduction to the physics of the high intensity laser interaction will be provided. Thorough understanding of heat transfer mechanism and energy conversion routes is of crucial importance for controlling the resulting modification of the target material in many practical applications. In the current studies femtosecond laser ablation was applied to complex biological molecules. Measurements of TOF mass spectra obtained from the laser–tissue interaction are presented. TOF mass spectroscopy has been applied to characterize the species produced in the femtosecond (fs) and nanosecond (ns) regimes. These studies aim to detect and give information on the photodissociation of these biological molecules and to compare the two ablation regimes. The morphological changes of the material were investigated using Environmental Scanning Electron Microscopy. The results will demonstrate the feasibility of the USLA-TOF method as a high sensitivity analytical technique for elemental analysis and for detection of fragile biological molecules. Some comments on the potential novel applications of ultra-short laser radiation are presented, namely efficient implementation in ophthalmology, dentistry, nanosurgery and innovative trends in femtosecond technology. Short Communication A - The authors report the dynamics of confined exctions when several exciton states are excited. The dynamics are measured by using a transient grating (TG) technique and a degenerate four-wave-mixing (DFWM) technique. In the system of the quantization of exciton center-of-mass motion, the excitons have several levels in the narrow energy region. The transient signals generated by the excitation of several exciton levels by using an ultrashort-pulse laser with a broadband spectrum are different from those generated by the excitation of single exciton level. The excitons confined in GaAs films with a specific thickness show enhanced excitonic optical nonlinearity, which enhancement is described by the nonlocal response theory, and an ultrafast response that is comparable to the pulse width of the DFWM signals. This result is an important factor in the development of ultrafast optical devices that exhibit large optical nonlinearity and ultrafast response. Moreover, the TG signals show a long-lived component, which is longer than that of the single exciton level. The changes in the response profile can be attributed to the excitation by a spectrally broadband pulse. Their results will provide impetus to the development of ultrafast optical devices based on the excitonic optical nonlinearity. Short Communication B - This publication is devoted to development of 100 W quasicontinues wave 950 nm long pulse width (5 ms) laser diode bars. Results on optical output power and degradations characteristics within wide temperature range (from -400C to +850C) are presented. Developed LDBs are based on advanced single quantum well separate confinement heterostructures with index-graded waveguide design optimized for generation wavelength 950 nm at +250C, low threshold current density (70 A/sm2), high characteristic (1,1 W/A). threshold current temperature (T0=150 K) and good slope efficiency Estimated LDB lifetime in long pulse width regime is more than 109 and 108 pulses at heat-sink temperature +250C and +850C, respectively.

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These laser diode bars are developed for effective pumping of Yb-Er glass solid state lasers (SSLs) with generation within the “eye-safe” spectral range (1.54 µm). Design of YbEr glass SSLs using for optical pumping two 950 nm laser diode bars was developed. Such SSLs have the pulse energy up to 8mJ at multimode regime, the pulse width 20 ns and repetition rate up to 20 Hz.

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RESEARCH AND REVIEW STUDIES

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In: High-Power and Femtosecond Lasers Editor: Paul-Henri Barret and Michael Palmer

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Chapter 1

RECENT PROGRESS OF HIGH PEAK POWER SOLID STATE LASERS Yung-Sheng Huang∗1, Jung-Sheng Huang1 and Fang-Ling Chang2 1

College of Electrical Engineering and Computer Science, Semiconductors Research Laboratory, I-Shou University, 840 Kaoshiung, Taiwan 2 Research Institute of Computer and Information Science, University of Oregon, Eugene OR 97405, USA

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ABSTRACT There has been a remarkable upsurge in the importance of lasers, especially in high power lasers, on optics in both pure science and in technology in recent years. Besides, by considering the development of the high power lasers with their rapidly growing list of applications, the obvious needs for an introduction to this newest field is the primary reason for this paper. In this article, we present an overall survey of recent advances in high peak power solid state lasers (SSLs). The contents include: Reviewing how the Degnan’s thermal Boltzman factor affects the inversion population which is resulted from the non-uniform temperature distribution in the laser crystal. The Auger effect (or so- called energy transfer up-conversion (ETU) effect) in the laser crystal could result in thermal loading which is a function of pulse repetition frequency (PRF). So the theoretical calculation on the thermo-optic effect and thermal focusing length are discussed to explain the experimental results of SSLs. An introduction to the spatial-time dependence laser model of rate equations for the active (A-O switch) and passive (Cr 4+ :YAG saturable absorber and semiconductor GaAs saturable absorber) Q-switched SSLs is presented. In the second part of this paper, we study the E-M transverse modes of laser output, especially in the generation of high order transverse modes, and calculate the threshold pump power. In order to obtain a high peak power and single mode laser pulse output, one can use

∗

Email: [email protected]

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2

Yung-Sheng Huang, Jung-Sheng Huang and Fang-Ling Chang

simultaneously the Q-switching and mode locking technique. In this article, we talk about its newest development in the past few years. In the third part of this article, we talk about the non-linear optical device which utilizes the intense radiation field of the nonlinear optical response of an optical media (i.e. KTP or KDP, QPM, and PPLN nonlinear crystals) to generate a new frequency emission from UV to far Infrared band. Thus, the frequency conversion is a useful technique for extending the utility of high power SSLs. We talk especially about the development of pulsed optical parametric oscillation (OPO) in SSLs. The discussion materials are based on some researcher’s recent works. Finally, the OPO tunable source may have impacts on the development of high power SSLs and important applications in some areas such as gravity detection, atmospheric detection, DNA detection, global remote sensing…etc.. But we skip this special issue in this article.

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1. THERMO-OPTIC EFFECTS In the literature "Heat Generation in Nd:YAG and Yb:YAG"[1] in 1993, T.Y. Fan reported that a small thermal load was observed in the diode-pumped Nd:YAG and Yb:YAG with a doped concentration of 1.04 at.% and 6.5 at.%, respectively. Chen et al. [2] gave a maximum stress fracture of the induced heat in the laser crystal caused by the pumping in power for a diode pumped optical-coupled laser system. Their research indicated that the value of the maximum stress fracture was influenced by both Nd-doped concentration and the absorption coefficient [3]. They therefore determined the ratio of thermal load to pumped laser mode[4] and the relation between ETU effect and second harmonic generation [5-7]. The non-uniform pumping power causes the non-uniform temperature distribution which results in the thermal dispersion effect, the lattice distortion, the variation of birefringence, and the thermal expansion in any direction resulted from thermal stress or displacement of the lattice site. These are the so-called thermal lensing effect. W. Koechner [8-9] had given both the theoretical and experimental results of the thermal lensing effect. In early years from 1960 to 1970, Foster[10], Osterink[11], Quelle[12]，Gordon[13] and Baldwin[14] had individually investigated the thermal lensing effect in the Yd:YAG laser, the limitation of the thermally induced diffraction loss resulting in thermal distortion in the laser rod, and negative thermal lensing effect. In 1970, Koechner reported the influence of thermally induced birefringence on the laser performance [9]。Therefore, the study of the thermal effect on the laser crystals has been developed very maturely. In 1999, Hardman et al. [15] studied the influence of thermal lensing effect and ETU effect on the laser performance when laser is lasing and nonlasing. J. J. Degnan presented some classical papers in 1989[16], 1995[17] and 1998[18] to work on the optimization theory of Q-switched solid state laser and discuss the thermal characteristics. In his research, the dynamical rate equation related to the atomic distributions on the excited states and ground state in thermal equilibrium according to the MaxwellBoltzmann statistical mechanics. Degnan derived a thermal equilibrium distribution function which he called the inversion reduction factor γ [16-18]. In the textbook of A. Yariv[19], γ equals to 2. Degnan also measured the fractional distribution function to be a constant at High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

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room temperature [18]. This fractional distribution function also appeared in the model of passively Q-switched laser, and end-pump quasi-three level Q-switched optimum laser model [20-21]. These models were developed by R. Beach independently [22]. However, Li et al. indicated in their recent paper that the equilibrium fractional distribution function derived by the Maxwell-Boltzmann statistic is not a constant but a function of both temperature and the lattice site for non-uniform temperature distribution [23]. Therefore, three equilibrium fractional distribution functions have to be interpreted from another point of view. Li et al. reported that their model could describe the laser system more accurate, since they considered the non-uniform thermal distribution in the end-pumped laser crystal. They analyzed the axial heating model with the cylindrically symmetric crystal and using the surface water cooling system resulting in the heat-convection diffusion toward its periphery. This boundary condition was used in their laser thermal model. It was shown that under this model, at certain cooling condition, the pulse output energy for once or twice circulated back and forth pumping geometry reduced about 21.7% and 14.5%, respectively. Their simulated results also suggested that the non-uniform temperature distribution reduced not only the pulse energy but also the output efficiency. Considering their theoretical approach, the authors adopted more accurate equations by using non-uniform thermal distribution along the axis of the crystal. Therefore, the excited and emission Blotzmann distribution factor between the excited and ground states has to be modified. Since the temperature is not a constant but varies along the axis of the crystal, the Blotzmann distribution factor depends on the axis of crystal as well. Therefore, further investigation is needed on how the quantum effects reach equilibrium with the temperature and thermal effect inside the laser crystal, and then influence the laser pulse output energy of the resonator under macroscopic condition. Liu et al. [24] had demonstrated an end-pumped frequency-doubled acoustic-optically Qswitched Nd:GdVO4 laser from which the green output at power level of several Watts obtained. The ETU influence and the dependence of the initial and residual inversion density on the Q-switching repetition frequency had not yet been considered in their theoretical model. The differences between their theoretical predictions and the experimental results became significantly remarkable at high power level. Huang et al. proposed a modified model where the ETU effect and the influence of Q-switching pulse repetition frequency were investigated [25]. They also reported that the thermal effect degrades the laser performance greatly especially in high output power.

2. THERMAL FOCAL LENGTH MEASUREMENT End pumping the solid-state laser is a standard method to produce the laser radiation with a single transverse mode. For the high power laser operation, the thermal lens of the laser crystal is an important parameter for optimization of the system. In 1995, B. Ozygus and J. Erhard [26] measured the beat frequency of adjacent transverse modes to determine the thermal lensing of end-pumped laser crystals. In 1997, B. Ozygus and Q. Zhang [27] presented a simple, effective method to determine the focal power of end-pumped lasers. At certain resonator parameters the transverse structures of the laser beam become a superposition of many transverse cavity modes of equal resonance frequencies. Because the resonator parameters depend on the thermally induced lens in the active medium, the strength

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of the lens can be determined by means of measuring the shift of the degeneration resonator length depending on the pumping power. Osterink et al. [28] presented an analysis model of the thermal effects in Nd YAG.. They considered the index of refraction variations in the rod due to index changes with temperature dn/dT, and photo-elastic effects from thermal strains. (But the variations are also undoubtedly effected by non-uniform pumping and cooling). The temperature distribution in the rod was computed by using an infinite heat generation and constant surface temperature. Temperature and hence refractive index were found to vary quadraticly with the radius. Then, the thermal stress distribution in the rod was determined and the photo-elastic index of refraction variations were calculated. The results were a quadratic radial variation in refractive index and an induced uniaxial birefringence whose extraordinary axis always lies in the radial direction and whose ordinary axis lies in the tangential direction. The focal length varies inversely with the internally generated heat (pump power), and the focal length is independent of the coolant temperature (flow rate). The average focal length in the rod is determined only by the term in the denominator which contains dn/dT, since the photo-elastic term will be averaged to approximate zero. The cylindrical geometry of laser rod is used generally. The heat is removed on the circumferential surface of the cylinder, thereby a radial thermal gradient is generated in the cylindrical geometry. The change in temperature within a laser rod causes a thermal distortion of the laser beam due to a temperature stress dependent variation of the refractive index. In addition, the stresses induce birefrigence is generated. An optical beam propagating along the rod axis suffers a quadratic spatial phase variation. This perturbation is equivalent to the effect of a spherical lens [29]. According to the early work by W. Koechner [8] under intense pumping in end-pump configuration, the end effects that account for the physical distortion of the flatness of the laser rod ends should be considered. The focal length of the rod caused by an end face curvature is obtained from the thick lens formula of geometric optics. Osterink et al.[28], Koechner et al.[8,30-31], and Innocenzi et al.[32] derived the theoretical analyses that the thermal focal length, f, which is inversely proportional to the input power. Comparing the results of these theoretical models with the experimental data measured by Ueda et al.[33] and Mukhopadhyay et al.[50], the calculated thermal focal length is not fit to the measured data. Ueda et al. considered the thermal load ξ being a constant (ξ=0.5 is adopted in their calculation) and a characteristic of the crystal. However, Huang et al. thought that the focal length is proportional to the thermal load, ξ, but it is not a constant. Instead, ξ is a function of pump power and it is proportional to the pumping power, namely, ξ(Pin). They used the experimental data measured by Ueda et al. (efficient and compact intracavity-frequency-doubled Nd:GdVO4/KTP laser end-pumped by a fiber-coupled laser diode) as an example to verify their model[34]. The results show that the variations of theξvalue is a linear function under lower input power, however, theξ value approaches to saturation when the pump power is getting to a large level as shown in Figure 1. Zhao et al.[35] combined some formulae to present the outline of the theoretical analysis for the whole thermal focal length of LD end-pumped solid state laser with stable resonator measuring process. They used slit-scanning method (SSM) to measure the beam quality for the multi-mode Gaussian beam field.

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Figure 1. Measured thermal focal length and the corresponding calculated thermal loading with the same plot.

Because this method can be operated easily and provide a more reliable beam information. They measured the beam width at different positions with different pump power and determined the corresponding TEM00 waist of the optical resonator based on ABCD matrix theory [36]. Thus the thermal focal length of the gain medium was determined. The accuracy of this experiment is nearly comparable with the previous researcher. D. C. Brown indicated that when laser are operating under the condition of high average power [37], and for the laser crystal, its thermal conductivity , thermal expansion coefficient, and the variations in index of refraction are all functions of temperature, then thermally induced variations in the index of refraction are generated. Therefore, the radial and tangential polarizations are no longer of the quadratic form. Hence a higher order spherical aberration needs to be considered, and the generated phase aberrations can be expressed as a Zernicks polynomial series. The author called this effect as nonlinear thermal distortion [38].

3. TRANSVERSE MODES The advantages of using passive Q-switch in laser resonator are the generation of high peak power laser, with tiny and compact sizes, and more sturdy and durable. However, there is a serious problem - the pulse delay on the application of the high peak power laser to distance measuring or remote sensing. The pulse delay is generated by the pulses time differences of the different laser transverse modes in the resonator. The results of distance measuring are affected by the quality of laser transverse mode output. With a laser of good transverse mode quality, the spot size still remains small after a long distance transmission. The errors of distance measuring results are caused by the time delays of the pulses arriving at

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the target. In general, the practical laser output seldom generating a single TEM00 mode, together with the imperfect optical system, the resonator without symmetry, the Brewster angle, the lens defects, the out-of-focus effect … etc., all these effects will generate high order transverse modes. For a fixed laser spot size, the lower the transverse modes order, the smaller the divergence angle is, and therefore is more suitable for the application to laser distance measuring. The key to the laser output power and the generation of transverse modes is the overlapping degree between the absorption distribution area of the gain medium and the intensity distribution area of the pump source in the laser resonator. If the area of the laser gain medium is small, the output of transverse mode will be a single mode. If the cross section is large, the output will be multi-modes. Laporta et al.[39] derived a formula indicating that the better the overlapping degree between the pump modes and the resonator modes, the lower pump threshold power is. Chen et al.[40] applied Laporta’s formula to calculate the threshold pumping power as a function of the off-focusing parameter as shown in Figure 2. The results indicate that when the off-focusing parameter approaching to zero, the TEM00 mode has the lowest threshold pumping power. In other words, the TEM00 mode is generated most easily at lower off-focusing. They also calculated the Hermite Gaussian mode and Laguerre Gaussian mode spatial distributions. The pure Hermite Gaussian mode distributions are shown in Figures 3 and 4.

Figure 2. The threshold pump power for fundament and different high order modes varies with different off focusing parameter.

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Figure 3. TEM 00 laser mode in the x-y plane.

Figure 4. TEM 5, 0 laser mode in the x-y plane.

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Figure 5. LG 1,5 laser mode in the polar coordinate.

Figure 6. LG 1, 5 with off focusing parameter laser mode in the polar coordinate.

The pure Laguerre Gaussian mode distribution is shown in Figure 5. The results show that the lowest-order mode on the off-focusing plane has the lowest threshold pump power. In High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

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other words, in this region, the low-order modes are generated more easily than the high-order modes. They adopted M. Arvidsson’s experimental structures [41] to generate the pure Hermite-Gaussian mode and Laguerre-Gaussian mode by using the optical fiber coupled offaxis technique. They also simulated the high-order modes generated from the different offfocusing and off-axis degrees of the Hermite-Gaussian mode and Laguerre-Gaissian mode as shown in Figure 6. They used these high-order modes investigating the effects of the time delay when the pulses arriving at the target at far field. Chen’s simulation results showed that the time delay is from the minimum, several hundreds ps, to the maximum, 20 ns, and this cause 6m length errors in the distance measuring.

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4. RECENT DEVELOPMENT OF HIGH POWER SIMULTANEOUSLY Q-SWITCHED AND MODE LOCKED LASERS Mode locking is a technique which phase-locks the longitudinal modes in the resonator. The larger the number of phase-locked longitudinal modes, the narrower the output width is. The electrical field intensity, which is caused by the effect of mode coupling with the longitudinal modes in the resonator, as a function of time is discussed by A. E. Siegman [36]. If the number of locked modes is increased, the ratio of intensities between the major pulses and the minor pulses will also be increased, but the widths of the pulse will be decreased. These pulses are periodic. Therefore, the wider the laser gain bandwidth, the larger the number of longitudinal modes are contained and the easier the short pulse laser is obtained. The pulse widths are influenced more by the phase relationship than by the amplitudes relationship of the longitudinal modes. It was indicated by Chen et al.[42-43] that if the initial transmission , T0, of the saturable absorber become smaller, then the pulse widths of the Q-switched lasers become narrower and the energy of these pulses become larger. The peak power of the mode-locked laser pulse is larger at small T0 values than at large T0 values. Because the smaller the T0 values, the shorter the build-up time of the Q-switched laser pulse is. Therefore, the remaining amount of longitudinal modes is increased after passing through the laser linear gain medium, and this is of benefit to generate the mode-locking mechanisms. Thus the number of the longitudinal modes involved in the mode-locking mechanisms is determined by the T0 value as shown in Figures 7-9. Another method to increase the number of longitudinal modes is by using a longer resonator. Chen et al. designed a z-configuration resonator to avoid the output instability caused by the thermal lens effect which is due to the longer resonator. As mentioned before, another factor which determines the quality of mode locking is the phases between the longitudinal modes. In general, the phases between the longitudinal modes are not all the same which causes the background noise signals distribution of the mode-locking laser output pulses. Therefore, the better the quality of the mode-locking, the larger the ratio of signal magnitudes between the mode locking pulses and background noises is. The results of numerical simulation are consistent with the experimental measurements in the number of mode-locking laser longitudinal modes inside one Q-switched laser pulse and relative intensities between mode locking laser pulses.

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Figure 7. Calculated simultaneously Q-switched and mode locked laser output under the initial transparency of saturable absorber T 0 =0.65.

Figure 8. The same conditions as in Figure 7 , except for T 0 =0.5.

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Figure 9. The same conditions as in Figure 7, except for T 0 =0.35.

Zhao et al.[44-49] reported a series of models and experimental data of the high power Qswitched solid state lasers from the year of 2004 to 2008. They considered a folded frequency doubling cavity system and proposed a new spatial-time dependence rate equation for LD end-pumped actively Q-switched intracavity frequency doubling laser. The equation includes the variations of photon densities along the resonant cavity axis because of the long resonant cavity and also includes the loss caused by the thermal lens effect of the laser crystal. The calculated and experimental generated green light pulse profile was in agreement quite well [44]. They replaced the active acoustic optic Q-switch by a GaAs saturable absorber and considered the single photon absorption (SPA), two-photon absorptions (TPA) and free carrier absorption (FCA) into rate equations. A model of LD end-pumped passively Qswitched intracavity frequency doubling Nd:GdVO4/KTP laser was developed. The numerical solutions of the theoretical calculation agreed with the experimental results [45]. Using the same procedure, by considering the Gaussian spatial distribution of the intracavity photon density and initial population inversion density as well as the influence of the AO Q-switch, Zhao et al. gave a coupled spatial-time dependent rate equations for a diode-pumped doubly Q-switched laser with both an AO modulator and a Cr4+-doped saturable absorber. These coupled rate equations were solved numerically. Some curves were generated to explain the optimal key parameters for the laser design [47]. In general, using a passive-passively double Q-switched laser with Cr4+:YAG and a GaAs saturable absorber can generate more symmetric and shorter pulses [48]. Some saturable absorbers, such as the Cr4+:YAG crystal, the GaAs wafer, the semiconductor saturable absorption mirrors … etc. are employed for simultaneously Qswitching and mode-locking. The GaAs wafer is more widely used in passively Q-switched and mode-locked 1-μm lasers than the other saturable absorbers. Combining the GaAs wafer with the Nd3+-doped laser crystal working at 1.06μm is especially used widely because of its

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low price, easy process, and having high threshold damage value. With the same model formalism mentioned above, Zhao et al. proposed a diode-pumped passively and simultaneously Q-switched and mode-locked frequency doubling green light laser by using the GaAs wafer as the saturable absorber [46]. Considering the free carrier absorption (FCA) process in GaAs wafer, a set of modified rate equations were used to describe the doubly Qswitched Cr4+:Nd3+:YAG laser with GaAs coupler in a short cavity. Their results showed that this laser can generate a more symmetric pulse shape, a shorter pulse width, the higher peak power [48]. In general, comparing with the passively Q-switched and mode-locked laser (QML), the actively QML generates more stable QML pulses. Zhao et al. established a relatively simple structure and a short resonant cavity length to generate a high efficiency and high average power actively Q-switched and mode-locked frequency doubling green light output [49]. The related researches of this subject can be referred to the recent works of Mukhopadhyay et al.[50].

5. COATING TECHNIQUE AFFECTING THE LASER OUTPUT BEAM QUALITY

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Coating on the nonlinear crystal surface can increase the structure compactness, decrease the device loss, and enhance the output power and stability. Figure 10 shows the reflection coefficient as a function of the wavelength for the three layers anti-reflecting (AR) coatings. It shows that the reflection coefficient is reduced effectively by the AR coating in the visible band.

Figure 10. Reflectivity of three layers anti-reflecting (AR) coating in the visible band.

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Figure 11. Multi-layers for high reflecting coating in the visible band.

The reflection coefficient as a function of the wavelength is shown in Figure 11 for multilayers high reflecting coatings. It shows that the reflection coefficient is increased effectively by the multi-layers high reflecting coating in the visible band. However, coating also increases the price and the coated film may be damaged under the high power output. In frequency doubling technique, the fundamental wave oscillates in optical resonant cavity and generates second harmonic wave through intracavity nonlinear crystal. If anti-reflecting coating technique on the output coupler mirror is not good enough, the generated second harmonic wave will return into the laser gain medium, and results in a non-linear polarized output wave. Therefore, coating techniques on the optical elements play an important role in determining the beam quality of the laser output. Chen et al.[51-52] has demonstrated a 532nm green CW laser of high pumping power, high repetition rate, and output with Watts, and a 671nm red laser with output level close to Watts. The system was designed to use an Nd:YVO4 laser crystal which is end-pumped with 808nm laser diode to radiate 1342nm infrared light source. Applying frequency-doubling technique, a 671nm red laser output is then obtained. Compared with the semiconductor laser diode, this all solid state laser with red light output has a much better beam quality than the laser diode. Experimental results show that when pump power is more than 17W, the red light output power starts saturation and the optical cavity is getting unstable because of the thermal lensing effect.

6. QPM TECHNIQUE AND QUASI PHASE MATCHING NONLINEAR CRYSTAL Quasi-phase matching (QPM) can offset the phase velocity dispersion problem during the frequency conversion processes. The phase mismatching between the fundamental waves and

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the harmonic waves caused by refraction index dispersion during the frequency conversion processes is offsetted by the periodic modulation of the crystal nonlinear polarization. The modulation period can be designed according to the refraction index dispersion of the crystal. In this way, not only the maximum effective nonlinear coefficients of the crystal can be chosen, but also QPM can reach the noncritical phase matching at some specific temperature that is not possible for the birefringent phase matching. Yariv et al. [53] investigated the theoretical analysis of QPM. The nonlinear polarization tensors used by PPLN, PPKTP, and PPLT are all d33. The light beam transmits along the x-axis, and thus the walk-off effect does not exist. Therefore, the crystals can be fabricated very long to raise the conversion efficiency. The general used nonlinear optical crystals, such as KTP, BBO, LBO … etc.[54], are cutting along some specific directions and works at some specific temperature to satisfy the phase matching condition. And only some specific non-diagonal element coefficients of these nonlinear crystals can be used because of the differences of the mutually interacted light wave polarization directions. During the frequency conversion processes, such as SHG or OPO, the phase mismatching will be accumulated proportional to the interactive length. After passing through the coherence length, the conversion efficiency and the output energy are decreasing because of the phase mismatching. When the crystal length is larger than the coherence length, the variations of the conversion efficiency from the fundamental waves to the harmonic waves are fluctuated from zero to the relative peak values according to the crystal mutually interactive length. If the nonlinear coefficient can be modulated every double coherent length, (In other words, the nonlinear coefficient changes the sign after each coherent length.) then the accumulated phase mismatching is canceled. Therefore, the conversion efficiency will keep increasing according to the interactive length. Thus the QPM technique is dividing the nonlinear crystal into several regions. Each region is equal to one coherent length, and the light axis rotates 180o in each region. Thus, the nonlinear polarization light rotates 180o after passing through one coherent length. The coherent length is usually equal to several μm long in the frequency conversion processes. Periodically poled KTP (PPKTP) is a nonlinear optical crystal of totally new type [55-56]. The PPKTP crystal is fabricated by several etching steps and electric polarized processes, and its nonlinear optical characteristics is changed permanently. PPKTP has the same transparent wave ranges as the bulk KTP but has no the phase mistmatching problem which the bulk KTP has troubles with. Compared with the widely used periodically poled LiNbO3 (PPLN)[52,5758], PPKTP has several advantages. Firstly, in the crystal fabrication stage, the required high electric field is about 21 KV/mm for the LiNbO3 crystal, but it takes only about 2 KV/mm for the PPKTP to accomplish the polization. Therefore, the maximum crystal thickness is limited to 0.5 mm for PPLN. But the crystal thickness for PPKTP is at least 1 mm. Secondly, the damage threshold of PPKTP is far more higher than PPLN. Hence the PPKTP crystal can operate at room temperature. Thirdly, PPKTP has better performances than PPLN at high power circumstances. The effective nonlinear coefficient, d33, of PPKTP is 17 pm/V which is lower than the value, 27 pm/V, of PPLN. However, the damage threshold of PPKTP is larger than 900 MW/cm2 for 5 ns pulse which is much higher than PPLN. At the same time, PPKTP has low susceptibility for photorefractive effect. Therefore, it can be operated at room temperature. Yang et al. [55-56] reported that using PPKTP nonlinear crystal in diode-pump

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Nd:GdVO4 laser operating both in CW and active Q-switched, the green laser output was obtained. Another group reported a model about PPLN OPO in case of CW wavelength with strong idle absorption condition [59].

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7. THEORY OF PARAMETRIC OSCILLATION (OPO) Consider a visible light impinging onto the cornea of the human eye, being focused by the eye lens, passing through the aqueous humor, and impinging onto the retina. At the retina the light is absorbed. The photon energy is converted by the retina into chemical signals which are transmitted to the brain by the optic nerve and stimulating optical sensations. The parallel rays of a laser (especially on the visible light range) can be focused through the eye lens to a point image of about 105 times larger in light intensity than the conventional sources of illumination. In fact, due to the high intensity of the laser radiation, the retina will be severely damaged only in a very short exposed time. When the amount of exposure to the laser radiation exceeds some critical value, the eyes will be damaged no matter what wavelength of the laser radiation is. The maximum permissible exposure of laser radiation to the eye depends on the wavelength [60]. Therefore, on the application of remote sensing, optical communications, and optical detections, using the safer laser wavelengths for human eyes is desired. Recently, the main technique for the application is to use OPO-generated pulse laser with 1.5-1.6 μm wavelengths. The pulsewidth is between the nano seconds to pico seconds. Chen et al. [51-52] have used hemispherical cavity to produce a pulse of 1.572 μm wavelength and 1.56 W output power at 58.8 KHz repetition rate frequency under 14.5 W input power. Louisell, Yariv and Siegman proposed the general quantum theory for the OPO single mode in 1961 [61-65]. They explained the sources of the quantum noise (or parametric fluorescence [66]) by using the quantum statistics, and derived its Hamiltonian form. Cassedy and Jain [67] continued Bjorkholm’s successful research on the injection tuning operation of OPO. They derived a more maturely theoretical analysis which employed the Gaussian-shape pump beam to achieve the successful injection and analyzed the time-dynamic behavior of OPO multi-modes in OPO’s. The theoretical calculation of injection usually stems from the equation of the single mode OPO quantum theory proposed by Louisell et al.. Ritsch et al. [68] and Schwob et al.[69] proposed the quantum theoretical analysis of the simultaneous multi-modes of OPO. The signal in an OPO is built up from the quantum noise. We use the OPO dynamic equations to illustrate a numerical example for the temporal evolution of DROPO pumped by the Gaussian beam profile as shown in Figure 12. It indicates that without seeding a quantity of the photon source (or the idle source) provided by the parametric fluorescence the signal wave can not grow up. In pulsed OPO, the macroscopic signal fluctuations are a function of time, pulse energy, frequency spectrum and transverse mode profile [70-71]. Oppo et al. proposed the theoretical analysis on the nanosecond SROPO spatial beam quality of output pulse combined with the idle wave absorption[72]. Smith concluded that the effects on the instability of CW pumped DROPO operation are due to pump frequency fluctuations causing the amplitude instability of the oscillator. In other words, the instability comes from the shift of the pump frequency[73-74].

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Figure 12. Temporal profile of OPO. The dash line indicates un-depletion pump field. The blue solid line represents depleted pump field, and the solid green line is the signal wave.

The spiking phenomenon caused by the behavior of oscillator mode hopping is observed from the experimental measuring. The oscillator output amplitude fluctuations are also caused by the variations of the resonant cavity length. Hence the oscillator tuning is resulted from the pump tuning. If we want to obtain a single mode output, an etalon element can be inserted inside the pulsed SROPO resonant cavity. An advantage of DROPO compared with SROPO is that DROPO has a lower threshold that comes from the resonance of both signal and idle waves in the optical cavity. Based on this reason, DROPO is widely used for CW operation, and the theoretical conversion efficiency can reach 100% when pumping power is four times than the threshold value. Such a low pump power makes it possible to use a semiconductor laser diode as a pumping source. Thus DROPO has a valuable potential on the commercial applications. However, the technique for generating DROPO operation is difficult because of the instability on oscillation frequency. At CW SROPO operation, there are several hundreds of modes within the bandwidth of the parametric gain envelope curve. These modes come from the variations of the cavity length and this results in the frequency tuning – a continuous variation of different cavity modes in the linear gain region. Through the mode competition mechanism, only the mode which has the nearest location to the center of gain curve is survived. DROPO is interesting contrast to SROPO. Many characteristics of DROPO attribute to its double resonance of the signal and idle waves. The essential condition for DROPO laser output is that the eigen modes of the signal and idle waves must overlap to each other within the parametric gain curve. This is because the dispersion relation existed in non-linear crystal and a little change in the OPO cavity length resulting in large variations between the signal wave modes and the idle wave modes. Only a few modes will locate within the gain curve. This phenomenon was demonstrated in Giordmaine-Miller’s diagram[75] and is called “mode clustering” or “mode-hopping”. And that is the main reason accounting for the unstable frequency output of DROPO operation.

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J Falk suggested reducing the feedback of signal waves via coating techniques on nonlinear crystal. And this method actually reduces the instability of DROPO, therefore it is called SROPO[76]. This method arranges the optical elements in the non-collinear geometry of optical cavity and the resulted signal wave path is not the same as the idle wave path. The IOPO configuration was also proposed by Falk[77]. The configuration includes any homogeneous broadened laser oscillator system. The effect of population inversions dynamics of the laser rode on the OPO performance is considered in Falk’s theory. And the population inversions dynamics is ignored by Harris[78]. Falk’s numerical solutions predicted the laser output behavior in a spiking regime, and showed that the repetition rate is increased as the pump power increases. Falk also used the Green function method to analyze the focusing effect[79]. This theory includes the diffraction effect and the Poynting vector of walk-off effect to evaluate the threshold pump power of OPO. Bjorkholm, Ashkin and Smith predicted that the non-resonant reflectivity of pump wave feedback into nonlinear crystal for DROPO and SROPO configurations can effectively improve OPO efficiency and reduce both threshold and build up time[74]. They also proposed the spatial non-uniform effect of OPO under Q-switched pulsed Gaussian beam profile. The results of the theoretical calculations and experimental measurements are in good agreement [80]. Injection tuning technique provides a precisely control of the output spectral frequency

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−1

in IR range). Bjorkholm and Danielmeyer proposed a theory and of OPO ( < 1cm experiments for explanation of the single mode and adjustable frequency output pulse for the pulsed injection tuned OPO. SROPO with a pump resonance is called PRSRO. This system has the advantages of single frequency output, mode-hop-free oscillation, and a lower threshold. These advantages had been theoretical and experimental confirmed by Schneider [81], Schneider and Mlnek. Siegman et al.[82] obtained a simple analytical solution for the ultra-short pulse generation in a degenerate mode-locked OPO pumped synchronously by a mode-locked laser. A very short pulse (~1 pico second) was predicted at the steady state which is very close to the threshold where pump depletion is negligible. Hence a mode-locked OPO can generate a tunable wavelength and ultra-short pulse which is impossible to obtain from the mode-locked laser. The author used FFT to solve the parametric equation of motion in the frequency domain for the coupled mode equation. There are two methods to produce narrow-band OPO. First, using an etalon element inserts into OPO cavity. This will result in high losses in optical cavity, and thus increases threshold, also reduces the output pulse energy. The disadvantage of this method is not only increasing complexity for OPO cavity but also making it more difficult on continue wave modulation. The second method is via injection seeding into OPO cavity. The advantage of this method is not only retaining its OPO efficiency but also keeping the simplicity of design for OPO cavity. It has been demonstrated by the experiment that pulsed seed source with nano Joules or continuous wave pump power with 1-2 micro Watts are enough to control wavelength and linewidth of an OPO. And this technique has been successfully applied to the spectroscopic measuring experiments. Injection seeding of OPO was first verified and given a quantitative explanation by Bjorkholm and Danielmeyer. A theoretical analysis was proposed by Cassedy and Jain [67]. This technique can control the spectral properties of an OPO in the transient behavior of operation and therefore it is applicable only to pulsed OPO. Contrast to unseeded OPO in which the output pulse energy of each mode shows a strong fluctuation

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Yung-Sheng Huang, Jung-Sheng Huang and Fang-Ling Chang

coming from pulse to pulse. These fluctuations attribute to build-on vacuum oscillation starting from statistical quantum noise [61]. Fix and Wallenstein gave a detailed analysis on numerical method and experiments about nano second BBO OPO at seeded sources and unseeded sources [70]. A special interest is the behavior of transition from seeded to unseeded operation. A numerical method for modeling a broad-bandwidth, nano second OPO in the plane wave approximation has been developed by A.V. Smith[83]. This method based on the split-step integration method and fast Fourier transform. His theory included diffraction effect and group velocity dispersion in OPO. A broadband width OPO is helpful to understand the unseeded spectral property of linewidth, the free running OPO efficiency, and the practical quantum noise method for injection seeding problem. An injection seeded OPO with walk off effect and with phase mismatch effect was reported by A.V. Smith and his co-workers [84]. In their model incorporated diffraction effect, birefringent walk off effect , pump depletion, absorption loss in nonlinear crystal, reflectivity of cavity mirror, and spatial temporal beam profile into numerical calculation (but the group velocity dispersion effect was not yet included), so the complexity of program consumed all the digital CPU time. This program is so-called SNLO. E. Rosencher et al. took into account the cylindrical symmetry of OPO, a numerical model based on quasi phase matching material (i.e., PPLN) pump by the Gaussian beam profile was studied [85]. In their model, since absence of the walk off effect, the isotropic of nonlinear crystal allows 1-D Hankel transform to replace a trditional 2-D FFT(fast Fourier transform) to evaluate the temporal behavior of cascading effect of SROPO output pulse. Peng et al. [86-87] gave a detail analysis on the high average power scaling behavior of OPOs. They considered thermally induced stress within the nonlinear crystal and the phase mismatch. Unlike in the solid state laser, the heat generating in OPO comes mainly from pump, signals, and the absorption of idle waves. The absorption coefficient depends on many complex factors such as the length of the nonlinear crystal, the wavelength of the resonant waves, the beam quality, the beam divergence, the length of the resonator, the reflection coefficient of the output coupling mirrors, and the whole conversion efficiency … etc.. The author established a multi-pass model to calculate the absorbed resonant-wave power and the heat generation in an OPO considering all the factors mentioned above.

8. PRACTICAL OPO PERFORMANCE AND RECENT DEVELOPMENT SROPO usually uses a Q-switched laser with the nano second pulse as a pumping source. In this situation, high peak power with ns pulse width not only can reach the OPO threshold, but also can generate a broad bandwidth (usually several nm) spectrum and a multi-mode output. Rosencher et al. reported a dual-cavity, single mode and stabilized output pulse DROPO, and derived a model of pulse ns OPO with time-dependent differential equations[88].Unlike the other models, this model directly adopted classical OPO coupled mode equations by J. A. Armstrong and N. Bloembergen[89]. Recently, Rosencher et al. proposed a theoretical model stating the possibility of OPO operation built on isotropic semiconductor microcavity[90]. Applying this model to the GaAs material, a OPO threshold condition which is lower than the optical damage can be obtained by modulating the

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19

reflectivity of output coupler. It had been demonstrated by the experiments with over 93% conversion efficiency of the signal and idle waves for pump depletion OPO devices. A theoretical simulation program called SNLO was developed by A. V. Smith at Sandia National Lab[83-84,91]. They also designed and set up two prototypes of the nano-second uvsources remote-sensing systems which were supposed to be used in space and operated by the satellite [92]. They employed the SNLO nonlinear optics software package to design the system parameters such as the pump beam’s spatial profile, the parameters for the resonant cavity, the length of the crystal … etc. to generate a 320nm, 10ns pulse. All these parameter values were obtained by numerical simulation. The systems measuring showed that the pulse energy was 200mJ and the whole light conversion efficiency from 1064nm to 320nm wavelengths was more than 20%. Peng et al. [86-87] developed a high efficiency, high repetition rate, all solid state tunable intracavity OPO pumped by using Nd:YLF laser. The average OPO output signal power is more than 1W in the tunable wavelength range from 1650nm to2100nm and in the repetition rate of 1kHz. The maximum OPO signal energy is 2.5mJ at 1900nm wavelength at which the pump to signal conversion efficiency is 42%. The maximum average output power is 4W at 3.5kHz. The widely used OPO configuration is the extracavity OPO configuration which makes use of Q-switched pulse as the pumping power and energy of OPO, the Q-switched pulse is required on the refraction limit condition and tight focus state strictly. However, the intracavity opo configuration was employed by Peng et al. Basically, the OPO locates inside the resonant cavity. The advantage of the intracavity configuration is generating a high peak power intensity and a small divergence angle in the laser resonant cavity, and hence it is more efficient to pump OPO. The numerical simulation of this system was based on the coupled mode equations proposed by Bass et al.. The quasi phase matching (QPM) has larger conversion coefficient of the nonlinear coefficient. Because QPM does not have the problem of Poynting vector walkoff in the process of the nonlinear frequency conversion. Hence, Zayhowski et al. in MIT first reported using PPLN nonlinear crystal in OPO. Huang et al. [58,93] in Taiwan investigated a distributed feedback (DFB) diode laser seeding PPLN OPO which generates a pulse of 200ps and 1549.6nm in wavelength (the IR wavelength range). This PPLN OPO with cavity length of 2.4cm is pumped by the passively Q-switched ND:YAG laser generating a 4.2ns, 10kW pulse. The output conversion efficiency is 22%. Vaidyanathan et al. in US Air Force Wright Lab, proposed a PPLN OPO operated at continuously tunable 1.3μm to 5μm wavelength range and 10ns pulse. They employed a long PPLN crystal with 25mm in length. And they reported that at the condition of high power pumping pulse OPO (more than 20 times of the threshold value), then the secondary parametric oscillation signal wave was generated. Their experiments allowed simultaneous multiple wavelength output. The theoretical calculations are agree with their experimental results. However, it is a technical challenge and formidable for the practical high average power OPO. R. L. Byer [94-98] reported his works on the laser interferometer gravitational wave detection (called LISA and LIGO) that were designed to detect the gravitational waves.

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Yung-Sheng Huang, Jung-Sheng Huang and Fang-Ling Chang

APPENDIX According to Laporta’s formula[39], we list below some interminable calculations about the threshold pump power of high order laser transverse modes under different off-focusing parameter, thereby obtain photon intensity in spatial distribution (see Figures 3-6). The original source see Chen’s paper[40]. * Pth (TEM n.0 ) =

γI sat ηPL

1

∫∫∫ S

n .0

( x, y, z )rP ( x, y, z )dv

2 2 ⎛ 2x ⎞ ⎡ ⎤ 2 ⎟ exp ⎢− 2( x +2 y ) ⎥ H n2 ⎜⎜ n ⎟ ω πω 2 n! L ω ⎣ ⎦ 1 ⎝ 1 ⎠ 2 ⎡ 2( x − Δ x ) ⎤ 2 2y2 α − 2 − αz ⎥ exp ⎢− rP ( x, y, z ) = 2 2 πω P (z ) 1 − exp[− αL ] ⎣ ω P (z ) ω P (z ) ⎦

S n.0 ( x, y, z ) =

2 1

⇒ S n.0 ( x, y , z )rP ( x, y , z ) =

⎡ − 2( x − Δx) 2 2 x 2 ⎤ 2α 2 − 2 − αz ⎥ exp ⎢ n 2 2 2 π 2 n! L(1 − exp[− αL ]) πω P ( z )ω1 ω1 ⎦ ⎣ ω P (z )

⎡ 1 1 ⎤ ⎛ 2 x ⎞⎟ × exp ⎢− 2 y 2 ( 2 + 2 )⎥ H n2 ⎜⎜ ω P (z ) ω1 ⎦ ⎝ ω1 ⎟⎠ ⎣ =

⎡ −2 ⎤ 2α 2 exp ⎢ 2 2 ( x 2 − 2 xΔx + Δx 2 )ω12 + x 2ω P2 (z ) ⎥ 2 2 π 2 n! L(1 − exp[− αL ]) πω P ( z )ω1 ⎣ ω1 ω P ( z ) ⎦

[

n

⎡ ⎛ ω 2 (z ) + ω 2 × exp[− αz ]exp ⎢− 2 y 2 ⎜⎜ P 2 2 1 ⎝ ω1 ω P (z ) ⎣⎢

⎞⎤ 2 ⎛ 2 x ⎞ ⎟ ⎟⎟⎥ H n ⎜ ⎜ ⎟ ⎠⎦⎥ ⎝ ω1 ⎠

⎛ ⎞ ⎡ ⎤ ⎜ exp ⎢ − 2 ⎟ ( x 2 − 2 xΔx + Δx 2 )ω12 + x 2ω P2 ( z ) ⎥ 2 2 ⎜ ⎟ ⎣ ω1 ω P ( z ) ⎦ ⎜ ⎟ 2 2 2 2 2 ⎡ ⎛ ω P (z ) + ω1 ⎞⎛ 2 ω1 ω1 Δx ⎞⎤ ⎜ ⎟ ⎜ = exp ⎢− 2⎜⎜ ω 2ω 2 ( z ) ⎟⎟⎜⎜ x − 2 xΔx ω 2 (z ) + ω 2 + ω 2 ( z ) + ω 2 ⎟⎟⎥ ⎟ ⎢⎣ ⎝ 1 P ⎠⎝ P P 1 1 ⎠⎥ ⎦ ⎜ ⎟ ⎜ ⎟ 2 2 2 2 4 ⎡ ⎛ ω 2 (z ) + ω 2 ⎞ ⎡⎛ ⎤ ⎤ ⎞ Δx ω ω ω ⎜ ⎟ 2 P 1 1 1 1 ⎢ ⎜ ⎟ ⎜ ⎟ ⎥⎥ Δx + 2 2 ⎜ = exp ⎢− 2⎜ ω 2ω 2 ( z ) ⎟ ⎢⎢⎜ x − ω 2 (z ) + ω 2 Δx ⎟ − 2 ⎟ 2 2 + ( ) ω z ω ⎥ ⎥ + ( ) z ω ω ⎠ ⎝ ⎠ ⎝ P P P 1 1 1 P 1 ⎣ ⎦⎦ ⎜ ⎟ ⎣ ⎜ ⎟ 2 ⎡ ⎛ ω 2 (z ) + ω 2 ⎞⎛ ⎡ ⎞ ⎤ ω12 ω12 1 ⎞⎤ ⎟ ⎜ 2⎛ P 1 ⎟ ⎟ ⎜ ⎟ ⎜ ⎜ ⎢ ⎥ Δ − − Δ = − exp 2 exp 2 x x x ⎢ ⎜ ⎜ ω 2 ( z ) ω 2 ( z ) + ω 2 ω 2 ( z ) ⎟⎥ ⎟ ⎟⎜ ⎜ 2 2 ω P2 ( z ) + ω12 ⎟⎠ ⎥ ⎢⎣ ⎝ ω1 ω P ( z ) ⎠⎝ ⎠⎦⎥ ⎟ ⎝ P P P 1 ⎣⎢ ⎜ ⎦ ⎜ ⎟ 2 2 2 2 ⎡ ⎛ ω 2 (z ) + ω 2 ⎞⎛ ⎡ ⎤ ⎞ ⎤ ω12 ⎜ ⎟ 2 ⎛ ω1 − ω1 − ω P ( z ) ⎞ P 1 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ = − − Δ Δ exp 2 exp 2 x x x ⎢ 2 2 ⎜ ⎟ ⎜ ω 2ω 2 ( z ) ⎟⎜ ⎟ ⎜ ω 2 ( z ) ω 2 ( z ) + ω 2 ⎟⎥ + ( ) ω z ω ⎢⎣ ⎝ 1 P ⎥ ⎠⎝ ⎠ ⎥⎦ ⎝ P P P 1 ⎠⎦ 1 ⎣⎢ ⎜ ⎟ ⎜ ⎟ 2 2 2 2 2 ⎡ ⎤ ⎞ ⎡ ⎤ ⎛ ω P (z ) + ω1 ⎞⎛ ω1 2Δx ⎜ ⎟ ⎟ ⎟ ⎜ ⎜ ⎢ ⎥ ⎜⎜ = exp − 2⎜ ω 2ω 2 ( z ) ⎟⎜ x − ω 2 ( z ) + ω 2 Δx ⎟ exp ⎢− ω 2 ( z ) + ω 2 ⎥ ⎟⎟ ⎢⎣ ⎝ 1 P ⎠ ⎥⎦ ⎣ ⎠⎝ P P 1 1 ⎦ ⎝ ⎠

[

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]

]

(

)

(

)

(

)

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Recent Progress of High Peak Power Solid State Lasers

21

∴ S n.0 ( x, y, z )rP ( x, y, z ) =

2α 2 π 2 n n! L(1 − exp[− αL ]) πω P2 (z )ω12 ⎡ ⎛ ω 2 (z ) + ω 2 × exp ⎢− 2⎜⎜ P 2 2 1 ⎢⎣ ⎝ ω1 ω P (z )

2 ⎞⎛ ⎞ ⎤ ω12 ⎟⎟⎜⎜ x − 2 Δx ⎟ ⎥ ω P (z ) + ω12 ⎟⎠ ⎥ ⎠⎝ ⎦

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⎡ ⎡ ⎛ ω 2 (z ) + ω 2 2Δx 2 ⎤ × exp ⎢− 2 exp[− αz ]exp ⎢− 2 y 2 ⎜⎜ P 2 2 1 2 ⎥ ⎣ ω P ( z ) + ω1 ⎦ ⎝ ω1 ω P ( z ) ⎣⎢ ⇒ γI 1 Pth (TEM n.0 ) = sat η P L ∫∫∫ S n.0 ( x, y, z )rP ( x, y, z )dv =

γI sat π 2 n n! L(1 − exp[− αL]) L 2α ηP L

=

πγI sat 2η P

⎞⎤ 2 ⎛ 2 x ⎞ ⎟ ⎟⎟⎥ H n ⎜ ⎜ ⎟ ⎠⎦⎥ ⎝ ω1 ⎠

1 ⎡ ⎤ 2Δx 2 ∫0 Qn exp⎢⎣− ω P2 (z ) + ω12 − αz ⎥⎦ dz 1 − exp[− αL ] 2 n n! L α ⎡ ⎤ 2Δx 2 ∫0 Qn exp⎢⎣− ω P2 (z ) + ω12 − αz ⎥⎦ dz

⎛ Qn ⎜ ⎜ ⎡ ⎛ 2x ⎞ ⎛ ω 2 (z ) + ω 2 ⎞⎤ 2 ⎟ exp ⎢− 2 y 2 ⎜⎜ P 2 2 1 ⎟⎟⎥ dy × H n2 ⎜⎜ ⎜ 2 2 ⎟ πω P (z )ω1 ⎝ ω1 ω P ( z ) ⎠⎦⎥ ⎝ ω1 ⎠ ⎜ ⎣⎢ ⎜ = ∫∫ 2 ⎡ ⎛ ω 2 ( z ) + ω 2 ⎞⎛ ⎞ ⎤ ω12 ⎜ P 1 ⎜ ⎟ ⎜ ⎟ ⎥ dx ⎢ − − Δ x x exp 2 ⎜ ⎜ 2 2 ⎟⎜ ω P2 (z ) + ω12 ⎟⎠ ⎥ ⎢⎣ ⎝ ω1 ω P ( z ) ⎠⎝ ⎜ ⎦ ⎜ 2 ω1 ⎜ 令 x′ = x − Δx ⎜ ω P2 ( z ) + ω12 ⎜ ⎡ ⎛ ω 2 (z ) + ω 2 ⎞ ⎤ ⎛ 2x ⎞ ⎜ πω P2 (z )ω12 4 ⎟ exp ⎢− 2⎜ P 2 2 1 ⎟( x ′)2 ⎥ dx ′ H n2 ⎜⎜ ⎜= ∫ 2 2 2 ⎜ ⎟ ⎟ 2 2 2 ω ( ) ( ) 2 ω P z + ω1 π ω P (z )ω1 ⎝ 1 ⎠ ⎣⎢ ⎝ ω1 ω P z ⎠ ⎦⎥ ⎜ ⎜ ⎡ ⎛ ω 2 (z ) + ω 2 ⎛ 2⎛ ⎞⎞ ω2 2 1 ⎜= ⎜⎜ x ′ + 2 1 2 Δx ⎟⎟ ⎟ exp ⎢− 2⎜⎜ P 2 2 1 H n2 ⎜ ∫ ⎟ ⎜ ⎜ π ω P2 ( z ) + ω12 ω1ω P ω P (z ) + ω1 ⎠⎠ ⎣⎢ ⎝ ω1 ω P ( z ) ⎝ ω1 ⎝ ⎜ ⎜ ⎝

(

)

(

)

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞ 2⎤ ⎟ ⎟⎟( x ′) ⎥ dx ′ ⎟ ⎠ ⎦⎥ ⎟ ⎟ ⎠

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22

Yung-Sheng Huang, Jung-Sheng Huang and Fang-Ling Chang

[

]

⎞ ⎛Q exp − x 2 H n2 ( x )dx = 2 n n! π ⎟ ⎜ ∫ ⎟ ⎜ ⎞ ⎛ ⎟ ⎜ ⎟ ⎜ ⎡ ⎛ ω P2 ( z ) + ω12 ⎞ 2 ⎤ ⎟ ⎜ ⎟ 2 ⎜ 2x′ 2 ⎟ ( x ′ ) ⎥ dx ′ ⎟ exp⎢− 2⎜⎜ 2 2 ⎜Q ∫ H k ⎜ ⎟ ω P2 ( z )ω12 ⎟ ( ) ω ω z ⎥⎦ ⎟ ⎢ 1 P ⎠ ⎣ ⎝ ⎜ ⎜⎜ 2 2 ⎟ ⎟ ω P ( z ) + ω1 ⎠ ⎟ ⎜ ⎝ ⎟ ⎜ 2 2 2 ⎜# g = ′ ′ dx ⎟ ∗ x → dg = ω P (z )ω12 ω P2 ( z )ω12 ⎟ ⎜ 2 2 2 2 ⎟ ⎜ ω P ( z ) + ω1 ω P ( z ) + ω1 ⎟ ⎜ ⎟ ⎜ 1 2 2 da ⎟ ⎜ ⇒ ∫ H k ( g ) exp − g 2 2 ⎟ ⎜ 2 ω P (z )ω1 ⎟ ⎜ ⎟ ⎜ ω P2 ( z ) + ω12 ⎟ ⎜ 1 ⎟ ⎜ 2 2 H k (g ) exp − g da ∫ ⎟ ⎜ = 2 2 2 ⎟ ⎜ ω P ( z )ω1 ⎟ ⎜ ω P2 ( z ) + ω12 ⎟ ⎜ ⎟ ⎜ 1 k ⎟ ⎜ = × 2 k! π ⎟ ⎜ 2 2 2 ⎟ ⎜ ω P ( z )ω1 ⎟⎟ ⎜⎜ ω P2 ( z ) + ω12 ⎠ ⎝

[

]

]

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[

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Recent Progress of High Peak Power Solid State Lasers

23

⇒ 1 2 k k! ⎛ 2ω P2 ( z ) ⎜ Qn = 2 ω P ( z ) + ω12 2 n ⎜⎝ ω P2 ( z ) + ω12

⎞ ⎟⎟ ⎠

k

⎡(n − k ) 2 ⎛ n ⎞ (k + 2 j )! ⎛ ω 2 ( z ) − ω 2 1 ⎜ P ⎟ × ⎢ ∑ ⎜⎜ ⎢ j =0 ⎝ k + 2 j ⎟⎠ k! j! ⎜⎝ ω P2 (z ) + ω12 ⎣ Q ω P (z ) = ω P = aω1 ⎛ ω (z ) − ω 1. ⎜⎜ ⎝ ω (z ) + ω 2 P 2 P

j

⎞ ⎛ 2ω Δx ⎟⎟ H n − k − 2 j ⎜⎜ 2 1 2 ⎠ ⎝ ω P (z ) + ω1

2

δ = Δx ω

j

( (

1

) )

j

j

⎞ ⎡ω a − 1 ⎤ ⎛ a2 −1⎞ ⎟⎟ = ⎢ ⎟⎟ ⎥ = ⎜⎜ 2 2 ⎝ a + 1⎠ ⎠ ⎣ω a + 1 ⎦

2 1 2 1

⎞⎤ ⎟⎟⎥ ⎠⎥⎦

2 1 2 1

⎛ 2ω Δx 2. H n − k − 2 j ⎜⎜ 2 1 2 ⎝ ω P ( z ) + ω1

2

⎞ ⎛ 2ω Δx ⎟⎟ = H n − k − 2 j ⎜⎜ 2 12 ⎝ ω1 a + 1 ⎠

(

⎛ 2ω 2 (z ) ⎞ ⎛ 2a 2ω12 ⎟ ⎜⎜ 2 2 = 3. ⎜⎜ 2 P 2 ⎟ ⎝ ω P (z ) + ω1 ⎠ ⎝ ω1 a + 1 2 2 2 4. ω P ( z ) + ω1 = ω1 a 2 + 1 k

(

(

)

)

k

)

⎞ ⎛ 2a 2 ⎞ ⎟⎟ = ⎜⎜ 2 ⎟⎟ ⎝ a +1⎠ ⎠

⎞ 2δ ⎞ ⎟⎟ = H n − k − 2 j ⎛⎜ 2 ⎟ ⎝ a + 1⎠ ⎠

k

⎡ ⎤ ⎡ − 2Δx 2 ⎤ ⎡ − 2δ 2 ⎤ 2 Δx 2 − = − = − αz ⎥ 5. exp ⎢− 2 exp exp z α α z ⎥ ⎢ 2 2 ⎥ ⎢ 2 2 ⎣a +1 ⎦ ⎣ ω P (z ) + ω1 ⎦ ⎣ ω1 a + 1 ⎦

(

)

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

NPth (TEM n.0 )

πγI satω12 2η P

= Pth (TEM n.0 )

1 − exp[− αL ] 2 n n! = α 1

1

1

2 ⎡ ⎛ 2δ ⎞⎤ ω1 + αz ⎟⎟⎥ dz Qn ∫ exp ⎢− ⎜⎜ 2 ⎠⎦ 0 ⎣ ⎝ a +1 2δ 2 1 − exp[− αL ] 2 n n! exp 1+ a2 1 = α ω12 Qn L [ ] − α z dz exp ∫ L

2

[

=

[

0

(1 − exp[− αL]) exp 2δ

2

1+ a2

α

[

= exp 2δ

2

2 n! 1 ] 1+ a Q ω

]

]

2 n n! 1 2 −1 (exp[− αL] − 1) Qn ω1 1

α

n

2

n

2 1

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Yung-Sheng Huang, Jung-Sheng Huang and Fang-Ling Chang

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

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[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

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Recent Progress of High Peak Power Solid State Lasers [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50]

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Chapter 2

LASER ANNEALING OF COMPOSITE MATERIALS WITH METAL NANOPARTICLES Andrey L. Stepanov∗ Laser Zentrum Hannover, 30419 Hannover, Germany Kazan Physical-Technical Institute, Russian Academy of Sciences, 420029 Kazan, Russian Federation

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ABSTRACT Recent results on the interaction of high power laser pulses with various dielectric materials containing metal nanoparticles are reviewed. Original results together with new publications are observed. In general, the excimer laser pulse modification of silver and copper nanoparticles synthesized by ion implantation in silicate glasses and sapphire are considered. One of features of composite samples prepared by the low energy ion implantation is the growth of metal particles with a wide size distribution in the thin depth from the irradiated substrate surface. Pulsed laser irradiation makes it possible to modify such composite layer, improving the uniformity in the size distribution of the nanoparticles. Changes induced by pulsed laser exposure suggest there are both reductions in average size of the metal nanoparticles, and some long-range dissolution of metal atoms in the matrix. Experimental data on laser modification are explained by photofragmentation and melting of the nanoparticles in the dielectric matrix. Combination of ion implantation and laser annealing is promising technology for fabrication of novel composite optical materials.

INTRODUCTION Composite materials, such as dielectrics with embedded metal nanoparticles (MNPs), are promising optoelectronic materials. An example of their application in optoelectronics is a prototype of integrated electronic circuit - chip that combines metallic wires as conductors of ∗

e-mail: [email protected] ; [email protected]

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electric signals with fibers as guides of optical signals. In practice, light guides are frequently made of synthetic sapphire (Al2O3) or silicon oxide (SiO2), which are deposited on or buried in semiconductor substrates. In this case, electrooptic emitters and that accomplish electric-tooptic signal conversion are fabricated inside the dielectric layer. This light signal from a microlaser is focused in a light guide and then transmitted through the optoelectronic chip to a high-speed photodetector, which converts the photon flux to the flux of electrons. It is expected that light guides used instead of metallic conductors will improve the data rate by at least two orders of magnitude. Moreover, there is good reason to believe that optical guide elements will reduce the energy consumption and heat dissipation, since metallic or semiconductor components of the circuits may be replaced by dielectric ones in this case. Prototype optoelectronic chips currently available are capable of handling data streams with a rate of 1 Gbit/s, with improvement until 10 Gbit/s in future. Key elements of dielectric waveguides used for light propagation are nonlinear optical switches, which must provide conversion of laser signal for pulse duration as short as pico- or femtoseconds.

Figure 1. A prototypes of optoelectronic chip with a dielectric waveguide combined with silicone substrate. Ion implantation can be applied to fabricate selective area doped by rear metal ions (marked by stars) to work as microlaser and to illuminate in waveguide, created by rear-gas ion radiation with MNPs to form an optical switcher.

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Laser Annealing of Composite Materials with Metal Nanoparticles

29

The nonlinear optical properties of MNP-containing dielectrics stem from the dependence of their refractive index and nonlinear absorption on incident light intensity [1, 2]. This effect is associated with MNPs, which exhibit an enhancement of local electromagnetic field in a composite and, as consequence, a high value of the third order nonlinear susceptibility when exposed to ultrashort laser pulses. Therefore, such MNP-containing dielectric materials may be used to advantage in integrated optoelectronic devices, for example, as shown in Figure 1. It is well known [1] that a local field enhancement in MNPs stimulates a strong linear optical absorption called as surface plasmon resonance (SPR). The electron transitions responsible for plasmon absorption in MNPs cause also a generation of an optical nonlinearity of a composite in the same spectral range. As a result, the manifestation of nonlinear optical properties is most efficient for wavelengths near the position of a SPR maximum. In practice, to reach the strong linear absorption of a composite in the SPR spectral region, attempts are made to increase the concentration (filling factor) of MNPs. Systems with a higher filling factor offer a higher nonlinear susceptibility, when all other parameters of composites being the same. Usually noble metals and copper are used to fabricate nonlinear optical materials with high values of third order susceptibility. There are variety ways to synthesis MNPs in dielectrics, such as magnetron sputtering, the convective method, ion exchange, sol–gel deposition, etc. One of the most promising enhanced fabrication methods is ion implantation [2-7] because it allows reaching a high metal filling factor in an irradiated matrix beyond the equilibrium limit of metal solubility and provides controllable synthesis of MNPs at various depths under the substrate surface. Nearly any metal–dielectric composition may be produced using ion implantation. This method allows for strict control of the doping ion beam position on the sample surface with implant dose as, for example, in the case of electron- and ion-beam lithography. Today, ion implantation is widely used in industrial semiconductor chip fabrication. Therefore, the combination of MNP-containing dielectrics with semiconductor substrates by same technological approach as ion implanattaion could be reached quite effective. Moreover, ion implantation can be applied for different steps in optoelectronic material fabrication such as creation of optical waveguides by implantation with rear gas ions (H+, He+ etc.) [6], a designing of electric-to-optic signal convectors and microlaser by irradiation of dialectics waveguides with rear metal ions (Er+, Eu+ etc.) [6, 8] and a synthesis of MNPs (Figure 1). The history of MNP synthesis in dielectrics by ion implantation dates back to 1973, when a team of researchers J. Davenas et al. at the Lyons University (France) pioneered this method to create particles of various metals (silver, sodium, calcium, etc.) in LiF and MgO ionic crystals [9, 10]. First work on ion-synthesis of noble nanoparticles was done in 1975 by Arnold in his study of Au-irradiated glasses [11]. Later developments have expanded from the metal implants to the use of many ions and the active formation of compounds, including metal alloys and totally different composition precipitate inclusions. In ion implantation practice MNPs were fabricated in various materials, such as polymers, glass, artificial crystals, and minerals [12]. Despite these steady advantages the use of ion implantation for nanoparticle synthesis there have not yet emerged clear mechanisms which allow precisely controlled particles sizes and depth distributions. Latter has a certain drawback which is the statistically nonuniform depth of penetration of implanted ions into a material [13, 14]. This leads to a wide size distribution of synthesized nanoparticles not only in the plane parallel to the irradiated surface but to a great extent also over the depth of the sample [15, 16]. Dispersion of nanoparticles with respect to sizes leads to a broadening of the SPR optical

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absorption band accompanied by a decrease it in the intensity [17]. This is also attributable to the dependence of the SPR spectral position on the particle size, i.e. the absorption spectrum in real sample is a superposition of several overlapping less intense bands that corresponding to particles of various sizes. The concern of the modern task is to increase the uniformity of the size distribution of MNPs synthesized by ion implantation using an approach of highpower pulse laser annealing with sequential furnace one. Experience gained from using the laser annealing techniques for various purposes allowed MNPs to be modified in various solid state dielectrics. In general, the interaction of the high-power laser pulses with dielectrics containing MNPs for modification of their optical properties has been the subject of intense investigation for the last few years. This interest was conditioned by both a development of microelectronics based on composites with nanoparticles and also on a need for a fundamental understanding of the influence of high-power light on properties of the nonuniform composite media. In particular, such researches are directed to the changes of the shape, the size, the size distribution, and the structure of the nanoparticles. The table 1 presents data, compiled from the available publications [18-61], on the types of MNPs in various matrixes and laser conditions for their changes. As seen from the table 1, depending on the laser wavelength, the power density or the pulse length, composite materials made by ion implantation can be successfully modified. For example, Nd:YAG laser irradiation in the visible and near-IR region converts implanted spherical titanium silicide particles into ellipsoidal ones in silica and soda-lime glass [61], or that there are changes of the internal crystallographic structure of implanted iron particles after ruby laser (690 nm) treatment [19]. The main feature most of all the experiments described in the table is that the laser light was applied directly into the spectral region of the transparency of the dielectric matrix, and consequently, the intense laser pulses were primarily absorbed by the metal particles [18, 19, 27, 28-31, 34-36, 42-50, 55, 57, 60]. Contrary to that, some years ago in 1993 by Wood et al. [23] a new approach for annealing was demonstrated, when float soda-lime glass with silver particles was irradiated by a laser light at wavelengths of glass absorption in the ultraviolet region. When applying high-power excimer ArF (193 nm) laser pulses, a decrease of the reflectance intensity of composite samples was observed. It was suggested that the implanted silver particles in glass can be dissolved and the glass matrix can be modified to be a silver rich metastable new glass phase. If this is correct then the new phase will be the potential to be destabilized to precipitate out the new silver particles in a controlled fashion by furnace. In reality, this new technique gives a variety of possibilities for controlled change of optical properties of implanted dielectrics, as suggested for the case of the combined laser annealing of float soda-lime glass implanted with metal ions [37]. However, a number of questions regarding mechanisms of such modifications and interactions with high-power excimer laser light with non-uniform composite materials are now just starting to be understood. The literature of the field is expanding rapidly and the references cited here are mostly limited to amorphous dielectrics, but with a rapid growth in the range of potential applications there are a much wider interests of interests in target materials and types of inclusions.

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Table 1. Laser annealing of MNPs in solid dielectric matrix (ASG – aluminosilicate glass, SLSG – soda-lime silicate glass). SPR – surface plasmon resonance, τ - laser pulse duration Types of metal nanoparticles K

Dielectric matrix MgO [100]

Synthesis method of nanoparticles Ion implantation and thermal annealing

Laser parameters YAG (1000 nm) laser τ=20 ns, energy per pulse 10 mJ

Laser annealing Irradiation close to the SPR spectral area of nanoparticles but of matrix transparence Irradiation in spectral area of matrix transparence Irradiation in the are of matrix transparence

K

MgO [100]

Ion implantation and thermal annealing

α-Fe

SiO2 glass

Ion implantation

Cu

Al2O3 crystal

Ion implantation

N2 (350 nm) laser τ=20 ns energy per pulse 10 mJ Rubin (690 nm) laser τ=40 ns, energy density 0.1 - 0.3 J/cm2 KrF (248 nm) excimer laser, τ=25 ns, 1 Hz energy density 0.3 J/cm2

Cu

SiO2 SLSG glasses

Ion implantation

KrF (355 nm) excimer laser, τ=25 ns, 1 Hz energy density 0,2-0.32 J/cm2, 1-250 pulses

Irradiation in the absorption bands of matrix

Reduction of the particles size and oxidation of Cu particles

Cu

SiO2

Ion implantation

Nd:YAG (248 nm) laser, τ=20 ns, 10 Hz energy density 0,2 J/cm2, 1-250 pulses

Irradiation in the absorption bands of matrix

Grow of the particless

Irradiation in the absorption bands of matrix

Main results of laser annealing Exfoliation of the surface layer with particles from sample

Authors

There are no recognized changes in the sample Ordering of the crystal structure of the particles Reduction of the particles size

Rankin et al. 1992 18]

Rankin et al. 1992 [18]

Bukharaev et al. 1991 [19] Stepanov et al. 2001 [20] Stepanov et al. 2002 [21] Stepanov 2005 [22] Stepanov and Khaibullin 2005 [23] Stepanov et al. 2000 [24] Stepanov et al. 2002 [25] Stepanov and Hole 2002 [16] Masuo et al. 2006 [27]

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Table 1. (Continued) Cu

SiO2

Ion implantation

Cu

Polymer

Ag

ASG glass

Simultaneous plasma polymerization and metal evaporation Ion-exchange

Ag

SiO2 glass

Ion implantation

Ag

SiO2 glass

Co-evaporation metal and glass

Ag

SiO2 SLSG glasses

Ion-exchange

Ag

SiO2 glass

Ion implantation

Nd:YAG (532 nm) laser, τ=20 ns, 10 Hz energy density 0,2 J/cm2, 1-250 pulses Nd:YAG (1064 nm) laser in the cw mode, the power from 8.6 to 1.1 W

Irradiation close to the SPR spectral area of nanoparticles but of matrix transparence Irradiation in spectral area of matrix transparence

Dissolution of the particles

Masuo et al. 2006 [27]

Changes of particle size and shape by coalescence

O-switched Nd:YAG (532 nm) laser, τ=10 ns, 10 Hz, energy density 0.18 and 0.6 J/cm2, 100 – 1000 pulses ArF (193 nm) excimer laser, 500 pulses, 10 Hz

Irradiation close to the SPR spectral area of nanoparticles but of matrix transparence

Photochromic effect – depletion of metallic particles by photoionization.

Werner et al. 1994 [28] Heilmann et al. 1995 [29] Heilmann 2003 [30] Akella et al. 1997 [31]

Irradiation in the absorption bands of matrix

Wood et al. 1993 [32] Townsend and Olivares 1997 [33]

Argon and krypton lasers (350 nm), power 0.24-1 W, 5 min O-switched Nd:YAG (532 and 1064 nm) laser, τ=10 ns, 10 Hz, energy density 0.3 and 5.0 J/cm2 Nd:YAG (532 nm) laser, , energy density 0.075 and 0.1 J/cm2

Irradiation close to the SPR spectral area of nanoparticles Irradiation close to the SPR spectral area of nanoparticles but of matrix transparence Irradiation close to the SPR spectral area of nanoparticles but of matrix transparence

Dissolution of particles into glass network or a separation particles into smaller ones Increasing of the particles size Increasing of the particles size and formation of new ones Dissolution of particles into glass network or a separation particles into smaller ones

Gonella et al. 1996 [35]

Ferrari et al. 1995 [34]

Townsend and Olivares 1997 [33]

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Ag

SiO2 SLSG glasses

Ion-exchange followed by ion irradiation

O-switched Nd:YAG (532 and 1064 nm) laser τ=10 ns, 10 Hz, energy density 0.3 and 5.0 J/cm2

Irradiation close to the SPR spectral area of nanoparticles but of matrix transparence

Ag

SiO2 SLSG glasses

Ion implantation

KrF (248 nm) excimer laser, τ=25 ns, 1 Hz energy density 0.2-0.25 J/cm2, 1-250 pulses

Irradiation in the absorption bands of matrix

Ag

SLSG glasses

Ion-exchange

Ti:sapphire (400, 500, 550 nm) laser, τ= 4 > 5, while the -ΔGCS values are 1 ≈ 2 > 3 > 4 > 5. From the -ΔGCS dependence of the kCS values, it seems that the CS processes in 1 - 5 are in the Marcus “normal” and “top region” [64]. As shown in Figure 15 (b), the CS state disappeared within 1 ps after the formation of the CS state. Because the CS states of 1 - 5 (1.33 - 1.71 eV relative to the ground state) are located at lower energies compared with the S1-state of SbTPP (2.08 eV), the charge recombination (CR) does not generate the S1-state but generates the ground state as indicated in Figure 16. Based on this energetic consideration, kinetic trace of 2 was fitted with 5.8 × 1012 and 2.2 × 1012 s-1 of rate constants for the appearance and disappearance of the CS state, respectively.

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Dae Won Cho, Mamoru Fujitsuka and Tetsuro Majima

S2 state S2

kr S1 state

knrS2

hν

kCS

[SbIVTPP(OCH3)] -N +C6H5CH3

kCR [SbVTPP(OCH3)]+-NC6H5CH3 Figure 16. Schematic energy diagram for the charge separation and recombination processes of 2.

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The agreement between the kCS and the disappearance rate of the CS state indicates that the CR rate (kCR) is larger than the kCS [65]. Consequently, this is the first example indicating that the S2-excited Sb-porphyrin acts as an electron acceptor.

5.2.2. Electron Transfer from Axial Ligand to Excited P-Porphyrins in the S2 State Fujitsuka et al. [21] also examined the CS and CR processes in P-tetraphenylporphyrin (PTPP) derivatives ([PTPP-(NHC6H4X)2]+Cl-, X = OCH3, CH3, H, Cl, CF3, and CN) (Scheme 8). Soret band and Q bands of 2 appeared at 423 and 549 and 590 nm, respectively. On the other hand, those of 1b were red-shifted to 429 and 568 nm, respectively. These shifts are attributable to the interaction with N atom of the axial ligand of PTPP. Upon excitation at 420 nm, which corresponds to the Soret band, fluorescence peak was observed at 434 nm indicating the fluorescence from the S2 state. The lifetime of the S2 fluorescence of 2 in CH3CN was estimated to be 1.5 ps. However, the S2 fuorescence lifetime of 1b was estimated to be 0.16 ps. The substantial decrease of the S2 fluorescence lifetime indicates that a new process other than internal conversion is included by introducing the axial ligands including N-phenyl groups, which have electron donating nature. For other compounds, i.e., 1a, 1c-1f, both S1 and S2 fluorescence bands were not observed. As the new deactivation pathway, electron transfer from the axial ligand to porphyrin ring is expected, because the axial ligand has an electron donating nature. + -

R

Cl N

N N

P

N

R

1a: R = NHC6H4OCH3 1b: R = NHC6H4CH3 1c: R = NHC6H5 1d: R = NHC6H4Cl 1e: R = NHC6H4CF3 1f: R = NHC6H4CN 2: R = OH

Scheme 8. Molecular structure of PTPP derivatives in this study. High-Power and Femtosecond Lasers: Properties, Materials and Applications : Properties, Materials and Applications, Nova Science Publishers,

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From the energy minimized structure of 1b, PTPP has a distorted structure, because of small radius of the included P atom. LUMO is localized on the TPP ring. HOMO is on the Nphenyl group. HOMO-1 is on another N-phenyl group of 1b, which is energetically degenerated with HOMO. HOMO-2 of 1b corresponds to HOMO of TPP ring. Thus, upon excitation of TPP ring, electron transfer from HOMO of 1b, i.e. N-phenyl group, is expected. That is, PTPP and N-phenyl ring are expected to act as an electron acceptor and a donor, respectively, in the electron transfer. Photoexcitation process upon excitation to the S2 state of PTPP was examined by measuring the transient absorption spectra during the laser flash photolysis using femtosecond laser at 400 nm. Figure 17 shows transient absorption spectra of 1b in CH3CN during the laser flash photolysis. Upon excitation, transient absorption peak appeared at 700 nm with (0.15 ps)-1 of rate constant, with the ground state bleaching at 565 nm. The absorption band around 700 nm indicates the generation of radical anion of PTPP. Furthermore, generation rate agreed well with the S2 fluorescence decay rate indicated above. These results indicate that CS occurred from the S2 state (eq. 1),

Δ O.D.

(A)

0.008 0.4 ps -0.1 ps

0.004

0.000 600 650 700 Wavelength / nm

750

(B) 0.008

Δ O.D.700

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550

0.004 0.000 -0.5

0.0

0.5

1.0 -12

Time / 10

1.5

2.0

s

Figure 17. (A) Transient absorption spectra at -0.1, 0, 0.1, 0.2, 0.3, and 0.4 ps of 1b in acetonitrile during the laser flash photolysis using 400 nm laser pulse (fwhm 100 fs). (B) Kinetic trace of ΔO.D. at 700 nm during the laser flash photolysis. Reprint with permission form [21], Fujitsuka, M. et al. J. Phys. Chem. B 2007, 111, 10574. © 2007, American Chemical Society.

[PTPP(NHC6H5CH3)]+(S2)-NHC6H5CH3 → [PTPP(NHC6H5CH3)]•- (NHC6H5CH3)•+. (1)

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The observed electron transfer rates, i.e., kCS and kCR, are discussed on the basis of the Marcus theory [64]. In Figure 18, the observed electron transfer rates are plotted against the free energy changes. Usually, electron transfer rate depends on free energy change according to eqs. (2) - (4),

k ET

π = V 2 h λS k BT

2

⎛ (λ S + ΔG + mh ω ) 2 ⎞ ⎟ ∑m (e (S / m!)) exp⎜⎜ − ⎟ 4 λ k T S B ⎝ ⎠ −S

m

⎛ 1 1 1 ⎞⎛ 1 1 ⎞ + − ⎟⎟⎜⎜ 2 − ⎟⎟ εS ⎠ ⎝ 2rD 2rA r ⎠⎝ n

(3)

λ S = e 2 ⎜⎜

S=

(2)

λV . hω

(4)

13

-1

10 kET / s

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In eq (2), λS is the solvent reorganization energy given by eq. (3), V is the electronic coupling, S is the electron-vibration coupling constant given by eq. (4), is the averaged angular frequency. In eq (3), rD, rA, r, and n are donor radius, acceptor radius, center-to-center distance, and refractive index, respectively. In eq. (4), λV is the internal reorganization energy. From the theoretical calculation, the rD, rA, and r values were estimated to be 2.1, 4.2, and 3.0 Å, respectively. Using these values, λS value was estimated to be 0.18 eV. In Figure 18, eq. (2) was calculated as a red line by assuming λV, V, and η are to be 0.57, 0.035, and 0.15 eV, respectively. The calculated curve well reproduced the kCS1, kCR1, and kCR2 values.

12

10

11

10

10

10

0.0

0.5

1.0

1.5

2.0

-ΔG / eV Figure 18. Free energy change (-ΔG) dependence of electron transfer rate (kET, i.e., kCS (filled mark) and kCR (opened mark)) of PTPP derivatives upon excitation to S1 (circle) and S2 (triangle) states. Solid lines were calculated using eq. (4) in text by assuming λs = 0.18 eV, V = 0.035 eV, h = 0.15 eV, and λv = 0.57 eV for S1 excitation (red line) and 1.65 eV for S2 excitation (blue line). Reprint with permission form [21], Fujitsuka, M. et al. J. Phys. Chem. B 2007, 111, 10574. © 2007, American Chemical Society.

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That is, CS from the S1 state is in the top region, while CR in the inverted region. On the other hand, although the kCS2 values are located at close position to the red line, kCS2 values become larger as -ΔGCS values, indicating that the kCS2 values are in the normal region of another parabola. This fact suggests that the total reorganization energy for CS from the S2 state is larger than that from the S1 state, probably because of difference in molecular structure in the S1 and S2 states, which causes difference in the λV value. The large difference in λS value cannot be expected. In Figure 18, the blue curve was obtained by just changing the λV value to be 1.65 eV, while other parameters are the same as the red line. The good fit supports above consideration. As indicated in above, the reports on the electron transfer from the S2 state of porphyrins are limited. Mataga et al. investigated free energy change dependence of electron transfer rate from the S2-excited Zn porphyrin derivatives, in which Zn porphyrin acts as an electron donor [57-59]. They showed that the observed electron transfer rates were well reproduced by the Marcus theory assuming 0.3 eV of λV, which is much smaller than the value employed in this study. Although they have not examined CS from the S1 state of the same compounds, the λV values for electron transfer from the various S1-excited Zn porphyrin derivatives have been reported to be 0.3 - 0.6 eV [66], which is similar to the λV for electron transfer from the S2 state reported by Mataga et al.. Thus, the Zn porphyrin derivatives, which have a planar structure, do not have large structural difference between the S1 and S2 states. On the other hand, present PTPP derivatives have a distorted structure in the ground state [21]. The excited PTPP possibly take a different structure depending on the excited state from the ground state, in order to reduce instability in the excited state. Such structural change causes the difference in the λV values.

5.2.3. Electron Transfer from Porphyrins to Axial Ligand in the S2 State Fujitsuka et al. [67] have been investigated that the electron transfer reactions from the S1 and S2 states of some Zn porphyrins (ZnTPP, ZnOEP), Zn phthalocyanine (ZnPc) and Zn naphthalocyanine (ZnNc) to the axial ligand. An axial ligand was synthesized as an acceptor, which an asymmetric pyromellitic diimide (PI) compound has an alkyl chain and a pyridine ring on N and N’ atoms, respectively. The pyridine ring of PI can coordinate to Zn of tetrapyrrole macrocycles as shown in scheme 9. When the ZnTPP-PI was excited to the S2 state by 400 nm laser pulse, the peak of PI•appeared obviously faster than the S1-excitation (Figure 19). This implies that the ET occurred from the S2 state in this complex. The apparent rate of ET from the S2 state was estimated to be (4.8 ps)-1. The CS rate constant from the S2 state was 5.5 times faster than ET from the S1 state. Because the S2-fluorescence lifetime of ZnTPP is reported to be 2.4-3 ps [68], the CS is not an efficient process due to the other deactivation processes such as internal conversion. Thus the quantum yield of ET from the S2 state is as low as 0.63. It should be stressed that CS in ZnPc-PI was also confirmed when ZnPc was excited to the S2 state. On the other hand, ZnOEP and ZnNc did not show CS even when they were excited to the S2 state, probably because of short S2 lifetime of ZnOEP and smaller driving force of ZnNc-PI in S2 state. In the case of ZnOEP and ZnNc, CS was observed only from their S1 state.

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Scheme 9. Structure of ZnTPP-PI complex.

Figure 19. Time profiles of ZnTPP-PI complex in short time scale. Excitation wavelength: 400 nm (circle) and 570 nm (square). The black and red lines were fitted curves. Reprint with permission form [67], Harada, K. et al. J. Phys. Chem. A 2007, 111, 11430. © 2007, American Chemical Society.

In Figure 20, the ET rate from the S2 state was also plotted against driving force. It is clear that the ET rate from the S2 state was not on the Marcus parabola for ET from the S1 state. This is a quite unique feature for ET from the S2 state. As a reason for this behavior, the following two possibilities can be pointed out. First, ET from the S2 state was not on the Marcus parabola for ET from the S1 state.

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Figure 20. (A) The rate constants, kET, were plotted against -ΔG under the assumption that ET from the S2 state was on another Marcus parabola from ET from the S1 state. The red curve was drawn with larger reorganization energy λ= 2.0 eV. (B) The energy level diagram of the complex including the hot CS state. (C) The rate constants, kET, were plotted against -ΔG under the assumption that ET from the S2 state has smaller -ΔG. Furthermore, ET from the S2 state of ZnTPP and ZnPc to PI was confirmed. ET from the S2 state of ZnPc was observed for the first time. The ET rate from the S2 state was faster than that from the S1 state. In the case of ZnOEP-PI and ZnNc-PI complexes, ET from the S2 state was not observed. Reprint with permission form [67], Harada, K. et al. J. Phys. Chem. A 2007, 111, 11430. © 2007, American Chemical Society.

To explain the ET rate from the S2 state, Marcus parabola with larger reorganization energy should be considered. Because solvent reorganization energy may not depend on excited state, internal reorganization energy varies to much extent. That is, when the complexes were excited to the S2 state, their structures might change larger than S1excitation. By assuming λ =2.0 eV, Marcus parabola can be drawn as the red line in Figure 20A. Second, ET from the S2 state to the hot CS state will be another possible ET process (Figure 20B). In this case, -ΔGCS value should be smaller as indicated in Figure 20C [69]. Thus, -ΔG(S2) may be overestimated. But the CR rates do not have a difference between S1excitation and S2-excitation. Thus, relaxation rate from the hot CS state to the CS state should be quite fast. Th rate will be