Semiconductor Laser Fundamentals-Toshiaki Suhara

Copyright © 2004 Marcel Dekker, Inc The Japanese edition of this book was published in the Kyoritsu Advanced Optoelectronics Series (Kyoritsu Shuppan, Tokyo, 1998) Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book The material contained herein is not intended to provide specific advice or recommendations for any specific situation Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 0-8247-5373-9 This book is printed on acid-free paper Headquarters Marcel Dekker, Inc., 270 Madison Avenue, New York, NY 10016, U.S.A tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Inc., Cimarron Road, Monticello, New York 12701, U.S.A tel: 800-228-1160; fax: 845-796-1772 Eastern Hemisphere Distribution Marcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities For more information, write to Special Sales/Professional Marketing at the headquarters address above Copyright ß 2004 by Marcel Dekker, Inc All Rights Reserved Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit): 10 PRINTED IN THE UNITED STATES OF AMERICA Copyright © 2004 Marcel Dekker, Inc Copyright © 2004 Marcel Dekker, Inc Copyright © 2004 Marcel Dekker, Inc Copyright © 2004 Marcel Dekker, Inc Copyright © 2004 Marcel Dekker, Inc Preface Semiconductor lasers are among the most important optoelectronics devices Remarkable development has been accomplished in the three decades since the first achievement in room-temperature continuous oscillation, which opened the possibility of practical applications of semiconductor lasers Today, various types of semiconductor lasers are mass-produced and widely used as coherent light sources for a variety of applications, including optical fiber communication systems and optical disk memory systems Advanced functions and high performance have been realized through distributed feedback lasers and quantum well lasers following the development of Fabry–Perot-type lasers Accordingly, new applications previously unfeasible (or difficult with other conventional lasers) have been found, and the replacement of gas and solid-state lasers by compact and economical semiconductor lasers is in progress Thus, semiconductor lasers are indispensable devices of increasing importance Extensive research and development is being conducted toward specific applications Remarkable progress is also being made in optoelectronic integrated circuits and integrated photonic devices using semiconductor lasers as the main component Implementation and advanced applications of semiconductor lasers require a deep understanding, and high technological expertise, in subareas including materials, crystal growth, device design, microfabrication, and device characterization (all of which comprise the field called semiconductor laser engineering) There already exist a number of authoritative books on semiconductor lasers, as given in the references in Chapter In Chapter 2, the fundamental quantum theory on the interaction of electrons and photons is outlined and summarized in a form that is convenient for the understanding and analysis of semiconductor lasers Chapter deals with stimulated emission in semiconductors as one of the most important principles for implementation of semiconductor lasers, and explains the basic theory and characteristics of light amplification Chapter covers Copyright © 2004 Marcel Dekker, Inc theoretical discussions on electron–photon interactions and stimulated emission, and considers characteristics of optical waveguide resonators for laser oscillator implementation In Chapter 6, rate equation analysis of semiconductor lasers is presented to clarify and explain the static and dynamic characteristics of semiconductor lasers using Fabry–Perot-type semiconductor lasers as a prototype device Chapter is devoted to distributed feedback lasers and distributed Bragg reflector lasers, which are dynamic single-mode lasers and allow advanced performance In Chapter 8, semiconductor laser amplifiers are discussed The Appendixes provide important theoretical topics and experimental techniques The chapters were carefully checked for mutual consistency and clarity of context Efforts were made to give a comprehensive explanation of mathematical formulae including the procedure of the deduction and physical meanings, rather than simple descriptions of the results, in order to ensure full understanding without skipping basic principles or referring to other materials Almost all the formulae are in such a form that they can actually be used by the readers for analysis and design It will give me great satisfaction if this book is helpful to researchers, engineers, and students interested in semiconductor lasers Finally, I would like to thank the staffs of Kyoritsu Pub., Ltd., and Marcel Dekker, Inc., for their cooperation Toshiaki Suhara Copyright © 2004 Marcel Dekker, Inc Contents Introduction 1.1 Principles and Device Structures of Semiconductor Lasers 1.2 Materials for Semiconductor Lasers 1.3 Features of Semiconductor Injection Lasers 1.4 Applications of Semiconductor Lasers References Interaction of Electrons and Photons 2.1 Quantization of Optical Waves and Photons 2.2 Interactions of Electrons and Photons 2.3 Absorption and Emission of Photons 2.4 Population Inversion and Light Amplification References Stimulated Emission and Optical Gain in Semiconductors 3.1 Band Structure of Semiconductors and Stimulated Emission 3.2 Direct-Transition Model 3.3 Gaussian Halperin–Lax Band-Tail Model with the Stern Energy-Dependent Matrix Element 3.4 Gain Spectrum and Gain Factor 3.5 Spontaneous Emission and Injection Current Density 3.6 Density Matrix Analysis References Stimulated Emission in Quantum Well Structures 4.1 Electron State in Quantum Well Structures 4.2 Direct-Transition Model 4.3 Gain Spectrum and Gain Factor Copyright © 2004 Marcel Dekker, Inc 4.4 4.5 Spontaneous Emission and Injection Current Density Strained Quantum Wells References Semiconductor Heterostructure Optical Waveguides 5.1 Outline of Optical Waveguides for Semiconductor Lasers 5.2 Fundamental Equations for the Optical Wave 5.3 Optical Wave in a Waveguide 5.4 Planar Waveguide 5.5 Perturbation Theory and the Optical Confinement Factor 5.6 Channel Waveguides 5.7 Reflection at Waveguide Facets 5.8 Waveguide Fabry–Perot Resonator 5.9 Far-Field Patterns References Characteristics of Semiconductor Lasers 6.1 Semiconductor Laser Structure and Outline of Oscillation 6.2 Rate Equations 6.3 Steady-State Oscillation Characteristics 6.4 Modulation Characteristics 6.5 Noise Characteristics 6.6 Single-Mode Spectrum and Spectrum Linewidth 6.7 Ultrashort Optical Pulse Generation References Distributed Feedback Lasers 7.1 Dynamic Single-Mode Lasers 7.2 Coupled-Mode Equations 7.3 Distributed Feedback Lasers 7.4 Distributed Bragg Reflector Lasers References Semiconductor Laser Amplifiers 8.1 Gain Spectrum and Gain Saturation 8.2 Resonant Laser Amplifiers 8.3 Traveling-Wave Laser Amplifiers 8.4 Tapered Laser Amplifiers 8.5 Master Oscillator Power Amplifier References Copyright © 2004 Marcel Dekker, Inc ~ i ~ð! À i Þ ¼ ~ð!Þ þ ðÀi Þ ¼ ~ À @! vg ð5:141Þ where g is the group velocity of the guided mode The validity of the above simple treatment can be shown by using the time-dependent wave equations Then the optical wave in the waveguide can be written as Eðx, y, z; tÞ ¼ Eðx, yÞEðzÞ expðÀi!tÞ expðÀ tÞ ð5:142Þ and E(z) can be expressed by using the complex propagation constant ~ð! À i Þ as EðzÞ ¼ Aþ exp½þi ~ð! À i ÞzŠ þ AÀ exp½Ài ~ð! À i ÞzŠ Copyright © 2004 Marcel Dekker, Inc ð5:143Þ 156 Chapter Using the power reflectivities Rb and Rf of the left- and right-hand facet mirrors, respectively, the boundary conditions can be written as À Aþ ¼ R1=2 b A , AÀ ¼ R1=2 Aþ exp½þ2i ~ð! À i ÞLŠ f ð5:144Þ For the above equations to have nontrivial solutions except for Aþ ¼ AÀ ¼ 0, ðRf Rb Þ1=2 exp½2i ~ð! À i ÞLŠ ¼ ð145Þ is required, and the above relation is decomposed into the real and imaginary parts as follows: Ref ~ð! À i ÞgL ¼ 2mp ðm is an integerÞ 1=2 ~ ðRf Rb Þ exp½À2Imf ð! À i ÞgLŠ ¼ ð5:146aÞ ð5:146bÞ Equation (5.145) indicates that in the resonator there can exist only such waves that are superimposed in phase after a round trip Each of the optical waves satisfying this condition is called a longitudinal mode The integer m is the order of the longitudinal mode From Eq (5.146), we see that the longitudinal mode function E(z) can be written as   ! mir imp þ EðzÞ ¼ A exp þ z L   ! mir imp À þ A exp À z þ L þ mir ¼   1 ln 2L Rf Rb ð5:147Þ To distinguish from the longitudinal mode presented here, the guided mode of the waveguide described by E(x, y) is referred to as the lateral mode From Eq (5.146a) we see that, for cases where ~ is given by Eq (5.131), the angular frequencies !m for the mth longitudinal mode are aligned with a separation Á! ¼ vg 2p c ¼ 2p ¼ 2p 2L @ =@! 2LNg 2L ð5:148Þ which is the same as the separation of the transmission peak frequencies The separation is called the longitudinal mode separation If the wavelength dependence of the effective index is neglected, the longitudinal modes are aligned with a constant separation Copyright © 2004 Marcel Dekker, Inc Semiconductor Heterostructure Optical Waveguides 157 When the lateral mode E(x, y) is normalized, the power flows Pþ and P , for the forward and backward waves, respectively, at t ¼ are given by the absolute squares of the first and second terms of the right-hand side of Eq (5.147), i.e., À Pþ ðzÞ ¼ jAþ j2 expðþmir zÞ À À P ðzÞ ¼ jA j expðÀmir zÞ ð5:149aÞ ð5:149bÞ The energies per unit length of the forward and backward waves stored in the waveguide are given by Pþ/vg and PÀ/vg, respectively, with the group velocity vg; the total optical energy stored in the resonator is given by the sum of Pþ/vg and PÀ/vg integrated over the waveguide section < z < L By normalizing the field so that the total stored energy equals to J, Aþ and AÀ are determined as jAþ j2 ¼ jAÀ j2 Rb ¼ vg mir Rf1=2 ½1 À ðRf Rb Þ1=2 ŠðR1=2 þ R1=2 f b Þ ð5:150Þ The normalized resonance mode is given by E(x, y)E(z) with the lateral mode E(x, y) and the longitudinal mode E(z) given by Eq (4.147) with the above Aþ and AÀ substituted Equation (5.142) indicates that the power in the resonator decays with time in a form of exp(À2 t) From Eqs (5.141) and (5.146b), the decay factor for cases where ... Distributed Feedback Lasers 7.1 Dynamic Single-Mode Lasers 7.2 Coupled-Mode Equations 7.3 Distributed Feedback Lasers 7.4 Distributed Bragg Reflector Lasers References Semiconductor Laser Amplifiers... of lasers by Schawlow and Townes [2] in 1958, followed by the experimental verifications of laser oscillation in a ruby laser and a He–Ne laser in 1960, the pioneering work on semiconductor lasers... xAs strained QW lasers as a pump source to excite fiber laser amplifiers for communication systems, broad-area lasers and arrayed lasers as a pump source to excite solid-state lasers such as yttrium