Fundamentals of semiconductor lasers ebook TLFeBOOK

Springer Series in optical sciences Founded by H.K.V Lotsch Editor-in-Chief: W T Rhodes, Atlanta Editorial Board: T Asakura, Sapporo K.-H Brenner, Mannheim T W Hänsch, Garching T Kamiya, Tokyo F Krausz, Vienna and Garching B Monemar, Linköping H Venghaus, Berlin H Weber, Berlin H Weinfurter, Munich Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo 93 Springer Series in optical sciences The Springer Series in Optical Sciences, under the leadership of Editor-in-Chief William T Rhodes, Georgia Institute of Technology, USA, and Georgia Tech Lorraine, France, provides an expanding selection of research monographs in all major areas of optics: lasers and quantum optics, ultrafast phenomena, optical spectroscopy techniques, optoelectronics, quantum information, information optics, applied laser technology, industrial applications, and other topics of contemporary interest With this broad coverage of topics, the series is of use to all research scientists and engineers who need up-to-date reference books The editors encourage prospective authors to correspond with them in advance of submitting a manuscript Submission of manuscripts should be made to the Editor-in-Chief or one of the Editors See also http://www.springer.de/phys/books/optical_science/ Editor-in-Chief William T Rhodes Ferenc Krausz Georgia Institute of Technology School of Electrical and Computer Engineering Atlanta, GA 30332-0250, USA E-mail: bill.rhodes@ece.gatech.edu Vienna University of Technology Photonics Institute Gusshausstrasse 27/387 1040 Wien, Austria E-mail: ferenc.krausz@tuwien.ac.at and Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Strasse 85748 Garching, Germany Editorial Board Toshimitsu Asakura Hokkai-Gakuen University Faculty of Engineering 1-1, Minami-26, Nishi 11, Chuo-ku Sapporo, Hokkaido 064-0926, Japan E-mail: asakura@eli.hokkai-s-u.ac.jp Karl-Heinz Brenner Chair of Optoelectronics University of Mannheim Institute of Computer Engineering B6, 26 68131 Mannheim, Germany E-mail: brenner@uni-mannheim.de Theodor W Hänsch Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Strasse 85748 Garching, Germany E-mail: t.w.haensch@physik.uni-muenchen.de Bo Monemar Department of Physics and Measurement Technology Materials Science Division Linköping University 58183 Linköping, Sweden E-mail: bom@ifm.liu.se Herbert Venghaus Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH Einsteinufer 37 10587 Berlin, Germany E-mail: venghaus@hhi.de Horst Weber Technische Universität Berlin Optisches Institut Strasse des 17 Juni 135 10623 Berlin, Germany E-mail: weber@physik.tu-berlin.de Takeshi Kamiya Ministry of Education, Culture, Sports Science and Technology National Institution for Academic Degrees 3-29-1 Otsuka, Bunkyo-ku Tokyo 112-0012, Japan E-mail: kamiyatk@niad.ac.jp Harald Weinfurter Ludwig-Maximilians-Universität München Sektion Physik Schellingstrasse 4/III 80799 München, Germany E-mail: harald.weinfurter@physik.uni-muenchen.de Takahiro Numai Fundamentals of Semiconductor Lasers With 166 Figures Professor Takahiro Numai Department of Electrical and Electronic Engineering Ritsumeikan University 1-1-1 Noji-Higashi, Kusatsu Shiga 525-8577 Japan numai@se.ritsumei.ac.jp Library of Congress Cataloging-in-Publication Data Numai, Takahiro Fundamentals of semiconductor lasers / Takahiro Numai p cm – (Springer series in optical sciences ; v 93) Includes bibliographical references and index ISBN 0-387-40836-3 (alk paper) Semiconductor lasers I Title II Series TA1700.N86 2004 2003060811 621.36 6–dc22 ISBN 0-387-40836-3 ISSN 0342-4111 Printed on acid-free paper © 2004 Springer-Verlag New York, Inc All rights reserved This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights Printed in the United States of America SPIN 10944981 www.springer-ny.com Springer-Verlag New York Berlin Heidelberg A member of BertelsmannSpringer Science+Business Media GmbH Dedicated to my grandparents in the U.S.A., Kenichiro and Asano Kanzaki This page intentionally left blank Preface Semiconductor lasers have been actively studied since the first laser oscillation in 1962 Through continuing efforts based on physics, characteristics of semiconductor lasers have been extensively improved As a result, they are now widely used For example, they are used as the light sources for bar-code readers, compact discs (CDs), CD-ROMs, magneto-optical discs (MOs), digital video discs (DVDs), DVD-ROMs, laser printers, lightwave communication systems, and pumping sources of solid-state lasers From these facts, it may be said that semiconductor lasers are indispensable for our contemporary life This textbook explains the physics and fundamental characteristics of semiconductor lasers with regard to system applications It is aimed at senior undergraduates, graduate students, engineers, and researchers The features of this book are as follows: The required knowledge to read this book is electromagnetism and introductory quantum mechanics taught in undergraduate courses After reading this book, students will be able to understand journal papers on semiconductor lasers without difficulty To solve problems in semiconductor lasers, sometimes opposite approaches are adopted according to system applications These approaches are compared and explained In the research of semiconductor lasers, many ideas have been proposed and tested Some ideas persist, and others have faded out These ideas are compared and the key points of the persisting technologies will be revealed The operating principles are often the same, although the structures seem to be different These common concepts are essential and important; they allow us to deeply understand the physics of semiconductor lasers Therefore, common concepts are emphasized in several examples, which will lead to both a qualitative and a quantitative understanding of semiconductor lasers This book consists of two parts The first part, Chapters 1–4, reviews fundamental subjects such as the band structures of semiconductors, optical transitions, optical waveguides, and optical resonators Based on these fundamentals, the second part, Chapters 5–8, explains semiconductor lasers viii Preface The operating principles and basic characteristics of semiconductor lasers are discussed in Chapter More advanced topics, such as dynamic singlemode lasers, quantum well lasers, and control of the spontaneous emission, are described in Chapters 6–8 Finally, the author would like to thank Professor emeritus of the University of Tokyo, Koichi Shimoda (former professor at Keio University), Professor Kiyoji Uehara of Keio University, Professor Tomoo Fujioka of Tokai University (former professor at Keio University), and Professor Minoru Obara of Keio University for their warm encouragement and precious advice since he was a student He is also indebted to NEC Corporation, where he started research on semiconductor lasers just after graduation from Keio University Thanks are extended to the entire team at Springer-Verlag, especially, Mr Frank Ganz, Mr Frank McGuckin, Ms Margaret Mitchell, Mr Timothy Taylor, and Dr Hans Koelsch, for their kind help Takahiro Numai Kusatsu, Japan September 2003 Contents Preface vii Band Structures 1.1 Introduction 1.2 Bulk Structures 1.2.1 k·p Perturbation Theory 1.2.2 Spin-Orbit Interaction 1.3 Quantum Structures 1.3.1 Potential Well 1.3.2 Quantum Well, Wire, and Box 1.4 Super Lattices 1.4.1 Potential 1.4.2 Period 1.4.3 Other Features in Addition to Quantum Effects 1 2 12 12 14 20 20 21 22 Optical Transitions 2.1 Introduction 2.2 Light Emitting Processes 2.2.1 Lifetime 2.2.2 Excitation 2.2.3 Transition States 2.3 Spontaneous Emission, Stimulated Emission, and Absorption 2.4 Optical Gains 2.4.1 Lasers 2.4.2 Optical Gains 25 25 26 27 27 27 28 29 29 30 Optical Waveguides 3.1 Introduction 3.2 Two-Dimensional Optical Waveguides 3.2.1 Propagation Modes 3.2.2 Guided Mode 3.3 Three-Dimensional Optical Waveguides 3.3.1 Effective Refractive Index Method 3.3.2 Marcatili’s Method 43 43 45 45 46 54 54 55 248 G Relative Intensity Noise (RIN) 2S˜δS1 (ω) S10 2 = |X X − Y Y |2 S10 2 RIN1 = × {|X2 |2 W1 − (X2 ∗ Y1 + X2 Y1 ∗ )W12 + |Y1 |2 W2 + |Z1 X2 − Z2 Y1 |2 Wn + [X2 ∗ (Z1 X2 − Z2 Y1 ) + X2 (Z1 X2 − Z2 Y1 )∗ ]W1n − [Y1 ∗ (Z1 X2 − Z2 Y1 ) + Y1 (Z1 X2 − Z2 Y1 )∗ ]W2n }, 2S˜δS2 (ω) RIN2 = S20 2 = S20 |X1 X2 − Y1 Y2 |2 (G.55) × {|Y2 |2 W1 − (X1 ∗ Y2 + X1 Y2 ∗ )W12 + |X1 |2 W2 + |Z2 X1 − Z1 Y2 |2 Wn − [Y2 ∗ (Z2 X1 − Z1 Y2 ) + Y2 (Z2 X1 − Z1 Y2 )∗ ]W1n + [X1 ∗ (Z2 X1 − Z1 Y2 ) + X1 (Z2 X1 − Z1 Y2 )∗ ]W2n } (G.56) References E O Kane: “Band structure of indium antimonide,” J Phys Chem Solids 1, 249 (1957) C Kittel: Quantum Theory of Solids, 2nd edn (John Wiley & Sons, New York 1987) G Bastard: Wave Mechanics Applied to Semiconductor Heterostructures (Halsted Press, New York 1988) S Datta: Quantum Phenomena (Addison-Wesley, Reading 1989) L I Schiff: Quantum Mechanics, 3rd edn (McGraw-Hill, New York 1968) A Messiah: Quantum Mechanics, vol.1, vol.2 (North-Holland, Amsterdam 1961) A Einstein: “Quantentheorie der Strahlung,” Phys Z 18, 121 (1917) J I Pankove: Optical Processes in Semiconductors (Dover, New York 1975) T Tamir, ed.: Integrated Optics, 2nd edn (Springer, Berlin 1979) 10 T Tamir, ed.: Guided-Wave Optoelectronics, 2nd edn (Springer, Berlin 1990) 11 R G Hunsperger: Integrated Optics: Theory and Technology, 3rd edn (Springer, Berlin 1991) 12 D Marcuse: Theory of Dielectric Waveguides, 2nd edn (Academic Press, San Diego 1991) 13 K J Ebeling: Integrated Optoelectronics (Springer, Berlin 1992) 14 E A J Marcatili: “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst Tech J 48, 2071 (1969) 15 T Numai: “1.5 µm phase-shift-controlled distributed feedback wavelength tunable optical filter,” IEEE J Quantum Electron QE-28, 1513 (1992) 16 H Kogelnik and C V Shank: “Coupled-wave theory of distributed feedback lasers,” J Appl Phys 43, 2327 (1972) 17 M Yamada and K Sakuda: “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl Opt 26, 3474 (1987) 18 H A Haus and C V Shank: “Antisymmetric taper of distributed feedback lasers,” IEEE J Quantum Electron QE-12, 532 (1976) 19 H A Haus: Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs 1984) 20 T Numai: A study on semiconductor wavelength tunable optical filters and lasers Ph.D Thesis, Keio University, Yokohama (1992) 21 T Numai: “1.5-µm wavelength tunable phase-shift-controlled distributed feedback laser,” IEEE/OSA J Lightwave Technol 10 199 (1992) 22 K Utaka, S Akiba, K Sakai, et al.: “λ/4-shifted InGaAsP/InP DFB lasers by simultaneous holographic exposure of positive and negative photoresists,” Electron Lett 20, 1008 (1984) 250 References 23 K Utaka, S Akiba, K Sakai, et al.: “λ/4-shifted InGaAsP/InP DFB lasers,” IEEE J Quantum Electron QE-22, 1042 (1986) 24 M Okai, S Tsuji, M Hirao, et al.: “New high resolution positive and negative photoresist method for λ/4-shifted DFB lasers,” Electron Lett 23, 370 (1987) 25 M Shirasaki, H Soda, S Yamakoshi, et al.: “λ/4-shifted DFB-LD corrugation formed by a novel spatial phase modulating mask,” European Conf Opt Commun./Integrated Opt and Opt Commun 25 (1985) 26 T Numai, M Yamaguchi, I Mito, et al.: “A new grating fabrication method for phase-shifted DFB LDs,” Jpn J Appl Phys., Part 26, L1910 (1987) 27 S Tsuji, A Ohishi, M Okai, et al.: “Quarter lambda shift DFB lasers by phase image projection method,” 10th Int Laser Conf 58 (1986) 28 Y Ono, S Takano, I Mito, et al.: “Phase-shifted diffraction-grating fabrication using holographic wavefront reconstruction,” Electron Lett 23, 57 (1987) 29 M Okai, S Tsuji, N Chinone, et al.: “Novel method to fabricate corrugation for a λ/4-shifted distributed feedback laser using a grating photomask,” Appl Phys Lett 55, 415 (1989) 30 H Sugimoto, Y Abe, T Matsui, et al.: “Novel fabrication method of quarterwave-shifted gratings using ECR-CVD SiNx films,” Electron Lett 23, 1260 (1987) 31 K Sekartedjo, N Eda, K Furuya, et al.: “1.5-µm phase-shifted DFB lasers for single-mode operation,” Electron Lett 20, 80 (1984) 32 T Nishida, M Nakao, T Tamamura, et al.: “Synchrotron radiation lithography for DFB laser gratings,” Jpn J Appl Phys 28, 2333 (1989) 33 Z I Alferov, V M Andreev, E L Portnoy, et al.: “AlAs-GaAs heterojunction injection lasers with a low room-temperature threshold,” Sov Phys Semicond 3, 1107 (1970) 34 I Hayashi, M B Panish, P W Foy, et al.: “Junction lasers which operate continuously at room temperature,” Appl Phys Lett 17, 109 (1970) 35 W E Lamb, Jr.: “Theory of an optical maser,” Phys Rev 134, A1429 (1964) 36 W H Louisell: Quantum Statistical Properties of Radiation (John Wiley & Sons, New York 1973) 37 M Sargent III, M O Scully, and W E Lamb, Jr.: Laser Physics (AddisonWesley, Reading 1974) 38 H Haken: Laser Theory (Springer, Berlin 1984) 39 K Shimoda: Introduction to Laser Physics, 2nd edn (Springer, Berlin 1986) 40 A E Siegman: Lasers (University Science Books, Mill Valley 1986) 41 A Yariv: Quantum Electronics, 3rd edn (John Wiley & Sons, New York 1989) 42 R Lang and K Kobayashi: “External optical feedback effects on semiconductor injection laser properties,” IEEE J Quantum Electron QE-16, 347 (1980) 43 Y Nakano, Y Luo, and K Tada: “Facet reflection independent, single longitudinal mode oscillation in a GaAlAs/GaAs distributed feedback laser equipped with a gain-coupling mechanism,” Appl Phys Lett 55, 1606 (1989) 44 K Iga, F Koyama, and S Kinoshita: “Surface emitting semiconductor lasers,” IEEE J Quantum Electron QE-24, 1845 (1988) 45 Z L Liau and J N Walpole: “ Large monolithic two-dimensional arrays of GaInAsP/InP surface-emitting lasers,” Appl Phys Lett 50, 528 (1987) 46 N W Carlson, G A Evans, D P Bour, et al.: “Demonstration of a gratingsurface-emitting diode laser with low-threshold current density ,” Appl Phys Lett 56, 16 (1990) References 251 47 Y Arakawa and A Yariv: “Quantum well lasers—gain, spectra, dynamics,” IEEE J Quantum Electron QE-22, 1887 (1986) 48 P S Zory, Jr., ed.: Quantum Well Lasers (Academic Press, San Diego 1993) 49 M Okai, M Suzuki, and T Taniwatari: “Strained multiquantum-well corrugation-pitch-modulated distributed feedback laser with ultranarrow (3.6 kHz) spectral linewidth,” Electron Lett 29, 1696 (1993) 50 J M Luttinger and W Kohn: “Motion of electrons and holes in perturbed periodic fields,” Phys Rev 97, 869 (1955) 51 G E Pikus and G L Bir: “Effect of deformation on the energy spectrum and the electrical properties of imperfect germanium and silicon,” Sov Phys Solid State 1, 136 (1959) 52 P Y Yu and M Cardona: Fundamentals of Semiconductors, Physics and Materials Properties, 2nd edn (Springer, Berlin 1999) 53 S Adachi: Physical Properties of III –V Semiconductor Compounds (John Wiley & Sons, New York 1992) 54 C Kittel: Introduction to Solid State Physics, 7th edn (John Wiley & Sons, New York 1996) 55 J F Nye: Physical Properties of Crystals (Oxford University Press, New York 1985) 56 H Yokoyama and K Ujihara, eds.: Spontaneous Emission and Laser Oscillation in Microcavities (CRC Press, New York 1995) 57 J Dalibard, J Dupont-Roc, and C Cohen-Tannoudji: “Vacuum fluctuations and radiation reaction: identification of their respective contributions,” J Phys 43, 1617 (1982) 58 F Stern and J M Woodall: “Photon recycling in semiconductor lasers,” J Appl Phys 45, 3904 (1974) 59 T Numai, H Kosaka, I Ogura, et al.: “Indistinct threshold laser operation in a pnpn vertical to surface transmission electro-photonic device with a vertical cavity,” IEEE J Quantum Electron 29, 403 (1993) 60 T Numai, K Kurihara, I Ogura, et al.: “Effect of sidewall reflector on current versus light-output in a pnpn vertical to surface transmission electro-photonic device with a vertical cavity,” IEEE J Quantum Electron 29, 2006 (1993) 61 T Numai: “Analysis of photon recycling in semiconductor ring lasers,” Jpn J Appl Phys., Part 1, 39, 6535 (2000) For further reading, the following articles will be useful 62 J K Butler, ed.: Semiconductor Injection Lasers (IEEE Press, New York 1979) 63 W Streifer and M Ettenberg, eds.: Semiconductor Diode Lasers, vol (IEEE Press, New York 1991) 64 H Kressel and J K Butler: Semiconductor Lasers and Heterojunction LEDs (Academic Press, San Diego 1977) 65 H C Casey, Jr., and M B Panish: Heterostructure Lasers A, B (Academic Press, San Diego 1978) 66 G H B Thompson: Physics of Semiconductor Laser Devices (John Wiley & Sons, New York 1980) 67 G P Agrawal and N K Dutta: Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York 1986) 68 Y Yamamoto, ed.: Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (John Wiley & Sons, New York 1991) 252 References 69 G P Agrawal and N K Dutta: Semiconductor Lasers, 2nd edn (Van Nostrand Reinhold, New York 1993) 70 H Kawaguchi: Bistabilities and Nonlinearlities in Laser Diodes (Artec House, Boston 1994) 71 W W Chow, S W Koch, and M Sargent III: Semiconductor-Laser Physics (Springer, Berlin 1994) 72 G P Agrawal, ed.: Semiconductor Lasers Past, Present, and Future (AIP Press, Woodbury 1995) 73 L A Coldren and S W Corzine: Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, New York 1995) 74 W W Chow and S W Koch: Semiconductor-Laser Fundamentals (Springer, Berlin 1999) 75 S E Miller and A G Chynoweth, eds.: Optical Fiber Telecommunications (Academic Press, San Diego 1979) 76 S E Miller and I P Kaminow, eds.: Optical Fiber Telecommunications II (Academic Press, San Diego 1988) 77 I P Kaminow and T L Koch, eds.: Optical Fiber Telecommunications IIIA (Academic Press, San Diego 1997) 78 I P Kaminow and T L Koch, eds.: Optical Fiber Telecommunications IIIB (Academic Press, San Diego 1997) 79 C Lin, ed.: Optoelectronic Technology and Lightwave Communications Systems (Van Nostrand Reinhold, New York 1989) 80 G Keiser: Optical Fiber Communications, 2nd edn (McGraw-Hill, New York 1991) 81 G P Agrawal: Fiber-Optic Communication Systems, 2nd edn (John Wiley & Sons, New York 1997) 82 A Yariv: Introduction to Optical Electronics, 2nd edn (Saunders, New York 1976) 83 A Yariv: Optical Electronics, 3rd edn (Saunders, New York 1985), 4th edn (Saunders, New York 1991) 84 A Yariv: Optical Electronics in Modern Communications, 5th edn (Oxford University Press, New York 1997) 85 B E A Saleh and M C Teich: Fundamentals of Photonics (John Wiley & Sons, New York 1991) Index absorption, 1, 28, 32 induced, 28 rate, 32 absorption loss, 78 ACC, see automatic current control (ACC) α parameter, 142 alternating current theory, 130 AM noise, see amplitude modulating (AM) noise amplitude modulating (AM) noise, 136 amplitude shift keying (ASK), 128 analog modulation, 132 angle of incidence, 46 antiguiding effect, 114 antireflection (AR), 169 anti-Stokes luminescence, 27 APC, see automatic power control (APC) AR, 169 aspect ratio, 54 astigmatism, 114 asymmetry measure, 52 Auger process, 25, 99 autocorrelation function, 140 automatic current control (ACC), 165 automatic power control (APC), 136, 162, 165 axial mode, 117 band edge emission, 28 band filling effect, 39 band offset, 14, 85 band-structure engineering, 190 bandgap, base function, 15 beam waist, 114 Bernard-Duraffourg relation, 36 BH, see buried heterostructure (BH) bias, 121 biaxial stress, 197 Biot-Savart’s law, bistable LD, 156 blackbody radiation theory, 33 Bloch function, Bloch oscillation, 21 Bloch theorem, Bohr angular frequency, 222 Bohr magneton, Boltzmann constant, 31 bra vector, Bragg wavelength, 67, 172 Brillouin zone, bending of, 21 buffer layer, 190 bulk, buried heterostructure (BH), 116 (C3 ) LD, see cleaved coupled cavity (C3 ) LD carrier concentration threshold, 93 carrier distribution, 30 carrier lifetime, 84, 91 carrier noise, 136 catastrophic optical damage (COD), 163 cathodoluminescence, 27 cavity distributed feedback (DFB), 57 Fabry-Perot, 57 optical, 30 cavity quantum electrodynamics (QED), 203 CGS-Gaussian units, 235 characteristic matrix, 69 254 Index characteristic temperature, 98 chemiluminescence, 27 chirped grating, 72 chirping, 127 chromatic dispersion, 73, 135 cladding layer, 45 cleaved coupled cavity (C3 ) LD, 177 cleaved facet, 57 COD, see catastrophic optical damage (COD) coherent, 128 complex refractive index, 43 compressive strain, 191 confinement of resonant radiation, 208 coupled cavity, 157 coupled wave equation, 67 coupled wave theory, 67 coupling coefficient, 66 coupling rate of a feedback light to the semiconductor laser, 158 critical angle, 45 critical thickness, 23, 190 crystal defect, 162 current versus light output (I-L), 90 cutoff, 46 condition, 52 cyclotron angular frequency, 212 cyclotron motion, 212 cyclotron resonance, 11, 212 dark line defect, 164 DBR, see distributed Bragg reflector (DBR) DBR-LD, see distributed Bragg reflector (DBR) LD decay coefficient, 125 decay rate, 158 decay time, 125 deformation potential, 196 degenerate, degradation, 162 δ function, 141 density of states, 16 effective, 31 derivative electrical resistance, 102, 103 light output, 102 measurement, 102 deviation, 124 DFB, see distributed feedback (DFB) DFB-LD, see distributed feedback (DFB) LD diagonal element, 191 diamond structure, dielectric film, 58 differential gain, 125 diffracted pattern, 108 diffraction grating, 57, 167 diffusion length, 115 digital modulation, 132 dipole moment, 37 Dirac’s constant, direct modulation, 128, 129 direct transition, 11, 26 discrete, discrete approach, 68 dislocation, 23 dislocations, 164 dispersion, 78, 118 chromatic, 73, 135 material, 135 mode, 135 structual, 135 dispersion curve, 51 distributed Bragg reflector (DBR), 57 distributed Bragg reflector (DBR) LD, 167 distributed feedback (DFB), 57 distributed feedback (DFB) LD, 167 double heterostructure, 22, 85 duty, 133 dynamic single-mode LD, 167 effective density of states, 31 effective mass, approximation, effective mass approximation, 15 effective refractive index, 50 method, 54 eigenvalue equation, 51 Einstein summation convention, 196 Einstein’s A coefficient, 34 Einstein’s B coefficient, 34 Einstein’s relation, 34 elastic strain, 23, 191 electric current noise, 137 electric dipole moment, 227 electric dipole transition, 227 Index 255 electroluminescence, 27 injection-type, 27 electron-beam exposure, 78 emission, induced, 28 spontaneous, 28 stimulated, 28 energy band, energy barrier layer, 14 energy barriers, 85 energy eigenvalue, energy level, ensemble average, 139 envelope function, 15 equivalent refractive index, 119 etching mask, 78 evanescent wave, 49 excitation, 25 excited state, 204 exciton, 27, 130 exciton recombination, 28 external cavity, 157 external cavity laser, 148 external cavity LD, 176 external differential quantum efficiency, 88 external modulation, 128, 129 extinction coefficient, 43 extinction ratio, 126 eye pattern, 133 free spectral range, 61 frequency fluctuation spectrum, 139 frequency modulating (FM) noise, 136 frequency shift keying (FSK), 128 Fresnel formulas, 47, 104 full width at half maximum (FWHM), 62 fundamental mode, 111 FWHM, see full width at half maximum (FWHM) Fabry-Perot cavity, 57 facet, 53 far-field pattern, 108 feedback, 29 Fermi level, 30 quasi-, 30 Fermi’s golden rule, 204 Fermi-Dirac distribution, 30 field spectrum, 139 finesse, 63 fluorescence, 27 FM noise, see amplitude modulating (FM) noise forward bias, 84 Franz-Keldysh effect, 130 free carrier absorption, 98 free carrier plasma effect, 113 free space, 43, 205 half width at half maximum (HWHM), 62 harmonic perturbation, 223 heat sink, 162 Heaviside function, 180 heavy hole band, 10 heterojunction, 85 heterostructure, 22 double, 22 high frequency modulation, 156 holographic exposure, 78 homojunction, 85 horizontal cavity surface emitting LD, 176 horizontal transverse mode, 108, 112 HWHM, see half width at half maximum (HWHM) hybrid orbital, gain optical, 30 gain flattening, 182 gain guiding, 43, 112 Gaussian distribution function, 145 Goos-Hă anchen shift, 49 graded index SCH (GRIN-SCH), 180 grating chirped, 72 phase-shifted, 72 tapered, 72 uniform, 72 GRIN-SCH, see graded index SCH (GRIN-SCH) ground state, 204 group theory, 189 guiding effect, 114 anti-, 114 guiding layer, 45 256 Index hydrostatic strain, 191 hysteresis, 160 hysteresis loop, 120 I-L, see current versus light output (I-L) impurity recombination, 27 incident light, 46 index guiding, 43 index-coupled grating, 168 indirect transition, 11, 26 induced absorption, 28 induced emission, 28 injection locking, 54 injection-type electroluminescence, 27 intensity fluctuation spectrum, 144 intensity-modulation/direct-detection, 128 intentionally accelerating degradation tests, 165 interaction energy, interband transition, 117 interference fringe pattern, 78 internal loss, 88 internal quantum efficiency, 89 intraband relaxation time, 120, 182 intrinsic, 84 inverse Laplace transform, 123 inverted population, 28 I-V , 100 k-selection rule, 40, 181 ket vector, kink, 114 k · p perturbation theory, Lagrange equation, 225 Lagrangian, 225 λ/4-shifted grating, 172 Laplace transform, 122 laser, 29 lateral mode, 106 lattice mismatching, 190 left-handed circularly polarized wave, 213 lifetime, 162 light hole band, 10 linearly polarized light, 46 linearly polarized wave, 213 longitudinal mode, 117 Lorentz equation, 225 Lorentz force, 211 Lorentzian, 40, 92, 146 luminescence, 26 anti-Stokes, 27 cathodo-, 27 chemi-, 27 electro-, 27 injection-type electro-, 27 photo-, 27 Stokes, 27 thermo-, 27 tribo-, 27 Luttinger parameter, 194 Luttinger-Kohn Hamiltonian, 193, 194 magnetic flux density, Marcatili’s method, 54 material dispersion, 135 Maxwell’s equations, 70, 229, 235 microcavity, 205 minizone, 21 mirror, 30, 57 mirror loss, 87 MKSA units, 235 modal gain, 182 mode competition, 115 mode density, 35 mode dispersion, 135 mode hopping, 115 mode number, 49 mode partition noise, 154 mode volume, 138 modified MQW, 179 modified Schawlow-Townes linewidth formula, 146 modulation efficiency, 130 MQW-LD, see multiple quantum well (MQW) LD multimode operation, 117 multiple quantum well (MQW) LD, 179 near-field pattern, 108 negative resistance, 21 node, 64 noise, 136 nondiagonal element, 191 nonradiative recombination, 25 Index nonradiative recombination lifetime, 91 nonradiative transition, nonreturn-to-zero (NRZ), 133 nonthermal equilibrium, 30 normalized frequency, 51 normalized waveguide thickness, 51 NRZ, see nonreturn-to-zero (NRZ) ohmic contacts, 162 optical cavity, 30, 57 optical confinement factor, 51 optical fiber, 43 optical fiber amplifier, 128 optical gain, 29, 30 optical isolator, 156 optical resonator, 30, 57 optical transition, optical waveguide, 43 planar, 44 strip, 44 three-dimensional, 44 two-dimensional, 44 orbit-strain interaction Hamiltonian, 195 orbital angular momentum, orbital angular momentum operator, 196 order of diffraction, 67, 172 orthonormalize, 138 oscillation, 86 overflow, 98 pattern effect, 133 Pauli exclusion principle, Pauli’s spin matrices, penetration depth, 49 periodic multilayer, 68 periodic potential, 13 perturbation, 215 perturbation parameter, perturbation theory k · p, first-order, second-order, phase shift, 47 phase shift keying (PSK), 128 phase velocity, 48 phase-shifted grating, 72 phonon, 25 257 phosphorescence, 27 photoluminescence, 27 photon, 25 photon lifetime, 91 photon recycling, 208 photoresist, 78 Pikus-Bir Hamiltonian, 193, 195 planar optical waveguide, 44 Planck’s constant, plane of incidence, 46 plane wave, 46 pn-junction, 115 pnpn structure, 115 point defect, 164 polarization, 46 polarization controller, 129 population inversion, 28 potential well, 14 power fluctuation spectrum, 139 Poynting vector, 226 propagate, 43 propagation constant, 48 propagation mode, 45 quantum box, 18 quantum confined Stark effect (QCSE), 130 quantum noise, 136 quantum number, quantum structures, 12 quantum well (QW), 4, 14 one-dimensional, 15 three-dimensional, 18 two-dimensional, 18 quantum well (QW) LD, 179 quantum wire, 18 quarter wavelength shifted grating, 172 quasi-Fermi level, 30 QW, see quantum well (QW) strained, 190 QW-LD, see quantum well (QW) LD radiation, 28 radiative recombination, 25 radiative recombination lifetime, 91 radiative transition, rate absorption, 32 spontaneous emission, 33 258 Index stimulated emission, 32 transition, 31 rate equations, 90, 91 reciprocal effective mass tensor, recombination, 25 impurity, 27 nonradiative, 25 radiative, 25 reflected light, 46 reflector, 30 refracted light, 46 refractive index, 43 complex, 43 relative electric susceptibility, 181 relative intensity noise (RIN), 149, 245 relaxation, 25 relaxation oscillation, 121 resonance angular frequency, 131 resonance condition, 61, 86 resonant tunneling effect, 21 resonator, 30 return-to-zero (RZ), 133 rib waveguide, 115 ridge, 54 ridge-waveguide, 116 right-handed circularly polarized wave, 212 ring cavity, 57 running wave, 64 RZ, see return-to-zero (RZ) S/N ratio, see signal-to-noise (S/N ) ratio saturable absorber, 156 scalar potential, 225 SCH, see separate connement heterostructure (SCH) Schră odinger equation, screening tests, 165 selection rule, 187 self-pulsation, 156 semiclassical theory, 137 semimetal, 21 separate confinement heterostructure (SCH), 180 separation-of-variables procedure, 236 shear strain, 191 signal-to-noise (S/N ) ratio, 126 single crystal, single quantum well (SQW) LD, 179 single-mode operation, 117 slope efficiency, 88 small-signal analysis, 124 Snell’s law, 45 spatial hole burning, 172 spatial hole-burning, 113 spectral density functions, 140 spectral linewidth, 62, 140 spectral linewidth enhancement factor, 142 spherical polar coordinate systems, spin angular momentum, magnetic moment, spin angular momentum operator, 196 spin-orbit interaction, Hamiltonian, split-off band, 10 split-off energy, 10 spontaneous emission, 28, 33 rate, 33 spontaneous emission coupling factor, 91 SQW-LD, see single quantum well (SQW) LD standing wave, 64 steady state, 93 step function, 180 stimulated emission, 28, 32 rate, 32 Stokes luminescence, 27 stop band, 68 strain, 190 compressive, 191 elastic, 23 hydrostatic, 191 shear, 191 tensile, 191 strain-dependent spin-orbit interaction Hamiltonian, 195 strained QW, 190 stress, 190 strip optical waveguide, 44 structural dispersion, 135 substrate, 45 super lattice, 20 Type I, 21 Index Type II, 21 Type III, 21 surface emitting LD horizontal cavity, 176 vertical cavity, 175 synchrotron radiation, 80 tapered grating, 72 TE mode, 46 tensile strain, 191 tensor, 191 thermal equilibrium, 28 thermoluminescence, 27 three-dimensional optical waveguide, 44, 54 threshold carrier concentration, 93 threshold current density, 93 thyristor, 115 time-average, 139 time-dependent quantum mechanical perturbation theory, 37 time-dependent Schră odinger equation, 221 TM mode, 46 total reection, 45 transfer matrix, 67, 238 transient response theory, 130 transition direct, 26 indirect, 26 nonradiative, optical, 259 radiative, transition rate, 31 transmission characteristics, 58 transverse electric (TE) mode, 46 transverse magnetic (TM) mode, 46 transverse mode, 106 horizontal, 108, 112 vertical, 106, 109 transverse resonance condition, 49 triboluminescence, 27 tunneling effect, 21 resonant, 21 turn-on delay time, 121 two-dimensional optical waveguide, 44 undoped, 84 uniform grating, 72 unisotropic optical gain, 183 unperturbed Hamiltonian, 215 valence band absorption, 99 VCSEL, see vertical cavity surface emitting LD (VCSEL) vector potential, 225 vertical cavity surface emitting LD, 175 vertical transverse mode, 106 wave function, wave vector, Wiener-Khintchine theorem, 140 window structure, 163 X-ray exposure, 78 zinc-blende structure, Springer Series in optical sciences New editions of volumes prior to volume 70 Solid-State Laser Engineering By W Koechner, 5th revised and updated ed 1999, 472 figs., 55 tabs., XII, 746 pages 14 Laser Crystals Their Physics and Properties By A A Kaminskii, 2nd ed 1990, 89 figs., 56 tabs., XVI, 456 pages 15 X-Ray Spectroscopy An Introduction By B K Agarwal, 2nd ed 1991, 239 figs., XV, 419 pages 36 Transmission Electron Microscopy Physics of Image Formation and Microanalysis By L Reimer, 4th ed 1997, 273 figs XVI, 584 pages 45 Scanning Electron Microscopy Physics of Image Formation and Microanalysis By L Reimer, 2nd completely revised and updated ed 1998, 260 figs., XIV, 527 pages Published titles since volume 70 70 Electron Holography By A Tonomura, 2nd, enlarged ed 1999, 127 figs., XII, 162 pages 71 Energy-Filtering Transmission Electron Microscopy By L Reimer (Ed.), 1995, 199 figs., XIV, 424 pages 72 Nonlinear Optical Effects and Materials By P Găunter (Ed.), 2000, 174 gs., 43 tabs., XIV, 540 pages 73 Evanescent Waves From Newtonian Optics to Atomic Optics By F de Fornel, 2001, 277 figs., XVIII, 268 pages 74 International Trends in Optics and Photonics ICO IV By T Asakura (Ed.), 1999, 190 figs., 14 tabs., XX, 426 pages 75 Advanced Optical Imaging Theory By M Gu, 2000, 93 figs., XII, 214 pages 76 Holographic Data Storage By H.J Coufal, D Psaltis, G.T Sincerbox (Eds.), 2000 228 figs., 64 in color, 12 tabs., XXVI, 486 pages 77 Solid-State Lasers for Materials Processing Fundamental Relations and Technical Realizations By R Ifăander, 2001, 230 gs., 73 tabs., XVIII, 350 pages 78 Holography The First 50 Years By J.-M Fournier (Ed.), 2001, 266 figs., XII, 460 pages 79 Mathematical Methods of Quantum Optics By R.R Puri, 2001, 13 figs., XIV, 285 pages 80 Optical Properties of Photonic Crystals By K Sakoda, 2001, 95 figs., 28 tabs., XII, 223 pages 81 Photonic Analog-to-Digital Conversion By B.L Shoop, 2001, 259 figs., 11 tabs., XIV, 330 pages 82 Spatial Solitons By S Trillo, W.E Torruellas (Eds), 2001, 194 figs., tabs., XX, 454 pages 83 Nonimaging Fresnel Lenses Design and Performance of Solar Concentrators By R Leutz, A Suzuki, 2001, 139 figs., 44 tabs., XII, 272 pages 84 Nano-Optics By S Kawata, M Ohtsu, M Irie (Eds.), 2002, 258 figs., tabs., XVI, 321 pages 85 Sensing with Terahertz Radiation By D Mittleman (Ed.), 2003, 207 figs., 14 tabs., XVI, 337 pages 86 Progress in Nano-Electro-Optics I Basics and Theory of Near-Field Optics By M Ohtsu (Ed.), 2003, 118 figs., XIV, 161 pages 87 Optical Imaging and Microscopy Techniques and Advanced Systems By P Tăorăok, F.-J Kao (Eds.), 2003, 260 figs., XVII, 395 pages 88 Optical Interference Coatings By N Kaiser, H.K Pulker (Eds.), 2003, 203 figs., 50 tabs., XVI, 504 pages 89 Progress in Nano-Electro-Optics II Novel Devices and Atom Manipulation By M Ohtsu (Ed.), 2003, 115 figs., XIII, 188 pages 90/1 Raman Amplifiers for Telecommunications Physical Principles By M.N Islam (Ed.), 2004, 488 figs., XXVIII, 328 pages 90/2 Raman Amplifiers for Telecommunications Sub-Systems and Systems By M.N Islam (Ed.), 2004, 278 figs., XXVIII, 420 pages 91 Optical Super Resolution By Z Zalevsky, D Mendlovic, 2004, 164 figs., XVIII, 232 pages 92 UV-Visible Reection Spectroscopy of Liquids By J.A Răaty, K.-E Peiponen, T Asakura, 2004, 131 figs., XII, 219 pages 93 Fundamentals of Semiconductor Lasers By T Numai, 2004, 166 figs., XII, 264 pages 94 Photonic Crystals Physics, Fabrication and Applications By K Inoue, K Ohtaka (Eds.), 2004, 214 figs., IX, 331 pages Springer Series in optical sciences 86 Progress in Nano-Electro-Optics I Basics and Theory of Near-Field Optics By M Ohtsu (Ed.), 2003, 118 figs., XIV, 161 pages 87 Optical Imaging and Microscopy Techniques and Advanced Systems By P Tăorăok, F.-J Kao (Eds.), 2003, 260 figs., XVII, 395 pages 88 Optical Interference Coatings By N Kaiser, H.K Pulker (Eds.), 2003, 203 figs., 50 tabs., XVI, 504 pages 89 Progress in Nano-Electro-Optics II Novel Devices and Atom Manipulation By M Ohtsu (Ed.), 2003, 115 figs., XIII, 188 pages 90/1 Raman Amplifiers for Telecommunications Physical Principles By M.N Islam (Ed.), 2004, 488 figs., XXVIII, 328 pages 90/2 Raman Amplifiers for Telecommunications Sub-Systems and Systems By M.N Islam (Ed.), 2004, 278 figs., XXVIII, 420 pages ... (former professor at Keio University), Professor Kiyoji Uehara of Keio University, Professor Tomoo Fujioka of Tokai University (former professor at Keio University), and Professor Minoru Obara of Keio... 4.3.6 Fabrication of Diffraction Gratings 57 57 58 61 61 62 63 63 64 64 68 Fundamentals of Semiconductor Lasers 5.1 Key Elements in Semiconductor Lasers ... structures of semiconductor crystals Most semiconductor crystals for semiconductor lasers have a zincblende structure, in which the bottom of the conduction bands is s-orbital-like and the tops of the