John wiley sons distributed feedback laser diodes and optical tunable filters ddu

Distributed Feedback Laser Diodes and Optical Tunable Filters Dr H Ghafouri–Shiraz The University of Birmingham, UK and Nanyang Technological University, Singapore Distributed Feedback Laser Diodes and Optical Tunable Filters Distributed Feedback Laser Diodes and Optical Tunable Filters Dr H Ghafouri–Shiraz The University of Birmingham, UK and Nanyang Technological University, Singapore Copyright # 2003 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770620 This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the Publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats Some of the content that appears in print may not be available in electronic books Library of Congress Cataloging-in-Publication Data Ghafouri–Shiraz, H Distributed feedback laser diodes and optical tunable filters / H Ghafouri–Shiraz p cm Includes bibliographical references and index ISBN 0-470-85618-1 (alk paper) Light emitting diodes Solid-state lasers Tunable lasers Light filters I Title TK7871.89.L53G43 2003 621.360 6–dc21 2003050194 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-85618-1 Typeset in 10/12pt Times by Thomson Press (India) Limited, New Delhi Printed and bound in Great Britain by TJ International, Padstow, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production This book is dedicated to My Father, the late Haji Mansour, for the uncompromising principles that guided his life and for his profound influence and inspiration My Mother, Rahmat, for leading her children into intellectual pursuits My Supervisor, the late Professor Takanori Okoshi, for his continuous guidance, encouragement, inspiring discussion and moral support A distinguished scientist and a great teacher who made me aware of the immense potential of optical fibre communications My Wife, Maryam, for her understanding support, affection and magnificent devotion to her family My constant companion and best friend, she has demonstrated incredible patience and understanding during the rather painful process of writing this book while maintaining a most pleasant, cheerful and comforting home My Children, Elham, Ahmad-Reza and Iman, for making everything worthwhile To all of my research and undergraduate students since 1987, for their excellent and fruitful research work, and for many stimulating discussions, which encouraged and motivated me to write this book Contents Preface Acknowledgements Glossary of Abbreviations Glossary of Symbols xiii xv xviii xix Introduction to Optical Communication Systems Introduction Historical Progress Optical Fibre Communication Systems 1.3.1 Intensity Modulation with a Direct Detection Scheme 1.3.2 Coherent Detection Schemes 1.4 System Requirements for High-Speed Optical Coherent Communication 1.4.1 Spectral Purity Requirements 1.4.2 Spectral Linewidth Requirements 1.5 Summary 1.6 References 7 18 25 26 31 31 32 32 33 36 38 38 41 43 45 48 51 56 57 58 60 60 An 1.1 1.2 1.3 Principles of Distributed Feedback Semiconductor Laser Diodes: Coupled Wave Theory 2.1 Introduction 2.2 Basic Principle of Lasers 2.2.1 Absorption and Emission of Radiation 2.2.2 The Einstein Relations and the Concept of Population Inversion 2.2.3 Dispersive Properties of Atomic Transitions 2.3 Basic Principles of Semiconductor Lasers 2.3.1 Population Inversion in Semiconductor Junctions 2.3.2 Principle of the Fabry–Perot Etalon 2.3.3 Structural Improvements in Semiconductor Lasers 2.3.4 Material Gain in Semiconductor Lasers 2.3.5 Total Radiative Recombination Rate in Semiconductors 2.4 Coupled Wave Equations in Distributed Feedback Semiconductor Laser Diodes 2.4.1 A Purely Index-coupled DFB Laser Diode 2.4.2 A Mixed-coupled DFB Laser Diode 2.4.3 A Gain-coupled or Loss-coupled DFB Laser Diode 2.5 Coupling Coefficient 2.5.1 A Structural Definition of the Coupling Coefficient for DFB Semiconductor Lasers 1 5 12 Conclusion, Summary and Suggestions 12.1 SUMMARY AND CONCLUSION In this book, the performance characteristics of distributed feedback semiconductor laser diodes and optical tunable filters based on DFB laser structures have been investigated As discussed in Chapter 1, these lasers can be used as optical sources and local oscillators in coherent optical communication networks, in which a stable single mode (in both the transverse plane and the longitudinal direction) and narrow spectral linewidth become crucial Based on the interaction of electromagnetic radiation with a two-energy-band system, the operating principles of semiconductor lasers were reviewed in Chapter With partially reflecting mirrors located at the laser facets, a Fabry–Perot laser forms the simplest type of optical resonator However, due to the broad gain spectrum, multi-mode oscillations and mode hopping are common for this type of laser Nevertheless, single longitudinal mode operation becomes feasible with the use of DFB LDs The characteristics of the DFB laser were explained using the coupled wave equations With a built-in periodic corrugation, travelling waves are formed along the direction of propagation in which a perturbed refractive index and/or gain are introduced In fact, DFB lasers act as optical bandpass filters, so that only frequency components near the Bragg frequency are allowed to pass The strength of optical feedback is measured by the strength of the coupling coefficient Based on the nature of the coupling coefficient, DFB semiconductor lasers can be classified into purely index-coupled, mixed-coupled and purely gain- or loss-coupled structures The discussion focused on the coupled wave equations in Chapter In the analysis, eigenvalue equations were derived for various structural configurations and consequently, their threshold currents and lasing wavelengths were determined From the lasing threshold characteristics, impacts due to the coupling coefficient, the laser cavity length, the facet reflectivities, the residue corrugation phases and phase discontinuities were discussed in a systematic way With a single %/2 phase shift introduced at the centre of the DFB cavity, the quarterly-wavelength-shifted DFB LD oscillates at the Bragg wavelength Due to nonuniform field distribution, however, the single-mode stability of this structure deteriorates quickly when the biasing current increases Based on a five-layer separate confinement heterostructure, the coupling coefficient of a trapezoidal corrugation was computed, from Distributed Feedback Laser Diodes and Optical Tunable Filters H Ghafouri–Shiraz # 2003 John Wiley & Sons, Ltd ISBN: 0-470-85618-1 304 CONCLUSION, SUMMARY AND SUGGESTIONS which coupling coefficients of other corrugation shapes, like triangular and rectangular gratings, were also evaluated [1] In Chapter 4, the idea of the transfer matrix was introduced and explored Compared with the boundary matching approach in deriving the eigenvalue equation, the transfer matrix method (TMM) is more robust and flexible By converting the coupled wave equations into a matrix formation, the characteristics of a corrugated DFB laser section can be represented by a  matrix This approach has been extended to include phase discontinuity and the effect of residue reflection at the facets By modifying the elements of the transfer matrix, they can also be used to represent other planar and corrugated structures including passive waveguides, the distributed Bragg reflector and planar Fabry–Perot sections Using these transfer matrices as building blocks, a general N-sectioned laser cavity model was constructed and the threshold analysis for such a laser model was discussed With perfectly matched boundaries between consecutive transfer matrices, the number of boundary conditions is reduced significantly Only the boundary condition located at the laser facet remains to be matched As compared with the eigenvalue equation, the TMM and/or TLLM simplifies the threshold analysis dramatically In a similar way, the transfer matrix has also been implemented to evaluate the below-threshold spontaneous emission power spectrum PN By combining the Poynting vector with the method of Green’s function, numerical results obtained from the three-phase-shift DFB LD were presented and the structural impact on the spectral behaviour discussed [2] In revealing the potential use of the TMM and/or TLLM in the practical design of DFB LDs, the threshold analysis of various DFB laser structures, including the 3PS [3] and distributed coupling coefficient [4], was carried out in Chapter In an attempt to minimise the effect of the SHB and hence improve the maximum available single-mode output power, it is necessary that a stable single longitudinal mode LD shows a high normalised gain margin ðÁLÞ and a uniform field intensity (i.e small value of flatness, F) Based on the lasing performance at threshold, selection criteria were set at ÁL > 0:25 and F < 0:05 for a 500 mm length laser cavity Using these optimised structures, complexities with respect to the design of DFB lasers may be reduced By changing the value of phase shifts, the coupling coefficient and their corresponding positions, results such as the gain margin ðÁLÞ and the uniformity of the field distribution (F) were presented A conventional single QWS DFB was selected for comparison purposes This structure is characterised by an intense electric field found at the centre of the cavity With the introduction of multiple phase shifts along the laser cavity, a 3PS DFB LD with three p/3 phase shifts and a position factor of 0.5 falls within the selection criteria of ÁL and F In an alternative approach, the introduction of the DCC also appears to be promising An improvement in the gain margin was shown for a DCC ỵ QWS DFB laser structure with a coupling ratio of = ¼ 1=3 and a corrugation change at 0.46 Despite the fact that the flatness of this design does not match the requirements of the selection criteria, a high gain margin and oscillation at the Bragg wavelength still count as an advantage in the DCC DFB laser design The N-sectioned laser cavity model has been used to determine both the threshold and the below-threshold performance of DFB LDs However, the TMM and/or TLLM used has to be modified when the stimulated emission becomes dominant in the above-threshold biasing regime In Chapter 6, a new technique [5] which combines the TMM and/or TLLM with the carrier rate equation was introduced In the model, multiple carrier recombination and a parabolic gain model were assumed To include any gain saturation effects, a non-linear gain coefficient was introduced The algorithm needs no first-order derivative and has been SUMMARY AND CONCLUSION 305 developed in such a way that, with minor modification, the same algorithm can be applied to various laser structures The TMM-based above-threshold laser model was applied to several DFB laser structures including the QWS, 3PS and the DCC DFB LDs The QWS DFB laser structure, which is characterised by its non-uniform field distribution, was shown to have a large dynamic range of spatially distributed refractive index Along the carrier concentration profile, a dip was shown at the centre of the cavity where the largest stimulated photon density was found By introducing more phase shifts along the corrugation, results from a 3PS DFB LD with 2 ¼ 3 ¼ 4 ¼ p=3 and PSP ¼ 0:5 were presented Uniform distributions were observed in the carrier density, photon density and the refractive index profile With an improved threshold gain margin, the abovethreshold characteristics of a QWS LD having non-uniform coupling coefficient were also shown As compared with the QWS structure, the introduction of a non-uniform coupling coefficient with = ¼ 1=3 and CP ¼ 0:46 increased the localised carrier concentration near the plane of corrugation change A significant reduction in the photon density difference between the central peak and the emitting photon density near the facet was also found Based on the TMM and/or TLLM, the above-threshold model was extended and applied to evaluate spectral and noise properties of DFB LDs in Chapter Based on the lasing mode distributions obtained for the carrier density, photon density, refractive index and the field intensity, characteristics like the single-mode stability, the spontaneous emission spectrum and the spectral linewidth were investigated At a fixed biasing current, the QWS structure having the smallest threshold gain was shown to have the smallest linewidth On the other hand, the non-lasing þ1 side mode became stronger with increasing bias current Comparatively, the 3PS structure was shown to have the smallest change in lasing wavelength With the introduction of multiple phase shifts along the corrugation, the internal field distribution becomes more uniform and hence a stable single-mode oscillation results It is shown that the DCC ỵ QWS structure has the largest gain margin The introduction of a distributed coupling coefficient improved the single-mode stability in such a way that the side mode suppression ratio remained at a high value Wavelength tunability is also improved in this structure From these results, it is apparent that the design of the DFB LD depends much on its applications On the other hand, the TMM and/or TLLM has proved to be a powerful tool when dealing with such a problem In Chapter the transmission line laser model was discussed TLLM can be classified as a distributed-element circuit model, which is based on the 1-D transmission line matrix method The building blocks of a TLM network are the TLM link lines and stub lines It has been shown how the scattering matrices of several TLM sub-networks may be derived by using Thevenin-equivalent circuits Scattering and connecting are the two main processes that form the basis of TLM The scattering matrix at a TLM node takes incident voltage pulses and operates on them to produce reflected pulses that travel away from the node The connecting matrix then directs the reflected pulses from one TLM node to adjacent TLM nodes, where they become incident pulses of the adjacent nodes in the next time iteration In TLLM, the voltage pulses represent the optical waves that circulate inside the laser cavity All the important optical processes in the laser are taken into account, such as the spectrallydependent gain of stimulated emission, material and scattering loss, spontaneous emission, carrier–photon interaction and carrier-dependent phase shift The microwave circuit elements of TLLM are used to describe these laser processes on an equivalence basis The baseband transformation method is used to enhance the computational efficiency by down-converting from the true optical carrier frequency to its equivalent baseband value 306 CONCLUSION, SUMMARY AND SUGGESTIONS The TLLM is a stochastic laser model because random noise effects are included, making it a highly realistic model compared to deterministic laser models However, intensive time averaging and smoothing techniques are required to obtain the wanted signal, which may otherwise be masked by noise In Chapter TLLM was modified to allow study of dynamic behaviour of distributed feedback laser diodes, in particular the effects of multiple phase shifts on the overall DFB LD performance We can easily model any arbitrary phase shift value by inserting some phase shifter stubs into the scattering matrices of TLLM This helps to make the electric field distribution and hence light intensity of DFB LDs more uniform along the laser cavity and hence minimise the hole burning effect In Chapter 10 optical tunable filters were introduced An active optical tunable filter with frequency characteristics that can be tailored to a desired response is an enabling technology for exploiting the full potential bandwidth of optical fibre communication systems Having seen the importance of such active optical tunable filters, it is highly desirable to design a tunable filter which can perform filtering and amplification of the filtered signal simultaneously In this chapter, active grating-embedded filters were analysed and designed based on the TMM outlined, where the coupled wave equations of the DFB LD amplifier filters were solved In addition, the dispersion relationship and the stop band were also discussed From the solutions of the eigenvalue equations, which were derived by matching the boundary conditions, the threshold current and the lasing wavelength were determined These included the analysis of the phase discontinuities and the below-threshold characteristics of DFB LDs The principle of the active tunability of DFB LD amplifier filters was discussed and the structural impacts of the performance of the filters were justified The effects of grating period and coupling coefficient on the performance characteristics of a novel multi-section and phase-shift-controlled DFB wavelength tunable optical filter have also been studied It was found that this filter structure offers a wide tuning range with narrow bandwidth, high gain and large SMSR The filter has over 30 dB peak gain within the ˚ for ¼ mmÀ1 and 42 A ˚ for ¼ 10 mmÀ1 The filter SMSR tuning range, which is 32.0 A varies between 12 dB and 30.2 dB Finally, some analyses on the three-section DBR LD amplifier filter were carried out It was found that this structure is not suitable for a multisection design since mode hopping occurs in the main lobe, though the tuning range can be increased Besides, it is very difficult to monolithically integrate the sections without error in practice, since the reflectivities of each section will contribute to the threshold amplitude Furthermore, the Bragg reflector is lossy and thus a higher threshold current will be required The effects of grating period and coupling coefficient on the performance characteristics of a !=4-phase-shifted double-phase-shift-controlled DFB wavelength tunable optical filter were studied in Chapter 11 It was found that the new laser-based filter structure offers a wide tuning range with narrow bandwidth, high gain and large SMSR The filter has over ˚ for ˚ for ¼ mmÀ1 and 34.3 A 30 dB peak gain within its tuning range, which is 28.3 A À1 ¼ 10 mm The filter SMSR varies between 15 and 34.7 dB Also, we investigated the effects of phase shifts 01 and 04 on tuning range, peak transmissivity and SMSR of single PSC DFB filters It was found that when 01 < p=2 and 04 > p=2, the filter tuning range increases Also, peak transmissivity of more than 35 dB and SMSR of better than 15 dB can be achieved The analytical investigation showed that the three-phase-shift-controlled DFB wavelength tunable optical filter has a wide tuning range with narrow bandwidth and high gain (see Figs 11.15 to 11.18) However, these two additional waveguide sections FUTURE RESEARCH 307 contribute to a larger amount of free carrier absorption which alters the threshold gain slightly The calculations are based on the assumption that the relationships of the grating phases at the two sides of the wavelength region are the same for the two O2 phase-control regions 12.2 THE TMM AND/OR TLLM ANALYSIS In the analysis, the most important characteristics, namely the single-mode stability, spectral linewidth and the spectral behaviour of DFB LDs, have been investigated using the QWS, 3PS and DCC laser structures The TMM and/or TLLM has provided the flexibility one needs in the design of DFB LDs There are other dynamic characteristics such as AM and FM response [6–9] and the use of multiple electrode configuration [10–11] which are also important in the characterisation of laser devices 12.3 FUTURE RESEARCH Based on the TMM and/or TLLM, the characteristics of DFB LDs have been investigated Detailed analysis covering both below- and above-threshold biasing regimes has been presented There are at least three possible research directions which may be worth further investigation 12.3.1 Extension to the Analysis of Quantum Well Devices In this book, we have concentrated on bulk devices only There is a potential to apply the same TMM and/or TLLM technique to quantum well structures [12] The major differences between QW lasers and bulk ones, which we have been examining, are the recombination mechanism [13], material gain characteristics, band structure [14] and confinement factor [15] One can replace some of the equations used in the bulk model with those appropriate for QW structures The analysis and the algorithm will remain the same as for the bulk devices described earlier 12.3.2 Extension to Gain-coupled Devices DFB LDs used in this book belong to the group of purely index-coupled devices The wavelength filtering mechanism is solely caused by the perturbation of refractive index In recent years, there has been a growing interest in the use of mixed-coupled and purely gaincoupled devices [16–20] With the coupling coefficient depending on the material gain, it has been shown both in theory [21] and experiment [22] that these devices exhibit stable single-mode oscillation at the Bragg wavelength Even for a small degree of gain coupling, a mixed-coupled device shows an improvement in the gain margin By introducing an imaginary term into the coupling coefficient used in the model, the characteristics of these devices can be investigated using the same methodology 308 CONCLUSION, SUMMARY AND SUGGESTIONS 12.3.3 Further Investigation of Optical Devices to be Used in WDM In this book, much of the emphasis has been on the threshold and above-threshold analysis of various DFB laser structures With the deployment of WDM techniques in optical communication networks [23], there is a growing demand for different types of optical device Optical filters which allow end users easy access to various information like television or interactive digital services [24] are important Recently, a four-channel notch filter based on a DCC DFB laser structure was demonstrated [25] Channel cross-talk levels between dB and 20 dB were obtained In this area of application, the flexible and robust TMM and/or TLLM may be used in the design of these devices 12.3.4 Switching Phenomena In high-speed optical communication networks employing single-mode semiconductor lasers like DFB laser diodes, there is increasing attention towards phenomena associated with high-speed switching [26–28] One of the system limitations is known to be the chirping effect induced by semiconductor lasers [29] Due to the strong coupling between gain and refractive index present in the semiconductor, any switching in the form of injection current results in a variation of optical gain and, hence, the refractive index of a semiconductor laser A dynamic shift in operating wavelength and broadening of spectral linewidth have been observed as a result of frequency chirping [29] Due to the dispersive nature of optical fibres, such a spectral broadening affects the pulse shape at the fibre output and consequently degrades the overall system performance To overcome the problem of frequency chirping, a number of methods have been proposed, including the use of an external modulator [30], pre-shaping of electrical signals [30], injection locking [31] and improvements in device structures [5] Using the flexible TMM and/or TLLM as a design tool, different structural designs of laser diode can be tested systematically, and hence improve the performance of laser devices 12.4 REFERENCES Ghafouri-Shiraz, H and Lo, B., Computation of coupling coefficient for a five-layer trapezoidal grating structure, Opt and Laser Technol., 27(1), 45–48, 1994 Ghafouri-Shiraz, H and Lo, B., Structural Impact on the below threshold spectral behavior of three phase shift (3PS) distributed feedback (DFB) lasers, Microwave Opt Tech Lett., 7(6), 296–299, 1994 Ghafouri-Shiraz, H and Lo, B S K., Structural dependence of three-phase-shift distributed feedback semiconductor laser diodes at threshold using the transfer-matrix method (TMM AND/ OR TLLM), Semi Sci Technol., 9(5), 1126–1132, 1994 Lo, B S K and Ghafouri-Shiraz, H., Spectral characteristics of distributed feedback laser diodes with distributed coupling coefficient, IEEE J Lightwave Technol., 13(2), 200–212, 1995 Lo, B S K and Ghafouri-Shiraz, H., A method to determine the above threshold characteristics of distributed feedback semiconductor laser diodes, IEEE J Lightwave Technol., in press Makino, T., Transfer-matrix analysis of the intensity and phase noise of multisection DFB semiconductor lasers, IEEE J Quantum Electron., QE-27(11), 2404–2415, 1991 Vankwikelberge, P., Morthier, G and Baets, R., CLADDISS–A longitudinal multimode model for the analysis of the static, dynamic and stochastic behaviour of diode lasers, IEEE J Quantum Electron., QE-26(10), 1728–1741, 1990 REFERENCES 309 Yoshikuni, Y and Motosugi, G., Multielectrode distributed feedback laser for pure frequency modulation and chirping suppressed amplitude modulation, J Lightwave Technol., LT-5, 516–522, 1987 Kikuchi, K and Okoshi, T., Measurement of FM noise, AM noise and field spectra of 1.3 mm InGaAsP/InP DFB lasers and determination of their linewidth enhancement factor, IEEE J Quantum Electron., QE-21(6), 1814–1818, 1985 10 Kikuchi, K and Tomofuji, H., Analysis of oscillation characteristics of separated-electrode DFB laser diodes, IEEE J Quantum Electron., QE-26(10), 1717–1727, 1985 11 Kikuchi, K and Tomofuji, H., Performance analysis of separated-electrode DFB laser diodes, Electron Lett., 25(2), 162–163, 1989 12 Zory, Jr., P S., Quantum Well Lasers New York: Academic Press, 1993 13 Agrawal, G P and Dutta, N K., Long-Wavelength Semiconductor Lasers Princeton, NJ: Van Nostrand, 1986 14 Yariv, A., Optical Electronics, 4th edition Orlando, FL: Saunders College Publishing, 1991 15 Ghafouri-Shiraz, H and Tsuji, S., Strain effects on refractive index and confinement factor of InxGa(1-x) laser diodes, Microwave Opt Tech Lett., 7(3), 113–119, 1994 16 David, K., Buus, J and Baets, R., Basic analysis of AR-coated partly gain-coupled DFB lasers: The standing wave effect, IEEE J Quantum Electron., 28(2), 427–433, 1992 17 David, K., Morthier, G., Vankvikelberge, P., Baets, R., Wolf, T and Borchert, B., Gain-coupled DFB lasers versus index-coupled and phase-shifted DFB lasers: A comparison based on spatial hole burning corrected yield, IEEE J Quantum Electron., 27(6), 1714–1724, 1991 18 David, K., Buus, J., Morthier, G and Baets, R., Coupling coefficient in gain-coupled DFB lasers: Inherent compromise between strength and loss, Photon Tech Lett., 3(5), 439–441, 1991 19 Luo, Y., Nakano, Y., Tada, K., Inoue, T., Homsomatsu, H and Iwaoka, H., Fabrication and characteristics of gain-coupled distributed feedback semiconductor lasers with a corrugated active layer, IEEE J Quantum Electron., QE-27(6), 1724–1732, 1991 20 Makino, T., Transfer matrix analysis of the spectral linewidth of a partly gain-coupled MQW DFB laser, Optical Quantum Electron., 25, 473–481, 1993 21 Kogelnik, H and Shank, C V., Coupled-wave theory of distributed feedback lasers, J Appl Phys., 43(5), 2327–2335, 1972 22 Luo, Y., Nakano, Y and Tada, K., Purely gain-coupled distributed feedback semiconductor lasers, Appl Phys Lett., 56(17), 1620–1622, 1990 23 Lee, T P and Zah, C N., Wavelength-tunable and single frequency semiconductor lasers for photonic communications networks, IEEE Communications Magazine, 73, 42–52, 73, 1989 24 Van Heijnngen, P., Muys, W., Van der Platts, J and Willems, F., Crosstalk in a fibre access network demonstrator carrying television and interactive digital services, Electron & Communication Eng J., 6, 49–55, 1994 25 Weber, J P., Stoltz, B., Dasler, M and Koek, B., Four channel tunable optical notch filter using InGaAsP/InP reflection gratings, IEEE Photon Techol Lett 6(1), 77–82, 1994 26 Lidoyne, O., Gallion, P., Chabran, C and Debarge, G., Locking range, phase noise and power spectrum of an injection-locked semiconductor laser, IEE Proc Pt J., 137, 147–153, 1990 27 Cartledge, J C., Improved transmission performance resulting from the reduced chirp of a semiconductor laser coupled to an external high-Q resonator, J Lightwave Technol., 8, 716–721, 1990 28 Mohrdiek, S., Burkhard, H and Walter, H., Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection, J Lightwave Technol., 12, 418–424, 1994 29 Linke, R A., Modulation induced transient chirping in single frequency lasers, IEEE J Quantum Electron., QE-21, 593–597, 1985 30 Petermann, K., Laser Diode Modulation and Noise Tokyo, Japan: KTK Scientific and Kluwer Academic Publishers, 1988 31 Hui, R., D’Ottavi, D., Mecozzi, A and Spano, P., Injection locking in distributed feedback semiconductor lasers, IEEE J Quantum Electron., QE-27, 344–351, 1931 Index above-threshold analysis DFB LDs 171–94 mathematical grid 156 above-threshold characteristics 3PS DFB LDs 161 DFB LDs 149–94 numerical processing 153–7 QWS DFB LDs 158–61 above-threshold lasing mode, TMM approach 149–53 above-threshold model, numerical results 157–68 above-threshold spontaneous emission spectrum 182–5 absorption of radiation 32–3 active tunability DFB LD amplifier filters 268–70 adjustable-length open-circuit stub 217 AlGaAs 5, 43 AM/FM noise spectrum measurement 21 amplification rate of optical intensity 210 amplified spontaneous emission spectrum formulation 111–20 amplitude coefficients 104, 259 amplitude gain 3PS DFB laser structure 177 and PSP 127 DCC ỵ QWS DFB laser structure 179 QWS DFB laser structure 176 versus normalised detuning parameter 262, 265, 281 amplitude gain coefficient 52 amplitude mirror loss 42 amplitude reflection coefficients 81 amplitude-shift keying (ASK) 6, 25 amplitude threshold gain 86, 87, 93, 94, 137 asymmetric facet reflectivities 88 atomic transitions, dispersive properties of 36–7 attenuators 221 backward coupling coefficient 56 backward transfer matrix 109 bandnumber 223 baseband transformation technique 221–3 below-threshold characteristics 266–8 below-threshold spontaneous emission power 115–17 numerical results 117–20 Bernard–Duraffourg condition 40 bit error rate (BER) 6, 8, 219 Bragg conditions 53, 55 Bragg diffraction 61, 151, 231 second-order 73–5 Bragg frequency 54, 279, 287 Bragg grating sections 17 Bragg propagation constant 53–5, 80, 103, 256, 287 Bragg reflector 280, 281 Bragg resonance 53 Bragg wavelength 54, 86, 87, 94, 95, 136, 142, 151, 231, 267, 268, 281, 286, 300 buried crescent (BC) 45 buried heterostructure (BH) 45, 208 carrier concentration change in 218 longitudinal distribution 159 carrier density distribution 3PS DFB LD 247 longitudinal 162, 164, 167 carrier density model 208–9 carrier density rate equation 209, 240–1 carrier-induced frequency chirp 216–18 carrier–photon resonance 208 Cauchy–Riemann condition 82–4, 257, 261 channelled substrate planar (CSP) 45 characteristic impedance 197–9 circuit modelling techniques 195–229 cleaved-coupled-cavity (CCC) lasers 206 coherent optical communication system 5–7 schematic diagram Distributed Feedback Laser Diodes and Optical Tunable Filters H Ghafouri–Shiraz # 2003 John Wiley & Sons, Ltd ISBN: 0-470-85618-1 312 INDEX complex field reflectivities 92 complex propagation constant 288 complex transcendental equations 82–4 solutions 260–2 computational efficiency baseband transformation 221–3 connection matrix 199–206, 239–40 for stubs within a section 239–40 continuous-pitch-modulated (CPM) DFB laser 136 continuous radiation regime 11 continuous wave (CW) linewidth 219 continuous wave (CW) operation 44 corrugated DFB LD 259 corrugated section, transfer matrix 151 corrugation phase 87–9 corrugation position, effects of change 138 corrugation shape 62–4 counter-running waves 90–1 coupled wave equations 51–9, 79–99, 103, 104, 253, 287 solution 255–62, 259–60 solutions 80–2 coupled wave theory 31–78 coupling coefficient 79, 127, 131, 133, 137, 139, 140, 257 effect of corrugation shape 62–4 structural definition 60–2 trapezoidal corrugation 69–75 see also DCC coupling ratio 139 effects on threshold characteristics 137 DBR lasers 16, 17, 206 DBR LD amplifier filter 279–81 DCC DFB laser structure, optimisation of 13841 DCC ỵ 3PS DFB laser structure, threshold analysis 1415 DCC ỵ 3PS DFB LDs 142, 1658 distributed coupling coefcient 1658 DCC ỵ QWS DFB laser structure amplitude gain 179 detuning coefficient 180 lasing characteristics 179 spontateous emission spectra 184 DCC ỵ QWS DFB LDs 1645 distributed coupling coefficient 164–5 DCC DFB laser 124 DCC DFB LDs, threshold analysis 136–41 degenerate homojunction 39 dense wavelength division multiplexing (DWDM) 253 density of state function 50 detuning coefficient 3PS DFB laser structure 178 and PSP 127 DCC ỵ QWS DFB laser structure 180 DFB LD 87 mirrorless index-coupled DFB LD 86 QWS DFB laser structure 176 detuning parameter 289 DFB laser 16 DFB laser diode 231–3 above-threshold analysis 171–94 above-threshold characteristics 149–94 amplifier filters, structural impacts 270–4 characteristics analysis 231–52 gain-coupled or loss-coupled 58–9 index-coupled 56–7 mixed-coupled 57 model with phase shift 234–6 optimisation 123–47 TLLM 231–52 DFB laser diode amplifiers 285 DFB lases 208 DFB semiconductor laser diodes 31–78 DFB semiconductor lasers 21, 232 diagonal transfer matrix 268 differential phase-shift keying (DPSK) digital modulation methods discrete Fourier transform (DFT) 223 dispersion equation 81 dispersion-flattened fibre dispersion relationship 257 dispersion-shifted fibre dispersive properties of atomic transitions 36–7 distributed Bragg reflector (DBR), semiconductor optical filters 253–84 distributed element model 196 double heterostructure 44 dual-channel planar buried heterostructure (DCPBH) 45 dynamic single-mode (DSM) operation 232 effective index method (EIM) 14 effective linewidth enhancement factor 21, 188 effective refractive index 210 at zero carrier injection 152 eigenvalue equation 82, 91, 97, 257 Einstein coefficient of absorption 33 Einstein coefficient of stimulated emission 34 INDEX Einstein coefficients 48–9 Einstein relations 33–6, 48 emission of radiation 32–3 erbium-doped fibre amplifiers (EDFA) external cavity (EC) mode-locked lasers 206 Fabry–Perot cavity 15, 280 Fabry–Perot etalon 31–2, 254 principle of 41–3 Fabry–Perot laser 23, 195, 206 fast Fourier transform (FFT) 208, 223, 225–6 Fermi–Dirac distribution function 40 fibre grating lasers 206 field-effect transistors (FETs) 196 field-intensity distribution 132 filter transmission spectra (FTS) 295–6 filtering technologies, comparison of 254 finite facet reflectivities 109–10 fixed-length stub 216, 218 free carrier plasma effect 269 frequency-division multiplexing (FDM) 4, frequency-domain models 233 frequency response 3PS DFB LD 244 QWS DFB LD 243 frequency-shift keying (FSK) 6, 25 full width at half maximum (FWHM) 17–18, 225, 255 GaAs 62, 269 gain filter, block diagram 211 gain margin 17, 84–5, 95, 131, 134, 135, 137, 139, 140, 143, 144, 300 numerical results 174–81 structural impacts on 128–30 variation of 180 gain profiles 267 gain spectrum 267 improvement 215 Gaussian noise statistics 221 grating-embedded semiconductor wavelength tunable filters 253 Green’s function method 112–15, 171 group refractive index 42 guided mode 11, 12 Henry’s linewidth enhancement factor 218 heterodyne receiver with coherent postdetection processing (HE/CP) 313 with incoherent postdetection processing (HE/IP) heterojunction double 44 single 44 heterojunction bipolar transistors (HBTs) 196 high-speed optical coherent communication, system requirements 7–26 homojunction 43 incident voltage pulses 204 index-coupled DFB LD 257, 258, 262, 266 InGaAsP 3, 62 intensity modulation with direct detection (IM/DD) scheme internal field distribution 132, 146 structural impacts on uniformity 130–4 inter-symbolic interference (ISI) intrinsic linewidth enhancement factor 20, 188 Kirchhoff’s law 196 Kramer–Kroenig relationship 48, 96 Kronecker delta function 114 laser amplification 210–16 laser diode amplifiers 206 as tunable filters 255 lasers, basic principle 32–7 lasing characteristics 88 3PS DFB laser structure 177 DCC ỵ QWS DFB laser structure 179 QWS DFB laser structure 175 lasing wavelength 93, 149 variation of 181 lateral carrier confinement 44–5 liquid phase epitaxy (LPE) 43 lithium niobate 269 longitudinal correction factor 24 longitudinal distribution 153, 244–7 carrier concentration 159 carrier density 162, 164, 167, 245 normalised intensity 160, 163, 166 photon concentration 159 photon density 162, 165 refractive index 160, 163, 166, 168 longitudinal intensity distribution 3PS DFB LDs 246 QWS DFB LDs 246 Lorentzian line shape 213 lossless transmission lines 219 314 INDEX lumped element model 196 lumped reactive elements 198 Mach–Zehnder integrated optic interferometer tunable filter 254 material parameters 157 matrix methods 102–10 types 103 maximum laser linewidth 25 Maxwell’s equations 8, 9, 37, 67, 196, 197, 219, 287 metal–organic chemical vapour deposition (MOCVD) 58 microwave circuit models for semiconductor lasers 196 Millman’s theorem 206 mode discrimination 84–5 momentum matrix 50, 51 moving average filter 223–4 multi-dielectric layers 52 multi-electrode DFB LD amplifier filter 269 multi-electrode DFB optical filter, transmission spectrum 270, 271 multi-mode oscillation 32 multiple-phase-shift 96, 101 multiple-phase-shift DFB LD 264 multiple-phase-shift DFB LD-based wavelength tunable optical filter 298–301 multi-section DFB LD amplifier filter 274–9 net amplitude gain coefficient 37 net gain difference 17 Newton–Raphson approximation 82–4, 260–2 Newton–Raphson iteration 82, 85 Newton–Raphson method 97, 154 nodal current 205 nodal voltage 204, 206 nominal threshold current density 48 normalised impedances 199–201 normalised intensity distribution 3PS DFB LDs 248 longitudinal 160, 163, 166 numerical processing, above-threshold characteristics 153–7 Nyquist’s sampling theorem 221 one-dimensional corrugated DFB LD 259 one-dimensional TLM 196 optical communication systems historical progress 1–4 overview 1–30 optical confinement factor 45, 210 optical devices optical fibres communication systems 4–7 components optical field 233 optical field amplitude 210 optical filtering 253 optical output power 149, 172 optical time-division-multiplexed (OTDM) communication systems 219 optical tunable filters see wavelength tunable optical filters optimisation DCC DFB laser structure 138–41 DFB LDs 123–47 optimum design of 3PS DFB laser 128–34 optoelectronic integrated circuit (OEIC) design 196 parasitic capacitance 199 parasitic inductance 199 Petermann’s gain guiding factor 24 phase (adjusting) stubs 216 phase discontinuities effects of 89–95 in DFB LDs 263–6 phase jitters phase noise 17–24 phase position and value effect on 3PS DFB LDs 249 phase shift 118, 119, 133–5, 140, 141, 143 DFB laser 89 DFB laser diode model with 234–6 effect of number of 247–9 effect on lasing characteristics 125–6 1PS DFB laser diode 92 introduction of 106–9 scattering matrix for DFB laser diode with 238 phase-shift-controlled DFB LD 268 phase-shift-controlled DFB LD amplifier filters 269–70, 272–4 characteristics of 273 phase-shift-controlled DFB LD optical filter structures 274–9 phase-shift keying (PSK) 6, 25 phase-shift position (PSP) 79, 263, 278 effect on lasing characteristics 126–8 of 1PS DFB laser diode 94–5 INDEX photon concentration, longitudinal distribution 159 photon density 209, 233 inside cavity 152 longitudinal distribution of 162, 165 photon density distribution of 3PS DFB LDs 246 photon distribution 158 photons 32 planar structure 108 Planck’s equation 32 population inversion concept 33–6 in semiconductor junctions 38–40 population inversion factor 23 post-processing methods 223–6 power matrix model (PMM) 208 power transmissivity 289 versus relative wavelength 277–8, 290–8, 301 pulse code modulation (PCM) 219 Q-factor 213, 215 QWS DFB LD-based wavelength tunable filter 289–94 QWS DFB LDs 79, 92, 123, 164–5, 232, 233, 241, 242 above-threshold characteristics 158–61 advantages and disadvantages 95–7 detuning coefficient 176 frequency response 243 lasing characteristics 175 longitudinal carrier density distribution 245 longitudinal intensity distribution 246 spontaneous emission spectra 183 transient longitudinal carrier density 244 transient response 242 see also DCC ỵ QWS DFB LDs radiative recombination coefficient 51 recombination rate 220 reflected voltage pulses 204 refractive index change in 216 distribution of 3PS DFB LDs 247 first-order approximation 151 longitudinal distribution 160, 163, 166, 168 spatially distributed 158 repeater spacing resonance modes 125, 126 ridge waveguide (RW) 45 315 sample and overlay method 225 scattering matrix 103, 199, 199–207, 212 DFB laser diode with phase shift 238 uniform DFB LD 236–8 semiconductor junction diodes semiconductor junctions, population inversion in 38–40 semiconductor laser amplifiers (SLA) semiconductor lasers basic principles 38–51 index-guided 47 material gain 45–8 structural improvements 43–5 separate confinement heterostructure (SCH) 44, 66 side mode suppression ratio (SMSR) 85, 119–20, 183, 271, 276, 278, 290, 291, 293, 295, 296, 298, 300 signal analysis 223–6 silica-based optical fibre single longitudinal mode (SLM) 15–17, 32, 84, 87, 89, 95 single mode along transverse plane 8–15 single-mode fibre (SMF) 6, 85 single-mode stability 96, 172–4 single-phase-shift-controlled double-phase-shift DFB wavelength tunable optical filter 294–8 single-phase-shifted (1PS) DFB LD 90, 263 slab dielectric waveguide smoothing algorithm 225 spatial hole burning effect (SHB) 123, 158 spatially distributed refractive index 158 spectral linewidth 185–91 formula limitations 26 formulation 17–24 measurement 21 numerical results 189–91 requirements 17–26 variation of 189–91 spectral purity requirements 7–17 spontaneous emission coupling factor 220 current source 220 distributed current source model 221 model 219–21 spontaneous emission rate 23, 186 spontaneous emission spectra 3PS DFB LD 184 DCC ỵ QWS DFB LD 184 QWS DFB LD 183 stable averaging method 224–5 316 INDEX steady-state carrier rate equation 152 stop bands 257 structural parameters 157, 161, 164, 167 stub-attenuator model 216 stub filter response 213 synchronised voltage pulses 199 system requirements 24–5 system transmission rate 25 telegraphist equations 197 Thevenin equivalent circuit 201, 203, 205, 211, 212 3PS DFB LDs 96, 97, 117–20, 241–2, 264 above-threshold characteristics 161 amplitude gain 177 carrier density distribution 247 detuning coefficient 178 dynamic characteristics 243 frequency response 244 lasing characteristics 177 longitudinal intensity distribution 246 normalised intensity distribution 248 optimum design 128–34 phase position and value effect 249 photon density distribution 246 refractive index distribution 247 spontaneous emission spectra 184 threshold analysis 124–8 transient longitudinal carrier density 245 transient response 243 see also DCC ỵ 3PS DFB LDs three-port circulator 216 threshold analysis 85, 123–47 3PS DFB laser 1248 DCC ỵ 3PS DFB laser structure 1415 DCC DFB LD 136–41 DFB LDs 262–8 threshold carrier density 48 threshold characteristics coupling ratio effects 137 DFB LDs 145 threshold condition 111 threshold equation 85 threshold gain 23, 276, 289 time-dependent Schroădinger equation 49 time-domain model (TDM) 208 time-domain optical-eld models 233 time-varying photon density 232 TLLM 196, 206–7, 233 basic construction 207–8 components 207 DFB LDs 234, 236–8 characteristics analysis 231–52 parameter values 241 techniques 195–229 TLLM MPS DFB model 241, 242 TLM 103, 196–9 link lines 197–8 stub filter 211, 215 stub lines 197, 198–9, 200 sub-network 201, 203, 205, 206 TMM 103, 123–47, 208, 253 above-threshold analysis of DFB laser structures 171–94 above-threshold characteristics of laser diodes 149–94 above-threshold lasing mode 149–53 laser structures 107 total radiative recombination rate 48–51 transcendental function 82 transfer matrix 153, 276 arbitrary section 150 corrugated section 151 formulation 103–6, 257–60 transfer matrix chain 106 transfer matrix method see TMM transfer matrix modelling 101–22, 208 transient longitudinal carrier density 3PS DFB LDs 245 QWS DFB LDs 244 transient response 3PS DFB LD 243 QWS DFB LD 242 transmission-line laser modelling see TLLM transmission-line matrix see TLM transmission-line modelling 196 transparency carrier concentration 46 transverse carrier confinement 43–4 transverse electric (TE) mode 9, 11–14, 60, 62, 67 transverse electromagnetic (TEM) field 196 transverse field distribution in unperturbed waveguide 66–9 transverse magnetic fiekd (TM) mode 9, 13, 14 trapezoidal corrugation, coupling coefficient 69–75 tunable fibre Fabry–Perot filters 254 tunable Mach–Zehnder (MZ) filters 254 unperturbed waveguide, transverse field distribution 66–9 INDEX variable phase length 218 vector wave equation 51 wave impedance 20 wave propagation, in periodic structures 51 wave propagation constant 52 wavelength division multiplexing (WDM) 4, 6, 253, 285 wavelength selection 254–5 mechanism 253 operation principle 254 wavelength selective amplifiers (AMP) 221 wavelength tunable optical filters 253–309 analytical model 286 power transmission spectra for type A 274 zero facet reflection 85 317 ... Distributed Feedback Laser Diodes and Optical Tunable Filters Distributed Feedback Laser Diodes and Optical Tunable Filters Dr H Ghafouri–Shiraz The University of Birmingham, UK and Nanyang Technological.. .Distributed Feedback Laser Diodes and Optical Tunable Filters Dr H Ghafouri–Shiraz The University of Birmingham, UK and Nanyang Technological University, Singapore Distributed Feedback Laser. .. Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons