FIBER OPTIC COMMUNICATIONS FIBER OPTIC COMMUNICATIONS FUNDAMENTALS AND APPLICATIONS Shiva Kumar and M. Jamal Deen Department of Electrical and Computer Engineering, McMaster University, Canada This edition first published 2014 © 2014 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved.
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pages cm Includes bibliographical references and index. Optical fiber communication.36′ 92–dc23 2013043803 A catalogue record for this book is available from the British Library. ISBN: 9780470518670 Set in 10/12pt TimesLTStd by Laserwords Private Limited, Chennai, India 1 2014 MJD To my late parents, Mohamed and Zabeeda Deen SK To my late parents, Saraswathi and Narasinga Rao Contents Preface xv Acknowledgments xvii 1 Electromagnetics and Optics 1 1.2 Coulomb’s Law and Electric Field Intensity 1 1.3 Ampere’s Law and Magnetic Field Intensity 3 1.1 Meaning of Curl 7 1.2 Ampere’s Law in Differential Form 9 1.1 Maxwell’s Equation in a Source-Free Region 10 1.3 Free-Space Propagation 11 1.4 Propagation in a Dielectric Medium 12 1.6 1-Dimensional Wave Equation 12 1.1 1-Dimensional Plane Wave 15 1.7 Power Flow and Poynting Vector 17 1.8 3-Dimensional Wave Equation 19 1.9 Reflection and Refraction 21 1.10 Phase Velocity and Group Velocity 26 1.11 Polarization of Light 31 Exercises 31 Further Reading 34 References 34 2 Optical Fiber Transmission 35 2.3 Ray Propagation in Fibers 36 2.1 Numerical Aperture 37 viii Contents 2.2 Multi-Mode and Single-Mode Fibers 39 2.3 Dispersion in Multi-Mode Fibers 39 2.4 Graded-Index Multi-Mode Fibers 42 2.4 Modes of a Step-Index Optical Fiber* 44 2.4 2-Dimensional Planar Waveguide Analogy 53 2.6 Excitation of Guided Modes 55 2.5 Pulse Propagation in Single-Mode Fibers 57 2.1 Power and the dBm Unit 60 2.6 Comparison between Multi-Mode and Single-Mode Fibers 68 2.7 Single-Mode Fiber Design Considerations 68 2.5 Polarization Mode Dispersion 78 2.8 Dispersion-Compensating Fibers (DCFs) 79 2.9 Additional Examples 81 Exercises 89 Further Reading 91 References 91 3 Lasers 93 3.3 Conditions for Laser Oscillations 101 3.5 Wave–Particle Duality 108 3.6 Laser Rate Equations 110 3.7 Review of Semiconductor Physics 113 3.1 The PN Junctions 118 3.2 Spontaneous and Stimulated Emission at the PN Junction 120 3.3 Direct and Indirect Band-Gap Semiconductors 120 3.8 Semiconductor Laser Diode 124 3.2 Radiative and Non-Radiative Recombination 126 3.3 Laser Rate Equations 126 3.4 Steady-State Solutions of Rate Equations 128 3.5 Distributed-Feedback Lasers 132 * Advanced material which may need additional explanation for undergraduate readers Contents ix 3.9 Additional Examples 133 Exercises 136 Further Reading 138 References 138 4 Optical Modulators and Modulation Schemes 139 4.4 Power Spectral Density 141 4.5 Digital Modulation Schemes 144 4.1 Amplitude-Shift Keying 144 4.2 Phase-Shift Keying 144 4.3 Frequency-Shift Keying 145 4.4 Differential Phase-Shift Keying 146 4.7 Optical Realization of Modulation Schemes 158 4.1 Amplitude-Shift Keying 158 4.2 Phase-Shift Keying 160 4.3 Differential Phase-Shift Keying 162 4.4 Frequency-Shift Keying 163 4.8 Partial Response Signals∗ 163 4.1 Alternate Mark Inversion 169 4.9 Multi-Level Signaling∗ 172 4.3 Quadrature Amplitude Modulation 178 4.10 Additional Examples 182 Exercises 185 Further Reading 186 References 187 5 Optical Receivers 189 5.2 Photodetector Performance Characteristics 190 5.2 Responsivity or Photoresponse 197 5.3 Photodetector Design Rules 199 5.5 Speed or Response Time 201 5.3 Common Types of Photodetectors 202 5.1 pn Photodiode 203 x Contents 5.3 Schottky Barrier Photodetector 204 5.4 Metal–Semiconductor–Metal Photodetector 204 5.4 Direct Detection Receivers 219 5.1 Optical Receiver ICs 220 5.3 Signal-to-Noise Ratio, SNR 227 5.1 Single-Branch Coherent Receiver 228 5.2 Balanced Coherent Receiver 232 5.3 Single-Branch IQ Coherent Receiver 234 5.4 Balanced IQ Receiver 237 5.5 Polarization Effects 239 Exercises 242 References 244 6 Optical Amplifiers 247 6.2 Optical Amplifier Model 247 6.3 Amplified Spontaneous Emission in Two-Level Systems 248 6.4 Low-Pass Representation of ASE Noise 249 6.5 System Impact of ASE 251 6.1 Signal–ASE Beat Noise 253 6.2 ASE–ASE Beat Noise 256 6.3 Total Mean and Variance 256 6.5 Amplifier Noise Figure 260 6.6 Optical Signal-to Noise Ratio 262 6.6 Semiconductor Optical Amplifiers 263 6.1 Cavity-Type Semiconductor Optical Amplifiers 264 6.2 Traveling-Wave Amplifiers 268 6.7 Erbium-Doped Fiber Amplifier 274 6.3 Amplified Spontaneous Emission 280 6.4 Comparison of EDFA and SOA 281 6.1 Governing Equations 283 Contents xi 6.3 Rayleigh Back Scattering 287 6.9 Additional Examples 288 Exercises 298 Further Reading 300 References 300 7 Transmission System Design 301 7.2 Fiber Loss-Induced Limitations 301 7.1 Balanced Coherent Receiver 306 7.3 Dispersion-Induced Limitations 313 7.4 ASE-Induced Limitations 315 7.1 Equivalent Noise Figure 317 7.2 Impact of Amplifier Spacing 318 7.3 Direct Detection Receiver 319 7.5 Additional Examples 327 Exercises 333 Further Reading 334 References 334 8 Performance Analysis 335 8.2 Optimum Binary Receiver for Coherent Systems 335 8.1 Realization of the Matched Filter 342 8.2 Error Probability with an Arbitrary Receiver Filter 345 8.1 PSK: Homodyne Detection 347 8.2 On–Off Keying 349 8.1 PSK: Synchronous Detection 351 8.2 OOK: Synchronous Detection 353 8.3 FSK: Synchronous Detection 356 8.4 OOK: Asynchronous Receiver 359 8.5 FSK: Asynchronous Detection 364 8.6 Comparison of Modulation Schemes with Heterodyne Receiver 367 8.4 Comparison of Modulation Schemes with Direct Detection 379 8.6 Additional Examples 381 Exercises 387 References 388 xii Contents 9 Channel Multiplexing Techniques 389 9.2 Polarization-Division Multiplexing 389 9.3 Wavelength-Division Multiplexing 391 9.2 Optical OFDM Transmitter 406 9.3 Optical OFDM Receiver 407 9.4 Optical OFDM Experiments 408 9.5 Time-Division Multiplexing 409 9.6 Additional Examples 413 Exercises 415 References 416 10 Nonlinear Effects in Fibers 419 10.2 Origin of Linear and Nonlinear Refractive Indices 419 10.1 Absorption and Amplification 423 10.4 Nonlinear Schrödinger Equation 428 10.5 Self-Phase Modulation 430 10.6 Combined Effect of Dispersion and SPM 433 10.7 Interchannel Nonlinear Effects 437 10.1 Cross-Phase Modulation 438 10.2 Four-Wave Mixing 448 10.8 Intrachannel Nonlinear Impairments 454 10.1 Intrachannel Cross-Phase Modulation 454 10.2 Intrachannel Four-Wave Mixing 455 10.3 Intra- versus Interchannel Nonlinear Effects 457 10.9 Theory of Intrachannel Nonlinear Effects 457 10.10 Nonlinear Phase Noise 471 10.1 Linear Phase Noise 471 10.2 Gordon–Mollenauer Phase Noise 474 10.11 Stimulated Raman Scattering 478 10.1 Time Domain Description 481 10.12 Additional Examples 483 Exercises 491 Further Reading 493 References 493 Contents xiii 11 Digital Signal Processing 497 11.3 Laser Phase Noise 498 11.4 IF Estimation and Compensation 501 11.5 Phase Estimation and Compensation 503 11.7 Polarization Mode Dispersion Equalization 513 11.8 Digital Back Propagation 516 11.1 Multi-Span DBP 521 11.9 Additional Examples 522 Exercises 524 Further Reading 525 References 525 Appendix A 527 Appendix B 533 Index 537 Preface The field of fiber-optic communications has advanced significantly over the last three decades. In the early days, most of the fiber’s usable bandwidth was significantly under-utilized as the transmission capacity was quite low and hence, there was no need to apply techniques developed in non-optical communication sys- tems to improve the spectral efficiency.
However, with the recent revival of coherent detection, high spectral efficiency can be realized using advanced modulation formats. This book grew out of our notes for undergraduate and graduate courses on fiber-optic communications. Chapters 1 to 6 discuss, in depth, the physics and engineering applications of photonic and optoelectronic devices used in fiber-optic communication systems. Chapters 7 to 11 focus on transmission system design, various propagation impairments, and how to mitigate them.
Chapters 1 to 7 are intended for undergraduate students at the senior level or for an introductory gradu- ate course. The sections with asterisks may be omitted for undergraduate teaching or they may be covered qualitatively without the rigorous analysis provided. Chapters 8 to 11 are intended for an advanced course on fiber-optic systems at the graduate level and also for researchers working in the field of fiber-optic com- munications. Throughout the book, most of the important results are obtained by first principles rather than citing research articles.
Each chapter has many worked problems to help students understand and reinforce the concepts. Optical communication is an interdisciplinary field that combines photonic/optoelectronic devices and communication systems. The study of photonic devices requires a background in electromagnetics. There- fore, Chapter 1 is devoted to a review of electromagnetics and optics.
The rigorous analysis of fiber modes in Chapter 2 would not be possible without understanding the Maxwell equations reviewed in Chapter 1. Chapter 2 introduces students to optical fibers. The initial sections deal with the qualitative understanding of light propagation in fibers using ray optics theory, and in later sections an analysis of fiber modes using wave theory is carried out. The fiber is modeled as a linear system with a transfer function, which enables students to interpret fiber chromatic dispersion and polarization mode dispersion as some kind of filter.
Two main components of an optical transmitter are the optical source, such as a laser, and the optical mod- ulator, and these components are discussed in Chapters 3 and 4, respectively. After introducing the basic concepts, such as spontaneous and stimulated emission, various types of semiconductor laser structures are covered in Chapter 3. Chapter 4 deals with advanced modulation formats and different types of optical mod- ulators that convert electrical data into optical data. Chapter 5 deals with the reverse process – conversion of optical data into electrical data.
The basic principles of photodetection are discussed.