Fiber Optic Communications

Shiva Kumar, Department of Electrical and Computer Engineering, McMaster University, Canada M. Jamal Deen, Department of Electrical and Computer Engineering, McMaster University, Canada

“The detailed, worked examples and first-principles derivations of key results are helpful pedagogical features. Students seeking their first exposure to this field who also wish to learn about advanced topics will find their requirements met by this book.”  (Optics and Photonics News, 28 August 2014)

• Preface xv Acknowledgments xvii1 Electromagnetics and Optics 11.1 Introduction 11.2 Coulomb’s Law and Electric Field Intensity 11.3 Ampere’s Law and Magnetic Field Intensity 31.4 Faraday’s Law 61.4.1 Meaning of Curl 71.4.2 Ampere’s Law in Differential Form 91.5 Maxwell’s Equations 91.5.1 Maxwell’s Equation in a Source-Free Region 101.5.2 Electromagnetic Wave 101.5.3 Free-Space Propagation 111.5.4 Propagation in a Dielectric Medium 121.6 1-Dimensional Wave Equation 121.6.1 1-Dimensional Plane Wave 151.6.2 Complex Notation 161.7 Power Flow and Poynting Vector 171.8 3-Dimensional Wave Equation 191.9 Reflection and Refraction 211.9.1 Refraction 221.10 Phase Velocity and Group Velocity 261.11 Polarization of Light 31Exercises 31Further Reading 34References 342 Optical Fiber Transmission 352.1 Introduction 352.2 Fiber Structure 352.3 Ray Propagation in Fibers 362.3.1 Numerical Aperture 372.3.2 Multi-Mode and Single-Mode Fibers 392.3.3 Dispersion in Multi-Mode Fibers 392.3.4 Graded-Index Multi-Mode Fibers 422.4 Modes of a Step-Index Optical Fiber* 442.4.1 Guided Modes 462.4.2 Mode Cutoff 512.4.3 Effective Index 522.4.4 2-Dimensional Planar Waveguide Analogy 532.4.5 Radiation Modes 542.4.6 Excitation of Guided Modes 552.5 Pulse Propagation in Single-Mode Fibers 572.5.1 Power and the dBm Unit 602.6 Comparison between Multi-Mode and Single-Mode Fibers 682.7 Single-Mode Fiber Design Considerations 682.7.1 Cutoff Wavelength 682.7.2 Fiber Loss 692.7.3 Fiber Dispersion 742.7.4 Dispersion Slope 762.7.5 Polarization Mode Dispersion 782.7.6 Spot Size 792.8 Dispersion-Compensating Fibers (DCFs) 792.9 Additional Examples 81Exercises 89Further Reading 91References 913 Lasers 933.1 Introduction 933.2 Basic Concepts 933.3 Conditions for Laser Oscillations 1013.4 Laser Examples 1083.4.1 Ruby Laser 1083.4.2 Semiconductor Lasers 1083.5 Wave–Particle Duality 1083.6 Laser Rate Equations 1103.7 Review of Semiconductor Physics 1133.7.1 The PN Junctions 1183.7.2 Spontaneous and Stimulated Emission at the PN Junction 1203.7.3 Direct and Indirect Band-Gap Semiconductors 1203.8 Semiconductor Laser Diode 1243.8.1 Heterojunction Lasers 1243.8.2 Radiative and Non-Radiative Recombination 1263.8.3 Laser Rate Equations 1263.8.4 Steady-State Solutions of Rate Equations 1283.8.5 Distributed-Feedback Lasers 1323.9 Additional Examples 133Exercises 136Further Reading 138References 1384 Optical Modulators and Modulation Schemes 1394.1 Introduction 1394.2 Line Coder 1394.3 Pulse Shaping 1394.4 Power Spectral Density 1414.4.1 Polar Signals 1424.4.2 Unipolar Signals 1424.5 Digital Modulation Schemes 1444.5.1 Amplitude-Shift Keying 1444.5.2 Phase-Shift Keying 1444.5.3 Frequency-Shift Keying 1454.5.4 Differential Phase-Shift Keying 1464.6 Optical Modulators 1494.6.1 Direct Modulation 1494.6.2 External Modulators 1504.7 Optical Realization of Modulation Schemes 1584.7.1 Amplitude-Shift Keying 1584.7.2 Phase-Shift Keying 1604.7.3 Differential Phase-Shift Keying 1624.7.4 Frequency-Shift Keying 1634.8 Partial Response Signals∗ 1634.8.1 Alternate Mark Inversion 1694.9 Multi-Level Signaling∗ 1724.9.1 M-ASK 1724.9.2 M-PSK 1744.9.3 Quadrature Amplitude Modulation 1784.10 Additional Examples 182Exercises 185Further Reading 186References 1875 Optical Receivers 1895.1 Introduction 1895.2 Photodetector Performance Characteristics 1905.2.1 Quantum Efficiency 1935.2.2 Responsivity or Photoresponse 1975.2.3 Photodetector Design Rules 1995.2.4 Dark Current 2005.2.5 Speed or Response Time 2015.2.6 Linearity 2025.3 Common Types of Photodetectors 2025.3.1 pn Photodiode 2035.3.2 pin Photodetector (pin-PD) 2035.3.3 Schottky Barrier Photodetector 2045.3.4 Metal–Semiconductor–Metal Photodetector 2045.3.5 Photoconductive Detector 2065.3.6 Phototransistor 2065.3.7 Avalanche Photodetectors 2075.3.8 Advanced Photodetectors∗ 2125.4 Direct Detection Receivers 2195.4.1 Optical Receiver ICs 2205.5 Receiver Noise 2245.5.1 Shot Noise 2245.5.2 Thermal Noise 2265.5.3 Signal-to-Noise Ratio, SNR 2275.6 Coherent Receivers 2275.6.1 Single-Branch Coherent Receiver 2285.6.2 Balanced Coherent Receiver 2325.6.3 Single-Branch IQ Coherent Receiver 2345.6.4 Balanced IQ Receiver 2375.6.5 Polarization Effects 239Exercises 242References 2446 Optical Amplifiers 2476.1 Introduction 2476.2 Optical Amplifier Model 2476.3 Amplified Spontaneous Emission in Two-Level Systems 2486.4 Low-Pass Representation of ASE Noise 2496.5 System Impact of ASE 2516.5.1 Signal–ASE Beat Noise 2536.5.2 ASE–ASE Beat Noise 2566.5.3 Total Mean and Variance 2566.5.4 Polarization Effects 2586.5.5 Amplifier Noise Figure 2606.5.6 Optical Signal-to Noise Ratio 2626.6 Semiconductor Optical Amplifiers 2636.6.1 Cavity-Type Semiconductor Optical Amplifiers 2646.6.2 Traveling-Wave Amplifiers 2686.6.3 AR Coating 2706.6.4 Gain Saturation 2716.7 Erbium-Doped Fiber Amplifier 2746.7.1 Gain Spectrum 2746.7.2 Rate Equations∗ 2756.7.3 Amplified Spontaneous Emission 2806.7.4 Comparison of EDFA and SOA 2816.8 Raman Amplifiers 2826.8.1 Governing Equations 2836.8.2 Noise Figure 2876.8.3 Rayleigh Back Scattering 2876.9 Additional Examples 288Exercises 298Further Reading 300References 3007 Transmission System Design 3017.1 Introduction 3017.2 Fiber Loss-Induced Limitations 3017.2.1 Balanced Coherent Receiver 3067.3 Dispersion-Induced Limitations 3137.4 ASE-Induced Limitations 3157.4.1 Equivalent Noise Figure 3177.4.2 Impact of Amplifier Spacing 3187.4.3 Direct Detection Receiver 3197.4.4 Coherent Receiver 3227.4.5 Numerical Experiments 3267.5 Additional Examples 327Exercises 333Further Reading 334References 3348 Performance Analysis 3358.1 Introduction 3358.2 Optimum Binary Receiver for Coherent Systems 3358.2.1 Realization of the Matched Filter 3428.2.2 Error Probability with an Arbitrary Receiver Filter 3458.3 Homodyne Receivers 3458.3.1 PSK: Homodyne Detection 3478.3.2 On–Off Keying 3498.4 Heterodyne Receivers 3508.4.1 PSK: Synchronous Detection 3518.4.2 OOK: Synchronous Detection 3538.4.3 FSK: Synchronous Detection 3568.4.4 OOK: Asynchronous Receiver 3598.4.5 FSK: Asynchronous Detection 3648.4.6 Comparison of Modulation Schemes with Heterodyne Receiver 3678.5 Direct Detection 3688.5.1 OOK 3688.5.2 FSK 3718.5.3 DPSK 3748.5.4 Comparison of Modulation Schemes with Direct Detection 3798.6 Additional Examples 381Exercises 387References 3889 Channel Multiplexing Techniques 3899.1 Introduction 3899.2 Polarization-Division Multiplexing 3899.3 Wavelength-Division Multiplexing 3919.3.1 WDM Components 3949.3.2 WDM Experiments 4019.4 OFDM 4029.4.1 OFDM Principle 4029.4.2 Optical OFDM Transmitter 4069.4.3 Optical OFDM Receiver 4079.4.4 Optical OFDM Experiments 4089.5 Time-Division Multiplexing 4099.5.1 Multiplexing 4099.5.2 Demultiplexing 4109.5.3 OTDM Experiments 4129.6 Additional Examples 413Exercises 415References 41610 Nonlinear Effects in Fibers 41910.1 Introduction 41910.2 Origin of Linear and Nonlinear Refractive Indices 41910.2.1 Absorption and Amplification 42310.2.2 Nonlinear Susceptibility 42410.3 Fiber Dispersion 42610.4 Nonlinear Schrödinger Equation 42810.5 Self-Phase Modulation 43010.6 Combined Effect of Dispersion and SPM 43310.7 Interchannel Nonlinear Effects 43710.7.1 Cross-Phase Modulation 43810.7.2 Four-Wave Mixing 44810.8 Intrachannel Nonlinear Impairments 45410.8.1 Intrachannel Cross-Phase Modulation 45410.8.2 Intrachannel Four-Wave Mixing 45510.8.3 Intra- versus Interchannel Nonlinear Effects 45710.9 Theory of Intrachannel Nonlinear Effects 45710.9.1 Variance Calculations 46310.9.2 Numerical Simulations 46610.10 Nonlinear Phase Noise 47110.10.1 Linear Phase Noise 47110.10.2 Gordon–Mollenauer Phase Noise 47410.11 Stimulated Raman Scattering 47810.11.1 Time Domain Description 48110.12 Additional Examples 483Exercises 491Further Reading 493References 49311 Digital Signal Processing 49711.1 Introduction 49711.2 Coherent Receiver 49711.3 Laser Phase Noise 49811.4 IF Estimation and Compensation 50111.5 Phase Estimation and Compensation 50311.5.1 Phase Unwrapping 50511.6 CD Equalization 50611.6.1 Adaptive Equalizers 51011.7 Polarization Mode Dispersion Equalization 51311.8 Digital Back Propagation 51611.8.1 Multi-Span DBP 52111.9 Additional Examples 522Exercises 524Further Reading 525References 525AppendixA 527Appendix B 533Index 537