Shiva Kumar, Department of Electrical and Computer Engineering, McMaster University, Canada

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

Acknowledgments xvii

1 Electromagnetics and Optics 1

1.1 Introduction 1

1.2 Coulomb’s Law and Electric Field Intensity 1

1.3 Ampere’s Law and Magnetic Field Intensity 3

1.4 Faraday’s Law 6

1.4.1 Meaning of Curl 7

1.4.2 Ampere’s Law in Differential Form 9

1.5 Maxwell’s Equations 9

1.5.1 Maxwell’s Equation in a Source-Free Region 10

1.5.2 Electromagnetic Wave 10

1.5.3 Free-Space Propagation 11

1.5.4 Propagation in a Dielectric Medium 12

1.6 1-Dimensional Wave Equation 12

1.6.1 1-Dimensional Plane Wave 15

1.6.2 Complex Notation 16

1.7 Power Flow and Poynting Vector 17

1.8 3-Dimensional Wave Equation 19

1.9 Reflection and Refraction 21

1.9.1 Refraction 22

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

2.1 Introduction 35

2.2 Fiber Structure 35

2.3 Ray Propagation in Fibers 36

2.3.1 Numerical Aperture 37

2.3.2 Multi-Mode and Single-Mode Fibers 39

2.3.3 Dispersion in Multi-Mode Fibers 39

2.3.4 Graded-Index Multi-Mode Fibers 42

2.4 Modes of a Step-Index Optical Fiber* 44

2.4.1 Guided Modes 46

2.4.2 Mode Cutoff 51

2.4.3 Effective Index 52

2.4.4 2-Dimensional Planar Waveguide Analogy 53

2.4.5 Radiation Modes 54

2.4.6 Excitation of Guided Modes 55

2.5 Pulse Propagation in Single-Mode Fibers 57

2.5.1 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

2.7.1 Cutoff Wavelength 68

2.7.2 Fiber Loss 69

2.7.3 Fiber Dispersion 74

2.7.4 Dispersion Slope 76

2.7.5 Polarization Mode Dispersion 78

2.7.6 Spot Size 79

2.8 Dispersion-Compensating Fibers (DCFs) 79

2.9 Additional Examples 81

Exercises 89

Further Reading 91

References 91

3 Lasers 93

3.1 Introduction 93

3.2 Basic Concepts 93

3.3 Conditions for Laser Oscillations 101

3.4 Laser Examples 108

3.4.1 Ruby Laser 108

3.4.2 Semiconductor Lasers 108

3.5 Wave–Particle Duality 108

3.6 Laser Rate Equations 110

3.7 Review of Semiconductor Physics 113

3.7.1 The PN Junctions 118

3.7.2 Spontaneous and Stimulated Emission at the PN Junction 120

3.7.3 Direct and Indirect Band-Gap Semiconductors 120

3.8 Semiconductor Laser Diode 124

3.8.1 Heterojunction Lasers 124

3.8.2 Radiative and Non-Radiative Recombination 126

3.8.3 Laser Rate Equations 126

3.8.4 Steady-State Solutions of Rate Equations 128

3.8.5 Distributed-Feedback Lasers 132

3.9 Additional Examples 133

Exercises 136

Further Reading 138

References 138

4 Optical Modulators and Modulation Schemes 139

4.1 Introduction 139

4.2 Line Coder 139

4.3 Pulse Shaping 139

4.4 Power Spectral Density 141

4.4.1 Polar Signals 142

4.4.2 Unipolar Signals 142

4.5 Digital Modulation Schemes 144

4.5.1 Amplitude-Shift Keying 144

4.5.2 Phase-Shift Keying 144

4.5.3 Frequency-Shift Keying 145

4.5.4 Differential Phase-Shift Keying 146

4.6 Optical Modulators 149

4.6.1 Direct Modulation 149

4.6.2 External Modulators 150

4.7 Optical Realization of Modulation Schemes 158

4.7.1 Amplitude-Shift Keying 158

4.7.2 Phase-Shift Keying 160

4.7.3 Differential Phase-Shift Keying 162

4.7.4 Frequency-Shift Keying 163

4.8 Partial Response Signals∗ 163

4.8.1 Alternate Mark Inversion 169

4.9 Multi-Level Signaling∗ 172

4.9.1 M-ASK 172

4.9.2 M-PSK 174

4.9.3 Quadrature Amplitude Modulation 178

4.10 Additional Examples 182

Exercises 185

Further Reading 186

References 187

5 Optical Receivers 189

5.1 Introduction 189

5.2 Photodetector Performance Characteristics 190

5.2.1 Quantum Efficiency 193

5.2.2 Responsivity or Photoresponse 197

5.2.3 Photodetector Design Rules 199

5.2.4 Dark Current 200

5.2.5 Speed or Response Time 201

5.2.6 Linearity 202

5.3 Common Types of Photodetectors 202

5.3.1 pn Photodiode 203

5.3.2 pin Photodetector (pin-PD) 203

5.3.3 Schottky Barrier Photodetector 204

5.3.4 Metal–Semiconductor–Metal Photodetector 204

5.3.5 Photoconductive Detector 206

5.3.6 Phototransistor 206

5.3.7 Avalanche Photodetectors 207

5.3.8 Advanced Photodetectors∗ 212

5.4 Direct Detection Receivers 219

5.4.1 Optical Receiver ICs 220

5.5 Receiver Noise 224

5.5.1 Shot Noise 224

5.5.2 Thermal Noise 226

5.5.3 Signal-to-Noise Ratio, SNR 227

5.6 Coherent Receivers 227

5.6.1 Single-Branch Coherent Receiver 228

5.6.2 Balanced Coherent Receiver 232

5.6.3 Single-Branch IQ Coherent Receiver 234

5.6.4 Balanced IQ Receiver 237

5.6.5 Polarization Effects 239

Exercises 242

References 244

6 Optical Amplifiers 247

6.1 Introduction 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

6.5.1 Signal–ASE Beat Noise 253

6.5.2 ASE–ASE Beat Noise 256

6.5.3 Total Mean and Variance 256

6.5.4 Polarization Effects 258

6.5.5 Amplifier Noise Figure 260

6.5.6 Optical Signal-to Noise Ratio 262

6.6 Semiconductor Optical Amplifiers 263

6.6.1 Cavity-Type Semiconductor Optical Amplifiers 264

6.6.2 Traveling-Wave Amplifiers 268

6.6.3 AR Coating 270

6.6.4 Gain Saturation 271

6.7 Erbium-Doped Fiber Amplifier 274

6.7.1 Gain Spectrum 274

6.7.2 Rate Equations∗ 275

6.7.3 Amplified Spontaneous Emission 280

6.7.4 Comparison of EDFA and SOA 281

6.8 Raman Amplifiers 282

6.8.1 Governing Equations 283

6.8.2 Noise Figure 287

6.8.3 Rayleigh Back Scattering 287

6.9 Additional Examples 288

Exercises 298

Further Reading 300

References 300

7 Transmission System Design 301

7.1 Introduction 301

7.2 Fiber Loss-Induced Limitations 301

7.2.1 Balanced Coherent Receiver 306

7.3 Dispersion-Induced Limitations 313

7.4 ASE-Induced Limitations 315

7.4.1 Equivalent Noise Figure 317

7.4.2 Impact of Amplifier Spacing 318

7.4.3 Direct Detection Receiver 319

7.4.4 Coherent Receiver 322

7.4.5 Numerical Experiments 326

7.5 Additional Examples 327

Exercises 333

Further Reading 334

References 334

8 Performance Analysis 335

8.1 Introduction 335

8.2 Optimum Binary Receiver for Coherent Systems 335

8.2.1 Realization of the Matched Filter 342

8.2.2 Error Probability with an Arbitrary Receiver Filter 345

8.3 Homodyne Receivers 345

8.3.1 PSK: Homodyne Detection 347

8.3.2 On–Off Keying 349

8.4 Heterodyne Receivers 350

8.4.1 PSK: Synchronous Detection 351

8.4.2 OOK: Synchronous Detection 353

8.4.3 FSK: Synchronous Detection 356

8.4.4 OOK: Asynchronous Receiver 359

8.4.5 FSK: Asynchronous Detection 364

8.4.6 Comparison of Modulation Schemes with Heterodyne Receiver 367

8.5 Direct Detection 368

8.5.1 OOK 368

8.5.2 FSK 371

8.5.3 DPSK 374

8.5.4 Comparison of Modulation Schemes with Direct Detection 379

8.6 Additional Examples 381

Exercises 387

References 388

9 Channel Multiplexing Techniques 389

9.1 Introduction 389

9.2 Polarization-Division Multiplexing 389

9.3 Wavelength-Division Multiplexing 391

9.3.1 WDM Components 394

9.3.2 WDM Experiments 401

9.4 OFDM 402

9.4.1 OFDM Principle 402

9.4.2 Optical OFDM Transmitter 406

9.4.3 Optical OFDM Receiver 407

9.4.4 Optical OFDM Experiments 408

9.5 Time-Division Multiplexing 409

9.5.1 Multiplexing 409

9.5.2 Demultiplexing 410

9.5.3 OTDM Experiments 412

9.6 Additional Examples 413

Exercises 415

References 416

10 Nonlinear Effects in Fibers 419

10.1 Introduction 419

10.2 Origin of Linear and Nonlinear Refractive Indices 419

10.2.1 Absorption and Amplification 423

10.2.2 Nonlinear Susceptibility 424

10.3 Fiber Dispersion 426

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

10.7.1 Cross-Phase Modulation 438

10.7.2 Four-Wave Mixing 448

10.8 Intrachannel Nonlinear Impairments 454

10.8.1 Intrachannel Cross-Phase Modulation 454

10.8.2 Intrachannel Four-Wave Mixing 455

10.8.3 Intra- versus Interchannel Nonlinear Effects 457

10.9 Theory of Intrachannel Nonlinear Effects 457

10.9.1 Variance Calculations 463

10.9.2 Numerical Simulations 466

10.10 Nonlinear Phase Noise 471

10.10.1 Linear Phase Noise 471

10.10.2 Gordon–Mollenauer Phase Noise 474

10.11 Stimulated Raman Scattering 478

10.11.1 Time Domain Description 481

10.12 Additional Examples 483

Exercises 491

Further Reading 493

References 493

11 Digital Signal Processing 497

11.1 Introduction 497

11.2 Coherent Receiver 497

11.3 Laser Phase Noise 498

11.4 IF Estimation and Compensation 501

11.5 Phase Estimation and Compensation 503

11.5.1 Phase Unwrapping 505

11.6 CD Equalization 506

11.6.1 Adaptive Equalizers 510

11.7 Polarization Mode Dispersion Equalization 513

11.8 Digital Back Propagation 516

11.8.1 Multi-Span DBP 521

11.9 Additional Examples 522

Exercises 524

Further Reading 525

References 525

AppendixA 527

Appendix B 533

Index 537

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