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Introduction 1

1．Maxwell's Equations,Power,and Energy 11

1.1 Maxwell's Field Equations 11

1.2 Poynting's Theorem 15

1.3 Energy and Power Relations and Symmetry of the Tensor？ 17

1.4 Uniqueness Theorem 22

1.5 The Complex Maxwell's Equations 23

1.6 Operations with Complex Vectors 25

1.7 The Complex Poynting Theorem 28

1.8 The Reciprocity Theorem 33

1.9 Summary 34

Problems 35

Solutions 37

2．Waveguides and Resonators 39

2.1 The Fundamental Equations of Homogeneous Isotropic Waveguides 39

2.2 Transverse Electromagnetic Waves 44

2.3 Transverse Magnetic Waves 47

2.4 Transverse Electric Waves 53

2.4.1 Mode Expansions 56

2.5 Energy,Power,and Energy Velocity 59

2.5.1 The Energy Theorem 59

2.5.2 Energy Velocity and Group Velocity 60

2.5.3 Energy Relations for Waveguide Modes 61

2.5.4 A Perturbation Example 62

2.6 The Modes of a Closed Cavity 64

2.7 Real Character of Eigenvalues and Orthogonality of Modes 67

2.8 Electromagnetic Field Inside a Closed Cavity with Sources 72

2.9 Analysis of Open Cavity 74

2.10 Open Cavity with Single Input 77

2.10.1 The Resonator and the Energy Theorem 78

2.10.2 Perturbation Theory and the Generic Form of the Impedance Expression 79

2.11 Reciprocal Multiports 83

2.12 Simple Model of Resonator 84

2.13 Coupling Between Two Resonators 88

2.14 Summary 91

Problems 92

Solutions 95

3．Diffraction,Dielectric Waveguides,Optical Fibers,and the Kerr Effect 99

3.1 Free-Space Propagation and Diffraction 100

3.2 Modes in a Cylindrical Piecewise Uniform Dielectric 106

3.3 Approximate Approach 109

3.4 Perturbation Theory 113

3.5 Propagation Along a Dispersive Fiber 113

3.6 Solution of the Dispersion Equation for a Gaussian Pulse 115

3.7 Propagation of a Polarized Wave in an Isotropic Kerr Medium 117

3.7.1 Circular Polarization 119

3.8 Summary 120

Problems 120

Solutions 123

4．Shot Noise and Thermal Noise 127

4.1 The Spectrum of Shot Noise 128

4.2 The Probability Distribution of Shot Noise Events 134

4.3 Thermal Noise in Waveguides and Transmission Lines 136

4.4 The Noise of a Lossless Resonator 140

4.5 The Noise of a Lossy Resonator 143

4.6 Langevin Sources in a Waveguide with Loss 144

4.7 Lossy Linear Multiports at Thermal Equilibrium 146

4.8 The Probability Distribution of Photons at Thermal Equilibrium 150

4.9 Gaussian Amplitude Distribution of Thermal Excitations 152

4.10 Summary 154

Problems 155

Solutions 156

5．Linear Noisy Multiports 157

5.1 Available and Exchangeable Power from a Source 159

5.2 The Stationary Values of the Power Delivered by a Noisy Multiport and the Characteristic Noise Matrix 160

5.3 The Characteristic Noise Matrix in the Admittance Representation Applied to a Field Effect Transistor 166

5.4 Transformations of the Characteristic Noise Matrix 168

5.5 Simplified Generic Forms of the Characteristic Noise Matrix 172

5.6 Noise Measure of an Amplifier 175

5.6.1 Exchangeable Power 175

5.6.2 Noise Figure 176

5.6.3 Exchangeable Power Gain 177

5.6.4 The Noise Measure and Its Optimum Value 179

5.7 The Noise Measure in Terms of Incident and Relected Waves 181

5.7.1 The Exchangeable Power Gain 183

5.7.2 Excess Noise Figure 184

5.8 Realization of Optimum Noise Performance 185

5.9 Cascading of Amplifiers 189

5.10 Summary 190

Problems 192

Solutions 193

6．Quantum Theory of Waveguides and Resonators 197

6.1 Quantum Theory of the Harmonic Oscillator 198

6.2 Annihilation and Creation Operators 203

6.3 Coherent States of the Electric Field 205

6.4 Commutator Brackets,Heisenberg's Uncertainty Principle and Noise 209

6.5 Quantum Theory of an Open Resonator 211

6.6 Quantization of Excitations on a Single-Mode Waveguide 215

6.7 Quantum Theory of Waveguides with Loss 217

6.8 The Quantum Noise of an Amplifier with a Perfectly Inverted Medium 220

6.9 The Quantum Noise of an Imperfectly Inverted Amplifier Medium 223

6.10 Noise in a Fiber with Loss Compensated by Gain 226

6.11 The Lossy Resonator and the Laser Below Threshold 229

6.12 Summary 237

Problems 238

Solutions 239

7．Classical and Quantum Analysis of Phase-Insensitive Systems 241

7.1 Renormalization of the Creation and Annihilation Operators 242

7.2 Linear Lossless Multiports in the Classical and Quantum Domains 243

7.3 Comparison of the Schr？dinger and Heisenberg Formulations of Lossless Linear Multiports 248

7.4 The Schr？dinger Formulation and Entangled States 251

7.5 Transformation of Coherent States 254

7.6 Characteristic Functions and Probability Distributions 256

7.6.1 Coherent State 256

7.6.2 Bose-Einstein Distribution 258

7.7 Two-Dimensional Characteristic Functions and the Wigner Distribution 259

7.8 The Schr？dinger Cat State and Its Wigner Distribution 263

7.9 Passive and Active Multiports 267

7.10 Optimum Noise Measure of a Quantum Network 272

7.11 Summary 276

Problems 277

Solutions 278

8．Detection 281

8.1 Classical Description of Shot Noise and Heterodyne Detection 282

8.2 Balanced Detection 285

8.3 Quantum Description of Direct Detection 288

8.4 Quantum Theory of Balanced Heterodyne Detection 290

8.5 Linearized Analysis of Heterodyne Detection 292

8.6 Heterodyne Detection of a Multimodal Signal 295

8.7 Heterodyne Detection with Finite Response Time of Detector 296

8.8 The Noise Penalty of a Simultaneous Measurement of Two Noncommuting Observables 298

8.9 Summary 300

Problems 301

Solutions 302

9．Photon Probability Distributions and Bit-Error Rate of a Channel with Optical Preamplification 305

9.1 Moment Generating Functions 305

9.1.1 Poisson Distribution 308

9.1.2 Bose-Einstein Distribution 308

9.1.3 Composite Processes 309

9.2 Statistics of Attenuation 311

9.3 Statistics of Optical Preamplification with Perfect Inversion 314

9.4 Statistics of Optical Preamplification with Incomplete Inversion 320

9.5 Bit-Error Rate with Optical Preamplification 324

9.5.1 Narrow-Band Filter,Polarized Signal,and Noise 324

9.5.2 Broadband Filter,Unpolarized Signal 327

9.6 Negentropy and Information 330

9.7 The Noise Figure of Optical Amplifiers 333

9.8 Summary 339

Problems 340

Solutions 342

10．Solitons and Long-Distance Fiber Communications 345

10.1 The Nonlinear Schr？dinger Equation 346

10.2 The First-Order Soliton 348

10.3 Properties of Solitons 352

10.4 Perturbation Theory of Solitons 354

10.5 Amplifier Noise and the Gordon-Haus Effect 357

10.6 Control Filters 361

10.7 Erbium-Doped Fiber Amplifiers and the Effect of Lumped Gain 365

10.8 Polarization 367

10.9 Continuum Generation by Soliton Perturbation 370

10.10 Summary 374

Problems 376

Solutions 377

11．Phase-Sensitive Amplification and Squeezing 379

11.1 Classical Analysis of Parametric Amplification 380

11.2 Quantum Analysis of Parametric Amplification 383

11.3 The Nondegenerate Parametric Amplifier as a Model of a Linear Phase-Insensitive Amplifier 386

11.4 Classical Analysis of Degenerate Parametric Amplifier 387

11.5 Quantum Analysis of Degenerate Parametric Amplifier 390

11.6 Squeezed Vacuum and Its Homodyne Detection 393

11.7 Phase Measurement with Squeezed Vacuum 395

11.8 The Laser Resonator Above Threshold 398

11.9 The Fluctuations of the Photon Number 403

11.10 The Schawlow-Townes Linewidth 406

11.11 Squeezed Radiation from an Ideal Laser 408

11.12 Summary 412

Problems 413

Solutions 414

12．Squeezing in Fibers 417

12.1 Quantization of Nonlinear Waveguide 418

12.2 The x Representation of Operators 420

12.3 The Quantized Equation of Motion of the Kerr Effect in the x Representation 422

12.4 Squeezing 424

12.5 Generation of Squeezed Vacuum with a Nonlinear Interferometer 427

12.6 Squeezing Experiment 432

12.7 Guided-Acoustic-Wave Brillouin Scattering 434

12.8 Phase Measurement Below the Shot Noise Level 436

12.9 Generation of Schr？dinger Cat State via Kerr Effect 440

12.10 Summary 442

Problems 442

Solutions 443

13．Quantum Theory of Solitons and Squeezing 445

13.1 The Hamiltonian and Equations of Motion of a Dispersive Waveguide 446

13.2 The Quantized Nonlinear Schr？dinger Equation and Its Linearization 449

13.3 Soliton Perturbations Projected by the Adjoint 453

13.4 Renormalization of the Soliton Operators 457

13.5 Measurement of Operators 461

13.6 Phase Measurement with Soliton-like Pulses 462

13.7 Soliton Squeezing in a Fiber 465

13.8 Summary 469

Problems 471

Solutions 472

14．Quantum Nondemolition Measurements and the"Collapse"of the Wave Function 473

14.1 General Properties of a QND Measurement 475

14.2 A QND Measurement of Photon Number 475

14.3 "Which Path"Experiment 481

14.4 The"Collapse"of the Density Matrix 484

14.5 Two Quantum Nondemolition Measurements in Cascade 490

14.6 The Schr？dinger Cat Thought Experiment 493

14.7 Summary 497

Problems 498

Solutions 499

Epilogue 503

Appendices 505

A.1 Phase Velocity and Group Velocity of a Gaussian Beam 505

A.2 The Hermite Gaussians and Their Defining Equation 506

A.2.1 The Defining Equation of Hermite Gaussians 506

A.2.2 Orthogonality Property of Hermite Gaussian Modes 507

A.2.3 The Generating Function and Convolutions of Hermite Gaussians 508

A.3 Recursion Relations of Bessel Functions 512

A.4 Brief Review of Statistical Function Theory 513

A.5 The Different Normalizations of Field Amplitudes and of Annihilation Operators 515

A.5.1 Normalization of Classical Field Amplitudes 515

A.5.2 Normalization of Quantum Operators 516

A.6 Two Alternative Expressions for the Nyquist Source 517

A.7 Wave Functions and Operators in the n Representation 518

A.8 Heisenberg's Uncertainty Principle 523

A.9 The Quantized Open-Resonator Equations 524

A.10 Density Matrix and Characteristic Functions 527

A.10.1 Example 1.Density Matrix of Bose-Einstein State 528

A.10.2 Example 2.Density Matrix of Coherent State 528

A.11 Photon States and Beam Splitters 529

A.12 The Baker-Hausdorff Theorem 530

A.12.1 Theorem 1 530

A.12.2 Theorem 2 531

A.12.3 Matrix Form of Theorem 1 531

A.12.4 Matrix Form of Theorem 2 532

A.13 The Wigner Function of Position and Momentum 533

A.14 The Spectrum of Non-Return-to-Zero Messages 535

A.15 Various Transforms of Hyperbolic Secants 538

A.16 The Noise Sources Derived from a Lossless Multiport with Suppressed Terminals 541

A.17 The Noise Sources of an Active System Derived from Suppression of Ports 542

A.18 The Translation Operator and the Transformation of Coherent States from theβRepresentation to the x Representation 543

A.19 The Heisenberg Equation in the Presence of Dispersion 544

A.20 Gaussian Distributions and Their e-1/2 Loci 544

References 549

Index 555