Electromagnetic Noise and Quantum Optical Measurements (Advanced Texts in Physics)

Cover......Page 1
Title Page......Page 3
Copyright Page......Page 4
Preface......Page 5
Contents......Page 9
Introduction......Page 17
1.1 Maxwell\'s Field Equations......Page 27
1.2 Poynting\'s Theorem......Page 31
1.3 Energy and Power Relations and Symmetry of the Tensor E......Page 33
1.4 Uniqueness Theorem......Page 38
1.5 The Complex Maxwell\'s Equations......Page 39
1.6 Operations with Complex Vectors......Page 41
1.7 The Complex Poynting Theorem......Page 44
1.8 The Reciprocity Theorem......Page 49
1.9 Summary......Page 50
Problems......Page 51
Solutions......Page 53
2.1 The Fundamental Equations of Homogeneous Isotropic Waveguides......Page 55
2.2 Transverse Electromagnetic Waves......Page 60
2.3 Transverse Magnetic Waves......Page 63
2.4 Transverse Electric Waves......Page 69
2.4.1 Mode Expansions......Page 72
2.5.1 The Energy Theorem......Page 75
2.5.2 Energy Velocity and Group Velocity......Page 76
2.5.3 Energy Relations for Waveguide Modes......Page 77
2.5.4 A Perturbation Example......Page 78
2.6 The Modes of a Closed Cavity......Page 80
2.7 Real Character of Eigenvalues and Orthogonality of Modes......Page 83
2.8 Electromagnetic Field Inside a Closed Cavity with Sources......Page 88
2.9 Analysis of Open Cavity......Page 90
2.10 Open Cavity with Single Input......Page 93
2.10.1 The Resonator and the Energy Theorem......Page 94
2.10.2 Perturbation Theory and the Generic Form of the Impedance Expression......Page 95
2.11 Reciprocal Multiports......Page 99
2.12 Simple Model of Resonator......Page 100
2.13 Coupling Between Two Resonators......Page 104
2.14 Summary......Page 107
Problems......Page 108
Solutions......Page 111
3. Diffraction, Dielectric Waveguides, Optical Fibers, and the Kerr Effect......Page 115
3.1 Free-Space Propagation and Diffraction......Page 116
3.2 Modes in a Cylindrical Piecewise Uniform Dielectric......Page 122
3.3 Approximate Approach......Page 125
3.5 Propagation Along a Dispersive Fiber......Page 129
3.6 Solution of the Dispersion Equation for a Gaussian Pulse......Page 131
3.7 Propagation of a Polarized Wave in an Isotropic Kerr Medium......Page 133
3.7.1 Circular Polarization......Page 135
Problems......Page 136
Solutions......Page 139
4. Shot Noise and Thermal Noise......Page 143
4.1 The Spectrum of Shot Noise......Page 144
4.2 The Probability Distribution of Shot Noise Events......Page 150
4.3 Thermal Noise in Waveguides and Transmission Lines......Page 152
4.4 The Noise of a Lossless Resonator......Page 156
4.5 The Noise of a Lossy Resonator......Page 159
4.6 Langevin Sources in a Waveguide with Loss......Page 160
4.7 Lossy Linear Multiports at Thermal Equilibrium......Page 162
4.8 The Probability Distribution of Photons at Thermal Equilibrium......Page 166
4.9 Gaussian Amplitude Distribution of Thermal Excitations......Page 168
4.10 Summary......Page 170
Problems......Page 171
Solutions......Page 172
5. Linear Noisy Multiports......Page 173
5.1 Available and Exchangeable Power from a Source......Page 175
5.2 The Stationary Values of the Power Delivered by a Noisy Multiport and the Characteristic Noise Matrix......Page 176
5.3 The Characteristic Noise Matrix in the Admittance Representation Applied to a Field Effect Transistor......Page 182
5.4 Transformations of the Characteristic Noise Matrix......Page 184
5.5 Simplified Generic Forms of the Characteristic Noise Matrix.......Page 188
5.6.1 Exchangeable Power......Page 191
5.6.2 Noise Figure......Page 192
5.6.3 Exchangeable Power Gain......Page 193
5.6.4 The Noise Measure and Its Optimum Value......Page 195
5.7 The Noise Measure in Terms of Incident and Reflected Waves......Page 197
5.7.1 The Exchangeable Power Gain......Page 199
5.7.2 Excess Noise Figure......Page 200
5.8 Realization of Optimum Noise Performance......Page 201
5.9 Cascading of Amplifiers......Page 205
5.10 Summary......Page 206
Problems......Page 208
Solutions......Page 209
6. Quantum Theory of Waveguides and Resonators......Page 213
6.1 Quantum Theory of the Harmonic Oscillator......Page 214
6.2 Annihilation and Creation Operators......Page 219
6.3 Coherent States of the Electric Field......Page 221
6.4 Commutator Brackets, Heisenberg\'s Uncertainty Principle and Noise......Page 225
6.5 Quantum Theory of an Open Resonator......Page 227
6.6 Quantization of Excitations on a Single-Mode Waveguide......Page 231
6.7 Quantum Theory of Waveguides with Loss......Page 233
6.8 The Quantum Noise of an Amplifier with a Perfectly Inverted Medium......Page 236
6.9 The Quantum Noise of an Imperfectly Inverted Amplifier Medium......Page 239
6.10 Noise in a Fiber with Loss Compensated by Gain......Page 242
6.11 The Lossy Resonator and the Laser Below Threshold......Page 245
6.12 Summary......Page 253
Problems......Page 254
Solutions......Page 255
7. Classical and Quantum Analysis of Phase-Insensitive Systems......Page 257
7.1 Renormalization of the Creation and Annihilation Operators......Page 258
7.2 Linear Lossless Multiports in the Classical and Quantum Domains......Page 259
7.3 Comparison of the Schrodinger and Heisenberg Formulations of Lossless Linear Multiports......Page 264
7.4 The Schrodinger Formulation and Entangled States......Page 267
7.5 Transformation of Coherent States......Page 270
7.6.1 Coherent State......Page 272
7.6.2 Bose-Einstein Distribution......Page 274
7.7 Two-Dimensional Characteristic Functions and the Wigner Distribution......Page 275
7.8 The Schrodinger Cat State and Its Wigner Distribution......Page 279
7.9 Passive and Active Multiports......Page 283
7.10 Optimum Noise Measure of a Quantum Network......Page 288
7.11 Summary......Page 292
Problems......Page 293
Solutions......Page 294
8. Detection......Page 297
8.1 Classical Description of Shot Noise and Heterodyne Detection......Page 298
8.2 Balanced Detection......Page 301
8.3 Quantum Description of Direct Detection......Page 304
8.4 Quantum Theory of Balanced Heterodyne Detection......Page 306
8.5 Linearized Analysis of Heterodyne Detection......Page 308
8.6 Heterodyne Detection of a Multimodal Signal......Page 311
8.7 Heterodyne Detection with Finite Response Time of Detector......Page 312
8.8 The Noise Penalty of a Simultaneous Measurement of Two Noncommuting Observables......Page 314
8.9 Summary......Page 316
Problems......Page 317
Solutions......Page 318
9.1 Moment Generating Functions......Page 321
9.1.2 Bose-Einstein Distribution......Page 324
9.1.3 Composite Processes......Page 325
9.2 Statistics of Attenuation......Page 327
9.3 Statistics of Optical Preamplification with Perfect Inversion.......Page 330
9.4 Statistics of Optical Preamplification with Incomplete Inversion......Page 336
9.5.1 Narrow-Band Filter, Polarized Signal, and Noise......Page 340
9.5.2 Broadband Filter, Unpolarized Signal......Page 343
9.6 Negentropy and Information......Page 346
9.7 The Noise Figure of Optical Amplifiers......Page 349
9.8 Summary......Page 355
Problems......Page 356
Solutions......Page 358
10. Solitons and Long-Distance Fiber Communications......Page 361
10.1 The Nonlinear Schrodinger Equation......Page 362
10.2 The First-Order Soliton......Page 364
10.3 Properties of Solitons......Page 368
10.4 Perturbation Theory of Solitons......Page 370
10.5 Amplifier Noise and the Gordon-Haus Effect......Page 373
10.6 Control Filters......Page 377
10.7 Erbium-Doped Fiber Amplifiers and the Effect of Lumped Gain......Page 381
10.8 Polarization......Page 383
10.9 Continuum Generation by Soliton Perturbation......Page 386
10.10 Summary......Page 390
Problems......Page 392
Solutions......Page 393
11. Phase-Sensitive Amplification and Squeezing......Page 395
11.1 Classical Analysis of Parametric Amplification......Page 396
11.2 Quantum Analysis of Parametric Amplification......Page 399
11.3 The Nondegenerate Parametric Amplifier as a Model of a Linear Phase-Insensitive Amplifier......Page 402
11.4 Classical Analysis of Degenerate Parametric Amplifier......Page 403
11.5 Quantum Analysis of Degenerate Parametric Amplifier......Page 406
11.6 Squeezed Vacuum and Its Homodyne Detection......Page 409
11.7 Phase Measurement with Squeezed Vacuum......Page 411
11.8 The Laser Resonator Above Threshold......Page 414
11.9 The Fluctuations of the Photon Number......Page 419
11.10 The Schawlow-Townes Linewidth......Page 422
11.11 Squeezed Radiation from an Ideal Laser......Page 424
11.12 Summary......Page 428
Problems......Page 429
Solutions......Page 430
12. Squeezing in Fibers......Page 433
12.1 Quantization of Nonlinear Waveguide......Page 434
12.2 The x Representation of Operators......Page 436
12.3 The Quantized Equation of Motion of the Kerr Effect in the x Representation......Page 438
12.4 Squeezing......Page 440
12.5 Generation of Squeezed Vacuum with a Nonlinear Interferometer......Page 443
12.6 Squeezing Experiment......Page 448
12.7 Guided-Acoustic-Wave Brillouin Scattering......Page 450
12.8 Phase Measurement Below the Shot Noise Level......Page 452
12.9 Generation of Schrodinger Cat State via Kerr Effect......Page 456
Problems......Page 458
Solutions......Page 459
13. Quantum Theory of Solitons and Squeezing......Page 461
13.1 The Hamiltonian and Equations of Motion of a Dispersive Waveguide......Page 462
13.2 The Quantized Nonlinear Schrodinger Equation and Its Linearization......Page 465
13.3 Soliton Perturbations Projected by the Adjoint......Page 469
13.4 Renormalization of the Soliton Operators......Page 473
13.5 Measurement of Operators......Page 477
13.6 Phase Measurement with Soliton-like Pulses......Page 478
13.7 Soliton Squeezing in a Fiber......Page 481
13.8 Summary......Page 485
Problems......Page 487
Solutions......Page 488
14. Quantum Nondemolition Measurements and the \"Collapse\" of the Wave Function......Page 489
14.2 A QND Measurement of Photon Number......Page 491
14.3 \"Which Path\" Experiment......Page 497
14.4 The \"Collapse\" of the Density Matrix......Page 500
14.5 Two Quantum Nondemolition Measurements in Cascade......Page 506
14.6 The Schrodinger Cat Thought Experiment......Page 509
14.7 Summary......Page 513
Problems......Page 514
Solutions......Page 515
Epilogue......Page 519
A.1 Phase Velocity and Group Velocity of a Gaussian Beam......Page 521
A.2.1 The Defining Equation of Hermite Gaussians......Page 522
A.2.2 Orthogonality Property of Hermite Gaussian Modes......Page 523
A.2.3 The Generating Function and Convolutions of Hermite Gaussians......Page 524
A.3 Recursion Relations of Bessel Functions......Page 528
A.4 Brief Review of Statistical Function Theory......Page 529
A.5.1 Normalization of Classical Field Amplitudes......Page 531
A.5.2 Normalization of Quantum Operators......Page 532
A.6 Two Alternative Expressions for the Nyquist Source......Page 533
A.7 Wave Functions and Operators in the n Representation......Page 534
A.8 Heisenberg\'s Uncertainty Principle......Page 539
A.9 The Quantized Open-Resonator Equations......Page 540
A.10 Density Matrix and Characteristic Functions......Page 543
A.10.2 Example 2. Density Matrix of Coherent State......Page 544
A.11 Photon States and Beam Splitters......Page 545
A.12.1 Theorem 1......Page 546
A.12.3 Matrix Form of Theorem 1......Page 547
A.12.4 Matrix Form of Theorem 2......Page 548
A.13 The Wigner Function of Position and Momentum......Page 549
A.14 The Spectrum of Non-Return-to-Zero Messages......Page 551
A. 15 Various Transforms of Hyperbolic Secants......Page 554
A. 16 The Noise Sources Derived from a Lossless Multiport with Suppressed Terminals......Page 557
A. 17 The Noise Sources of an Active System Derived from Suppression of Ports......Page 558
A. 18 The Translation Operator and the Transformation of Coherent States from the 3 Representation to the x Representation......Page 559
A.20 Gaussian Distributions and Their e-1/2 Loci......Page 560
References......Page 565
Index......Page 571