CHAPTER1 Baslc Theorems and Postulates of Quantum Mechanics 1
1.0 Introduction 1
1.1 The Schr?dinger Wave Equation 1
1.2 The Time-Independent Schrōdinger Wave Equation 7
CHAPTER2 Soms Solutions of the Time-lndependent Schrōdinger E?u?tion 18
2.0 Introduction 18
2.1 Parlty 18
2.2 The Harmonic Oscillator 19
2.3 The Schrǒdinger Equation in Spherically Symmetric Potential Fields 27
2.4 The Angular Momentum Operators and Their Eigenfunctions 30
CHAPTER3 Matrix Formulation of Quantum Mechanics 34
3.0 Introduction 34
3.1 Some Basic Matrix Properties 34
3.2 Transformation of a Square Matrix 35
3.3 Matrix Diagonalization 36
3.4 Representations of Operators as Matrices 36
3.5 Transformation of Operator Representations 38
3.6 Deriving the Eigenfunctions and Eigenvalues of an Operator by the Matrix Method 39
3.7 The Heisenberg Equations of Motion 41
3.8 Matrix Elements of the Angular Momentum Operators 42
3.9 Spin Angular Momenta 45
3.10 Addition of Angular Momentum 45
3.11 Time-Independent Perturbation Theory 47
3.12 Time-Dependent Perturbation Theory-Relation to Line Broadening 50
3.13 Density Matrices-Introduction 56
3.14 The Density Matrix 56
3.15 The Ensemble Average 57
3.16 Time Evolution of the Density Matrix 58
3.17 The Time Evolution Operator-Feynman Diagrams 58
CHAPTER4 Lattice Vibratione and Their Quantization 68
4.0 Introduction 68
4.1 Motion of Homogeneous Line 68
4.2 Wave Motion of a Line of Similar Atoms 69
4.3 A Line with Two Different Atoms 71
4.4 Lattice Sums 74
4.5 Quantization of the Acoustic Branch of Lattice Vibrations 76
4.6 Average Thermal Excitation of Lattice Modes 80
CHAPTER5 Electromagnetic Fields and Their Quantization 83
5.0 Introduction 83
5.1 Power Transport,S?orage,and Dissipation in Electromagnetic Fields 83
5.2 Propagation of Electromagnetic Waves in Anisotropic Crystals 87
5.3 The Index Ellipsoid 90
5.4 Propagation in Uniaxial Crystals 92
5.5 Normal Mode Expansion of the Electromagnetic Field in a Resonator 94
5.6 The Quantization of the Radiation Field 96
5.7 Mode Density and Blackbody Radiation 99
5.8 The Coherent State 100
CHAPTER6 The P?opa?tion of Optical Beams in Homogeneous and L?e Media 106
6.0 Introduction 106
6.1 The Lens Waveguide 106
6.2 The Identical-Lens Waveguide 111
6.3 The Propagation of Rays Between Mirrors 111
6.4 Rays in Lenslike Media 112
6.5 The Wave Equ?tion in Quadratic Index Media 115
6.6 The Gaussian Beam in a Homogeneous Medium 116
6.7 The Fundamental Gaussian Beam in a Lenslike Medium-The ABCD Law 120
6.8 A Gaussian Beam in a Lens Waveguide 123
6.9 High-Order Gaussian Beam Modes in a Homogeneous Medium 124
6.10 High-Order Gaussian Beam Modes in Quadratic Index Media 125
6.11 Propagation in Media with a Quadratic Gain Profile 127
6.12 Elliptic Gaussian Beams 129
CHAPTER7 Optical Resonators 136
7.0 Introduction 136
7.1 Spherical Mirror Resonators 136
7.2 Mode Stability (Confinement)Criteria and the Self-Consistent Resonator Solutions 141
7.3 The Resonance Frequencies 145
7.4 Losses in Optical Resonators 147
7.5 Unstable Optical Resonators 149
CHAPTER8 Interaction of Radiation and Atomic Systems 155
8.0 Introduction 155
8.1 Density Matrix Derivation of the Atomic Susceptibility 155
8.2 The Significance of X(v) 162
8.3 Spontaneous and Induced Transitions 164
8.4 The Gain Coefficient 169
8.5 The Einstein Treatment of Induced and Spontaneous Transitions 171
8.6 Homogeneous and Inhomogeneous Broadening 173
8.7 Gain Saturation in Systems with Homogencous and Inhomogeneous Broadening 176
CHAPTER9 L?er O?cillation 183
9.0 Introduction 183
9.1 The Laser Oscillation Condition 183
9.2 Laser Oscillation--General Treatment 189
9.3 Power Output from Lasers 191
CHAPTER10 So? Specific Laser Systems 202
10.0 Introduction 202
10.1 Pumping and Laser Efficiency 202
10.2 The Ruby Laser 202
10.3 The Nd3+:YAG Laser 208
10.4 The Neodymium-Glass Laser 211
10.5 The He-Ne Laser 214
10.6 The Carbon Dioxide Laser 216
10.7 Organic-Dye Lasers 224
CHAPTER11 Semiconductor Diode Lasers 232
11.0 Introduction 232
11.1 Some Semiconductor Background 232
11.2 Optically Induced Band-to-Band Transitions in Semiconductors 236
11.3 Diode Lasers 243
11.4 GaInAsP Lasers 251
11.5 Some Real Lasers 251
11.6 Direct-Current Modulation of Semiconductor Lasers 255
CHAPTER12 Quantu? Well Lasers 264
12.0 Introduction 264
12.1 The Quantum Mechanics 264
12.2 Gain in Quantum Well Lasers 269
12.3 Some Numerical Considerations 271
CHAPTER13 The Free-Electron Laser 277
13.0 Introduction 277
13.1 The Kinematics of Free-Electron-Photon Interaction 277
13.2 Theory of Optical Gain in Free-Electron Lasers 283
13.3 The Pondermotive Potential 289
CHAPTER14 The Modulation of Optical Radiation 298
14.0 Introduction 298
14.1 The Electrooptic Effect 298
14.2 Electrooptic Retardation 307
14.3 Electrooptic Amplitude Modulation 310
14.4 Phase Modulation of Light 313
14.5 Transverse Electrooptic Modulators 315
14.6 High-Frequency Modulation Considerations 318
14.7 Eiectrooptic Beam Deflection 323
14.8 The Photoelastic Effect 325
14.9 Bragg Diffraction of Light by Acoustic Waves 327
14.10 Deflection of Light by Sound 335
14.11 Bragg Scattering in Naturally Birefringent Crystals 337
CHAPTER15 Coherent Interactions of a Radiation Fieid and An Atomic Sy?tem 342
15.0 Introduction 342
15.1 Vector Representation of the Interaction of a Radiation Field with a Two-Level Atomic System 342
15.2 Superradiance 352
15.3 Photon Echoes 355
15.4 Self-Induced Transparency 357
CHAPTER16 Introduction to Nonlinear Optics-Second-Harmonlc G?n?tion 378
16.0 Introduction 378
16.1 The Nonlinear Optical Susceptibility Tensor 379
16.2 The Nonlinear Field Hamiltonian 383
16.3 On the Physical Origins of the Nonllnear Optical Coefficlents 384
16.4 The Electrmagnetic Formulation of the Nonlinear Interaction 389
16.5 Optical Second-Harmonic Generation 392
16.6 Second-Harmonic Generation with a Depleted Input 398
16.7 Second-Harmonic Generation with Gaussian Beams 400
16.8 Internal Second-Harmonic Generation 402
CHAPTER17P Parametric Amplification,Oscillation,and Fluorescence 407
17.0 Introduction and Lumped Circuit Analog 407
17.1 The Basic Equations of Parametric Amplification 409
17.2 Parametric Oscillation 411
17.3 Power Output and Pump Saturation in Parametric Oscillators 418
17.4 Frequency Turning in Parametric Oscillation 419
17.5 Quantum Mechanical Treatment of Parametric Interactions 421
17.6 Frequency Up-Conversion 425
17.7 Spontaneous Parametric Fluoresceoce 430
17.8 Backward Parametric Amplification and Oscillation 435
17.9 Squeezed States of the Electromagnetic Field 437
CHAPTER18 Third-Order Optical Nonlinearities--Stimulated Raman and Brillouin Scattering 453
18.0 Introduction 453
18.1 The Nonlinear Constants 453
18.2 molecular Raman Scattering 457
18.3 Stimulated Molecular Raman Scattering 465
18.4 Electromagnetic Treatment of Stimulated Raman Scattering 469
18.5 Anti-Stokes Scattering 473
18.6 Stimulated Brillouin Scattering 475
18.7 A Classical Treatment of Brillouin Scattering 475
18.8 Self-Focusing of Optical Beams 482
CHAPTER19 P?-Conjugate-Optics and Photorefractive Beam Coupling 495
19.0 Introduction 495
19.1 Propagation Through a Distorting Medium 495
19.2 Image Transmission in Fibers 495
19.3 Theory of Phase Conjugation by Four-Wave Mixing 498
19.4 Optical Resonators with Phase-Conjugate Reflectors 506
19.5 The ABCD Formalism of Phase-Conjugate Optical Resonators 507
19.6 Some Practical Applications of Phase Conjugation 510
19.7 Optical Phase Conjuation by Stimulated Nonlinear Scattering 513
19.8 Beam Coupling and Phase Conjugation by the Photorefractive Effect 516
CHAPTER20 Q-Switching and Mode Locking of Lasers 534
20.0 Introduction 534
20.1 Q-Switching 534
20.2 Mode Locking in Inhomogeneously Broadened Laser Systems 542
20.3 Mode Locking in Homogeneously Broadened Laser Systems 553
20.4 Relaxation Oscillation in Lasers 560
20.5 Passive Mode Locking 565
CHAPTER21 Noise and Spectra of Laser Amplifiers and O?cillators 570
21.0 Introduction 570
21.1 Noise in Laser Amplifiers 570
21.2 Spontaneous Emission Noise in Laser Oscillators 577
21.3 Some Mathematical Background 582
21.4 The Laser Equations 584
21.5 The Laser Spectra 586
21.6 The Laser Spectra Experiments 592
21.7 The a Parameter 594
21.8 The Measurement of(Δv)laset 596
CHAPTER22 Guided Wave Optics-Propagation in Optical Fibers 600
22.0 Introduction 600
22.1 The Waveguide Modes 600
22.2 Mode Characteristics of the Planar Waveguide 603
22.3 Goupling Between Guided Modes 606
22.4 The Periodic Waveguide--Distributed Feedback Lasers 608
22.5 The Coupled-Mode Solutions 611
22.6 The Distributed Feedback Laser 615
22.7 Electrooptic Modulation and Mode Coupling in Dielectric Waveguides 623
22.8 Directional Coupling-Supermodes 627
22.9 The Eigenmodes of a Coupled Waveguide System( Supermodes ) 631
22.10 Propagation in Optical Fibers 640
APPENDIX1 The Kramer?-Kronlg Relations 651
APPENDIX2 Solid Angle Associated with a Blackbody Mode 653
APPENDIX3 The Spontaneous Emission Lifetime for a Vibrational-Rotational Transition in a Linear Molecule 655
APPENDIX4 Quantum Mechanical Derivation of Nonlinear Optical Constants 658
APPENDIX5 The Interaction of An Electron and An Electromagnetic Field 663
APPENDIX6 The Derivation of the Spontaneous Emission Langevin Fluctuation“Power” 666
Index 669