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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