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CHAPTER1 Baslc Theorems and Postulates of Quantum Mechanics1

1.0 Introduction1

1.1 The Schr?dinger Wave Equation1

1.2 The Time-Independent Schrōdinger Wave Equation7

CHAPTER2 Soms Solutions of the Time-lndependent Schrōdinger E?u?tion18

2.0 Introduction18

2.1 Parlty18

2.2 The Harmonic Oscillator19

2.3 The Schrǒdinger Equation in Spherically Symmetric Potential Fields27

2.4 The Angular Momentum Operators and Their Eigenfunctions30

CHAPTER3 Matrix Formulation of Quantum Mechanics34

3.0 Introduction34

3.1 Some Basic Matrix Properties34

3.2 Transformation of a Square Matrix35

3.3 Matrix Diagonalization36

3.4 Representations of Operators as Matrices36

3.5 Transformation of Operator Representations38

3.6 Deriving the Eigenfunctions and Eigenvalues of an Operator by the Matrix Method39

3.7 The Heisenberg Equations of Motion41

3.8 Matrix Elements of the Angular Momentum Operators42

3.9 Spin Angular Momenta45

3.10 Addition of Angular Momentum45

3.11 Time-Independent Perturbation Theory47

3.12 Time-Dependent Perturbation Theory-Relation to Line Broadening50

3.13 Density Matrices-Introduction56

3.14 The Density Matrix56

3.15 The Ensemble Average57

3.16 Time Evolution of the Density Matrix58

3.17 The Time Evolution Operator-Feynman Diagrams58

CHAPTER4 Lattice Vibratione and Their Quantization68

4.0 Introduction68

4.1 Motion of Homogeneous Line68

4.2 Wave Motion of a Line of Similar Atoms69

4.3 A Line with Two Different Atoms71

4.4 Lattice Sums74

4.5 Quantization of the Acoustic Branch of Lattice Vibrations76

4.6 Average Thermal Excitation of Lattice Modes80

CHAPTER5 Electromagnetic Fields and Their Quantization83

5.0 Introduction83

5.1 Power Transport,S?orage,and Dissipation in Electromagnetic Fields83

5.2 Propagation of Electromagnetic Waves in Anisotropic Crystals87

5.3 The Index Ellipsoid90

5.4 Propagation in Uniaxial Crystals92

5.5 Normal Mode Expansion of the Electromagnetic Field in a Resonator94

5.6 The Quantization of the Radiation Field96

5.7 Mode Density and Blackbody Radiation99

5.8 The Coherent State100

CHAPTER6 The P?opa?tion of Optical Beams in Homogeneous and L?e Media106

6.0 Introduction106

6.1 The Lens Waveguide106

6.2 The Identical-Lens Waveguide111

6.3 The Propagation of Rays Between Mirrors111

6.4 Rays in Lenslike Media112

6.5 The Wave Equ?tion in Quadratic Index Media115

6.6 The Gaussian Beam in a Homogeneous Medium116

6.7 The Fundamental Gaussian Beam in a Lenslike Medium-The ABCD Law120

6.8 A Gaussian Beam in a Lens Waveguide123

6.9 High-Order Gaussian Beam Modes in a Homogeneous Medium124

6.10 High-Order Gaussian Beam Modes in Quadratic Index Media125

6.11 Propagation in Media with a Quadratic Gain Profile127

6.12 Elliptic Gaussian Beams129

CHAPTER7 Optical Resonators136

7.0 Introduction136

7.1 Spherical Mirror Resonators136

7.2 Mode Stability (Confinement)Criteria and the Self-Consistent Resonator Solutions141

7.3 The Resonance Frequencies145

7.4 Losses in Optical Resonators147

7.5 Unstable Optical Resonators149

CHAPTER8 Interaction of Radiation and Atomic Systems155

8.0 Introduction155

8.1 Density Matrix Derivation of the Atomic Susceptibility155

8.2 The Significance of X(v)162

8.3 Spontaneous and Induced Transitions164

8.4 The Gain Coefficient169

8.5 The Einstein Treatment of Induced and Spontaneous Transitions171

8.6 Homogeneous and Inhomogeneous Broadening173

8.7 Gain Saturation in Systems with Homogencous and Inhomogeneous Broadening176

CHAPTER9 L?er O?cillation183

9.0 Introduction183

9.1 The Laser Oscillation Condition183

9.2 Laser Oscillation--General Treatment189

9.3 Power Output from Lasers191

CHAPTER10 So? Specific Laser Systems202

10.0 Introduction202

10.1 Pumping and Laser Efficiency202

10.2 The Ruby Laser202

10.3 The Nd3+:YAG Laser208

10.4 The Neodymium-Glass Laser211

10.5 The He-Ne Laser214

10.6 The Carbon Dioxide Laser216

10.7 Organic-Dye Lasers224

CHAPTER11 Semiconductor Diode Lasers232

11.0 Introduction232

11.1 Some Semiconductor Background232

11.2 Optically Induced Band-to-Band Transitions in Semiconductors236

11.3 Diode Lasers243

11.4 GaInAsP Lasers251

11.5 Some Real Lasers251

11.6 Direct-Current Modulation of Semiconductor Lasers255

CHAPTER12 Quantu? Well Lasers264

12.0 Introduction264

12.1 The Quantum Mechanics264

12.2 Gain in Quantum Well Lasers269

12.3 Some Numerical Considerations271

CHAPTER13 The Free-Electron Laser277

13.0 Introduction277

13.1 The Kinematics of Free-Electron-Photon Interaction277

13.2 Theory of Optical Gain in Free-Electron Lasers283

13.3 The Pondermotive Potential289

CHAPTER14 The Modulation of Optical Radiation298

14.0 Introduction298

14.1 The Electrooptic Effect298

14.2 Electrooptic Retardation307

14.3 Electrooptic Amplitude Modulation310

14.4 Phase Modulation of Light313

14.5 Transverse Electrooptic Modulators315

14.6 High-Frequency Modulation Considerations318

14.7 Eiectrooptic Beam Deflection323

14.8 The Photoelastic Effect325

14.9 Bragg Diffraction of Light by Acoustic Waves327

14.10 Deflection of Light by Sound335

14.11 Bragg Scattering in Naturally Birefringent Crystals337

CHAPTER15 Coherent Interactions of a Radiation Fieid and An Atomic Sy?tem342

15.0 Introduction342

15.1 Vector Representation of the Interaction of a Radiation Field with a Two-Level Atomic System342

15.2 Superradiance352

15.3 Photon Echoes355

15.4 Self-Induced Transparency357

CHAPTER16 Introduction to Nonlinear Optics-Second-Harmonlc G?n?tion378

16.0 Introduction378

16.1 The Nonlinear Optical Susceptibility Tensor379

16.2 The Nonlinear Field Hamiltonian383

16.3 On the Physical Origins of the Nonllnear Optical Coefficlents384

16.4 The Electrmagnetic Formulation of the Nonlinear Interaction389

16.5 Optical Second-Harmonic Generation392

16.6 Second-Harmonic Generation with a Depleted Input398

16.7 Second-Harmonic Generation with Gaussian Beams400

16.8 Internal Second-Harmonic Generation402

CHAPTER17P Parametric Amplification,Oscillation,and Fluorescence407

17.0 Introduction and Lumped Circuit Analog407

17.1 The Basic Equations of Parametric Amplification409

17.2 Parametric Oscillation411

17.3 Power Output and Pump Saturation in Parametric Oscillators418

17.4 Frequency Turning in Parametric Oscillation419

17.5 Quantum Mechanical Treatment of Parametric Interactions421

17.6 Frequency Up-Conversion425

17.7 Spontaneous Parametric Fluoresceoce430

17.8 Backward Parametric Amplification and Oscillation435

17.9 Squeezed States of the Electromagnetic Field437

CHAPTER18 Third-Order Optical Nonlinearities--Stimulated Raman and Brillouin Scattering453

18.0 Introduction453

18.1 The Nonlinear Constants453

18.2 molecular Raman Scattering457

18.3 Stimulated Molecular Raman Scattering465

18.4 Electromagnetic Treatment of Stimulated Raman Scattering469

18.5 Anti-Stokes Scattering473

18.6 Stimulated Brillouin Scattering475

18.7 A Classical Treatment of Brillouin Scattering475

18.8 Self-Focusing of Optical Beams482

CHAPTER19 P?-Conjugate-Optics and Photorefractive Beam Coupling495

19.0 Introduction495

19.1 Propagation Through a Distorting Medium495

19.2 Image Transmission in Fibers495

19.3 Theory of Phase Conjugation by Four-Wave Mixing498

19.4 Optical Resonators with Phase-Conjugate Reflectors506

19.5 The ABCD Formalism of Phase-Conjugate Optical Resonators507

19.6 Some Practical Applications of Phase Conjugation510

19.7 Optical Phase Conjuation by Stimulated Nonlinear Scattering513

19.8 Beam Coupling and Phase Conjugation by the Photorefractive Effect516

CHAPTER20 Q-Switching and Mode Locking of Lasers534

20.0 Introduction534

20.1 Q-Switching534

20.2 Mode Locking in Inhomogeneously Broadened Laser Systems542

20.3 Mode Locking in Homogeneously Broadened Laser Systems553

20.4 Relaxation Oscillation in Lasers560

20.5 Passive Mode Locking565

CHAPTER21 Noise and Spectra of Laser Amplifiers and O?cillators570

21.0 Introduction570

21.1 Noise in Laser Amplifiers570

21.2 Spontaneous Emission Noise in Laser Oscillators577

21.3 Some Mathematical Background582

21.4 The Laser Equations584

21.5 The Laser Spectra586

21.6 The Laser Spectra Experiments592

21.7 The a Parameter594

21.8 The Measurement of(Δv)laset596

CHAPTER22 Guided Wave Optics-Propagation in Optical Fibers600

22.0 Introduction600

22.1 The Waveguide Modes600

22.2 Mode Characteristics of the Planar Waveguide603

22.3 Goupling Between Guided Modes606

22.4 The Periodic Waveguide--Distributed Feedback Lasers608

22.5 The Coupled-Mode Solutions611

22.6 The Distributed Feedback Laser615

22.7 Electrooptic Modulation and Mode Coupling in Dielectric Waveguides623

22.8 Directional Coupling-Supermodes627

22.9 The Eigenmodes of a Coupled Waveguide System( Supermodes )631

22.10 Propagation in Optical Fibers640

APPENDIX1 The Kramer?-Kronlg Relations651

APPENDIX2 Solid Angle Associated with a Blackbody Mode653

APPENDIX3 The Spontaneous Emission Lifetime for a Vibrational-Rotational Transition in a Linear Molecule655

APPENDIX4 Quantum Mechanical Derivation of Nonlinear Optical Constants658

APPENDIX5 The Interaction of An Electron and An Electromagnetic Field663

APPENDIX6 The Derivation of the Spontaneous Emission Langevin Fluctuation“Power”666

Index669