Description
Book SynopsisThis book is based on tried and tested courses taught by the author, George Stegeman, who is one of the experimental pioneers in nonlinear optics. The book starts with second order phenomena, goes on to explain the derivation of nonlinear susceptibilities, and finishes with a thorough discussion of third order nonlinear effects.
Table of ContentsPreface xi
1. Introduction 1
1.1 What is Nonlinear Optics and What is it Good for? 1
1.2 Notation 2
1.3 Classical Nonlinear Optics Expansion 4
1.4 Simple Model: Electron on a Spring and its Application to Linear Optics 6
1.5 Local Field Correction 10
Suggested Further Reading 13
Part A: Second-order Phenomena 15
2. Second-Order Susceptibility and Nonlinear Coupled Wave Equations 17
2.1 Anharmonic Oscillator Derivation of Second-Order Susceptibilities 18
2.2 Input Eigenmodes, Permutation Symmetry, and Properties of χ (2) 23
2.3 Slowly Varying Envelope Approximation 25
2.4 Coupled Wave Equations 26
2.5 Manley–Rowe Relations and Energy Conservation 31
Suggested Further Reading 38
3. Optimization and Limitations of Second-Order Parametric Processes 39
3.1 Wave-Vector Matching 39
3.2 Optimizing d(2)eff 53
3.3 Numerical Examples 59
References 67
Suggested Further Reading 67
4. Solutions for Plane-Wave Parametric Conversion Processes 69
4.1 Solutions of the Type 1 SHG Coupled Wave Equations 69
4.2 Solutions of the Three-Wave Coupled Equations 77
4.3 Characteristic Lengths 80
4.4 Nonlinear Modes 81
References 84
Suggested Further Reading 85
5. Second Harmonic Generation with Finite Beams and Applications 86
5.1 SHG with Gaussian Beams 86
5.2 Unique and Performance-Enhanced Applications of Periodically Poled LiNbO3 (PPLN) 98
References 107
Suggested Further Reading 107
6. Three-Wave Mixing, Optical Amplifiers, and Generators 108
6.1 Three-Wave Mixing Processes 108
6.2 Manley–Rowe Relations 110
6.3 Sum Frequency Generation 111
6.4 Optical Parametric Amplifiers 113
6.5 Optical Parametric Oscillator 119
6.6 Mid-Infrared Quasi-Phase Matching Parametric Devices 128
References 139
Selected Further Reading 140
7. χ (2) Materials and Their Characterization 141
7.1 Survey of Materials 141
7.2 Oxide-Based Dielectric Crystals 143
7.3 Organic Materials 144
7.4 Measurement Techniques 149
Appendix 7.1: Quantum Mechanical Model for Charge Transfer Molecular Nonlinearities 153
References 157
Suggested Further Reading 158
Part B: Nonlinear Susceptibilities 159
8. Second- and Third-Order Susceptibilities: Quantum Mechanical Formulation 161
8.1 Perturbation Theory of Field Interaction with Molecules 162
8.2 Optical Susceptibilities 169
Appendix 8.1: χ (3)ijk‘
Symmetry Properties for Different Crystal Classes 192
Reference 196
Suggested Further Reading 196
9. Molecular Nonlinear Optics 197
9.1 Two-Level Model 198
9.2 Symmetric Molecules 210
9.3 Density Matrix Formalism 215
Appendix 9.1: Two-Level Model for Asymmetric Molecules—Exact Solution 216
Appendix 9.2: Three-Level Model for Symmetric Molecules—Exact Solution 218
References 222
Suggested Further Reading 223
Part C: Third-order Phenomena 225
10. Kerr Nonlinear Absorption and Refraction 227
10.1 Nonlinear Absorption 228
10.2 Nonlinear Refraction 238
10.3 Useful NLR Formulas and Examples (Isotropic Media) 243
Suggested Further Reading 250
11. Condensed Matter Third-Order Nonlinearities due to Electronic Transitions 251
11.1 Device-Based Nonlinear Material Figures of Merit 252
11.2 Local Versus Nonlocal Nonlinearities in Space and Time 253
11.3 Survey of Nonlinear Refraction and Absorption Measurements 255
11.4 Electronic Nonlinearities Involving Discrete States 256
11.5 Overview of Semiconductor Nonlinearities 266
11.6 Glass Nonlinearities 281
Appendix 11.1: Expressions for the Kerr, Raman, and Quadratic Stark Effects 284
References 286
Suggested Further Reading 289
12. Miscellaneous Third-Order Nonlinearities 290
12.1 Molecular Reorientation Effects in Liquids and Liquid Crystals 291
12.2 Photorefractive Nonlinearities 300
12.3 Nuclear (Vibrational) Contributions to n2|| (-ω; ω) 306
12.4 Electrostriction 310
12.5 Thermo-Optic Effect 312
12.6 χ(3) via Cascaded χ(2) Nonlinear Processes: Nonlocal 314
Appendix 12.1: Spontaneous Raman Scattering 317
References 328
Suggested Further Reading 329
13. Techniques for Measuring Third-Order Nonlinearities 330
13.1 Z-Scan 332
13.2 Third Harmonic Generation 339
13.3 Optical Kerr Effect Measurements 343
13.4 Nonlinear Optical Interferometry 344
13.5 Degenerate Four-Wave Mixing 345
References 346
Suggested Further Reading 346
14. Ramifications and Applications of Nonlinear Refraction 347
14.1 Self-Focusing and Defocusing of Beams 348
14.2 Self-Phase Modulation and Spectral Broadening in Time 352
14.3 Instabilities 354
14.4 Solitons (Nonlinear Modes) 363
14.5 Optical Bistability 372
14.6 All-Optical Signal Processing and Switching 375
References 382
Suggested Further Reading 383
15. Multiwave Mixing 384
15.1 Degenerate Four-Wave Mixing 385
15.2 Degenerate Three-Wave Mixing 397
15.3 Nondegenerate Wave Mixing 399
Reference 413
Suggested Further Reading 413
16. Stimulated Scattering 414
16.1 Stimulated Raman Scattering 415
16.2 Stimulated Brillouin Scattering 431
References 441
Suggested Further Reading 442
17. Ultrafast and Ultrahigh Intensity Processes 443
17.1 Extended Nonlinear Wave Equation 444
17.2 Formalism for Ultrafast Fiber Nonlinear Optics 448
17.3 Examples of Nonlinear Optics in Fibers 452
17.4 High Harmonic Generation 460
References 462
Suggested Further Reading 463
Appendix: Units, Notation, and Physical Constants 465
A.1 Units of Third-Order Nonlinearity 465
A.2 Values of Useful Constants 467
Reference 467
Index 469
