Nonlinear Optics

GEORGE I. STEGEMAN, PhD, is Chair Professor in the College of Engineering at KFUPM, Saudi Arabia, and Emeritus Professor at the College of Optics and Photonics (CREOL) of the University of Central Florida (UCF). He is the first recipient of the Cobb Family Eminent Chair in Optical Sciences and Engineering at UCF. Dr. Stegeman is a Fellow of the Optical Society of America and has received the Canadian Association of Physicists's Herzberg Medal for achievement in physics and the Optical Society of America's R.W. Wood Prize.ROBERT A. STEGEMAN, PhD, has held professional positions at the College of Optical Sciences at The University of Arizona, as well as various industrial companies.

• Preface xi1. Introduction 11.1 What is Nonlinear Optics and What is it Good for? 11.2 Notation 21.3 Classical Nonlinear Optics Expansion 41.4 Simple Model: Electron on a Spring and its Application to Linear Optics 61.5 Local Field Correction 10Suggested Further Reading 13Part A: Second-order Phenomena 152. Second-Order Susceptibility and Nonlinear Coupled Wave Equations 172.1 Anharmonic Oscillator Derivation of Second-Order Susceptibilities 182.2 Input Eigenmodes, Permutation Symmetry, and Properties of χ (2) 232.3 Slowly Varying Envelope Approximation 252.4 Coupled Wave Equations 262.5 Manley–Rowe Relations and Energy Conservation 31Suggested Further Reading 383. Optimization and Limitations of Second-Order Parametric Processes 393.1 Wave-Vector Matching 393.2 Optimizing d(2)eff 533.3 Numerical Examples 59References 67Suggested Further Reading 674. Solutions for Plane-Wave Parametric Conversion Processes 694.1 Solutions of the Type 1 SHG Coupled Wave Equations 694.2 Solutions of the Three-Wave Coupled Equations 774.3 Characteristic Lengths 804.4 Nonlinear Modes 81References 84Suggested Further Reading 855. Second Harmonic Generation with Finite Beams and Applications 865.1 SHG with Gaussian Beams 865.2 Unique and Performance-Enhanced Applications of Periodically Poled LiNbO3 (PPLN) 98References 107Suggested Further Reading 1076. Three-Wave Mixing, Optical Amplifiers, and Generators 1086.1 Three-Wave Mixing Processes 1086.2 Manley–Rowe Relations 1106.3 Sum Frequency Generation 1116.4 Optical Parametric Amplifiers 1136.5 Optical Parametric Oscillator 1196.6 Mid-Infrared Quasi-Phase Matching Parametric Devices 128References 139Selected Further Reading 1407. χ (2) Materials and Their Characterization 1417.1 Survey of Materials 1417.2 Oxide-Based Dielectric Crystals 1437.3 Organic Materials 1447.4 Measurement Techniques 149Appendix 7.1: Quantum Mechanical Model for Charge Transfer Molecular Nonlinearities 153References 157Suggested Further Reading 158Part B: Nonlinear Susceptibilities 1598. Second- and Third-Order Susceptibilities: Quantum Mechanical Formulation 1618.1 Perturbation Theory of Field Interaction with Molecules 1628.2 Optical Susceptibilities 169Appendix 8.1: χ (3)ijk‘Symmetry Properties for Different Crystal Classes 192Reference 196Suggested Further Reading 1969. Molecular Nonlinear Optics 1979.1 Two-Level Model 1989.2 Symmetric Molecules 2109.3 Density Matrix Formalism 215Appendix 9.1: Two-Level Model for Asymmetric Molecules—Exact Solution 216Appendix 9.2: Three-Level Model for Symmetric Molecules—Exact Solution 218References 222Suggested Further Reading 223Part C: Third-order Phenomena 22510. Kerr Nonlinear Absorption and Refraction 22710.1 Nonlinear Absorption 22810.2 Nonlinear Refraction 23810.3 Useful NLR Formulas and Examples (Isotropic Media) 243Suggested Further Reading 25011. Condensed Matter Third-Order Nonlinearities due to Electronic Transitions 25111.1 Device-Based Nonlinear Material Figures of Merit 25211.2 Local Versus Nonlocal Nonlinearities in Space and Time 25311.3 Survey of Nonlinear Refraction and Absorption Measurements 25511.4 Electronic Nonlinearities Involving Discrete States 25611.5 Overview of Semiconductor Nonlinearities 26611.6 Glass Nonlinearities 281Appendix 11.1: Expressions for the Kerr, Raman, and Quadratic Stark Effects 284References 286Suggested Further Reading 28912. Miscellaneous Third-Order Nonlinearities 29012.1 Molecular Reorientation Effects in Liquids and Liquid Crystals 29112.2 Photorefractive Nonlinearities 30012.3 Nuclear (Vibrational) Contributions to n2|| (-ω; ω) 30612.4 Electrostriction 31012.5 Thermo-Optic Effect 31212.6 χ(3) via Cascaded χ(2) Nonlinear Processes: Nonlocal 314Appendix 12.1: Spontaneous Raman Scattering 317References 328Suggested Further Reading 32913. Techniques for Measuring Third-Order Nonlinearities 33013.1 Z-Scan 33213.2 Third Harmonic Generation 33913.3 Optical Kerr Effect Measurements 34313.4 Nonlinear Optical Interferometry 34413.5 Degenerate Four-Wave Mixing 345References 346Suggested Further Reading 34614. Ramifications and Applications of Nonlinear Refraction 34714.1 Self-Focusing and Defocusing of Beams 34814.2 Self-Phase Modulation and Spectral Broadening in Time 35214.3 Instabilities 35414.4 Solitons (Nonlinear Modes) 36314.5 Optical Bistability 37214.6 All-Optical Signal Processing and Switching 375References 382Suggested Further Reading 38315. Multiwave Mixing 38415.1 Degenerate Four-Wave Mixing 38515.2 Degenerate Three-Wave Mixing 39715.3 Nondegenerate Wave Mixing 399Reference 413Suggested Further Reading 41316. Stimulated Scattering 41416.1 Stimulated Raman Scattering 41516.2 Stimulated Brillouin Scattering 431References 441Suggested Further Reading 44217. Ultrafast and Ultrahigh Intensity Processes 44317.1 Extended Nonlinear Wave Equation 44417.2 Formalism for Ultrafast Fiber Nonlinear Optics 44817.3 Examples of Nonlinear Optics in Fibers 45217.4 High Harmonic Generation 460References 462Suggested Further Reading 463Appendix: Units, Notation, and Physical Constants 465A.1 Units of Third-Order Nonlinearity 465A.2 Values of Useful Constants 467Reference 467Index 469