Preface to the First Edition Preface to the Second Edition Authors 1 Introduction 1.1 Historical Background 1.2 Unifying Themes 1.3 Overview of Nonlinear Effects Covered in This Book 1.4 Labeling Conventions and Terminology 1.5 Units Problems References Further Reading 2 Linear Optics 2.1 Introduction 2.1.1 Linearity 2.1.2 Maxwel's Equations 2.1.3 Poynting's Theorem 2.1.4 Intensity 2.1.5 Linear Polarization 2.1.6 Complex Representation of Polarization 2.1.7 Energy Exchange between a Field and Polarization 2.2 Tensor Properties of Materials 2.2.1 Tensors 2.3 Wave Equation 2.3.1 Constitutive Relationships for Complex Amplitudes 2.3.2 Wave Equation in Homogeneous lsotropic Materials 2.3.3 Dispersion 2.3.4 Wave Equation in Crystals 2.3.5 Fresnel's Equation 2.3.6 o-Waves and e-Waves 2.3.7 Poynting Vector Walk-Off 2.4 Determining e-Waves and o-Waves in Crystals 2.4.1 Homogeneous Isotropic 2.4.2 Uniaxial Crystal 2.4.3 Biaxial Crystals 2.5 Index Elipsoid 2.6 Applications 2.6.1 Slowly Yaying EnvelopE Approximaion and Gausian Beam 2.6.2 Gaussian Beam Propagation Using the q-Parameter 2.6.3 M2 Propagation Factor 2.6.4 Example of Formatting a Beam for SHG Problems References Further Reading 3 Introduction to the Nonlinear Susceptibility 3.1 Introduction 3.1.1 Nonlinear Polarization 3.1.2 Parametric Processes 3.2 Classical Origin of the Nonlinearity 3.2.1 One-Dimensional Linear Harmonic Oscillator 3.2.2 One-Dimensional Anharmonic Oscilator 3.2.3 Third-Order Effects in Centrosymmetric Media 3.3 Details of the Nonlinear Susceptibility,X (2) 3.3.1 Degeneracy and Subtleties of Squaring the Field 3.3.2 Tensor Properties of Susceptibility 3.3.3 Permuting the Electric Fields in the Nonlinear Polarization 3.3.4 Full Permutation Symmetry in Lossless Media 3.3.5 Kleinman's Symmetry 3.3.6 Contracting the Indices in x (2) ijk 3.3.7 Effective Nonlinearity and deff 3.3.8 Example Calculation of deff 3.4 Connection between Crystal Symmetry and the d-Matrix 3.4.1 Centrosymmetric Crystals 3.4.2 Example Calculation of d-Matrix for 3m Crystals 3.5 Electro-Optic Effect 3.5.1 EO Effects and the r-Matrix 3.5.2 Example Calculation of EO Effect in KH2DPO4 3.5.3 EO Wave Plates 3.5.4 EO Sampling: Terahertz Detection 3.5.5 Connection between d and r Problems References Further Reading 4 Three-Wave Processes in the Small-Signal Regime 4.1 Introduction to the Wave Equation for Three Fields 4.1.1 Wave Equation for a Three-Wave Process 4.1.2 Slowly Varying Envelope Approximation Extended …… 5 Quasi-Phase Matching 6 Three-Wave Mixing beyond the Small-Signal Limit 7 x(2) Devices 8 x(3) Processes 9 Raman and Brillouin Scattering 10 Nonlinear Optics Including Diffraction and Dispersion 11 Quantum Nonlinear Optics Appendix A: Complex Notation Appendix B: Sellmeier Equations Appendix C: Programming Techniques Appendix D: Exact Solutions to the Coupled Amplitude Equations Appendix E: Optical Fibers-Slowly Varying Envelope Equations Index