Nonlinear Optical Technology

Preface xxi Acronyms xxiii Introduction: Why Nonlinear Optics? xxvii Summary 1: What is Nonlinear Optics Technology? S1 Summary 2: Second-Order Nonlinearity S5 Summary 3: Third-Order Nonlinearity S24 Summary 4: Nonlinear Scattering and Loss S47 Part I Technical Chapters on Second-Order Nonlinearity 1 1 Second Harmonic Generation 3 1.1 Introduction 3 1.2 Second Harmonic Generation at the Beginning 3 1.3 How Do We Begin? 5 1.4 Approaches to Second Harmonic Generation 8 1.5 Electromagnetic Response to Dielectric 11 1.6 Nonlinear Static Field 13 1.7 Second Harmonic Has No Inversion Symmetry 14 1.8 Photon Picture of SHG 15 1.9 Nonlinear Optics (a Look Ahead) 16 1.10 Applications: SHG at Interfaces 17 1.11 Discussion 22 2 Generating Second Harmonic Efficiently 23 2.1 Introduction 23 2.2 Traveling Waves for SHG 25 2.3 Phase-Matched Growth of Intensity 28 2.4 SHG from Crystal Under Refractive-Index Mismatch 32 2.5 When SH Power Diminishes Due to Phase Mismatch, Where Does It Go? 36 2.6 Phase-Matched Depleted Pump 37 2.7 SH Intensity with Phase Mismatch and Depleted Pump 39 2.8 Applications of SHG 40 2.9 Sum and Difference Frequency Generation 44 2.10 Optical Field Rectification 45 2.11 Review 47 3 Extending Coherence Lengths 49 3.1 Introduction 49 3.2 How Important Is Matching Phases? 51 3.3 Experimental Demonstration of SHG With/Without PM 53 3.4 Anisotropic Crystals 59 3.5 Anisotropic Crystals for SHG Phase Matching 62 3.6 Quasi-Phase Matching 66 3.7 Challenge of Alternating SHG Domains 71 3.8 Periodically-Poled Lithium Niobate (PPLN) 73 3.9 Gaussian Beam Diffraction 77 3.10 Resonators for Enhanced SHG: Fabry-Perot Interferometer 82 3.11 Cavity Enhancement in Green Laser Pointer 85 4 Optical Parametric Amplification 87 4.1 Optical Parametric Amplifier: Tunable Source of Coherent Light 87 4.2 Optical Parametric Amplifiers: Engineering Perspective 92 4.3 Amplification by Parametric Nonlinearities 95 4.4 OPA as Reverse of Difference Frequency Generation 99 4.5 Understanding Parametric Oscillators 100 4.6 Operating an OPO System 104 4.7 OPO Is OPA in Optical Cavity 107 4.8 Relate Electric Field and Intensity to Photon Density 109 4.9 Understanding Degenerate Oscillators and Amplifiers 111 4.10 Practical Applications of OPOs 116 Part II Technical Chapters on Third-Order Nonlinearity 119 5 Third-Order Nonlinearity 121 5.1 Introduction to Third-order Nonlinearity x3 121 5.2 Third-Harmonic Generation 121 5.3 Higher Order Nonlinearities in Pressurized Gases 125 5.4 High-Harmonic Generation Experimental Results 127 5.5 Toward Commercialization 130 5.6 Analyzing fs Pulses: Frequency Resolved Optical Gate 132 5.7 Chirped-Pulse Amplification Systems 134 5.8 Race to Achieve the Highest Intensity 137 5.9 Next Chapter 138 6 Nonlinear Index and Pulses 139 6.1 Intensity-Induced Refractive Index Change 139 6.2 Impact of Phase Delay Due to Δn 143 6.3 Solitons: Temporal Pulse Shape Never Changes 146 6.4 Self-intensity-Modulated Phase 148 6.5 Frequency Shift Equals Time Slope of Changing Phase 152 6.6 XPM: Cross-phase Modulation 159 6.7 XPM to Transfer Phase Information 166 6.8 Applications of Lossless Quantum Information Transfer 167 6.9 Next Chapter 169 7 Spatial Nonlinear Index 171 7.1 Introduction 171 7.2 Self-trapping in the Spatial Domain by Nonlinear Index 171 7.3 Spatial Solitons 175 7.4 Derivation of 1D Spatial Soliton Wave Equation 177 7.5 Self-focusing with Power Higher than Critical 181 7.6 Experimental Improvements 185 7.7 Nonlinear Fabry-Perot Etalon: Optical Bistability 186 7.8 Measuring Nonlinear Coefficients: Z-scan Technique 190 7.9 Kerr Lens Mode-locking 191 7.10 Next Chapter 192 8 Coherent Wave-Mixing 193 8.1 Introduction 193 8.2 Lateral Grating from Two-wave Mixing 195 8.3 Bragg Gratings 202 8.4 Pulsed Gratings 204 8.5 Four-wave-Mixing 206 8.6 Four-wave Mixing Backward Waves 210 8.7 Spatial Analysis to Find Fourth Wave D in χ(3) 211 8.8 Time-dependence of E3 and E4 213 8.9 Phase Conjugation (Changing Sign of Phase) 214 8.10 Fiber Optical Parametric Amplification 216 8.11 Four Wave Mixing as Four-photon Scattering 221 8.12 Next Chapter 224 Part III Technical Chapters on Nonlinear Optical Scattering and Loss 225 9 Stimulated Raman Scattering 227 9.1 Introduction 227 9.2 Spontaneous Raman Scattering 229 9.3 Introduction to Stimulated Raman Scattering 233 9.4 Understanding Stokes Generation 236 9.5 Stokes Generates Coherent Molecular Vibrations 240 9.6 Anti-Stokes Waves 243 9.7 Raman Laser 246 9.8 Applications: SRS Optical Nonlinearity is Both Useful and Detrimental 251 9.9 Raman SRS Fiber Amplifiers 252 9.10 High-power Raman Lasers in Special Fibers 255 9.11 Photonic Raman Lasers 255 9.12 Stimulated Raman Spectroscopy 259 9.13 Review: Short List of Main Uses for SRS 262 10 Stimulated Brillouin Scattering 265 10.1 Spontaneous Brillouin Scattering 265 10.2 Spontaneous or Parametric Brillouin Scattering 269 10.3 Stimulated Brillouin Scattering 270 10.4 SBS as Stokes Power Amplifier 275 10.5 Historical Background 279 10.6 Phase Conjugation and SBS Reflection 283 10.7 Brillouin Fiber Lasers 289 10.8 Brillouin Fiber Sensors 291 10.9 Photonic Brillouin Ring Laser 293 10.10 Prospective SBS Applications 296 11 Nonlinear Absorption 299 11.1 Nonlinear Absorption 299 11.2 Two-photon Absorption 300 11.3 Saturable Absorption 308 11.4 Rate Equation for Absorption Transition 309 11.5 Solve for Saturable Absorption 311 11.6 Application: Creating Pulsing Lasers 312 11.7 Classes of Pulsed Lasers 314 11.8 Final Thoughts 317 Appendix A Light Beams in Transparent Media 319 Appendix B Optical Materials and Light Fields 345 Appendix C Understanding Resonators 373 Appendix D Waveguides to Avoid Diffraction 385 Problem Assignments 399 Index 415