Nonlinear Optics (eBook)

Preface 5
Contents 8
About the Author 14
Abstract 16
1 Introduction 17
1.1 Importance of Nonlinear Optics 17
1.1.1 Status of Nonlinear Optics in Modern Physics 17
1.1.2 Status of Nonlinear Optics in Modern Optics 18
1.1.3 Nonlinear Optics Is a Basis of Photonic Technology 19
1.2 Physical Meaning of Nonlinear Optics 21
1.2.1 Phenomenon Related with High-Order Polarization 21
1.2.2 Nonlinear Response of Medium to the Optical Field 22
1.2.3 Parameters of Medium Are Function of Optical Field 23
1.3 Research Content of Nonlinear Optics 24
1.3.1 Typical Nonlinear Optical Effects 24
1.3.2 Two Kinds of Nonlinear Optical Effects 29
1.3.3 Nonlinear Optical Materials 30
1.4 Development History of Nonlinear Optics 31
1.4.1 Brief History of Nonlinear Optics 31
1.4.2 Development Tendency of Nonlinear Optics 32
1.5 Applications of Nonlinear Optics 33
1.5.1 Application in Laser Technology 34
1.5.2 Application in Information Technology 34
1.5.3 Application in Material Technology 35
References 37
2 Polarization Theory of Nonlinear Medium 39
2.1 Wave Equations of Nonlinear Medium 39
2.1.1 Maxwell’s Equations for Nonlinear Medium 39
2.1.2 Time-Domain Wave Equation in Anisotropic Nonlinear Medium 41
2.1.3 Time-Domain Wave Equation in Isotropic Nonlinear Medium 42
2.1.4 Frequency-Domain Wave Equation in Anisotropic Nonlinear Medium 44
2.1.5 Frequency-Domain Wave Equation in Isotopic Nonlinear Medium 44
2.2 Polarization and Susceptibility of Nonlinear Medium 46
2.2.1 Frequency-Domain Expressions of Polarization and Susceptibility 46
2.2.2 Degeneration Factor of Polarization 50
2.2.3 Symmetry of Susceptibility Tensor 53
2.3 Real Part and Imaginary Part of Susceptibility 56
2.3.1 Relation Between Real Part and Imaginary Part of Susceptibility (K–K Relation) 56
2.3.2 Physical Significance of Real Part and Imaginary Part of Susceptibility 57
2.3.3 Relation Between Nonlinear Refractive Index and Nonlinear Absorption Coefficient 61
Appendix A: Derivation of K–K Relation [9, 10] 62
Appendix B: Two Systems of Units [11] 64
I. Fundamental Formula 65
II. Conversion of Two Unit Systems 65
References 65
3 Optical Three-Wave Coupling Processes 67
3.1 Three-Wave Coupled Equations 67
3.1.1 Review of Second-Order Nonlinear Optics Effects in Isotopic Medium 67
3.1.2 Approximate Description of Second-Order Nonlinear Optics Effect in Anisotropic Medium 69
3.1.3 Three-Wave Coupled Equations in Anisotropic Medium 71
3.2 Optical Second-Harmonic Generation 73
3.2.1 Small Signal Approximation 74
3.2.2 High Fundamental Wave Consumption 77
3.2.3 Phase Matching Technology 80
3.2.4 Experimental Facilities for Second Harmonic Generation 85
3.3 Optical Sum Frequency, Difference Frequency and Parameter Amplification 87
3.3.1 Optical Sum Frequency and Frequency Up-Conversion 87
3.3.2 Optical Difference Frequency and Frequency Down-Conversion 91
3.3.3 Optical Parametric Amplification 94
3.3.4 Comparison of Four Kinds of Three-Wave Mixing Processes and Experimental Facilities 95
3.4 Optical Parametric Oscillator 97
3.4.1 Threshold Value Equations of Optical Parametric Oscillation 97
3.4.2 Double Resonant Parametric Oscillator 99
3.4.3 Singly Resonant Parametric Oscillator 101
References 104
4 Optical Four-Wave Coupling Process 105
4.1 Introduction to Third-Order Nonlinear Optical Effects 105
4.2 Optical Third Harmonic and Optical Four-Wave Mixing 107
4.2.1 Optical Third Harmonic 107
4.2.2 Optical Four-Wave Mixing 110
4.2.3 Degenerated Four-Wave Mixing 111
4.3 Optical Phase Conjugation 113
4.3.1 Definition and Characteristic of Optical Phase Conjugation 113
4.3.2 Optical Phase Conjugation in Four-Wave Mixing Process 115
4.3.3 Application of Optical Phase Conjugation 121
References 123
5 Optical Kerr Effect and Self-focusing 124
5.1 Optical Kerr Effect 124
5.1.1 Self-phase Modulation Optical Kerr Effect 126
5.1.2 Cross-Phase Modulation Optical Kerr Effect 129
5.1.3 Optical-Kerr-Effect Induced Birefringence 131
5.2 Self-focusing of Light Beam 134
5.2.1 Steady State Self-focusing 134
5.2.2 Dynamic State Self-focusing 142
5.2.3 Self-phase Modulation Based on Self-focusing 147
5.3 Z-scan Measurement of Nonlinear Optical Parameter 150
5.3.1 Experimental Method of Z-scan Measurement 150
5.3.2 Theoretical Calculation of Z-scan Measurement [23] 153
5.3.3 Other Z-scan Technologies 158
References 161
6 Nonlinear Stimulated Scattering 163
6.1 Introduction to Light Scattering 163
6.1.1 Classification of Light Scattering 163
6.1.2 Stimulated Radiation Light Scattering Characteristics 165
6.2 Stimulated Raman Scattering 166
6.2.1 Physical Picture of Stimulated Raman Scattering 166
6.2.2 Classical Theory of Stimulated Raman Scattering 171
6.2.3 Experiments of Stimulated Raman Scattering 177
6.3 Stimulated Brillouin Scattering 178
6.3.1 Physical Picture of Stimulated Brillouin Scattering 178
6.3.2 Classical Theory of Stimulated Brillouin Scattering 181
6.3.3 Experiments of Stimulated Brillouin Scattering 186
References 189
7 Nonlinear Absorption and Refraction of Light 190
7.1 Single-Photon Absorption and Two-Photon Absorption 190
7.1.1 Light-Intensity Transmission Equations 190
7.1.2 Single-Photon Nonlinear Absorption and Refraction 193
7.1.3 General Theory of Two-Photon Absorption 196
7.1.4 Two-Photon Absorption and Refraction in Semiconductor 199
7.2 Saturable Absorption and Reverse Saturable Absorption 206
7.2.1 Molecular-Energy-Level Model of Saturable Absorption 206
7.2.2 Relation Between Saturable Absorption and Three-Order Nonlinear Absorption 212
7.2.3 Molecular-Energy-Level Mode of Reverse Saturable Absorption 213
7.2.4 Application of Reverse Saturable Absorption in All-Optical Limiting 219
7.3 Saturable Refraction and Reverse Saturable Refraction 220
7.3.1 Description of Saturable Refraction and Reverse Saturable Refraction [19, 20] 220
7.3.2 Physical Significance of Sign Symbol of Nonlinear Refraction Coefficient 224
References 227
8 Optical Bistability and Its Instability 228
8.1 Introduction to Optical Bistability 228
8.1.1 Basic Conception of Optical Bistability [1–4] 228
8.1.2 Classification of Optical Bistable Device 230
8.2 Optical Bistable Device 232
8.2.1 Principle of F–P Etalon Intrinsic Optical Bistable Device 232
8.2.2 Principle of Electro-Optical Hybrid Optical Bistable Device 242
8.2.3 Application of Optical Bistable Devices 248
8.3 Optical Instability of Optical Bistability 250
8.3.1 Stability Analysis of Optical Bistability 250
8.3.2 Instability of Optical Bistability 255
References 263
9 Propagation of Light Pulse in Fiber and Optical Soliton 264
9.1 Nonlinear Schrodinger Equation [1] 264
9.1.1 Helmholtz Equation 265
9.1.2 Derivation of Frequency-Domain Wave Equation in Fiber 268
9.1.3 Derivation of Nonlinear Schrodinger Equation 270
9.2 Group Velocity Dispersion and Self-phase Modulation [1] 273
9.2.1 Pulse Propagation Excluding Dispersion and Nonlinearity 275
9.2.2 Influence of Dispersion to Pulse Propagation 275
9.2.3 Influence of Self-phase Modulation to Pulse Propagation 279
9.2.4 Combined Action of Dispersion and Self-phase Modulation 281
9.3 Time Soliton and Space Soliton 285
9.3.1 Time Soliton 285
9.3.2 Space Soliton 289
References 291
10 All-Optical Switch Based on Nonlinear Optics 292
10.1 Summarization of All-Optical Switch 292
10.1.1 Research Direction of All-Optical Switch [1] 292
10.1.2 Classification of All-Optical Switch [1] 297
10.2 Nonlinear Optical Coupler All-Optical Switch 302
10.2.1 Symmetric Coupler Under Low Incident Power 303
10.2.2 Symmetric Coupler All-Optical Switch in Self-phase Modulation 306
10.2.3 Asymmetric Coupler All-Optical Switch in Cross-Phase Modulation 309
10.3 Nonlinear Sagnac Interferometer All-Optical Switch 313
10.3.1 Symmetric Sagnac Interferometer in Low Incident Power 313
10.3.2 Sagnac Interferometer All-Optical Switch with a Non-3 dB Coupler 318
10.3.3 Sagnac Interferometer All-Optical Switch in Cross-Phase Modulation 320
10.3.4 Sagnac Interferometer All-Optical Switch with a Optical Amplifier 322
10.4 Nonlinear M–Z Interferometer All-Optical Switch 324
10.4.1 M–Z Interferometer All-Optical Switch with Different Arm Materials 324
10.4.2 M–Z Interferometer All-Optical Switch with Different Arm Lengths 326
10.5 Nonlinear Ring Resonator All-Optical Switch 327
10.5.1 All-Optical Switch in a M–Z Interferometer Coupled with a SCRR 328
10.5.2 All-Optical Switch in a DCRR 334
10.6 Nonlinear Fiber Grating All-Optical Switch 338
10.6.1 Single Nonlinear FBG All-Optical Switch 339
10.6.2 Single Nonlinear LPFG All-Optical Switch 347
10.6.3 Nonlinear Fiber Connected LPFG-Pair All-Optical Switch 352
10.6.4 Nonlinear Fiber Connected FBG-Pair Optical Bistable Switch 361
10.7 Nanoscale All-Optical Switches 368
10.7.1 Nano-waveguide Interferometer All-Optical Switches 370
10.7.2 Photonic Crystal All-Optical Switch 376
10.7.3 Surface Plasmon Polariton All-Optical Switch 385
10.7.4 Silicon Nano-waveguide Resonant Cavity All-Optical Switch 395
References 397