Banerjee P.P. Nonlinear optics: theory, numerical modeling, and applications
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Banerjee P.P. Nonlinear optics: theory, numerical modeling, and applications / Banerjee P.P. - New York: Dekker, 2004. - 315 p. - (Optical engineering; vol.86). - ISBN 0-8247-0965-9.
 
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Preface ............................................................ iii

 1 Optical Propagation in Linear Media ............................... 1
   1.1 Maxwell's Equations ........................................... 1
   1.2 Linear Wave Propagation in Homogeneous, Linear Isotropic
       Media ......................................................... 4
   1.3 Wave Propagation in Anisotropic Media ........................ 12
   1.4 Diffraction .................................................. 25
   1.5 Dispersion ................................................... 31
   1.6 Problems ..................................................... 34
       References ................................................... 35

 2 The Origin and Modeling of Optical Nonlinearity .................. 37
   2.1 A Simple Physical Model for Optical Nonlinearity ............. 38
   2.2 Physical Effects of Nonlinear Polarization ................... 42
   2.3 Mathematical Modeling of Optical Nonlinearities .............. 43
   2.4 An Alternative Approach ...................................... 54
   2.5 Summary ...................................................... 56
   2.6 Problems ..................................................... 57
       References ................................................... 57

 3 Second Harmonic Generation ....................................... 59
   3.1 The Physics of Second Harmonic Generation .................... 59
   3.2 SHG in Crystals—Mathematical Formulation ..................... 62
   3.3 Phase Matching in Anisotropic Crystal ........................ 70
   3.4 Nonlinear Transverse Effects in Second Harmonic Generation ... 71
   3.5 SHG in a Medium with Second-Order and
       Third-Order Nonlinear Susceptibilities ....................... 73
   3.6 Summary ...................................................... 76
   3.7 Problems ..................................................... 77
       References ................................................... 77

 4 Self-Refraction of Optical Beams ................................. 79
   4.1 The Nonlinear Refractive Index Coefficient n2 ................ 80
   4.2 Self-Refraction of Gaussian Beams ............................ 81
   4.3 Focused Gaussian Beam in a Kerr-Slice: The z-Scan Method ..... 90
   4.4 Self-Bending of Optical Beams ................................ 96
   4.5 Self-Phase Modulation Due to χ(2): Effective χ(3) .............. 97
   4.6 Summary ...................................................... 98
   4.7 Problems ..................................................... 99
       References .................................................. 100

 5 Optical Bistability ............................................. 101
   5.1 The Nonlinear Ring Cavity ................................... 101
   5.2 Transverse Optical Bistability .............................. 109
   5.3 Linear-Nonlinear Interface .................................. 110
   5.4 Conclusion .................................................. 119
   5.5 Problems .................................................... 120
       References .................................................. 120

 6 Optical Phase Conjugation ....................................... 123
   6.1 Comparison with Holography .................................. 124
   6.2 The k-Space Formalism ....................................... 125
   6.3 Semiclassical Analysis: CW Case ............................. 132
   6.4 Phase Conjugation of Pulses and Transient Phase
      Conjugate Response ........................................... 137
   6.5 Discussion .................................................. 142
   6.6 Problems .................................................... 142
       References .................................................. 144

 7 Stimulated Brillouin and Raman Scattering ....................... 145
   7.1 Stimulated Brillouin Scattering ............................. 145
   7.2 Stimulated Raman Scattering ................................. 151
   7.3 Problems .................................................... 153
       References .................................................. 154

 8 Solitons in Optical Fibers ...................................... 155
   8.1 Background on Linear Optical Fibers ......................... 156
   8.2 Fiber Dispersion and Nonlinearity ........................... 158
   8.3 Fiber-Optic Solitons and the NLS Equation ................... 161
   8.4 Dispersion Managed Soliton Communication Systems ............ 164
   8.5 Dark Solitons ............................................... 166
   8.6 Optical Shocks and Self-Steepemiag of Pulses ................ 171
   8.7 Problems .................................................... 173
       References .................................................. 173

 9 Photorefractive Nonlinear Optics ................................ 175
   9.1 Introduction ................................................ 175
   9.2 The Kukhtarev Equations and Their Simplification ............ 177
   9.3 Beam Fanning and Distortion in Photorefractive Materials .... 181
   9.4 Two-Wave Mixing in Photorefractive Materials ................ 194
   9.5 Four-Wave Mixing and Phase Conjugation in Photorefractive
       Materials ................................................... 196
   9.6 Self-Phase Conjugation and Edge Enhancement ................. 200
   9.7 Organic Photorefractive Materials ........................... 202
   9.8 Problems .................................................... 206
       References .................................................. 207

10 Nonlinear Optical Properties of Nematic Liquid Crystals ......... 209
   10.1 The Liquid Crystalline State of Matter ..................... 210
   10.2 Classification of Liquid Crystals .......................... 210
   10.3 Liquid Crystal Alignment ................................... 211
   10.4 Principles of the Continuum Theory ......................... 213
   10.5 Director Distribution of Homogeneously Aligned Nematic
        Liquid Crystal Under an External Electrical Field .......... 215
   10.6 Nonlinear Optical Properties from Optically Induced
        Molecular Reorientation .................................... 224
   10.7 Optically Induced Reorientational Nonlinearity
        with External Voltage ...................................... 228
   10.8 Analysis of Beam Propagation in Liquid Crystals
        and z-Scan ................................................. 235
   10.9 Problems ................................................... 240
        References ................................................. 241

11 Self-Organization in Nonlinear Optical Systems .................. 243
   11.1 Introduction ............................................... 243
   11.2 Nonlinear Two-Dimensional Systems with Feedback ............ 245
   11.3 Self-Organization in Photorefractive Materials ............. 249
   11.4 Theory of Self-Organization in Photorefractive Materials ... 255
   11.5 Instability Criterion and the Dispersion Relation .......... 257
   11.6 Nonlinear Eigenmodes in the Steady State ................... 259
   11.7 Model of Hexagonal Formation Based on Transverse
        Electrical Instability ..................................... 264
   11.8 Potential Applications ..................................... 265
   11.9 Problems ................................................... 267
        References ................................................. 268

12 Nonlinear Optics of Photonic Bandgap Structures ................. 271
   12.1 Introduction ............................................... 271
   12.2 The Linear Dispersion Relation ............................. 272
   12.3 The Effect of Cubic Nonlinearity ........................... 276
   12.4 Second Harmonic Generation in Photonic Bandgap
        Structures ................................................. 282
   12.5 Problems ................................................... 287
        References ................................................. 288

Appendix A  The Split Step Beam Propagation Method ................. 289
            A.1 Examples ........................................... 290
                References ......................................... 294

Appendix B  Wavelet Transforms and Application to Solution
            of Partial Differential Equations ...................... 295
            B.1 Introduction to Wavelets ........................... 295
            B.2 Wavelet Properties and Scaling Functions ........... 296
            B.3 Digital Filters and Multi-Resolution Analysis ...... 298
            B.4 Application of Wavelet Transform to the NLS
                Equation ........................................... 302
                References ......................................... 306

Index .............................................................. 307


Вверх Banerjee P.P. Nonlinear optics: theory, numerical modeling, and applications / Banerjee P.P. - New York: Dekker, 2004. - 315 p. - (Optical engineering; vol.86). - ISBN 0-8247-0965-9.

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