ISBN-10:
0824709659
ISBN-13:
9780824709655
Pub. Date:
12/04/2003
Publisher:
Taylor & Francis
Nonlinear Optics(Optical Engineering Series) / Edition 1

Nonlinear Optics(Optical Engineering Series) / Edition 1

by Partha P. Banerjee
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Overview

Nonlinear Optics probes in great depth quadratic and cubic nonlinearities, photorefractive nonlinear optics, the nonlinear optical properties of nematic liquid crystals, and photonic bandgap structures. This reference places core physical principles and theoretical concepts in dialogue with contemporary applications and research and presents the essential physics behind the products and promise of this very fertile field. It presents new developments in the dispersion management in nonlinear optical fibers and the combined effects of quadratic and cubic nonlinearities on harmonic generation. Coverage includes a review of linear wave propagation and the origins of optical nonlinearity.

Product Details

ISBN-13: 9780824709655
Publisher: Taylor & Francis
Publication date: 12/04/2003
Series: Optical Science and Engineering Series
Edition description: New Edition
Pages: 314
Product dimensions: 6.25(w) x 9.25(h) x 1.00(d)

Table of Contents

Prefaceiii
1Optical Propagation in Linear Media1
1.1Maxwell's Equations1
1.2Linear Wave Propagation in Homogeneous, Linear Isotropic Media4
1.3Wave Propagation in Anisotropic Media12
1.4Diffraction25
1.5Dispersion31
1.6Problems34
References35
2The Origin and Modeling of Optical Nonlinearity37
2.1A Simple Physical Model for Optical Nonlinearity38
2.2Physical Effects of Nonlinear Polarization42
2.3Mathematical Modeling of Optical Nonlinearities43
2.4An Alternative Approach54
2.5Summary56
2.6Problems57
References57
3Second Harmonic Generation59
3.1The Physics of Second Harmonic Generation59
3.2SHG in Crystals--Mathematical Formulation62
3.3Phase Matching in Anisotropic Crystal70
3.4Nonlinear Transverse Effects in Second Harmonic Generation71
3.5SHG in a Medium with Second-Order and Third-Order Nonlinear Susceptibilities73
3.6Summary76
3.7Problems77
References77
4Self-Refraction of Optical Beams79
4.1The Nonlinear Refractive Index Coefficient n[subscript 2]80
4.2Self-Refraction of Gaussian Beams81
4.3Focused Gaussian Beam in a Kerr-Slice: The z-Scan Method90
4.4Self-Bending of Optical Beams96
4.5Self-Phase Modulation Due to x[superscript (2)]: Effective x[superscript (3)]97
4.6Summary98
4.7Problems99
References100
5Optical Bistability101
5.1The Nonlinear Ring Cavity101
5.2Transverse Optical Bistability109
5.3Linear-Nonlinear Interface110
5.4Conclusion119
5.5Problems120
References120
6Optical Phase Conjugation123
6.1Comparison with Holography124
6.2The k-Space Formalism125
6.3Semiclassical Analysis: CW Case132
6.4Phase Conjugation of Pulses and Transient Phase Conjugate Response137
6.5Discussion142
6.6Problems142
References144
7Stimulated Brillouin and Raman Scattering145
7.1Stimulated Brillouin Scattering145
7.2Stimulated Raman Scattering151
7.3Problems153
References154
8Solitons in Optical Fibers155
8.1Background on Linear Optical Fibers156
8.2Fiber Dispersion and Nonlinearity158
8.3Fiber-Optic Solitons and the NLS Equation161
8.4Dispersion Managed Soliton Communication Systems164
8.5Dark Solitons166
8.6Optical Shocks and Self-Steepening of Pulses171
8.7Problems173
References173
9Photorefractive Nonlinear Optics175
9.1Introduction175
9.2The Kukhtarev Equations and Their Simplification177
9.3Beam Fanning and Distortion in Photorefractive Materials181
9.4Two-Wave Mixing in Photorefractive Materials194
9.5Four-Wave Mixing and Phase Conjugation in Photorefractive Materials196
9.6Self-Phase Conjugation and Edge Enhancement200
9.7Organic Photorefractive Materials202
9.8Problems206
References207
10Nonlinear Optical Properties of Nematic Liquid Crystals209
10.1The Liquid Crystalline State of Matter210
10.2Classification of Liquid Crystals210
10.3Liquid Crystal Alignment211
10.4Principles of the Continuum Theory213
10.5Director Distribution of Homogeneously Aligned Nematic Liquid Crystal Under an External Electrical Field215
10.6Nonlinear Optical Properties from Optically Induced Molecular Reorientation224
10.7Optically Induced Reorientational Nonlinearity with External Voltage228
10.8Analysis of Beam Propagation in Liquid Crystals and z-Scan235
10.9Problems240
References241
11Self-Organization in Nonlinear Optical Systems243
11.1Introduction243
11.2Nonlinear Two-Dimensional Systems with Feedback245
11.3Self-Organization in Photorefractive Materials249
11.4Theory of Self-Organization in Photorefractive Materials255
11.5Instability Criterion and the Dispersion Relation257
11.6Nonlinear Eigenmodes in the Steady State259
11.7Model of Hexagonal Formation Based on Transverse Electrical Instability264
11.8Potential Applications265
11.9Problems267
References268
12Nonlinear Optics of Photonic Bandgap Structures271
12.1Introduction271
12.2The Linear Dispersion Relation272
12.3The Effect of Cubic Nonlinearity276
12.4Second Harmonic Generation in Photonic Bandgap Structures282
12.5Problems287
References288
Appendix AThe Split Step Beam Propagation Method289
A.1Examples290
References294
Appendix BWavelet Transforms and Application to Solution of Partial Differential Equations295
B.1Introduction to Wavelets295
B.2Wavelet Properties and Scaling Functions296
B.3Digital Filters and Multi-Resolution Analysis298
B.4Application of Wavelet Transform to the NLS Equation302
References306
Index307

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