Applied Nonlinear Optics

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ISBN: 9780486453606 | 048645360X
Cover: Paperback
Copyright: 10/6/2006

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Directed toward physicists and engineers interested in the device applications enabled by nonlinear optics, this text is suitable for advanced undergraduates and graduate students. Its content is presented entirely on a classical basis and requires only an elementary knowledge of quantum mechanics.

Linear Optics: Wave Propagation in Anisotropic Materials

(24)

Lorentz Model---harmonic oscillator model of the refractive index; dispersion and absorption

(5)

Anisotropy---tensor form of the dielectric constant; rotation to the principal dielectric axes

(2)

Wave Propagation in an Anisotropic Crystal---the two allowed polarizations

(2)

The Index Ellipsoid---method to find the polarization directions; uniaxial and biaxial crystals; the extraordinary index at an angle Ø to the optic axis

(3)

Refraction at the Surface of an Anisotropic Crystal---the k vector construction

(2)

Applications of Birefringence---compensation of the dispersion of a material; quarter-wave plates and half-wave plates

(1)

Orientation of the Crystal

(1)

Biaxial Crystals---the two-sheeted k vector surface; the polarization on these surfaces

(3)

Optical Activity

(1)

Induced Anisotropy

(1)

Electrooptic Effect---the contracted notation for the 18 independent elements; electrooptic modulation; the halfwave voltage

(4)

Nonlinear Optics

(29)

Introduction---the nonlinearity of the polarization and the generation of sidebands

(1)

Nonlinearities of the Polarization---generation of second-harmonic, dc, sum and difference frequencies

(3)

The Anharmonic Oscillator

(1)

Definition of the Electric Field---the definition of the electric field with many frequency components; definition of positive and negative frequencies

(1)

The Nonlinear Polarization---solution of the anharmonic oscillator equation; expression for the first- and second-order polarization

(2)

Extension to Three Dimensions in Three Mutually Interacting Fields---permutation of the frequencies and the indices

(1)

Miller's Rule---relation between the second-order susceptibility and the linear susceptibilities

(1)

The Coefficients Used Experimentally---relation between d and x

(1)

Contraction of the Indices---definition of a column vector F, contraction of the indices; an example

(1)

Crystal Symmetry---derivation of the matrix elements of a representative class; Kleinman's symmetry condition; the nonlinear susceptibility matrix and the piezoelectric matrix

(2)

Definition of dett

(2)

An Example

(2)

The Coupled Amplitude Equations---derivation of the three coupled amplitude equations that govern a general three-frequency interaction; expressions for output power in the small-signal approximation

(3)

The Manley---Rowe Relations---gain in difference frequency generation; the parametric oscillator

(2)

Second-Harmonic Generation---the output power per unit area for the small-signal approximation; exact solution of the coupled amplitude equations in the phase-matched case

(2)

Output Angle

(3)

The Electrooptic Coefficient---relation between the classical electrooptical coefficient and the nonlinear optical coefficient

(1)

Nonlinear Interactions in Reflection

(1)

Dimensions---relation between MKS units and c.g.s. units

(2)

Phase Matching

(19)

Introduction---the importance of phase matching to non-linear interactions

(1)

Power Flow in the Non-Phase-Matched Case---coupling of the power back and forth between input and harmonics

(4)

Quasi-Phase-Matching Methods---methods to adjust the phase difference periodically

(1)

Angle Phase Matching---phase-matching using the birefringence of a crystal. Type I and Type II phase matching---diagrams showing possible interactions for a given phase-matching angle

(2)

The Expression for dett for the Different Crystal Classes---equations and tables giving the polarization of the output as a function of the polarizations and the direction of transmission of the input

(6)

Disadvantages of Angle Phase Matching---the effects of walk-off between the extraordinary and the ordinary rays; divergence of a focused beam

(1)

Temperature-Dependent Phase Matching---noncritical phase matching in the x-y plane by temperature tuning of the indices

(1)

Phase Matching in Biaxial Crystals

(1)

Other Phase-Matching Methods---phase matching in optically active media; phase matching using Faraday rotation; interactions between noncollinear beams

(1)

Competing Interactions---simultaneous phase matching between several interactions; absorbtion of the pump radiation

(2)

Nonlinear Materials

(29)

Historical Introduction---brief history of the development of nonlinear materials, their use, measurement, and characterization

(4)

Quality Assessment of Nonlinear Materials---linear and non-linear SHG characteristics; effective crystal length

(4)

The Accurate Measurement of Optical Nonlinearity---absolute measurements; Maker fringe technique; sign of nonlinearity; pulsed-laser techniques

(3)

Kurtz Powder Assessment of Nonlinear Materials

(2)

Lithium Niobate---general properties; growth; poling; assessment; refractive indices; effects of composition; damage problems; ``hot'' LiNbO3

(6)

Barium Sodium Niobate---general properties; growth; poling; detwinning; refractive indices

(2)

ADP and KDP---General properties; refractive indices

(4)

Lithium Iodate---general properties; refractive indices

(1)

Proustite---general properties; refractive indices

(3)

Second-Harmonic Generation

102

(22)

Introduction

102

(1)

Plane Wave Interactions---low-conversion efficiency solutions; high conversion

102

(3)

Finite Beam Size---small beam area: limitations of focusing; optimum focusing for TEM00 mode; phase-matching limitations for multimode beams; effects of source linewidth

105

(3)

Effects of Mode Structure on SHG---SHG from randomly phased modes

108

(3)

SHG from Mode-Locked Lasers

111

(1)

Intracavity SHG---Three- and four-level laser rate equations with SHG; optimum coupling

112

(8)

Picosecond Time Domain Measurements by SHG

120

(4)

Parametric Up-Conversion

124

(29)

Introduction---sum frequency generation; limitation to up-conversion; introductory theory; infrared detection; single-and multiple-mode approaches

124

(3)

General Points---Manley-Rowe relations; quantum-conversion efficiency for multimode converter

127

(1)

Focused Beams---Small area A; single-mode operations; optimum focusing

128

(2)

Effects of Phase Matching

130

(9)

Tuning---tunable infrared frequency; tuning ranges

130

(2)

Frequency Bandwidth---narrow- and broad-band operation

132

(2)

Solid Acceptance Angle for Infrared Radiation---critical, noncritical, and noncollinear phase matching

134

(5)

Comparison of the Single-Mode and Multimode Up-Converters---blackbody modes and number of quanta per mode; relative sensitivity of multimode and single-mode up-converters in various situations; optimization

139

(3)

Noise Properties---comparison of up-converter and photoconductive detectors; characteristics of the up-converter as infrared detector; parametrically generated noise in the up-converter

142

(4)

Parametric Image Converters Principles---simple theory of image transfer

146

(6)

Mode Analysis---use of analysis of Section 6.5 for evaluation of image converter; sensitivity to blackbody sources

149

(3)

Experimental Status of Up-Conversion

152

(1)

Optical Parametric Amplification and Oscillation

153

(24)

Introduction---the Manley--Rowe relations; gain indifference frequency generation; comparison with microwave parametric oscillators

153

(1)

Amplifier and Oscillator Gain Coefficients---solution of the coupled equations; gain coefficient for the amplifier and for the oscillator

154

(2)

Effects of Phase Mismatch

156

(1)

Parametric Oscillation---the first oscillator of Giordmaine and Miller; the continuous-wave oscillator of Smith

157

(4)

Mode Hopping and the Cluster Effect---frequency and amplitude instabilities of the doubly resonant oscillator

161

(3)

Power Limiting and Gain Saturation---Siegman's power limiter; saturation of the gain; coupling between the oscillator and the pump; the ring resonant oscillator

164

(5)

More Stable Configurations---servo control of the doubly resonant oscillator; the backward wave oscillator; the singly resonant parametric oscillator

169

(4)

Noise in the Optical Parametric Amplifier

173

(1)

Requirements for the Laser Pump---the multimode pump of Harris; pump requirements for the singly resonant oscillator

174

(3)

Appendix 1 Tensors

177

(3)

Appendix 2 Nonlinear Optical Susceptibilities

180

(6)

References

186

(9)

Index

195

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Applied Nonlinear Optics

Summary

Table of Contents

Supplemental Materials