Cover

Title Page

Copyright

Contents

Preface

List of Figures

Chapter 1: From Optics to Photonics

1.1 The Charm and Challenge of Photonics

1.2 The Nature of Optical Nonlinearity

1.3 Overcoming the Materials Bottleneck

1.4 The Expanding Frontiers

1.5 Explorations

Chapter 2: A Phenomenological View of Nonlinear Optics

2.1 Optics in the Nonlinear World

2.1.1 Introduction

2.1.2 First Order Susceptibility

2.1.3 Second Order Susceptibility

2.1.4 Third Order Susceptibility

2.2 Time Domain Response

2.2.1 First Order Polarization- Time Domain Response

2.2.2 Higher Order Polarizations - Time Domain Response

2.3 Frequency Domain Response

2.3.1 First Order Susceptibility

2.3.2 Second Order Susceptibility

2.3.3 General Order (n) Susceptibility

2.4 The nth order Polarization

2.5 Monochromatic Waves

2.6 Calculation of the Factor K

2.6.1 Optical Rectification

2.6.2 Second Harmonic Generation

2.6.3 Pockels Effect

2.6.4 Sum and Difference Frequency generation

2.6.5 Third Harmonic Generation

2.6.6 Nondegenerate Four Wave Mixing

2.7 Explorations

Chapter 3: Symmetry and Susceptibility Tensors

3.1 Introduction

3.2 Crystal Symmetry and Susceptibility Tensors

3.2.1 Neumann Principle

3.2.2 Symmetry of Second Order Susceptibility

3.2.3 Second Harmonic Generation

3.2.4 Kleinman Symmetry

3.2.5 Symmetry of Third Order Susceptibility

3.3 The Dielectric Permittivity Tensor

3.4 The Refractive Index Ellipsoid

3.5 Explorations

Chapter 4: Calculation of Non-linear Susceptibilities

4.1 Introduction

4.1.1 Physical Quantities in Quantum Physics

4.1.2 The Projection Operator

4.2 The Equation of Motion

4.3 Ensembles of Particles

4.4 Time-dependent Perturbation

4.5 Dipolar Interaction

4.6 First Order Density Matrix

4.7 Second Order Density Matrix

4.8 Third Order Density Matrix

4.9 Double Integrals in the Expressions for Density Matrix

4.10 Second Harmonic Susceptibility

4.11 Relaxation Effects

4.12 Applications to Color Centers

4.12.1 Third Order Susceptibility

4.12.2 Second Order Susceptibility

4.13 Explorations

Chapter 5: Nonlinear Wave Mixing Processes

5.1 Introduction

5.2 Elements of Electromagnetism

5.3 Travelling Electromagnetic Waves in Free Space

5.3.1 Energy Density in the Travelling Wave

5.4 Propagation of Electromagnetic Waves in Linear Materials

5.5 Propagation of Electromagnetic Waves in Nonlinear Materials

5.5.1 The Wave Equation

5.5.2 Energy Transfer Rate

5.6 Three Wave Mixing

5.6.1 An Approximation

5.7 Second Harmonic Generation

5.7.1 Phase Matching Schemes

5.7.2 Accurate Treatment of Second Harmonic Generation

5.8 Explorations

Chapter 6: Optical Phase Conjugation and Bistability

6.1 Optical Phase Conjugation

6.1.1 Phase Conjugation as Time Reversal

6.1.2 Phase Conjugation through Four-Wave-Mixing

6.1.3 Practical Realization

6.1.4 Peculiar Properties of the Phase Conjugate Beam

6.1.5 The Grating Picture

6.1.6 Applications of Phase Conjugation

6.2 Optical Bistability and Photonic Switching

6.2.1 Refractive Index at High Intensities : An Overview

6.2.2 Fabry-Perot Etalon

6.2.3 Photonic Switching in a Nonlinear Fabry-Pėrot Etalon

6.3 Explorations

Chapter 7: Self Focusing, Phase Modulation and Pulse Shaping

7.1 Self Focusing of Light

7.1.1 The Concept of Self Focusing

7.1.2 Self Trapping and Spatial Solitons

7.1.3 The z-scan Experiment

7.1.4 Analysis of the z- scan Trace

7.1.5 Measurement of Nonlinear Optical Absorption

7.1.6 Mechanisms of Nonlinear Absorption

7.2 Self Phase Modulation (SPM)

7.3 Pulse Shaping and Optical Soliton Propagation

7.3.1 Solitary Waves and Optical Solitons

7.4 Explorations

Chapter 8: Mechanisms and Materials

8.1 Introduction

8.2 Mechanisms of Nonlinearity

8.2.1 Anharmonicity of Potential

8.2.2 Thermal Mechanism

8.2.3 Orientational Mechanism

8.2.4 Inelastic Photon Scattering

8.2.5 Photorefractivity

8.2.6 Saturable Absorption

8.2.7 Band Gap Distortion (Franz-Keldysh Effect)

8.2.8 Band Filling Mechanism

8.2.9 Non-parabolicity of Bands

8.2.10 Delocalization of Electrons

8.3 A Perspective on Newer Materials and Processes

8.3.1 Low Dimensional Materials

Understanding Quantum Confinement

Optical Nonlinearity in Nanomaterials

Nonlinear Absorption and Optical Limiting

8.3.2 Photonic Bandgap Materials

The Concept of Photonic Bandgap

Nonlinear Photonic Crystal Fibers and Integrated Circuits

8.3.3 Slowing of Light and the Effect on Nonlinearity

8.4 Explorations

References

Bibliography

Index