Essentials of Nonlinear Optics

Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.

Professor Y.V.G.S. Murti, IIT Madras, India
Y.V.G.S. Murti joined the premier institution of IIT Madras, where his teaching and research activities spanned over a few decades. Professor Murti's Condensed Matter research included experimental and theoretical investigations addressing problems on lattice defects and related transport and optical phenomena. Establishing a school of research on Photonics, he led work on experiments on Nonlinear Wave Mixing as well as on theoretical evaluation of Optical Nonlinearities of color centers.

Professor C. Vijayan, IIT Madras, India
C. Vijayan achieved his M.Sc. and PhD in physics from the Indian Institute of Technology, Madras, Chennai. His early work includes Solid State Transport Phenomena, and Photonic Memories. Over the last two decades, he has been actively pursuing research on nonlinear optical properties of Novel Materials. A professor of physics at the Indian Institute of Technology, Madras, he heads the Photonics laboratory directing work on Quantum Confined Materials and Nanophotonic Materials.

1.1 The Charm and Challenge of Photonics 2

1.2 The Nature of Optical Nonlinearity 3

1.3 Overcoming the Materials Bottleneck 5

1.4 The Expanding Frontiers 7

1.5 Explorations 9

2 A Phenomenological View of Nonlinear Optics 11

2.1 Optics in the Nonlinear World 12

2.2 Time Domain Response 16

2.3 Frequency Domain Response 19

2.4 The n^th order Polarization 21

2.5 Monochromatic Waves 21

2.6 Calculation of the Factor K 24

2.7 Explorations 27

3 Symmetry and Sysceptibility Tensors 29

3.1 Introduction 30

3.2 Crystal Symmetry and Susceptibility Tensors 30

3.3 The Dielectric Permittivity Tensor 47

3.4 The Refractive Index Ellipsoid 50

3.5 Explorations 52

4 Calculation of Non-linear Susceptibilities 55

4.1 Introduction 56

4.2 The Equation of Motion 59

4.3 Ensembles of Particles 60

4.5 Dipolar Interaction 63

4.6 First Order Density Matrix 65

4.7 Second Order Density Matrix 66

4.8 Third Order Density Matrix 67

4.9 Double Integrals in the Expressions for Density Matrix 68

4.10 Second Harmonic Susceptibility 70

4.11 Relaxation Effects 71

4.12 Applications to Color Centers 72

4.13 Explorations 75

5 Nonlinear Wave Mixing Processess 77

5.1 Introduction 78

5.2 Elements of Electromagnetism 78

5.3 Travelling Electromagnetic Waves in Free Space 81

5.4 Propagation of Electromagnetic Waves in Linear Materials 83

5.5 Propagation of Electromagnetic Waves in Nonlinear Materials 85

5.6 Three Wave Mixing 88

5.7 Second Harmonic Generation 91

5.8 Explorations 98

6 Optical Phase Conjugation and Bistability 101

6.1 Optical Phase Conjugation 102

6.2 Optical Bistability and Photonic Switching 114

6.3 Explorations 119

7 Self Focusing, Phase Modulation and Pulse Shaping 125

7.1 Self Focusing of Light 126

7.2 Self Phase Modulation (SPM) 137

7.3 Pulse Shaping and Optical Soliton Propagation 140

7.4 Explorations 143

8 Mechanisms and Materials 147

8.1 Introduction 148

8.2 Mechanisms of Nonlinearity 149

8.3 A Perspective on Newer Materials and Processes 162

8.4 Explorations 171

Bibliography 173

References 175

Index 185

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