Table of Contents

Dedication v

Preface vii

About the Authors ix

1 Geometrical Optics 1

1.1 Fermat's Principle 2

1.2 Reflection and Refraction 5

1.3 Ray Propagation in an Inhomogeneous Medium: Ray Equation 8

1.4 Matrix Methods in Paraxial Optics 24

1.4.1 The ray transfer matrix 25

1.4.2 Illustrative examples 33

1.4.3 Cardinal points of an optical system 38

1.5 Reflection Matrix and Optical Resonators 43

1.6 Ray Optics using MATLAB 49

2 Wave Propagation and Wave Optics 59

2.1 Maxwell's Equations: A Review 59

2.2 Linear Wave Propagation 63

2.2.1 Traveling-wave solutions 63

2.2.2 Maxwell's equations in phasor domain: Intrinsic impedance, the Poynting vector, and polarization 68

2.2.3 Electromagnetic waves at a boundary and Fresnel's equations 74

2.3 Wave Optics 90

2.3.1 Fourier transform and convolution 90

2.3.2 Spatial frequency transfer function and spatial impulse response of propagation 97

2.3.3 Examples of Fresnel diffraction 101

2.3.4 Fraunhofer diffraction 102

2.3.5 Fourier transforming property of an ideal lens 105

2.3.6 Resonators and Gaussian beams 113

2.4 Gaussian Beam Optics and MATLAB Examples 125

2.4.1 q-transformation of Gaussian beams 127

2.4.2 MATLAB example: Propagation of a Gaussian beam 130

3 Beam Propagation in Inhomogeneous Media and in Kerr Media 142

3.1 Wave Propagation in a Linear Inhomogeneous Medium 142

3.2 Optical Propagation in Square-Law Media 143

3.3 The Paraxial Wave Equation 151

3.4 The Split-Step Beam Propagation Method 153

3.5 MATLAB Examples Using the Split-Step Beam Propagation Method 157

3.6 Beam Propagation in Nonlinear Media: The Kerr Media 168

3.6.1 Spatial soliton 169

3.6.2 Self-focusing and self-defocusing 173

4 Acousto-Optics 188

4.1 Qualitative Description and Heuristic Background 188

4.2 The Acousto-Optic Effect: General Formalism 198

4.3 Raman-Nath Equations 201

4.4 Contemporary Approach 204

4.5 Raman-Nath Regime 206

4.6 Bragg Regime 208

4.7 Numerical Examples 215

4.8 Modern Applications of the Acousto-Optic Effect 222

4.8.1 Intensity modulation of a laser beam 222

4.8.2 Light beam deflector and spectrum analyzer 225

4.8.3 Demodulation of frequency-modulated (FM) signals 226

4.8.4 Bistable switching 228

4.8.5 Acousto-optic spatial filtering 234

4.8.6 Acousto-optic heterodyning 242

5 Electro-Optics 254

5.1 The Dielectric Tensor 254

5.2 Plane-Wave Propagation in Uniaxial Crystals: Birefringence 260

5.3 Applications of Birefringence: Wave Plates 268

5.4 The Index Ellipsoid 271

5.5 Electro-Optic Effect in Uniaxial Crystals 276

5.6 Some Applications of the Electro-Optic Effect 281

5.6.1 Intensity modulation 281

5.6.2 Phase modulation 292

5.6.3 Frequency shifting 294

Index 301