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Preface v

1. Geometrical Optics
1.1 Fermat's Principle 2
1.2 Reflection and Refraction 3
1.3 Ray Propagation in an Inhomogeneous Medium: Ray Equation 6
1.4 Matrix Methods in Paraxial Optics 16
1.4.1 The Ray Transfer Matrix 17
1.4.2 Illustrative examples 25
1.4.3 Cardinal points of an optical system 27
1.5 Reflection Matrix and Optical Resonators 32
1.6 Ray Optics using MATLAB 37

2. Wave Propagation and Wave Optics
2.1 Maxwell's Equations: A Review 46
2.2 Linear Wave Propagation 50
2.2.1 Traveling-wave solutions 50
2.2.2 Maxwell's equations in phasor domain: Intrinsic
impedance, the Poynting vector, and polarization 55
2.2.3 Electromagnetic waves at a boundary and Fresnel's equations 60
2.3 Wave Optics 73
2.3.1 Fourier transform and convolution 74
2.3.2 Spatial frequency transfer function and spatial impulse response of propagation 75
2.3.3 Examples of Fresnel diffraction 79
2.3.4 Fraunhofer diffraction 80
2.3.5 Fourier transforming property of ideal lenses 83
2.3.6 Resonators and Gaussian beams 86
2.4 Gaussian Beam Optics and MATLAB Examples 97
2.4.1 q-transformation of Gaussian beams 99
2.4.2 MATLAB example: propagation of a Gaussian beam. 102

3. Beam Propagation in Inhomogeneous Media
3.1 Wave Propagation in a Linear Inhomogeneous Medium Il l
3.2 Optical Propagation in Square-Law Media 112
3.3 The Paraxial Wave Equation 119
3.4 The Split-Step Beam Propagation Method 121
3.5 MATLAB Examples Using the Split-Step Beam Propagation Method 124
3.6 Beam Propagation in Nonlinear Media: The Kerr Media 134
3.6.1 Spatial soliton 136
3.6.2 Self-focusing and self-defocusing 139

4. Acousto-Optics
4.1 Qualitative Description and Heuristic Background 152
4.2 The Acousto-optic Effect: General Formalism 158
4.3 Raman-Nath Equations 161
4.4 Contemporary Approach 164
4.5 Raman-Nath Regime 165
4.6 Bragg Regime 166
4.7 Numerical Examples 172
4.8 Modern Applications of the Acousto-Optic Effect 178
4.8.1 Intensity modulation of a laser beam 178
4.8.2 Light beam deflector and spectrum analyzer 181
4.8.3 Demodulation of frequency modulated (FM) signals... 182
4.8.4 Bistable switching 184
4.8.5 Acousto-optic spatial filtering 188
4.8.6 Acousto-optic heterodyning 196

5. Electro-Optics
5.1 The Dielectric Tensor 205
5.2 Plane-Wave Propagation in Uniaxial Crystals; Birefringence 210
5.3 Applications of Birefringence: Wave Plates 217
5.4 The Index Ellipsoid 219
5.5 Electro-Optic Effect in Uniaxial Crystals 223
5.6 Some Applications of the Electro-Optic Effect equations 227
5.6.1 Intensity modulation 227
5.6.2 Phase modulation 236

Index 241
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