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Part Ⅰ Fundamentals of Matrix Optics 3

Chapter 1 Geometrical Optics 3

1.1 Maxwell's equations and ray equation 3

1.2 Definition of ray transfer matrix 5

1.3 Derived methods for matrix elements 7

1.4 Reference plane moving technique 9

1.5 Ray transfer matrix in reverse propagation 10

1.6 Factoring the matrix 11

1.7 Image for mingmatrix 13

1.8 Conjugate distance equation and magnifications 14

1.9 Relation between matrix and classical expressions 15

Exercises 16

References 17

Chapter 2 Physical Optics 18

2.1 Eikonal function 18

2.2 Fresnel number 19

2.3 Diffraction 23

2.4 Optical transfer function 25

2.5 Fractional Fourier optics 26

2.6 Interference 32

Exercises 34

References 36

Chapter 3 Laser Optics 38

3.1 Gaussian beam and ABCD law 38

3.2 Transformation of Gaussian beam outside and inside cavity 41

3.3 Self-consistence,self-reproducing and optical axis 46

3.4 gfactorand G factor 47

3.5 Single-pass matrix representation of resonators 49

3.6 Multi-element resonators and scaled fractional Fourier transforms 52

3.7 Resonators with complex elements 55

3.8 Confinement,dynamic stability and insensitivity to perturbations 58

3.9 Primary considerations for resonator with apertures 60

3.10 Fresnel number ofGaussian beams 62

3.11 Beam quality factor M2 65

3.12 Arbitrary beams and ABCD law 67

3.13 ABCD matrix for an axial symmetrical beam through Kerr medium 70

3.14 Temporal ABCD law for pulsed laser beams 71

3.15 Temporal ABCD matrix 73

Exercises 75

References 77

Chapter 4 Phase Conjugation 80

4.1 The two transfer matrices for phase conjugation 80

4.2 Phase-conjugate resonators 83

4.3 Pseudo phase-conjugate properties of slab lasers 97

4.4 The fourth retroreflector 103

4.5 Retroreflective properties of the human eye 107

Exercises 107

References 108

Part Ⅱ Progress in Matrix Optics 113

Chapter 5 Misaligned Optical Systems 113

5.1 Augmented 4×4 matrices 113

5.2 Propagation of optical beams through asymmetrically inhomogeneous media 117

5.3 Geometrical variations ofthe optical axis caused by misalignment 122

5.4 Physical optics variations caused by misalignment 131

5.5 Topological structure ofraytransferflow graph 137

5.6 Flow graphical analyses oflaser alignment 145

5.7 Laser safety monitoring considerations for dams 150

Exercises 155

References 158

Chapter 6 Array Optics 160

6.1 Difficulty of classical optics 160

6.2 Matrix treatment for optical arrays 162

6.3 Synthetical aberrations of arrays and αβγδ condition 169

6.4 Arrays as pseudo-conjugators 170

6.5 Arrayswith Det=0 178

6.6 Interferencetheoryfor arrays 180

6.7 A new type retroreflective film formed by laser generating glass beads 184

Exercises 188

References 188

Chapter 7 Asymmetric Spatial-temporal Domain 190

7.1 Expanded 4×4 matrices for typically asymmetric elements 190

7.2 Skew rays for short waveguides 200

7.3 Beam complex curvature tensor and tensor ABCD law 206

7.4 Mutual transformation between nonsymmetric and symmetric beams 220

7.5 Spatial-temporal coupling ofpulsed Gaussian beams 232

7.6 Beam quality factor for pulsed beams 236

Exercises 239

References 241

Chapter 8 Diffractive Optics 244

8.1 Apertured uniform waves 244

8.2 Fresnel zone plate and its astigmatism 251

8.3 Apertured Gaussian beams 256

8.4 Apertured resonators 262

8.5 "Non-diffracting beams" 264

8.6 On the nature of diffraction-πphasejump 271

Exercises 275

References 276

Appendix 1 279

Illustration for Appendix 1 284

Appendix 2 285

Appendix 3 288

Illustration for Appendix 3 292

Appendix4 293