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Part Ⅰ Fundamentals of Matrix Optics3

Chapter 1 Geometrical Optics3

1.1 Maxwell's equations and ray equation3

1.2 Definition of ray transfer matrix5

1.3 Derived methods for matrix elements7

1.4 Reference plane moving technique9

1.5 Ray transfer matrix in reverse propagation10

1.6 Factoring the matrix11

1.7 Image for mingmatrix13

1.8 Conjugate distance equation and magnifications14

1.9 Relation between matrix and classical expressions15

Exercises16

References17

Chapter 2 Physical Optics18

2.1 Eikonal function18

2.2 Fresnel number19

2.3 Diffraction23

2.4 Optical transfer function25

2.5 Fractional Fourier optics26

2.6 Interference32

Exercises34

References36

Chapter 3 Laser Optics38

3.1 Gaussian beam and ABCD law38

3.2 Transformation of Gaussian beam outside and inside cavity41

3.3 Self-consistence,self-reproducing and optical axis46

3.4 gfactorand G factor47

3.5 Single-pass matrix representation of resonators49

3.6 Multi-element resonators and scaled fractional Fourier transforms52

3.7 Resonators with complex elements55

3.8 Confinement,dynamic stability and insensitivity to perturbations58

3.9 Primary considerations for resonator with apertures60

3.10 Fresnel number ofGaussian beams62

3.11 Beam quality factor M265

3.12 Arbitrary beams and ABCD law67

3.13 ABCD matrix for an axial symmetrical beam through Kerr medium70

3.14 Temporal ABCD law for pulsed laser beams71

3.15 Temporal ABCD matrix73

Exercises75

References77

Chapter 4 Phase Conjugation80

4.1 The two transfer matrices for phase conjugation80

4.2 Phase-conjugate resonators83

4.3 Pseudo phase-conjugate properties of slab lasers97

4.4 The fourth retroreflector103

4.5 Retroreflective properties of the human eye107

Exercises107

References108

Part Ⅱ Progress in Matrix Optics113

Chapter 5 Misaligned Optical Systems113

5.1 Augmented 4×4 matrices113

5.2 Propagation of optical beams through asymmetrically inhomogeneous media117

5.3 Geometrical variations ofthe optical axis caused by misalignment122

5.4 Physical optics variations caused by misalignment131

5.5 Topological structure ofraytransferflow graph137

5.6 Flow graphical analyses oflaser alignment145

5.7 Laser safety monitoring considerations for dams150

Exercises155

References158

Chapter 6 Array Optics160

6.1 Difficulty of classical optics160

6.2 Matrix treatment for optical arrays162

6.3 Synthetical aberrations of arrays and αβγδ condition169

6.4 Arrays as pseudo-conjugators170

6.5 Arrayswith Det=0178

6.6 Interferencetheoryfor arrays180

6.7 A new type retroreflective film formed by laser generating glass beads184

Exercises188

References188

Chapter 7 Asymmetric Spatial-temporal Domain190

7.1 Expanded 4×4 matrices for typically asymmetric elements190

7.2 Skew rays for short waveguides200

7.3 Beam complex curvature tensor and tensor ABCD law206

7.4 Mutual transformation between nonsymmetric and symmetric beams220

7.5 Spatial-temporal coupling ofpulsed Gaussian beams232

7.6 Beam quality factor for pulsed beams236

Exercises239

References241

Chapter 8 Diffractive Optics244

8.1 Apertured uniform waves244

8.2 Fresnel zone plate and its astigmatism251

8.3 Apertured Gaussian beams256

8.4 Apertured resonators262

8.5 "Non-diffracting beams"264

8.6 On the nature of diffraction-πphasejump271

Exercises275

References276

Appendix 1279

Illustration for Appendix 1284

Appendix 2285

Appendix 3288

Illustration for Appendix 3292

Appendix4293