RANDOM LIGHT BEAMS. THEORY AND APPLICATIONS
Olga Korotkova
CRC Press 2013.
TABLE OF CONTENTS
1
Preface 25
Symbol 27
1 Introduction 1
2
1.1 Brief history 1
1.2 Preliminary mathematics 4
3
1.2.1 Random processes 4
1.2.2 Spectral representation of random processes 7
1.2.3 Analytic representation of complex signals 10
1.2.4 Gaussian random processes 11
2
1.3 Preliminary optics 12
3
1.3.1 Maxwell’s, wave and Helmholtz equations 12
1.3.2 Angular spectrum representation and beam conditions 15
1.3.3 Exact beams 19
4
1.3.3.1 Plane waves and cosine beams 20
1.3.3.2 Bessel beams 22
1.3.3.3 Mathieu beams 24
1.3.3.4 Parabolic beams 25
3
1.3.4 Vectorial nature of optical fields: polarization 28
4
1.3.4.1 Polarization ellipse 28
1.3.4.2 Jones calculus 29
1.3.4.3 Stokes vectors 31
3
1.3.5 Spatial interference in light fields 33
Bibliography 35
2
1
2 Deterministic paraxial beams 39
2
2.1 Basic family of Gaussian beams 39
3
2.1.1 Fundamental Gaussian beam 40
2.1.2 Hermite-Gaussian beams 46
2.1.3 Laguerre-Gaussian beams 47
2
2.2 Superposition of Gaussian beams 50
3
2.2.1 Flat-top beams 50
2.2.2 Cusp-Gaussian beams 54
2.2.3 Dark-hollow beams 57
2
2.3 Other deterministic beams 59
Bibliography 61
1
3 Scalar stochastic beams: theory 65
2
3.1 Statistical description 65
3
3.1.1 Mutual coherence function 66
3.1.2 Cross-spectral density function 67
3.1.3 Spectral and coherence properties 69
3.1.4 Total, encircled and fractional power 70
3.1.5 Higher-order statistical properties 71
3.1.6 Coherent mode decomposition 72
3.1.7 Angular spectrum decomposition 74
2
3.2 Mathematical models 77
3
3.2.1 General structure 77
3.2.2 Gaussian Schell-model sources 79
3.2.3 J0-Bessel correlated sources 87
3.2.4 Multi-Gaussian correlated sources 93
3.2.5 Bessel-Gaussian-correlated and Laguerre-Gaussian-correlated Schell-model sources 100
3.2.6 Non-uniformly correlated sources 104
3.2.7 I0-Bessel correlated sources 108
2
3.3 Methods of generation 113
Bibliography 119
1
4 Electromagnetic stochastic beams: theory 123
2
4.1 Statistical description 123
3
4.1.1 Beam coherence polarization matrix 123
4.1.2 Cross-spectral density matrix 124
4.1.3 Spectral, coherence and polarization properties 126
4.1.4 Classic and generalized Stokes parameters 130
4.1.5 Coherent mode decomposition 132
4.1.6 Angular-spectrum decomposition 134
2
4.2 Electromagnetic quasi-homogeneous sources 138
3
4.2.1 Far-field analysis and the reciprocity relations 138
4.2.2 Conditions for spectral invariance 142
4.2.3 Conditions for polarization invariance 143
2
4.3 Propagation in free space and linear media 146
3
4.3.1 Propagation in free space 146
4.3.2 Conservation laws for electromagnetic stochastic free fields 147
4.3.3 Propagation in linear deterministic media with arbitrary index of refraction 151
2
4.4 Generalized Jones-Mueller calculus 152
3
4.4.1 Transmission through deterministic devices 152
4.4.2 Transmission through random devices 157
4.4.3 Combination of several devices 157
2
4.5 Electromagnetic Gaussian Schell-model sources and beams 159
3
4.5.1 Realizability and beam conditions 159
4.5.2 Methods of generation 165
4.5.3 Propagation in free space 168
2
4.6 Electromagnetic beams with Gaussian statistics 170
3
4.6.1 Higher-order statistical moments of fields 170
4.6.2 Higher-order moments of beams with Gaussian statistics 175
4.6.3 Fluctuations in power 176
4.6.4 Higher-order moments of Stokes parameters 179
2
4.7 Other stochastic electromagnetic beams 185
3
4.7.1 Electromagnetic multi-Gaussian Schell-model beams 185
4.7.2 Electromagnetic non-uniformly correlated beams 188
Bibliography 195
2
1
5 Interaction of random electromagnetic beams with optical systems 201
2
5.1 ABCD matrix method for beam interaction with imageforming optical systems 201
5.2 Random beams in the human eye 207
5.3 Random beams in negative phase materials 213
5.4 Imaging by twisted random beams 219
5.5 Tensor method for random beam interaction with astigmatic ABCD systems 225
5.6 Electromagnetic random beams in optical resonators 227
Bibliography 233
1
6 Random beams in linear random media 237
2
6.1 Natural random media: turbulence 237
3
6.1.1 Atmospheric turbulence 239
6.1.2 Oceanic turbulence 242
6.1.3 Biological tissues 243
2
6.2 Scalar randombeam interaction with random media 246
3
6.2.1 Extended Huygens-Fresnel principle 247
6.2.2 Angular spectrum method 250
6.2.3 Fractional power changes 254
6.2.4 Correlation-induced spectral changes 255
2
6.3 Electromagnetic random beam interaction with random media 263
3
6.3.1 General theory 263
6.3.2 Polarization changes in randommedia 264
6.3.3 Propagation in non-Kolmogorov atmospheric turbulence 267
6.3.4 Propagation in oceanic turbulence 272
Bibliography 279
2
1
7 Mitigation of random media effects with random beams 285
2
7.1 Free-space optical communications 285
3
7.1.1 Communication link quality criteria 286
7.1.2 The pdf models for beam intensity in the atmosphere 288
2
7.2 Mitigation of scintillations by different randomization schemes 292
3
7.2.1 Non-uniform polarization 292
7.2.2 Partial coherence 295
7.2.3 Combination of non-uniform polarization and partial coherence 296
2
7.3 Active LIDAR systems with rough targets 299
3
7.3.1 Beam propagation in optical systems in the presence of random medium 300
7.3.2 Beam passage through a LIDAR system with a semirough target 302
7.3.3 Target characterization: inverse problem 311
Bibliography 315
2
1
8 Weak scattering of random beams 319
2
8.1 Classic theory of weak scattering 319
8.2 Description of scattering media 322
3
8.2.1 Single scatterer 322
8.2.2 Collections of scatterers 326
8.2.3 Random scatterers 326
2
8.3 Weak scattering for scalar fields 327
3
8.3.1 Cross-spectral density function of scattered field 327
8.3.2 Coherence effects on Mie scattering 332
8.3.3 Scattering from turbulent medium containing particles 333
2
8.4 Weak scattering of electromagnetic fields 335
3
8.4.1 Cross-spectral density matrix of scattered field 335
8.4.2 Scattering from a delta-correlated slab 341
8.4.3 Scattering from a thin bio-tissue layer 344
Bibliography 351
2
1
Index 355
0
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