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

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