Random Light Beams: Theory and Applications

399 Pages·2013·39.526 MB·English

by  Olga Korotkova

Electrical Engineering K
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Random Light Beams k
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Theory and Applications
“This book is a remarkably thorough discussion of the physics of
optical beam propagation. Random Light Beams serves as a great
overview of the last 30 years of classical coherence theory, as well.”
– G reg Gbur, Department of Physics and Optical Science, University T R
of North Carolina, Charlotte, USA h
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Random Light Beams: Theory and Applications discusses the o
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various phenomena associated with beam-like fields. It explores r
natural and man-made light fields, and gives an overview of y
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recently introduced families of random light beams. It also outlines
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mathematical tools for analysis, suggests schemes for realization, o
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and discusses possible applications.
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The book introduces the essential concepts needed for a deeper
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understanding of the subject, discusses various classes of
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deterministic paraxial beams and examines random scalar beams.
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It highlights electromagnetic random beams and matters relating
to generation, propagation in free space and various media, li i
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and discusses transmission through optical systems. It includes g
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applications that benefit from the use of random beams, as well as
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the interaction of beams with deterministic optical systems.
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• Includes detailed mathematical description of different model n

sources and beams s
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• Offers information that is based on the scientific results of the
last several years
• Contains more than 100 illustrations on beam behavior e
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This book gives examples of light propagation through the human eye,
laser resonators, and negative phase materials. It discusses in detail, m
propagation of random beams in random media, the scattering of
random beams and thin random layers as well as the possible uses
for these beams in imaging, tomography, and smart illumination. s
K11026
ISBN: 978-1-4398-1950-0
90000
9 781439 819500
K11026_COVER_final.indd 1 7/8/13 11:53 AM

Random
Light Beams
Theory and Applications

Random
Light Beams
Theory and Applications
Olga Korotkova
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2014 by Taylor & Francis Group, LLC
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Version Date: 20130725
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Contents
1 Introduction 1
1.1 Brief history . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Preliminary mathematics . . . . . . . . . . . . . . . . . . . . 4
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
1.3 Preliminary optics . . . . . . . . . . . . . . . . . . . . . . . . 12
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
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
1.3.4 Vectorial nature of optical fields: polarization . . . . . 28
1.3.4.1 Polarization ellipse . . . . . . . . . . . . . . . 28
1.3.4.2 Jones calculus . . . . . . . . . . . . . . . . . 29
1.3.4.3 Stokes vectors . . . . . . . . . . . . . . . . . 31
1.3.5 Spatial interference in light fields . . . . . . . . . . . . 33
Bibliography 35
2 Deterministic paraxial beams 39
2.1 Basic family of Gaussian beams . . . . . . . . . . . . . . . . 39
2.1.1 Fundamental Gaussian beam . . . . . . . . . . . . . . 40
2.1.2 Hermite-Gaussian beams . . . . . . . . . . . . . . . . 46
2.1.3 Laguerre-Gaussian beams . . . . . . . . . . . . . . . . 47
2.2 Superposition of Gaussian beams . . . . . . . . . . . . . . . . 50
2.2.1 Flat-top beams . . . . . . . . . . . . . . . . . . . . . . 50
2.2.2 Cusp-Gaussian beams . . . . . . . . . . . . . . . . . . 54
2.2.3 Dark-hollow beams . . . . . . . . . . . . . . . . . . . . 57
2.3 Other deterministic beams . . . . . . . . . . . . . . . . . . . 59
Bibliography 61
v
vi
3 Scalar stochastic beams: theory 65
3.1 Statistical description . . . . . . . . . . . . . . . . . . . . . . 65
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
3.2 Mathematical models . . . . . . . . . . . . . . . . . . . . . . 77
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-correlatedandLaguerre-Gaussian-correlated
Schell-model sources . . . . . . . . . . . . . . . . . . . 100
3.2.6 Non-uniformly correlated sources . . . . . . . . . . . . 104
3.2.7 I0-Bessel correlated sources . . . . . . . . . . . . . . . 108
3.3 Methods of generation . . . . . . . . . . . . . . . . . . . . . . 113
Bibliography 119
4 Electromagnetic stochastic beams: theory 123
4.1 Statistical description . . . . . . . . . . . . . . . . . . . . . . 123
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
4.2 Electromagnetic quasi-homogeneous sources . . . . . . . . . 138
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
4.3 Propagation in free space and linear media . . . . . . . . . . 146
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 arbi-
trary index of refraction . . . . . . . . . . . . . . . . . 151
4.4 Generalized Jones-Mueller calculus . . . . . . . . . . . . . . . 152
4.4.1 Transmission through deterministic devices . . . . . . 152
4.4.2 Transmission through random devices . . . . . . . . . 157
4.4.3 Combination of several devices . . . . . . . . . . . . . 157
4.5 Electromagnetic Gaussian Schell-model sources and beams . 159
vii
4.5.1 Realizability and beam conditions . . . . . . . . . . . 159
4.5.2 Methods of generation . . . . . . . . . . . . . . . . . . 165
4.5.3 Propagation in free space . . . . . . . . . . . . . . . . 168
4.6 Electromagnetic beams with Gaussian statistics . . . . . . . 170
4.6.1 Higher-order statistical moments of fields . . . . . . . 170
4.6.2 Higher-order moments of beams with Gaussian statis-
tics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
4.6.3 Fluctuations in power . . . . . . . . . . . . . . . . . . 176
4.6.4 Higher-order moments of Stokes parameters . . . . . . 179
4.7 Other stochastic electromagnetic beams . . . . . . . . . . . . 185
4.7.1 Electromagnetic multi-Gaussian Schell-model beams . 185
4.7.2 Electromagnetic non-uniformly correlated beams . . . 188
Bibliography 195
5 Interaction of random electromagnetic beams with optical
systems 201
5.1 ABCD matrix method for beam interaction with image-
forming 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
6 Random beams in linear random media 237
6.1 Natural random media: turbulence . . . . . . . . . . . . . . . 237
6.1.1 Atmospheric turbulence . . . . . . . . . . . . . . . . . 239
6.1.2 Oceanic turbulence . . . . . . . . . . . . . . . . . . . . 242
6.1.3 Biological tissues . . . . . . . . . . . . . . . . . . . . . 243
6.2 Scalar random beam interaction with random media . . . . . 246
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
6.3 Electromagnetic random beam interaction with random media 263
6.3.1 General theory . . . . . . . . . . . . . . . . . . . . . . 263
6.3.2 Polarization changes in random media . . . . . . . . . 264
6.3.3 Propagation in non-Kolmogorov atmospheric turbu-
lence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
6.3.4 Propagation in oceanic turbulence . . . . . . . . . . . 272
Bibliography 279
viii
7 Mitigation of random media effects with random beams 285
7.1 Free-space optical communications . . . . . . . . . . . . . . . 285
7.1.1 Communication link quality criteria . . . . . . . . . . 286
7.1.2 The pdf models for beam intensity in the atmosphere 288
7.2 Mitigation of scintillations by different randomization schemes 292
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
7.3 Active LIDAR systems with rough targets . . . . . . . . . . 299
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 semi-
rough target . . . . . . . . . . . . . . . . . . . . . . . 302
7.3.3 Target characterization: inverse problem . . . . . . . . 311
Bibliography 315
8 Weak scattering of random beams 319
8.1 Classic theory of weak scattering . . . . . . . . . . . . . . . . 319
8.2 Description of scattering media . . . . . . . . . . . . . . . . . 322
8.2.1 Single scatterer . . . . . . . . . . . . . . . . . . . . . . 322
8.2.2 Collections of scatterers . . . . . . . . . . . . . . . . . 326
8.2.3 Random scatterers . . . . . . . . . . . . . . . . . . . . 326
8.3 Weak scattering for scalar fields . . . . . . . . . . . . . . . . 327
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
8.4 Weak scattering of electromagnetic fields . . . . . . . . . . . 335
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
Index 355