Introduction to the Theory of Coherence and Polarization of Light

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ISBN: 9780521822114 | 0521822114
Cover: Hardcover
Copyright: 10/22/2007

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All optical fields undergo random fluctuations. They may be small, as in the output of many lasers, or they may be appreciably larger, as in light generated by thermal sources. The underlying theory of fluctuating optical fields is known as coherence theory. An important manifestation of the fluctuations is the phenomenon of partial polarization. Actually, coherence theory deals with considerably more than fluctuations. Unlike usual treatments, it describes optical fields in terms of observable quantities and elucidates how such quantities, for example, the spectrum of light, change as light propagates.

Preface	p. xi
Elementary coherence phenomena	p. 1
Interference and statistical similarity	p. 1
Temporal coherence and the coherence time	p. 4
Spatial coherence and the coherence area	p. 5
The coherence volume	p. 8
Problems	p. 10
Mathematical preliminaries	p. 11
Elementary concepts of the theory of random processes	p. 11
Ergodicity	p. 17
Complex representation of a real signal and the envelope of a narrow-band signal	p. 19
The autocorrelation and the cross-correlation functions	p. 22
The autocorrelation function of a finite sum of periodic components with random amplitudes	p. 24
The spectral density and the Wiener-Khintchine theorem	p. 25
Problems	p. 29
Second-order coherence phenomena in the space-time domain	p. 31
Interference law for stationary optical fields. The mutual coherence function and the complex degree of coherence	p. 31
Generation of spatial coherence from an incoherent source. The van Cittert-Zernike theorem	p. 37
Illustrative examples	p. 46
Michelson's method for measuring stellar diameters	p. 46
Michelson's method for determining energy distribution in spectral lines	p. 51
Propagation of the mutual intensity	p. 54
Wave equations for the propagation of mutual coherence in free space	p. 56
Problems	p. 58
Second-order coherence phenomena in the space-frequency domain	p. 60
Coherent-mode representation and the cross-spectral density as a correlation function	p. 60
The spectral interference law and the spectral degree of coherence	p. 63
An illustrative example: spectral changes on interference	p. 69
Interference of narrow-band light	p. 73
Problems	p. 76
Radiation from sources of different states of coherence	p. 79
Fields generated by sources with different coherence properties	p. 79
Correlations and the spectral density in the far field	p. 81
Radiation from some model sources	p. 88
Schell-model sources	p. 88
Quasi-homogeneous sources	p. 90
Sources of different states of spatial coherence which generate identical distributions of the radiant intensity	p. 95
Coherence properties of Lambertian sources	p. 97
Spectral changes on propagation. The scaling law	p. 102
Problems	p. 108
Coherence effects in scattering	p. 111
Scattering of a monochromatic plane wave on a deterministic medium	p. 111
Scattering of partially coherent waves on a deterministic medium	p. 115
Scattering on random media	p. 118
General formulas	p. 118
Examples	p. 121
Scattering on a quasi-homogeneous medium	p. 123
Problems	p. 127
Higher-order coherence effects	p. 129
Introduction	p. 129
Intensity interferometry with radio waves	p. 131
The Hanbury Brown-Twiss effect and intensity interferometry with light	p. 134
Einstein's formula for energy fluctuations in blackbody radiation and the wave-particle duality	p. 140
Mandel's theory of photoelectric detection of light fluctuations	p. 143
Mandel's formula for photocount statistics	p. 143
The variance of counts from a single photodetector	p. 145
Correlation between count fluctuations from two detectors	p. 147
Determination of statistical properties of light from photocount measurements	p. 149
Problems	p. 151
Elementary theory of polarization of stochastic electromagnetic beams	p. 154
The 2 X 2 equal-time correlation matrix of a quasi-monochromatic electromagnetic beam	p. 154
Polarized, unpolarized and partially polarized light. The degree of polarization	p. 158
Completely polarized light	p. 158
Natural (unpolarized) light	p. 160
Partially polarized light and the degree of polarization	p. 161
The geometrical significance of complete polarization. The Stokes parameters of completely polarized light. The Poincare sphere	p. 165
Problems	p. 171
Unified theory of polarization and coherence	p. 174
The 2 X 2 cross-spectral density matrix of a stochastic electromagnetic beam	p. 174
The spectral interference law, the spectral degree of coherence and the spectral degree of polarization of stochastic electromagnetic beams	p. 175
Determination of the cross-spectral density matrix from experiments	p. 179
Changes in random electromagnetic beams on propagation	p. 181
Propagation of the cross-spectral density matrix of a stochastic electromagnetic beam - general formulas	p. 181
Propagation of the cross-spectral density matrix of an electromagnetic Gaussian Schell-model beam	p. 183
Examples of correlation-induced changes tn stochastic electromagnetic beams on propagation	p. 186
Coherence-induced changes of the degree of polarization in Young's interference experiment	p. 191
Generalized Stokes parameters	p. 194
Problems	p. 197
Appendices	p. 202
Cells of phase space and the degeneracy parameter	p. 202
Cells of phase space of a quasi-monochromatic light wave (Section 1.4)	p. 202
Cells of phase space of radiation in a cavity (Sections 7.4 and 7.5)	p. 204
The degeneracy parameter	p. 206
Derivation of Mandel's formula for photocount statistics [Eq. (2) of Section 7.5.1]	p. 208
The degree of polarization of an electromagnetic Gaussian Schell-model source	p. 210
Some important probability distributions	p. 212
The binomial (or Bernoulli) distribution and some of its limiting cases	p. 212
The Bose-Einstein distribution	p. 214
Author index	p. 216
Subject index	p. 220
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Introduction to the Theory of Coherence and Polarization of Light

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