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Physical Review A

Photoelectron statistics and autocorrelation of a mixture of chaotic and coherent light of same and different frequencies

T. Aoki, Y. Endo, Hiromitsu Takayanagi, Kenji Sakurai

Published Feb 1, 1976• 4 citations
Publisher

Abstract

The statistics and autocorrelation function of Rayleigh-scattered light mixed with coherent light were experimentally studied. The factorial moments were measured for the cases of both heterofrequencies and homofrequencies. In the case of heterofrequencies, the mean frequency of the scattered light was shifted from that of the coherent light by using a flowing scatterer. The second- and third-order factorial moments obtained were compared with the theory of Jaiswal and Mehta and were found to be experimental proof for the theory. The autocorrelation function was also measured in the case of a heterofrequency, and the result was explained well by the theoretical expression deduced here.

DOI
10.1103/physreva.13.853

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Canadian Journal of Physics•Jun 15, 1972•3 citations
The statistics and autocorrelation function of Rayleigh-scattered light mixed with coherent light were experimentally studied. The factorial moments were measured for the cases of both heterofrequencies and homofrequencies. In the case of heterofrequencies, the mean frequency of the scattered light was shifted from that of the coherent light by using a flowing scatterer. The second- and third-order factorial moments obtained were compared with the theory of Jaiswal and Mehta and were found to be experimental proof for the theory. The autocorrelation function was also measured in the case of a heterofrequency, and the result was explained well by the theoretical expression deduced here.
The statistics and autocorrelation function of the light scattered from polystyrene latex have been studied with a light-detecting system on-line with a small digital computer. The distributions of photoelectric counts have been measured during count intervals from 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ to 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ sec. The results were well accounted for by the approximate theory of Mandel. The factorial moments have been measured to sixth order and the results were in excellent agreement with theoretical calculations. For the first time, we have directly measured the autocorrelation function without using a clipping or scaling method. With this direct method, the comparison between the results of the composite measurements and the theoretical predictions can be quantitatively discussed.
Statistical properties of partially polarized Gaussian light were studied experimentally for degrees of polarization PPP from 0.03 to 1 by a standard technique of photon counting. The Gaussian light with an arbitrary degree of polarization was obtained from Rayleigh scattering of orthogonally polarized laser beams. The factorial moments up to sixth order of the photoelectron distribution were measured with an arbitrary temporal and spatial coherence. After corrections were taken for the experimental conditions, the theoretical values of these factorial moments were compared with the experimental results. It is shown that the theoretical predictions were quantitatively well verified by the present measurements. The microscopic process is discussed from the standpoint of the light scattering system used in the present measurements, and it is shown that the orthogonally polarized components of the scattered light observed are statistically independent.
In this paper, we consider the photoelectron counting distribution when the wave field incident on the detector is a mixture of harmonic signal and thermal noise. An expression for the factorial moment-generating function of the number of counts is obtained in terms of the eigenvalues of an associated integral equation. This expression is then used to evaluate the factorial cumulants of the number of counts. The results are valid for an arbitrary counting interval. The extension to photoelectron counting with several detectors is considered in paper II of the present investigation.
General formulas for the factorial cumulants of the photocounting distribution and the cumulants of the integrated intensity are obtained for chaotic light superposed with coherent light, for experiments involving NNN different counting intervals. The chaotic light may be partially polarized, need not be time stationary or single mode, may differ in frequency from the coherent light, and may have any spectral distribution.
The statistical behavior of photoelectrons emitted at L points of a photocathode in partially coherent Gaussian light is considered. The exact formula for the cumulants and the factorial moment generating function is derived. An exact expression for the photocount distribution and for the factorial moments is obtained in the case when the detection time is much smaller than the coherence time. Two cases of interest which were treated earlier by the same authors are also considered. In particular, the case of two points of detection is of special interest because a physical meaning can be given to the difference of the normalized eigenvalues. Finally, both the exact and approximate theories are compared with the experimental photocount distribution for four different geometrical arrangements.