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Physical Review A

Photon statistics of partially polarized Gaussian light

Tadashi Aoki, Katsumi Sakurai

Published Oct 1, 1979• 5 citations
Publisher

Abstract

Statistical properties of partially polarized Gaussian light were studied experimentally for degrees of polarization $P$ 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.

DOI
10.1103/physreva.20.1593

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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.
The photon counting statistics of light is studied, in which the various types of photon counting distribution can be represented by Nakagami'sm-distribution. To investigate this theoretical utility we have measured the photon counting distribution of laser light scattered by a very dilute solution in which non-Gaussian statistics appear. The comparison is also made by the factrial moment between the experimental value and theoretical one. The experimental distribution is in agreement with the theoretical distribution.
We study the photocounting statistics and the integrated intensity distribution of partially polarized Gaussian light. Expressions for the characteristic functions of the two distributions are obtained in terms of the eigenvalues of an associated integral equation. Closed-form expressions for these characteristic functions are derived for the special case when the spectral profile of the light is Lorentzian. Results from a numerical evaluation of the factorial moments of the number of photoelectrons in a given time interval and of the integrated intensity distribution are also presented.
Exact formulas are derived for the factorial cumulants of the photoelectric counting distribution of partially polarized Gaussian and Gaussian-plus-coherent light for arbitrary detector areas. The results make it possible to follow the transition from Bose-Einstein statistics in the small-area limit to Poisson statistics in the large-area limit. Numerical results are presented for a circular geometry. These methods, which enable experimentally measured photocount statistics to be extrapolated to zero detector area, are expected to be useful in measurements of small departures from Gaussian statistics. Other theoretical results make it possible to express the statistics of the sum of photocounts from different photocathodes, or the multiaperture, single-cathode (MASC) photocount statistics of light of arbitrary coherence properties, in terms of the multicathode (MC) counting statistics. Explicit expressions are derived for the MASC photocount cumulants for the special case of partially polarized Gaussian light.
Microscopic scattering processes are discussed for two structures of light incident on thermal particles. One is composed of two collinear light beams originating from different oscillating modes of a laser, and another is composed of two counter propagating beams originating from the same oscillating mode. A comparison of the cumulant expansions for the above two cases has allowed discerning which terms in the scattering structures led to the same statistical properties of the scattered photons. It is shown that, for the scattering of multimode-laser light, the statistical properties of scattered photons are not affected by the noncorrelating random phases of the incident laser fields but are the same as those in the case of single-mode laser light under practical scattering experiments. The factorial moments ${F}_{k}[=〈n(n\ensuremath{-}1)\ensuremath{\cdots}(n\ensuremath{-}k+1)〉]$ up to sixth order of the scattered photons were measured for various scattering situations including the above two cases, and they were found to support the theoretical results.
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.
The probability distribution of photoelectrons detected simultaneously at L different points of a photocathode is studied under the assumptions that the incident light is Gaussian with arbitrary state of coherence and polarization. The generating function is expressed as an infinite product of eigenvalues of a matrix integral equation, the kernel being the correlation matrix. The case of spectrally pure light beams is discussed in detail and the relation to previous work is given. The notion of polarizationally pure beams is introduced, for which the polarization state of light is independent of the spatial and temporal coherence. The generating function is then expressed in terms of eigenvalues of a simpler integral equation. An approximate distribution valid up to the second moment is derived.