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Journal of Physics A Mathematical Nuclear and General

Single-interval statistics of light scattered by identical independent scatterers

P. N. Pusey, Dale W. Schaefer, D E Koppel

Published Mar 1, 1974• 39 citations
Publisher

Abstract

The authors consider the statistical properties of coherent light Rayleigh-scattered by a solution containing an arbitrary number N of independent, identical particles. Expressions are obtained for the single-interval intensity probability distribution and the moments of this distribution, which are equivalent to the measurable photocount factorial moments.

DOI
10.1088/0305-4470/7/4/016

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Journal of the Optical Society of America•Sep 1, 1983•1 citation
The authors consider the statistical properties of coherent light Rayleigh-scattered by a solution containing an arbitrary number N of independent, identical particles. Expressions are obtained for the single-interval intensity probability distribution and the moments of this distribution, which are equivalent to the measurable photocount factorial moments.
Onefold photoelectron counting distributions are evaluated for coherent light scattered by an ensemble of particles. The ensemble contains, in general, a random number of nonidentical particles. Expressions are obtained for the probability density function and the moments of the scattering intensity. These results reduce to those of Pusey, Schaefer, and Koppel when the particles are identical. Photocount probabilities are also evaluated. The variance, coefficient of skewness, and coefficient of excess are evaluated when the probability density of the intensity contributed by each scatterer is specified by a narrow Gaussian distribution centered about the deterministic mean.
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 quantum theory of the statistical properties and the photocount statistics of intense radiation in Raman scattering are presented making use of the coherent-state techniques. Both the Heisenberg-Langevin and Fokker-Planck equations approaches are developed. The existence of the conditional Glauber-Sudarshan quasi-distribution is also discussed. The time dependences of the photocount distribution and its factorial moments are demonstrated in the case of stimulated scattering and anticorrelation and antibunching of scattered photons are found.