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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Experimental photon statistics of multiscattered light

G. F. Lorusso, Vito Capozzi, Antonio Minafra

Published Apr 1, 1994• 2 citations
Publisher

Abstract

The concentration dependence of the statistical properties of light scattered by a monodisperse sphere suspension has been studied. Theoretical predictions for photon-counting distributions, obtained by supposing the scattered field is a superposition of coherent signal S and noise excitation N, agree well with the experimental results, thus providing an alternative method to obtain quantitative information on the influence of multiple scattering on measurements. Moreover, the autocorrelation function is deformed from an exponential law to a stretched-exponential law, as expected, and the experimental results show that the parameter ${\mathit{d}}_{\mathit{w}}$, quantifying the exponential stretching, and the ratio S/N exhibit a similar dependence on the level of multiple scattering.

DOI
10.1103/physreve.49.3531

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The concentration dependence of the statistical properties of light scattered by a monodisperse sphere suspension has been studied. Theoretical predictions for photon-counting distributions, obtained by supposing the scattered field is a superposition of coherent signal S and noise excitation N, agree well with the experimental results, thus providing an alternative method to obtain quantitative information on the influence of multiple scattering on measurements. Moreover, the autocorrelation function is deformed from an exponential law to a stretched-exponential law, as expected, and the experimental results show that the parameter dw{\mathit{d}}_{\mathit{w}}dw​, quantifying the exponential stretching, and the ratio S/N exhibit a similar dependence on the level of multiple scattering.
We have studied the amplitude and temporal correlations of intensity fluctuations of multiply scattered light transmitted through a colloidal suspension. When the coherence length lc{\mathit{l}}_{\mathit{c}}lc​ of the incident light becomes comparable to the width of the probability distribution of photon-path lengths, both the amplitude and dynamics of intensity fluctuations become functions of lc{\mathit{l}}_{\mathit{c}}lc​. In this article we present a simple theory that relates these coherence effects to the photon path-length distribution P(L). We have tested this theory using P(L) calculated from computer simulations and from the diffusion approximation, and find that our theory qualitatively accounts for the observed dependences on coherence length. Our results indicate when the effects of finite laser coherence must be taken into account in quasielastic multiple scattering. In the few-scattering regime of quasielastic multiple scattering, we find that the intensity autocorrelation function generally has a stretched-exponential form, and we discuss the origin of this behavior.
In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.
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.
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Under usual laboratory conditions the absorption of a beam of light by a dilute two-level medium depends on the intensity and spectrum of the incident light. If the incident photon flux is small compared to the decay rate of the absorber’s excited state, saturation effects can be neglected and only the spectrum of the light is important; thus, weak-field absorption depends only on the firstorder correlation function of the incident light. This result relies, however, on a requirement that the incident beam cross-section be much larger than the absorption cross-section of an atom. Then individual atoms act as low efficiency scatterers and the statistics of the scattering process is governed by the law of large numbers applied to many scattering sites. In contrast, if it is arranged that just one atom significantly absorbs (scatters) a beam of photons, correlation functions of the incident light beyond the first-order must be considered. For a beam that is focused within an absorption cross-section, we might naively predict that every photon will be scattered and none transmitted. In fact, even for a very weak beam there is a finite probability for two photons to arrive at the atom within the excited state lifetime, and in this event at least one of them will be transmitted (statistical saturation). In this paper we calculate the transmitted photon flux for a weak beam of photons focussed strongly onto a single, resonant two-state atom. We study the dependence of the transmitted flux on the statistics of the incident photons. Photon beams derived from sources of coherent, chaotic, squeezed, coherent-antibunched, and broadband-antibunched light are considered. our calculations are based on a recently developed theory of cascaded open systems,1,2 and serve to illustrate the usefulness of this theory.