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arXiv:cond-mat/0511402 · Physical Review Letters

Photocount Statistics in Mesoscopic Optics

Sandor Balog, P. Zakharov, Frank Scheffold, S. E. Skipetrov

Published Sep 7, 2006• 25 citations
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Abstract

We report the first observation of the impact of mesoscopic fluctuations on the photocount statistics of coherent light scattered in a random medium. A Poisson photocount distribution of the incident light widens and gains additional asymmetry upon transmission through a suspension of small dielectric spheres. The effect is only appreciable when the average number n of photocounts becomes comparable or larger than the effective dimensionless conductance g of the sample.

DOI
10.1103/physrevlett.97.103901

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We report the first observation of the impact of mesoscopic fluctuations on the photocount statistics of coherent light scattered in a random medium. A Poisson photocount distribution of the incident light widens and gains additional asymmetry upon transmission through a suspension of small dielectric spheres. The effect is only appreciable when the average number n of photocounts becomes comparable or larger than the effective dimensionless conductance g of the sample.
The asymmetry of photocount statistics in respect of the spatial and temporal coherence factors is demonstrated and explained. This asymmetry appears because of the of a counter receiving a non-Poisson photoelectron flux. A statistical model of an optical field, photoelectron flux, and counting flux is used in a computer study of the dependences of the distributions and moments of the number of counts in a given time interval on the ratio of the coherence factors. An explanation of the features of these dependences is provided. A determination is made of the range of conditions in which the asymmetry is significant. In particular, the asymmetry disappears in the case of a Poisson photoelectron flux and for a very short dead time.
We study fluctuations of the number of photocounts measured by an ideal photodetector illuminated by light scattered in an amplifying disordered medium, below the threshold for random lasing. We show that the variance of fluctuations and their correlation function carry information about fluctuating properties of the medium. A direct link is established between the fluctuations of the number of photocounts due to the amplified spontaneous emission (ASE) and the dimensionless conductance ggg of the medium. Our results suggest a possibility of probing amplifying disordered media by analyzing statistics of their ASE, without illuminating them from outside by a probe beam.
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.
It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of n photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photocounting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.
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.