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IEEE Journal of Quantum Electronics

1A4 - Photocount distributions and field statistics

F. T. Arecchi, A. Berne, A. Sona, Pio Burlamacchi

Published Sep 1, 1966• 46 citations
Publisher

Abstract

The statistical properties of a radiation field (either Gaussian or laser) have been investigated by photon counting distributions. Two methods (nonlinear and linear) are here introduced and compared from the viewpoint of the accuracy of the measurement and of the associated information capacity. Finally, the method of the "joint photocount distributions" is here introduced as a new tool for the investigation of the time evolution of a random field.

DOI
10.1109/jqe.1966.1074084

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Reconstruction of Photon Statistics in the Presence of Photodetection Noise

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An original approach has been developed to extract information on the photon distribution function recorded by the photocount method in the presence of interference. Photon statistics reconstruction has been studied in the presence of two types of interference: dark counts and background radiation. The calculation has been performed using a characteristic function. Correctly reconstructing photon statistics and appropriate experimental conditions have been discussed. The obtained results can be used in measuring photon statistics of low-photon radiation sources and non-classical light fields.

Journal of Experimental and Theoretical Physics Letters•Mar 1, 2026•0 citations
The statistical properties of a radiation field (either Gaussian or laser) have been investigated by photon counting distributions. Two methods (nonlinear and linear) are here introduced and compared from the viewpoint of the accuracy of the measurement and of the associated information capacity. Finally, the method of the "joint photocount distributions" is here introduced as a new tool for the investigation of the time evolution of a random field.
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.
Results have been presented by Bedard (see abstr. A33736 of 1967) on the derivation of the N-fold joint photocount distribution of a Gaussian (thermal) radiation field of arbitrary spectral profile, when the counting-time intervals are short compared with the coherence time of the light. In this paper these results are extended for arbitrary counting-time intervals. The authors assume that the fluctuating radiation field has a fixed direction of propagation and that all the photodetector surfaces lie within one coherence area on a plane normal to this direction of propagation. The evaluation of the -fold joint photocount distribution and the photocount moments can be reduced to the solution of either a homogeneous or an inhomogeneous (Fredholm) integral equation of the second kind.
The transient phase-independent solutions of the laser Fokker-Planck equation are analyzed for a short range of time following the moment of the switching on of the oscillations. The evolution of the laser light in time is then represented as a nonstationary Gaussian random process. On the basis of this fact, the factorial moment generating function of the photocount probability distribution is derived, which accounts automatically for all the finite-counting-time corrections. The time development of the first two moments is compared with the recent results of Arecchi and Degiorgio.
An original approach has been developed to extract information on the photon distribution function recorded by the photocount method in the presence of interference. Photon statistics reconstruction has been studied in the presence of two types of interference: dark counts and background radiation. The calculation has been performed using a characteristic function. Correctly reconstructing photon statistics and appropriate experimental conditions have been discussed. The obtained results can be used in measuring photon statistics of low-photon radiation sources and non-classical light fields.