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Physical Review A

Photon counting statistics with thermal light having a multiple-peak spectrum

C. L. Mehta, Sushma Gupta

Published May 1, 1975• 4 citations
Publisher

Abstract

We consider the photon-counting statistics with polarized thermal light having arbitrary rational spectral profile. The method is illustrated for a light beam having a two-peak symmetric Lorentzian spectrum. The associated integral equation is converted into a differential equation and the eigenvalues are determined. Using the standard techniques of contour integration, an explicit expression is obtained for the generating function valid for an arbitrary value of the counting interval.

DOI
10.1103/physreva.11.1634

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We consider the photon-counting statistics with polarized thermal light having arbitrary rational spectral profile. The method is illustrated for a light beam having a two-peak symmetric Lorentzian spectrum. The associated integral equation is converted into a differential equation and the eigenvalues are determined. Using the standard techniques of contour integration, an explicit expression is obtained for the generating function valid for an arbitrary value of the counting interval.
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It is well known that the photocount distribution associated with the photoelectric detection of fluctuating light beams carries information about the probability density of the light intensity. In this paper, we present an exact solution to a problem of particular interest which arises in connection with the photoelectric detection of narrow-band Gaussian (thermal or pseudothermal) light, namely, the problem of determining the photocount distribution when the counting-time interval is not necessarily short compared to the coherence time of the light. The method developed in this paper is applied to the case where the spectral profile of the light is Lorentzian; it leads to an exact expression for the photocount generating function and it provides simple recurrence relations for the photocount distribution and for its factorial moments.
In this paper, we consider the photoelectron counting distribution when the wave field incident on the detector is a mixture of harmonic signal and thermal noise. An expression for the factorial moment-generating function of the number of counts is obtained in terms of the eigenvalues of an associated integral equation. This expression is then used to evaluate the factorial cumulants of the number of counts. The results are valid for an arbitrary counting interval. The extension to photoelectron counting with several detectors is considered in paper II of the present investigation.