Photocount statistics of Gaussian light of arbitrary spectral profile

Abstract

A general method of deriving the generating function of the photocounts due to Gaussian light of arbitrary spectral profile is presented. The eigenvalues of the basic integral equation corresponding to a general real-valued autocorrelation function are related to the usual infinite product representation of the generating function of the photocounts. The integral equation is solved by the Laplace transform technique. The eigenvalues are determined by imposing analyticity requirement on the Laplace transform and the eigenvalues are identified to be the zeros of an alternant. By appropriate parametrization and multiplication by an alternant the eigenvalues are directly related to the zeros of an entire function. By the use of the Hadamard factorization theorem the generating function is identified to be the reciprocal of the entire function evaluated at a chosen point. The method is extended to cover the superposition of two incoherent beams.