Second-order statistics of integrated intensities and detected photons, the exact analysis I. Theory

Abstract

We express the exact probability density distribution function as the product of a gamma distribution and a series of associated Laguerre polynomials, with the expansion coefficients determined by moments of the integrated intensity. Orthogonal polynomials with respect to the exact probability distribution function are then expanded in similar fashion. These polynomials are then used to construct an expansion of the joint probability distribution function in the second-order photoelectron statistics. Since the polynomials are identical with the corresponding Laguerre polynomials when the exact probability distribution function is the gamma distribution, the new polynomials are generalized versions of the associated Laguerre polynomials. The joint photoelectron statistics may be studied with these new polynomials.