Dynamical Computation of Photon Correlations and Counting Statistics

Equations of motion are derived for generating functions of field correlations and detector counting probabilities for an arbitrary system of electromagnetic fields in the presence of their sources. For a system with linear constitutive relations, the equations are solved exactly. Such systems are shown to be always Gaussian, and some representative counting distributions are computed. A perturbative treatment of a system with a cubic nonlinearity in its constitutive relation is made to find the counting distribution to first order in the nonlinear coefficient. A comparison is made with the below-threshold limit of a recent laser-fluctuation theory, and a possible application to measurement of phonon-phonon interactions is mentioned.