N-Fold Joint Photon Counting Distributions Associated with the Photodetection of Gaussian Light

Recently, Arecchi, Bern\'e, and Sona reported results of theoretical and experimental investigations on the twofold joint photocount distributions of a stationary Gaussian-Markovian radiation field. In this paper, we generalize their results by deriving the $N$-fold joint photocount distribution of a Gaussian (thermal) radiation field of arbitrary spectral profile, when the counting-time intervals are short compared to the coherence time of the light. The present analysis provides simple recurrence relations for the $N$-fold joint photocount distributions and for their generalized factorial moments. These relations are derived with the help of an $N\ifmmode\times\else\texttimes\fi{}N$ generating matrix which is introduced here. The present analysis also indicates to what extent the $N$-fold joint photocount distributions contain useful information about the higher-order coherence properties of the radiation field.