Linking equations between photon statistics and photocurrent statistics for time-varying stochastic photon rates

Abstract

Detected photons originating from classical light beams can be described either by means of photon statistics or by means of photocurrent statistics on a semiclassical basis. The statistical parameters of these two descriptions have, up to now, only been related to each other using vague, effective-time-constant arguments. We show that these relations are invalid for the general case of time-varying stochastic photon rates and arbitrary detector impulse responses and derive generally valid linking equations for the ensemble average, the shot noise variance and the excess noise variance of the photon statistics and the photocurrent statistics due to a random optical field. The derivations are based on a general definition of the time average that allows an elegant treatment in the Fourier domain.