Exact photocount statistics of linearly unstable gaussian light

Abstract

The theory of the long-time photocount statistics of a linear gaussian light wave is extended into the unstable region characterized by a gain constant Λ. Exact recurrence relations for the photocount distribution and the normalized factorial moments are given and the distribution function P(E) of the integrated light intensity E is discussed. Due to the exponential increase of mean intensity during the counting interval T only a limited amount of amplitude stabilization can occur in E provided ΛT ≲1. For ΛT ⪡1 and ΛT ⪢1 the distribution P(E) is thermal. A new parameter r appears in the theory measuring the initial wave intensity in relation to the quantum fluctuations. For r ⪢ 1, P(E) is practically thermal for all values of ΛT. For r≲1 characteristic deviations from a thermal distribution appear which provide a means to measure the linear gain Λ of the light wave by photon counting.