Trivariate characteristics of intensity fluctuations for heavily saturated optical systems

Trivariate cumulants of intensity fluctuations have been computed starting from a trivariate intensity probability distribution function, which rests on the assumption that the variation of intensity has a maximum entropy distribution with the constraint that the total intensity is constant. The assumption holds for optical systems such as a thin, long, mirrorless gas laser amplifier where under heavy gain saturation the total output approaches a constant intensity, although intensity of any mode fluctuates rapidly over the average intensity. The relations between trivariate cumulants and central moments that were needed for the computation of trivariate cumulants were derived. The results of the computation show that the cumulants have characteristic values that depend on the number of interacting modes in the system. The cumulant values approach zero when the number of modes is infinite, as expected. The results will be useful for comparison with the experimental triavariate statistics of heavily saturated optical systems such as the output from a thin, long, bidirectional gas laser amplifier.