Probability-density function for energy perturbations of isolated optical pulses

The mathematical methods required to model simple stochastic processes are reviewed briefly. These methods are used to determine the probability-density function (PDF) for noise-induced energy perturbations of isolated (solitary) optical pulses in fiber communication systems. The analytical formula is consistent with the numerical solution of the energy-moment equation. System failures are caused by large energy perturbations. For such perturbations the actual PDF differs significantly from the (idealized) Gauss PDF that is often used to predict system performance. This report is a revised version of Lucent ITD-03-44739E and ITD-03-44750R, with additional references to related work.