Higher Order Statistics of Parametric Amplifier Gain Variation Due to Dispersion Fluctuation

Currently, there are no analytical formulas or ordinary differential equations (ODEs) to investigate the higher order statistics for the gain variations in fiber parametric amplifiers (FOPAs) with dispersion fluctuation. This is mainly due to the tedious efforts to derive the related ODEs. In this article, a comprehensive generalized stochastic coupled mode equation approach for the ODE derivation is proposed to study the gain variations in FOPAs, which greatly simplifies the derivation process. Based on the systematic approach, one may find the higher order statistics of the FOPA gain without the time consuming Monte Carlo simulations. The analytical and numerical solutions of the ODEs agree well with the Monte Carlo simulations. The approach can be extended to other practical problems like the higher order statistics of the mode amplitudes in the multimode fibers with random coupling.