Influence of stochasticity on multiple four-wave-mixing processes in an optical fiber

In this paper, we present the results of a computational study of the dynamical evolution of multiple four-wave-mixing processes in a single mode optical fiber with spatially and temporally δ-correlated phase noise. A generalized nonlinear Schrödinger equation (NLSE) with stochastic phase fluctuations along the length of the fiber is solved using the split-step Fourier method. A good agreement is obtained with previous experimental and computational results based on a truncated-ODE (ordinary differential equation) model, in which stochasticity was seen to play a key role in determining the nature of the dynamics. The full NLSE allows for simulations with high frequency resolution (60 MHz) and frequency span (16 THz) compared to the truncated-ODE model (300 GHz and 2.8 THz, respectively), thus enabling a more detailed comparison with observations. A physical basis for this hitherto phenomenological phase noise is discussed and quantified.