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 delta-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.

Self- and Cross-phase modulation of asymmetric femtosecond pulses (~ 810 nm) propagating through a birefringent single-mode optical fiber (~ 6.9 cm) is studied both experimentally (using GRENOUILLE) and numerically (by solving a set of coupled nonlinear Schrödinger equations or CNLSEs). An optical spectrogram representation is derived from the electric field of the pulses and is linearly juxtaposed with the corresponding optical spectrum and optical time-trace. The simulations are shown to be in good qualitative agreement with the experiments. Measured input pulse asymmetry, when incorporated into the simulations, is found to be the dominant cause of output spectral asymmetry. The results indicate that it is possible to modulate short pulses both temporally and spectrally by passage through polarization maintaining optical fibers with specified orientation and length.

Implications of spontaneous and stimulated Raman scattering (SSRS) and phase noise on the spatial evolution of multiple-order sidebands arising from four-wave mixing (FWM) along the length of an optical fiber are investigated. A modified split-step Fourier method is used to solve the governing coupled nonlinear Schrödinger equations. The phase noise overcomes the depletive nature of SSRS and stabilizes the FWM sidebands, in good agreement with experimental results.