Numerical Study of Non-Schell Model Pulses in Nonlinear Dispersive Media with the Monte Carlo-Based Pseudo-Mode Superposition Method

Recently, we introduced random complex and phase screen methods as powerful tools for numerically investigating the evolution of partially coherent pulses (PCPs) in nonlinear dispersive media. However, these methods are restricted to the Schell model type. Non-Schell model light has attracted growing attention in recent years for its distinctive characteristics, such as self-focusing, self-shifting, and non-diffraction properties as well as its critical applications in areas such as particle trapping and information encryption. In this study, we incorporate the Monte Carlo method into the pseudo-mode superposition method to derive the random electric field of any PCPs, including non-Schell model pulses (nSMPs). By solving the nonlinear Schrödinger equations through numerical simulations, we systematically explore the propagation dynamics of nSMPs in nonlinear dispersive media. By leveraging the nonlinearity and optical coherence, this approach allows for effective control over the focal length, peak power, and full width at half the maximum of the pulses. We believe this method offers valuable insights into the behavior of coherence-related phenomena in nonlinear dispersive media, applicable to both temporal and spatial domains.