Spatiotemporal decoupled split-step Fourier method for simulating spatiotemporal coupling dynamics in supercontinuum generation from ultrashort pulses

Supercontinuum generation from ultrashort pulses represents a significant phenomenon in nonlinear optics, with extensive applications in optical communications, biomedical imaging, and high-precision spectroscopy. However, the supercontinuum generation process involves complex spatiotemporal coupled nonlinear effects, where conventional numerical simulation methods inadequately address the evolutionary characteristics in both temporal and spatial domains simultaneously. To address this limitation, we propose a spatiotemporal decoupled split-step Fourier method (STD-SSFM) for solving the nonlinear Schrödinger equation governing the spatiotemporal evolution of optical fields. This method distinctively separates temporal, spatial, and nonlinear terms within each propagation step and preserves complete spatiotemporal coupling dynamics through multi-step accumulation, thereby significantly simplifying computational procedures while maintaining the physical accuracy of spatiotemporal simulations. We have conducted numerical simulations of Ti:Sapphire femtosecond pulse laser beam propagation in fused silica. The results verify that this method can accurately capture the key pulse propagation features, including spectral broadening, temporal reshaping, spatial self-focusing, and nonlinear phase modulation. Compared to conventional approaches, our method fully preserves spatiotemporal correlation distributions and phase information during optical field evolution, and provides an efficient and reliable tool for a deeper understanding of supercontinuum generation mechanisms.