Light Propagation in Nonlinear Media

In this article, we investigate light propagation in nonlinear media. To accurately characterize this phenomenon, we employ the Split-Step Fourier Method (SSFM). This numerical approach serves as a powerful tool for modeling light transmission through complex media with high precision. The implementation typically involves alternating between spatial and spectral domains using Fast Fourier Transforms (FFTs), where nonlinear effects are calculated in the spatial domain while linear dispersion effects are handled in the Fourier domain. When applying this method, we carefully analyze the physical properties of the medium under study, incorporating parameters like nonlinear coefficients and dispersion profiles into our computational model. Key functions would include calculating phase shifts from nonlinear effects and applying dispersion operators through frequency-domain multiplications. Furthermore, we examine how propagation velocity and direction influence light behavior in the medium, which translates to implementing adaptive step-size control and directional propagation algorithms in code. This comprehensive analysis aims to provide deeper insights into light propagation dynamics in nonlinear media, with practical implementations potentially involving Python/Matlab code structures with FFT libraries and nonlinear coefficient arrays.