Split-Step Fourier Method for Solving Nonlinear Schrödinger Equations

In nonlinear optics research, the Schrödinger equation is widely employed as the governing equation for wave propagation. This program implements the split-step Fourier method to solve the nonlinear Schrödinger equation through discrete computational steps. The algorithm decomposes the equation into manageable time segments, alternating between Fourier-domain operations for linear terms and spatial-domain calculations for nonlinear components using iterative methods. This numerical approach enables precise simulation of wave evolution by handling dispersion effects in the frequency domain and nonlinear effects in the temporal domain separately at each step. The method's implementation involves critical functions such as FFT/IFFT transformations for linear propagation and iterative solvers for nonlinear phase modulation. Such computational techniques hold significant value in nonlinear optics studies, providing accurate modeling capabilities that enhance our understanding and exploration of complex nonlinear optical phenomena.