Solving Nonlinear Schrödinger Equation for Pulse Propagation in Optical Fibers Using Split-Step Fourier Method

This paper applies the Split-Step Fourier Method (SSFM) to model pulse propagation in optical fibers and solve the nonlinear Schrödinger equation. The SSFM is a numerical technique that decomposes the optical fiber into small segments, alternating between linear and nonlinear operators. In code implementation, the linear dispersion effects are computed in the frequency domain using Fast Fourier Transforms (FFT), while nonlinear effects are handled in the time domain. The algorithm typically involves: initializing pulse parameters, defining fiber characteristics, implementing the split-step loop with appropriate step sizes, and applying FFT/iFFT operations for domain conversion. This method provides accurate solutions for pulse evolution during fiber transmission, which is crucial for designing and optimizing fiber-optic communication systems. Key implementation aspects include proper step-size selection to balance accuracy and computational efficiency, handling boundary conditions, and managing numerical dispersion effects.