Split-Step Fourier Method

In optical fiber communication systems, dispersion and self-phase modulation (SPM) represent two primary distortion mechanisms. To better understand and optimize fiber optic communication systems, precise calculation and analysis of dispersion and SPM effects are essential. The Split-Step Fourier Method (SSFM) provides an effective numerical approach for solving the nonlinear Schrödinger equation, which governs pulse propagation in optical fibers. This algorithm alternately handles the linear dispersive effects in the frequency domain using fast Fourier transforms (FFT) and nonlinear phase modulation effects in the time domain through exponential operators. The method significantly improves computational accuracy while providing deeper physical insights into optical phenomena in fibers, thereby facilitating more advanced research and optimization of fiber communication systems. Code implementation typically involves iterating through propagation steps with FFT/IFFT operations for dispersion calculation and pointwise multiplication for nonlinear phase shifts.