Solving Nonlinear Schrödinger Equation Using Split-Step Fourier Method

The split-step Fourier method is employed to solve the nonlinear Schrödinger equation, which accurately models light propagation in optical fibers. This equation enables the investigation of key nonlinear transmission characteristics in fibers, including attenuation and dispersion effects. The numerical implementation typically involves alternating between nonlinear phase shift calculations in the time domain and linear dispersion operations in the frequency domain using Fast Fourier Transforms (FFT). Studying these nonlinear properties is crucial for applications in optical communication systems and laser design, where fiber behavior under high-power conditions must be precisely characterized. The algorithm structure generally consists of iterative steps: applying nonlinear effects through power-dependent phase rotation, transforming to spectral domain via FFT, applying dispersion compensation, and inverse FFT transformation back to time domain.