Step-by-Step Method for Solving Coupled Nonlinear Schrödinger Equations

This implementation uses the split-step method to solve coupled nonlinear Schrödinger equations, primarily applied to digital simulation of high-power mode-locked gain fiber lasers. The simulation procedure is divided into the following four computational steps: 1. Fiber Loss Transmission This step simulates the attenuation of laser beams during propagation through optical fibers, accounting for absorption and scattering effects. Code implementation typically involves applying an exponential decay operator to the optical field amplitude in the frequency domain using Fourier transforms. 2. Dispersion This phase models chromatic dispersion effects in optical fibers, where light propagation speed varies with wavelength causing phase shifts. The computational approach usually employs Fourier domain operators to handle group velocity dispersion (GVD) through multiplication with dispersion-specific phase terms. 3. Nonlinear Effects This component simulates nonlinear optical phenomena arising from the nonlinear response of the fiber medium. Implementation commonly uses the nonlinear Schrödinger equation's nonlinear term, calculating Kerr effects and self-phase modulation through power-dependent phase shifts in the time domain. 4. Gain This stage models optical amplification in gain fibers, where light energy amplification induces phase changes. The code typically implements gain saturation models and amplification factors using exponential gain operators with appropriate saturation parameters. The program structure features 'finding' as the main driver function that coordinates the sequential execution of these physical processes. Supporting functions encapsulate each simulation step, allowing modular computation of the nonlinear Schrödinger equation solutions through operator splitting techniques.