Light Propagation in Nonlinear Media with Algorithm Implementation

The propagation of light through nonlinear media constitutes a complex physical process involving interactions between light and the material medium. When light intensity reaches sufficiently high levels, the medium's response deviates from linear proportionality to intensity, giving rise to nonlinear effects including self-phase modulation, cross-phase modulation, and four-wave mixing. These phenomena find significant applications in optical fiber communications, laser physics, and optical signal processing systems.

The Split-Step Fourier Method (SSFM) stands as a widely adopted numerical algorithm for simulating light propagation in nonlinear media. This computational approach decomposes the propagation process into alternating linear and nonlinear operations: The linear component primarily handles dispersion and diffraction effects, typically solved efficiently in the frequency domain using Fast Fourier Transform (FFT) algorithms. The nonlinear component computes directly in the time domain, accounting for medium responses such as the Kerr effect and Raman scattering. In code implementation, SSFM typically employs a loop structure where each propagation step alternates between FFT-based linear operations and point-wise nonlinear calculations, with step size adjustment crucial for balancing accuracy and computational efficiency.

SSFM's advantages lie in its computational efficiency and precision, making it suitable for studying ultrashort pulse propagation, soliton dynamics, and optical field evolution in complex nonlinear media. Through appropriate step size partitioning, the method effectively balances calculation accuracy with speed, establishing itself as an essential tool in nonlinear optics simulations. The algorithm's modular structure allows straightforward incorporation of additional physical effects through separate linear and nonlinear operator definitions.