Beam Propagation Method (BPM) for Optical Waveguide Simulation

The Beam Propagation Method (BPM) is a numerical technique for simulating light propagation in optical devices. Widely employed in designing and analyzing optical components such as optical fibers and waveguides, BPM represents light propagation through matrix operations that calculate wave evolution at each propagation step. This approach enables detailed investigation of light propagation characteristics and optical device performance. Key implementation aspects include using split-step Fourier algorithms to handle refractive index variations, where the propagation is typically divided into thin slices with phase corrections applied between Fourier transforms. The core computation involves solving the Helmholtz equation discretely through operators that account for both diffraction and medium effects, often implemented using MATLAB's fft2/ifft2 functions for efficient Fourier domain processing. Practical implementations may include boundary handling techniques like perfectly matched layers (PML) to minimize reflections and specialized functions for modeling nonlinear effects or waveguide coupling.