RCWA Algorithm Application: Computing 2D Optical Gratings

This document discusses the implementation of RCWA (Rigorous Coupled Wave Analysis) algorithm for computing 2D optical gratings in MATLAB environment. RCWA is a numerical method for calculating electromagnetic field distributions, particularly useful for analyzing the performance of optical devices. The core implementation involves matrix operations for solving Maxwell's equations in periodic structures through eigenmode decomposition. For 2D grating calculations, the code requires precise input parameters including grating periodicity (both x and y directions), groove depth, material properties (refractive indices), and incident wave conditions. The algorithm handles these parameters through structured input objects that validate dimensional consistency and physical feasibility. Key computational steps include Fourier series expansion of dielectric permittivity, construction of wave coupling matrices, and solving eigenvalue problems for propagation constants. The provided code example demonstrates practical implementation with modular functions for parameter initialization, RCWA core computation, and results visualization. Users can modify grating geometrical parameters and material characteristics to investigate different optical properties such as diffraction efficiency, transmission spectra, and field distributions. The implementation includes error checking for parameter boundaries and convergence monitoring for numerical stability. This MATLAB-based framework serves as an educational tool for understanding RCWA fundamentals while providing a functional foundation for advanced optical grating design and analysis. The code structure separates computational routines from visualization modules, allowing easy integration with additional optical simulation components.