MATLAB Source Code for Rigorous Coupled-Wave Analysis of Diffraction Gratings

The following provides a detailed technical breakdown of the MATLAB source code implementing rigorous coupled-wave analysis for diffraction grating simulations: First, understanding fundamental grating physics is essential. Diffraction gratings are optical devices that spatially disperse light into constituent wavelengths using periodic groove patterns. When illumination passes through these structures, wave diffraction occurs based on groove spacing and incident wavelength relationships. This MATLAB implementation employs the rigorous coupled-wave analysis (RCWA) method, grounded in Fourier modal formalism for electromagnetic analysis of periodic structures. The algorithm excels in handling high groove-density gratings through eigenvalue decomposition of Maxwell's equations in Fourier space, achieving computational efficiency without sacrificing accuracy. Key code sections include: - Parameter initialization: Defining grating period, refractive indices, and illumination conditions through structured input variables - Grating profile generation: Implementing Fourier series expansion for complex groove geometries using matrix transformation methods - Electromagnetic solver: Applying eigenmode analysis to coupled-wave equations via MATLAB's matrix computation libraries (e.g., eig() function) - Post-processing modules: Visualizing diffraction patterns with plotting functions (plot, imagesc) and calculating efficiency metrics through power flux integration The code structure demonstrates modular design principles, separating physical modeling, numerical computation, and result visualization into distinct functions. Critical algorithms include: 1. Fourier coefficient calculation for permittivity profiles 2. Eigenvalue problem resolution for wave propagation constants 3. Boundary condition matching at layer interfaces 4. Diffraction order efficiency normalization This computational tool enables precise analysis of light-grating interactions for applications spanning spectroscopic instrument design, optical communications, and photovoltaic device optimization. The implementation balances numerical rigor with practical usability through commented code sections and parameter adjustment guidelines.