MATLAB Implementation of Transfer Matrix Method for Photonic Crystal Band Structure Calculation

In this paper, we employ the transfer matrix method to calculate the band structure of one-dimensional photonic crystals. The MATLAB implementation involves constructing layer-by-layer propagation matrices that characterize electromagnetic wave behavior through periodic dielectric structures. The algorithm efficiently handles matrix multiplications using MATLAB's optimized linear algebra functions, significantly accelerating computation compared to manual calculations. Our code implementation includes proper boundary condition handling and frequency domain sampling to generate accurate dispersion relations. Additionally, the program calculates transmission coefficients by computing the ratio of transmitted to incident wave amplitudes, providing deeper insights into the system's optical properties. This approach enables comprehensive investigation of photonic crystal behaviors and characteristics, establishing a detailed foundation for future research through parameterized scripts that allow easy modification of structural parameters like refractive indices and layer thicknesses.