FDTD Calculation of 2D Photonic Crystal Bandgap

The Finite-Difference Time-Domain (FDTD) method is employed to calculate the bandgap properties of two-dimensional photonic crystals. The implementation involves solving Maxwell's equations using Yee's algorithm with spatial and temporal discretization, requiring extensive computation loops for electromagnetic field updates across the crystal lattice. The core algorithm includes perfectly matched layer (PML) boundary conditions for absorption and Fourier transform operations for frequency domain analysis. While the program contains substantial code due to the complex numerical computations involving electric and magnetic field iterations, it maintains user accessibility through modular functions for parameter configuration and results visualization. Key components include the dielectric constant distribution setup, field initialization routines, and time-stepping mechanisms with stability criteria enforcement. The simulation accommodates various structural parameters including lattice constants, rod radii, and dielectric contrasts, enabling analysis of different photonic crystal configurations. Post-processing features extract transmission spectra and identify bandgap regions through eigenvalue solvers. Although computational demands are significant due to the fine meshing requirements, the systematic implementation provides reliable performance for investigating photonic crystal behaviors under diverse conditions, making it a valuable research tool for photonic device design and optimization.