Band Structure Calculation of Rectangular Lattice Cylindrical Photonic Crystals

We implemented a computational approach utilizing supercell and plane wave methods to calculate the band structure of rectangular lattice cylindrical photonic crystals. This methodology employs Fourier expansion techniques within a periodic boundary condition framework, achieving high precision in predicting photonic crystal properties. Our implementation involves key computational steps including: geometric modeling of cylindrical rods arranged in rectangular lattices, dielectric constant mapping using spatial discretization, and eigenvalue solution of Maxwell's equations through plane wave expansion algorithms. The computational parameters comprehensively account for multiple factors such as lattice dimensions, cylindrical rod geometry, and material refractive indices. Through iterative convergence testing and parameter optimization, we obtained detailed band structure information including photonic band gaps and dispersion relations. These computational results provide valuable insights for understanding photonic crystal properties and applications in optical devices, with the implementation featuring automated parameter sweeping and visualization routines for efficient analysis of structural variations.