Photonic Crystal Bandgap Calculation Program Using the Two-Plane Wave Expansion Method

This methodology presents a program for calculating photonic crystal bandgaps using the two-plane wave expansion method. The program employs Fourier space discretization to solve Maxwell's equations in periodic dielectric structures, where key algorithmic components include eigenvalue solvers for calculating electromagnetic mode frequencies and matrix construction for dielectric constant Fourier components. This computational tool enables researchers to better understand photonic crystal characteristics and behaviors through systematic band structure analysis. For instance, by calculating photonic crystal bandgaps, the program can predict material optical properties and electronic structures through frequency domain simulations. The implementation typically involves plane wave cutoff energy optimization and Brillouin zone sampling for accurate dispersion relation calculations. Furthermore, the program can be utilized for developing novel photonic crystal materials and designing optical devices by performing parametric studies on lattice constants, dielectric contrasts, and crystal symmetries. Thus, this program holds significant importance for advancing research in the photonic crystal field, particularly for photonic bandgap engineering and optical device optimization applications.