Improved Finite-Difference Frequency-Domain Scheme for the Analysis of 2-D Photonic Crystals

An improved finite-difference frequency-domain approach was developed for the analysis of two-dimensional photonic crystals. This newly proposed finite-difference scheme can deal with piecewise homogenous structures with slanted interfaces, thus provide the capability to analyze the structures with arbitrary shapes. We utilized this scheme to calculate the band diagrams of 2-D photonic crystals with the square lattice. Only one unit cell area need be calculated with proper periodical boundary conditions. We also demonstrated the convergence behavior to verify the efficiency of adopting the improved scheme.