Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals

A finite-difference frequency-domain method based on the Yee's cell is utilized to analyze the band diagrams of two-dimensional photonic crystals with square or triangular lattice. The differential operator is replaced by the compact scheme and the index average scheme is introduced to deal with the curved dielectric interfaces in the unit cell. For the triangular lattice, the hexagonal unit cell is converted into a rectangular one for easier mesh generation. The band diagrams for both square and triangular lattices are obtained and the numerical convergence of computed eigen frequencies is examined and compared with other methods.