Dispersion relation and optical transmittance of a hexagonal photonic crystal slab

The dispersion relation and the optical transmittance of a two-dimensional photonic crystal composed of the hexagonal array of cylindrical air holes fabricated in a dielectric slab were analyzed by group theory and the numerical calculation based on the finite-difference time-domain method. The decay rate of the leaky modes that exist above the light line (the dispersion relation in air) in the band diagram was also evaluated, from which the absence of the coupling between certain internal eigenmodes and the external radiation field was shown. This phenomenon was related to symmetry mismatching by the group-theoretical argument. It was also shown that a certain leaky band has a quality factor as large as 3000 over its entire spectral range. These features as well as the opaque frequency regions due to symmetry mismatching were clearly demonstrated by the calculated optical transmission spectra.