Optimal higher-lying band gaps for photonic crystals with large dielectric contrast

We investigate the characteristics of higher-lying band gaps for two-dimensional photonic crystals with large dielectric contrast. An optimal common band gap is attained on a hexagonal lattice of circular dielectric cylinders at relatively higher bands. The corresponding TM and TE modes exhibit simultaneous band edges, around which the frequency branches tend to be dispersionless. Unlike the fundamental band gap which usually appears between the dielectric and air bands, the optimal higher-lying gap in the present study occurs between two consecutive dielectric-like bands with high energy fill factors. The underlying mechanism is illustrated with the apparent change of eigenmode patterns inside the dielectric regions for both polarizations. In particular, the common gap region is bounded by two successive orders of Mie resonance frequencies on a single dielectric cylinder with the same geometry and material, where the Mie resonance modes show similar internal fields with the respective eigenmodes for the photonic crystal.