Photonic band gaps in two-dimensional square and hexagonal lattices

Abstract

Two-dimensional square and hexagonal lattices exhibit photonic band gaps common to s- and p-polarized waves. These gaps occur from an overlap of the gaps between the first and second p bands and higher s bands. A dielectric structure with a hexagonal lattice of air holes requires a lower index contrast to generate a band gap and gives rise to larger gaps than a square lattice. Furthermore, square and hexagonal lattices of dielectric rods in air do not give rise to band gaps even when asymmetry is introduced to lift the degeneracies.