The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice

The photonic band structures of a two-dimensional photonic crystal consisting of a honeycomb lattice with triangular dielectric rods embedded in air are studied numerically. In a honeycomb lattice, the largest absolute photonic bandgap is achieved by the use of triangular rods which have the same shape as that of the coordination polygon of a lattice point; the reason why triangular dielectric rods in a honeycomb lattice can generate the largest gap is also discussed.