Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes

Abstract

Despite the considerable amount of research undertaken on various lattice structures, the photonic band gap (PBG) for a triangular lattice remains the largest both in the transverse magnetic (TM) and transverse electric (TE) modes. The PBG for a square lattice can be doubled by using square air holes rather than air cylinders. Reducing the symmetry was effective in terms of a honeycomb lattice in that the PBG can be increased 40% by deforming the lattice and using oval dielectric rods instead of cylindrical rods. The PBGs for all the examined structures increase monotonously as the refractive index is increased. The overlap PBG between the TM and TE gaps (polarization-independent PBG) is the largest for a triangular lattice of circular air rods. The overlap PBG for a hybrid square lattice of air rods is the next largest, and is twice as large as that for the well-known honeycomb lattice consisting of dielectric cylinders. When the refractive index of a dielectric material is increased to more than 3.50, the magnitude of the overlap PBG for almost all the photonic crystals that exhibit an overlap PBG saturates or decreases, except for the largest and next largest overlap PBG’s mentioned above.