Photonic band gaps in two-dimensional square lattices: Square and circular rods

Periodic arrays of rods with either a square or circular cross section located at the corners of a square lattice exhibit photonic band gaps common to s and p polarizations. The overlap of s and p gaps is generated in arrays of low-index rods embedded in a dielectric background of higher index. The overlap does not occur between the same bands in arrays of rods with a square cross section and a circular cross section. Arrays of rods with a circular cross section require a lower index contrast to generate a band gap than rods with a square cross section, but do not necessarily yield larger gaps at higher index contrasts.