Photonic band structure of two-dimensional systems: The triangular lattice

By the use of a position-dependent dielectric constant and the plane-wave method, we have calculated the photonic band structure for electromagnetic waves in a structure consisting of a periodic array of parallel dielectric rods of circular cross section, whose intersections with a perpendicular plane form a triangular lattice. The rods are embedded in a background medium with a different dielectric constant. The electromagnetic waves are assumed to propagate in a plane perpendicular to the rods, and two polarizations of the waves are considered. Absolute gaps in the resulting band structures are found for waves of both polarizations, and the dependence of the widths of these gaps on the ratio of the dielectric constants of the rods and of the background, and on the fraction of the total volume occupied by the rods, is investigated.