Two-dimensional photonic band structures

By the use of a position-dependent dielectric constant we have calculated the photonic band structure for electromagnetic waves in a structure that consists of a periodic array of parallel dielectric rods of circular cross section, whose intersections with a perpendicular plane constitute a square lattice. The rods are embedded in a background medium with a different dielectric constant. Two polarizations of the electromagnetic waves are considered, and they are assumed to propagate in the plane perpendicular to the rods. Absolute gaps in the resulting band structures are found for both polarizations, and the properties of these gaps as functions of the ratio of the dielectric constants of the rods and of the background, and of the fraction of the total volume occupied by the rods, are investigated.