Photonic band structure of a truncated, two-dimensional, periodic dielectric medium

We calculate the photonic band structure for the propagation of electromagnetic waves through a structure that consists of parallel, identical, dielectric rods of finite length, whose intersections with a perpendicular plane form a two-dimensional crystal. The rods are embedded in a medium with a different dielectric constant, and the composite system is confined between a pair of perfectly conducting plates that are perpendicular to the rods. The electromagnetic waves propagate in a plane perpendicular to the rods. The resulting photonic band structure can display absolute band gaps if the separation between the perfectly conducting plates is sufficiently large or sufficiently small.