Soluble two-dimensional photonic-crystal model

We present an analytical treatment of a two-dimensional square photonic lattice constructed from two infinite arrays of dielectric sheets at right angles, in the limit of very small sheet thickness and very high dielectric constant, such that their product is constant. The photonic band structures for s- and p-polarized electromagnetic waves are calculated analytically. This approach enables two varieties of band to be identified and understood in terms of locally propagating and locally evanescent field distributions in the primitive cell. The densities of states are interpreted in terms of one- and two-dimensional contributions from the two kinds of band. As preliminaries to the two-dimensional calculations, we derive the photonic properties of the single dielectric sheet and of the infinite one-dimensional array of such sheets.