SOLUBLE 2-DIMENSIONAL PHOTONIC-CRYSTAL MODEL

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