Band structures of two-dimensional surface-plasmon polaritonic crystals

By the use of the homogeneous form of the reduced Rayleigh equation for the electric field above and on the rough surface of a metal in contact with a vacuum, we have obtained the dispersion relation for surface-plasmon polaritons propagating across such an interface. This dispersion relation is exact within the domain of validity of the Rayleigh hypothesis upon which it is based. It is applied to a two-dimensional vacuum-metal interface formed from a periodic array of hemiellipsoids on the planar surface of the same metal. Nonperturbative numerical solutions of the resulting dispersion relation are obtained for wave vectors along the boundary of the irreducible element of the first Brillouin zone for a square and a triangular array of the hemiellipsoids. Absolute band gaps in the frequency spectrum, where the density of states vanishes, are found, and the dependence of the position and width of these gaps on various geometrical parameters of each array is investigated. We also study the influence of radiative damping and ohmic losses on the dispersion curves. Our theoretical results are compared with existing experimental data.