Bulk and surface plasmons and localization effects in finite superlattices

We consider the propagation of bulk and surface plasmons in a finite superlattice structure composed of alternating layers of materials A and B, with the whole structure resting on a substrate. An implicit dispersion relation is derived allowing the dielectric constant of each material to be a function of frequency. We then present numerical examples for the case where material A is a metal and the remaining materials have frequency-independent dielectric constants. We explore three types of material configurations: (1) a finite number of layers of A and all other materials being taken with ε=1; (2) the same as case (1), but here with the dielectric constant of material B increased by 5%; and (3) a realistic geometry appropriate for Al films separated by ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ layers on a ${\mathrm{SiO}}_2$ substrate. The dispersion curves in case (1) are similar to those for an infinite superlattice of the same material parameters. The primary difference is that for thin superlattice structures, there is a splitting of the frequencies of the surface modes. In case (2) the symmetry of the system is lowered and there is strong localization, particularly for the surface modes. Case (3) also shows unique features, the most interesting being the existence of a mode which changes character from bulk nature to a surface mode and then back to a bulk mode.