Phase diagrams of surface plasmon polaritonic crystals

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Abstract
The homogenous form of the reduced Rayleigh equation has been employed in this work to study absolute photonic band gaps in the frequency spectrum of surface plasmon polaritons propagating across a vacuum-metal interface formed from a hexagonal array of hemiellipsoids. The complex dielectric function that characterizes a specific metal within this approach is obtained from experimental data for silver, aluminum, and gold. Nonperturbative numerical solutions of the resulting dispersion relation are analyzed for the occurrence of absolute band gaps while the geometrical parameters of the surface are varied. This approach is exact within the domain of validity of the Rayleigh hypothesis and produces phase diagrams that reveal suitable parameters for the design of surface plasmon polaritonic crystals. The lifetimes of characteristic surface plasmon polariton modes are calculated to judge the applicability of these designs. The numerical predictions in this work are compared with existing experimental data.