We consider the optical properties of a periodic array of silver spherical particles with diameters of a few hundred nanometers on top of a thin Ag film. Maxwell's equations are solved using a multiple-scattering formalism which combines high accuracy with efficiency. We study the interaction between flat-surface and localized particle plasmons. Interestingly, the presence of a periodic array can lead to an enhanced transmission through the metallic film due to leakage of the surface plasmon-polaritons in the substrate.
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N. Papanikolaou (2007) studied this question.
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