Abstract
The dielectric properties of metamaterials consisting of periodically arranged metallic nanoparticles of spherical shape are calculated by rigorously solving Maxwell's equations. Effective dielectric functions are obtained by comparing the reflectivity of planar surfaces limiting these materials with Fresnel's formulas for equivalent homogeneous media, showing mixing and splitting of individual-particle modes due to interparticle interaction. Detailed results for simple-cubic and fcc crystals of aluminum spheres in vacuum, silver spheres in vacuum, and silver spheres in a silicon matrix are presented. The filling fraction of the metal $f$ is shown to determine the position of the plasmon modes of these metamaterials. Significant deviations are observed with respect to Maxwell-Garnett effective-medium theory for large $f$, and multiple plasmons are predicted to exist in contrast to Maxwell-Garnett theory.
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