  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 inter-particle 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.
