Effective parameters and quasi-static resonances for periodic arrays of dielectric spheres

We investigate the effective parameters and quasi-static resonances for periodic arrays of dielectric spheres. The effective medium model based on the homogenization of normal modes for spherical particles is used to determine the effective permittivity epsilon(eff) and permeability mu(eff) in the quasi-static regime. Major features of epsilon(eff) and mu(eff) are characterized by the Lorentz-type anomalous dispersion around the frequencies pertaining to the leading-order electric and magnetic resonances, respectively. In particular, the anomalous dispersion is depicted by a resonance function associated with the spherical cavity. The underlying mechanism of quasi-static resonance is illustrated with the localized and dipole-like field patterns at the resonant frequencies. A comparison with the effective parameters for periodic arrays of dielectric circular cylinders is also discussed. (C) 2010 Optical Society of America