Finite-difference frequency-domain method for the extraction of effective parameters of metamaterials

Here, we report a numerical implementation of the nonlocal homogenization approach recently proposed in [M. G. Silveirinha, Phys. Rev. B 75, 115104 (2007)], using the finite-difference frequency-domain method to discretize the Maxwell equations. We apply the developed formalism to characterize the nonlocal dielectric function of several structured materials formed by dielectric and metallic particles and, in particular, we extract the local permittivity, permeability, and magnetoelectric coupling parameters when these are meaningful. It is shown that the finite-difference frequency-domain implementation of the homogenization method is stable and robust, yielding very accurate results.