Effective permittivity of a medium with stratified dielectric host and metallic inclusions

The homogenization of artificial materials is an important problem in electromagnetics. The metamaterial concept enables the development of new composite structures with propagation properties not available in natural materials. The class of artificial materials with planar metallic inclusions is particularly interesting, because it can be fabricated using planar circuit technology. A composite material with planar inclusions can be regarded as a stack of dielectric slabs that sustain the metallic elements. In a practical realization, it may be of interest to interleave the slabs on which the inclusions are imprinted with a different dielectric material. It is of interest to assess the effect of the stratification of the dielectric host on the effective permittivity of a composite structure. To this end, we investigate the homogenization of an array of metallic inclusions embedded in a stratified dielectric host. We propose a periodic Green function based approach to homogenize the composite structure. The method is an extension of the formalism developed by us (Silveirinha, M. and Fernandes, C.A., Electromagnetics Journal, vol.23, no.8, p.647-63, 2003). That formalism only applies when the dielectric host is homogeneous. To the best of our knowledge, the homogenization of artificial materials with the described geometry was not considered before.