Integral effective medium approach for a metamaterial with radially-inhomogeneous spherical inclusions

Abstract

In this study, a novel integral effective medium approach (IEMA) to obtain the complex effective permittivity and permeability tensors of 3-D metal-dielectric composite is developed. An infinite isotropic homogenous dielectric medium with periodically imbedded spherical inclusions with spherical inhomogeneity is considered here as an artificial dielectric in subwavelength. Within full-scattering theory, it is shown that such composite belongs to a general class of metamaterials with spherical inclusions.The obtained expressions for the elements of the effective tensors are valid in the entire subwavelength range. In order to test the proposed IEMA, the problem for metallic spherical particles coated by a layer of dielectric is solved analytically in greater detail by using the approach proposed earlier by the first author of the study.We were able to show that a metal-dielectric composite/metamaterial with spherical inhomogeneous inclusions can be considered as a quasi-periodic artificial crystal with a tunable band gap in the subwavelength range. In certain sub-ranges in subwavelength, such crystals can exhibit the properties of homogeneous ferrite material.