Analytical Verification of Effective Constitutive Parameter Increasing Using Metamaterial Inserts

We propose a concept to upgrade the constitutive parameters of a homogeneous magneto dielectric material. The concept is based on metamaterial inserts embedded in the magneto dielectric host material. This results in a hybrid composite material of higher permittivity and permeability than the original host material. In this paper, we verify the upgrading concept by using the Clausius-Mossotti equations, which describe the macroscopic response of the composite material in terms of the polarizabilities of the inserts. Sub-wavelength spheres made of Barium Strontium Titanate (BST), are considered as dielectric metamaterial inserts. The polarizabilities of a single sphere are derived using Mie theory. The constitutive parameters of the composite material are then calculated, showing the permittivity and permeability upgrading.