Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles

In this paper we present a method for retrieving the effective parameters of a metamaterial composed of a regular rectangular orthorhombic lattice of linear biaxially anisotropic particles suspended in free space. By assuming the point–dipole interaction approximation, equations are derived which extract the electric and magnetic polarizabilities of the individual particles given the measured or simulated scattering parameters of a single planar array of particles. These results are in turn substituted into the Clausius–Mossotti equations to find the bulk effective permittivity and effective permeability. To demonstrate our approach, the extraction method is applied to a metamaterial consisting of a cubic arrangement of magnetodielectric spheres using the scattering parameters obtained by simulating the structure with Ansoft HFSS. Our results show good agreement with a known analytical solution at frequencies in which the Clausius–Mossotti approximation is valid.