Effective Permittivity of Heterogeneous Substrates With Cubes in a 3-D Lattice

This letter studies the behavior of heterogeneous dielectric substrates created by including micro-sized cubes of different electromagnetic (EM) properties to an otherwise homogenous host medium. The letter looks at the effect of the volume fraction of cubic inclusions (dielectric or metallic) to the effective EM properties of the heterogeneous medium. It is well known that the effective permittivity of the mixture is dependent on the properties of the host and inclusions as well as the size and spacing of the cubes. EM simulations using a plane-wave excitation have been used to carry out these studies. An inversion process using a rectification algorithm was employed to correctly obtain the effective permittivity from the scattering parameters of the mixture. The analytical results of the infinite medium using canonical equations and a volume equivalence showed good agreement with the EM simulations and measurement of our samples of finite thickness. This letter shows that cubic inclusions can produce a higher effective permittivity than was previously found with spheres.