Calculation of effective parameters of high permittivity integrated artificial dielectrics

An analysis is presented of the effective electromagnetic parameters of high-permittivity, anisotropic artificial dielectrics which are built by stacking arrays of metallic elements and conventional dielectric films, with adjacent arrays shifted with respect to each other. The effective parameters of the artificial dielectric are extracted from the scattering coefficients of plane electromagnetic waves which are normally or obliquely incident on a slab of the artificial material with finite thickness. These coefficients are derived from the generalised scattering matrix of a single layer of metallic elements which is computed using the integral equation technique. Both two-dimensional and three-dimensional configurations are considered. Calculations demonstrate the feasibility of artificial dielectric films with extremely high values of effective relative permittivity (several thousands) in the plane of the film at millimetre-wave (mm-wave) frequencies. These artificial dielectrics have a high potential for application in microwave and mm-wave integrated circuits because of their high-permittivity and planar layout. As a potential application, the authors propose an artificial dielectric waveguide integrated on a silicon substrate.