Field calculation of electric dipole excitation of a metafilm printed on a finite‐thickness dielectric slab using the susceptibility homogenization method

Abstract

Here, the authors calculate the fields due to the electric dipole that excites a homogenized metasurface which is printed on a finite thickness dielectric slab. The problem is solved by replacing the total parts below the periodic array which contain the dielectric slab and the half-space under it, with an effective homogenous half-space. Furthermore, the static interaction constants between dipoles which are located at two different materials' interface are calculated. Then, with the help of the Lorentz method, the analytical formulae are presented to calculate the surface susceptibility densities of the homogenized metasurface located at two materials' interface. These analytical formulae can be applied to arrays with both square and rectangular periodicity. An array of circular patches printed on dielectric slabs with different thicknesses is considered to verify the results. The results show good agreement compared to the fields calculated by commercial numerical software FEKO. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Closed-Form Dyadic Green’s Functions for Dipole Excitation of Planar Periodic Structures

“…The approach in [32] is extended for metafilms at the interface of two half spaces in [33] and for metasurfaces placed on a dielectric slab in [34]. Since the numerical results are reported for total fields, a significant difference between the results for two different dielectric constants (5 and 16), [33], and for two slabs of same permittivity but with different heights (2 mm and 10 mm), [34], is not observed again due to the dominance of the incident field.…”