Closed form basis function fourier spectra for dispersion calculation of metasurfaces made by circular and elliptical ring patches

Circular and elliptical ring patches are considered as possible unit cells for metasurfaces, showing that the loading of very thin rings is higher if compared with full circular or elliptical patches. Moreover, it has been shown that entire domain basis functions with closed form spectra can be defined for circular and elliptical ring patches, and only a few basis functions can be used for the efficient description of electric current on the rings. This result allows for an important speedup in periodic MoM algorithms adopted to calculate wavenumber dispersion.