Gaussian ring basis functions for the analysis of modulated metasurface antennas

This paper presents a novel type of basis functions, whose spectral-and space-domain properties can be exploited for the efficient method of moments (MoM) analysis of planar metasurface (MTS) antennas. The effect of the homogenized MTS is introduced in the integral equation as an impedance boundary condition (IBC). The proposed basis functions are shaped as Gaussian-type rings with small width and linear azimuthal phase. The analytical form of the spectrum of the Gaussian ring basis allows for a closed-form evaluation of the MoM impedance matrix's entries. Moreover, these basis functions account for the global evolution of the surface current density in an effective manner, reducing the size of the MoM system of equations with respect to the case of subdomain basis functions. These features allow one to carry out a direct solution for problems with a diameter of up to 15 wavelengths in less than 1 min using a conventional laptop. The applicability on practical antennas has been tested through the full-wave analysis of MTS antennas implemented with small printed elements.