Power balance and efficiency of metasurface antennas

This paper presents two methods for the efficient evaluation of the power balance in circular metasurface (MTS) antennas implementing arbitrary modulated surface impedances on a grounded dielectric slab. Both methods assume the surface current in the homogenized MTS to be known. The first technique relies on the surface current expansion with Fourier-Bessel basis functions (FBBF) and proceeds by integration of the Poynting vector on a closed surface. The second method is based on the evaluation of the residue of the electric field spectrum at the surface-wave (SW) pole, and is demonstrated by using a current expansion in Gaussian ring basis functions (GRBF). The surface current expansions can be directly obtained either by analyzing the antenna with a Method of Moments (MoM) tool for homogenized MTSs based on FBBF or GRBF, or derived by a projection process. From there, the power contributions, namely the total power delivered by the feed, the radiated power, the SW power, and the Ohmic power losses in the dielectric are computed. Several efficiency metrics are presented and discussed: tapering efficiency, conversion efficiency, loss factor, and diffraction factor. Since the MTS apertures at hand are leaky-wave (LW) antennas, the designer must find a compromise between the aperture efficiency and the conversion efficiency. This requires accurate and fast computational techniques for the efficiency. The present paper demonstrates for the first time that the efficiency of MTS antenna devices can be accurately evaluated in a few minutes. The compromise that should be made during the design process between the tapering efficiency and the conversion efficiency is highlighted. The impact on the efficiency of isotropic versus anisotropic MTS, uniform versus non-uniform modulation index, is analyzed. An excellent agreement is obtained between both approaches, commercial software, and experimental data.