Closed-form analytical design of a beamforming reflective metagrating with a relatively low number of meta-atoms

Abstract

Metagrating, a periodic metamaterial structure proposed in recent years, is characterized by its structural simplicity and sparsity, compared to a metasurface. It is able to guarantee very high efficiency, even for wide-angle beam deflections, where only a few meta-atoms are required. In such cases, numerical optimization can be avoided and our goal in this work is to provide a fully analytical design study of a metagrating containing only two meta-atoms in a supercell. A series of closed-form design formulas are given, such as the impedance density expression of the meta-atoms, the passive and lossless conditional equations, as well as equations for the power ratio control of the diffraction modes. Four metagratings composed of microstrip capacitor structures working at 10 GHz for wide-angle beam steering and beam splitting are numerically demonstrated. The simulation results agree well with the theoretical predictions, which validates the correctness and effectiveness of the proposed theoretical method.