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Analytical and Numerical Modeling of Reconfigurable Beamforming Metasurfaces

Analytical-numerical models of reconfigurable reflecting metasurfaces formed by chessboard-patterned metallic patch arrays with nonlinear capacitive loads are formulated. Two methods are used for the analytical modeling: One based on the effective medium theory and another based on the dispersion equation for the Bloch waves in a two-dimensional transmission line metamaterial. It is shown that the first approach is efficient to predict the reflectivity of a periodic metasurface, while the second approach is efficient to describe the excitation of surface waves on a finite-size structure. The analytical models are validated with numerical simulations. Finite size arrays with varying numbers of unit cells and array geometries are considered. It is observed that the proposed chessboard patterned arrays exhibit excellent angular stability of the resonant frequency independently of the incident wave polarization. Possible methods of beamforming and electronic control in the considered metasurface arrays are discussed.