Metasurface characterization based on eigenmode analysis and averaging of electromagnetic fields

A fully numerical homogenization technique for the retrieval of the effective surface susceptibilities of a periodic composite metasurface is developed in this work. We utilize the so-called dual field-flux finite element formulation scheme to accurately calculate the eigenmodes of a composite periodic metasurface, a scheme that possesses a crucial advantage: The capability of evaluating all field components and their derivatives accurately and with the same order of approximation is a requirement for our proposed technique. Next, we derive the generalized sheet transition condition equations for a general bianisotropic metasurface, which correlate the field components on either sides of the metasurface with its surface susceptibilities. At this point, we establish a new field averaging scheme for the acquisition of the average field components of the modes supported by the metasurface. Combining this computational information, we derive a set of linear algebraic equations based on the GSTCs and the average electromagnetic fields and numerically solve it, so as to obtain the effective surface susceptibilities of a bianisotropic metasurface. Comparison with the results of other techniques in the literature shows very good agreement, relatively to the resonance behavior of the returned values and their position at the frequency spectrum. The advantages that distinguish the proposed technique over other related methods are its foundation on the intrinsic modal information of the eigenmodes supported by the metasurface and its independence of any wave excitation schemes or involvement of analytical polarizability calculations.