On the Averaging of the Electromagnetic Field in Metasurface Modeling

In this work, we present a fully numerical modeling technique for 2D-periodic composite electromagnetic structures known as metasurfaces. Utilizing the field-flux eigenmode Finite Element formulation, we outline the treatment of the general eigenvalue problem pertaining to metasurfaces. Subsequently, we propose an averaging process of the associated electromagnetic fields at paths prescribed by the Generalized Sheet Transition Conditions. Average field components of a metasurface consisting of split-ring resonators are illustrated and discussed.