Analytical model of a metasurface consisting of a regular array of sub-wavelength circular holes in a metal sheet

In this work, a metasurface consisting of an array of circular holes in a metal conducting sheet with a sub-wavelength periodicity is considered. The surface partially reflects the incident field according to the shape and geometrical dimensions of the inclusions and, due to this property, is widely employed in antenna systems to improve the radiation pattern of regular radiators. Since the reflection properties of the metasurface are determined by the current density distribution on the metal, we inspect this distribution and coherently develop a new, easy, and accurate analytical model to describe the grid impedance of the metasurface. In order to validate the model, we compare the reflection coefficient of the array obtained through our approach to the one resulting from full-wave numerical simulations and to other accurateanalytical methods available in the open technical literature.