Metasurfaces homogenization technique based on the computation of the average value of the contravariant tensors elements

Abstract

The purpose of this paper is to present a 2D metasurfaces homogenization based on the computation of the average value of the contravariant tensors elements. A simple semi-analytical model for the comprehension of the extraordinary optical transmission (EOT) through a 2D array of periodic subwavelength metasurface is analyzed through the proposed method. In this single mode model, the mono layer of the metasurface film is considered as homogeneous medium. Therefore, the electromagnetic response of this structure to a plane wave excitation is equivalent to that of a slab with homogeneous equivalent properties. In a coordinates system where the coordinate curves xj coincide with the physical discontinuity of the material, the covariant formalism involving contravariant components of density flux and covariant components of the electromagnetic field, allows to efficiently handle the continuity properties of the electromagnetic field. By averaging all these quantities involving local fields over the periods of the unit cell, and assuming that, these macroscopic fields and densities satisfy a constitutive relationship, the electromagnetic parameters such as averaged permittivity and permeability can be defined.