Generalized Sheet Transition Conditions for a Metascreen—A Fishnet Metasurface

Abstract

We used a multiple-scale homogenization method to derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen-a metasurface with a "fishnet" structure. These surfaces are characterized by periodically-spaced arbitrary-shaped apertures in an otherwise relatively impenetrable surface. The parameters in these GSTCs are interpreted as effective surface susceptibilities and surface porosities, which are related to the geometry of the apertures that constitute the metascreen. Finally, we emphasize the subtle but important difference between the GSTCs required for metascreens and those required for metafilms (a metasurface with a "cermet" structure, i.e., an array of isolated (non-touching) scatterers).

Retrieval Approach for Determining Surface Susceptibilities and Surface Porosities of a Symmetric Metascreen From Reflection and Transmission Coefficients

“…1a), a term coined in [10]. Metasurfaces with a "fishnet" structure are called metascreens [11], see Fig. 1b.…”

“…Alternatively, a dipole-interaction model can be used to obtain the GSTCs [16] and [17]. However they are obtained, the GSTCs for a metascreen take on a different form than those required for the metafilm, and their features are discussed in [11], [16] and [17]. The issue with a metascreen is that there is the possibility of having tangential surface currents (flowing on the surface of the screen along the z and x directions) that do not vanish as the lattice constant of the metascreen approaches zero, as such, a GSTC that constrains the tangential H cannot be used, see [11] for details.…”

“…However they are obtained, the GSTCs for a metascreen take on a different form than those required for the metafilm, and their features are discussed in [11], [16] and [17]. The issue with a metascreen is that there is the possibility of having tangential surface currents (flowing on the surface of the screen along the z and x directions) that do not vanish as the lattice constant of the metascreen approaches zero, as such, a GSTC that constrains the tangential H cannot be used, see [11] for details. The GSTCs allow the surface distribution of apertures to be replaced with a boundary condition on the averaged fields that is applied across an infinitely thin equivalent surface (hence the name metascreen), as indicated in Fig.…”

“…2. In [11], the GSTCs relating the electromagnetic fields on both sides of the metascreen shown in Fig. 1 and Fig.…”

“…In this paper, we use the GSTCs to derive the planewave reflection (R) and transmission (T ) coefficients for a metascreen. The derivation presented in [11] laid out the framework for calculating the required surface susceptibilities and surface porosities, which require the solution of a set of static field problems-this can be computationally challenging for generally shaped apertures. Thus, we will also derive expressions allowing the surface parameters to be retrieved from measured or simulated values of R and T .…”