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

## TL;DR

This paper introduces a method to determine the effective surface susceptibilities and porosities of symmetric metascreens using reflection and transmission data, enabling better design and analysis of metasurfaces with various aperture geometries.

## Contribution

It develops a retrieval approach based on GSTCs to extract surface parameters from R and T coefficients, validated across different aperture types and resonances.

## Key findings

- Successfully retrieved surface parameters for various aperture geometries.
- Identified resonances in filled apertures not present in unfilled ones.
- Validated retrieval method against other approaches.

## Abstract

Recently we derived generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen (a metasurface with a ``fishnet'' structure, i.~e., a periodic array of arbitrary spaced apertures in a relatively impenetrable surface). The parameters in these GSTCs are interpreted as effective surface susceptibilities and surface porosities, which themselves are related to the geometry of the apertures that constitute the metascreen. In this paper, we use these GSTCs to derive the plane-wave reflection ($R$) and transmission ($T$) coefficients of a symmetric metascreen, expressed in terms of these surface parameters. From these equations, we develop a retrieval approach for determining the uniquely defined effective surface susceptibilities and surface porosities that characterize the metascreen from measured or simulated data for the $R$ and $T$ coefficients. We present the retrieved surface parameters for metascreens composed of five different types of apertures (circular holes, square holes, crosses, slots, and a square aperture filled with a high-contrast dielectric). The last example exhibits interesting resonances at frequencies where no resonances exist when the aperture is not filled, which opens up the possibility of designing metasurfaces with unique filtering properties. The retrieved surface parameters are validated by comparing them to other approaches.