A General Expression for Homogeneous Metasurface Scattering

TL;DR

This paper presents a universal analytical model for homogeneous metasurface scattering, simplifying the design process by providing explicit expressions for scattering under arbitrary illumination conditions.

Contribution

It introduces a general susceptibility-based model that yields analytical scattering expressions, reducing the complexity of metasurface analysis and design.

Findings

Provides explicit formulas for specular scattering with arbitrary illumination.

Simplifies metasurface design by using symmetry-exploitable expressions.

Enables faster analysis compared to traditional boundary condition methods.

Abstract

The general approach in metasurface design is to find the unit-cell properties required to achieve a given functionality. This is usually done by modeling the metasurface as a combination of surface electric and magnetic polarization densities, whose parameters are determined by solving the generalized sheet transition conditions. This is a time consuming task, as the so-called boundary conditions needs to be solved per-case basis, depending on the source polarization, angle of incidence, and intended functionality. Evermore, the task complexity increases as factors such as different media around the metasurface and more than one illumination scenario are taken into account. In this work, we provide a general solution for a uniform metasurface homogenized in terms of susceptibilities. With this model, it is possible to obtain analytical expressions for the specular scattering produced by a metasurface illuminated with arbitrary illumination and angle of incidence. It is expected that the proposed model can ease the analysis and design of metasurfaces, by providing straight-forward expressions which can be simplified by exploiting the unit-cell symmetries.