Perfect control of reflection and refraction using spatially dispersive metasurfaces

TLDR

Nonuniform metasurfaces can shape refracted and reflected waves, yet conventional design methods based on generalized laws inevitably produce parasitic reflections. This work proposes a general synthesis approach that enables full control of transmitted and reflected plane waves with perfect performance. The method employs an equivalent impedance‑matrix model linking tangential fields on both sides of the metasurface, from which the required polarizabilities and suitable unit‑cell structures are derived. The results show that only spatially dispersive metasurfaces can achieve perfect refraction and reflection, and ideal refraction requires weak spatial dispersion (bianisotropy) while perfect reflection without polarization change demands a strongly nonlocal response.

Abstract

Nonuniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected plane waves and show that perfect performance can be realized. The method is based on the use of an equivalent impedance matrix model which connects the tangential field components at the two sides on the metasurface. With this approach we are able to understand what physical properties of the metasurface are needed in order to perfectly realize the desired response. Furthermore, we determine the required polarizabilities of the metasurface unit cells and discuss suitable cell structures. It appears that only spatially dispersive metasurfaces allow realization of perfect refraction and reflection of incident plane waves into arbitrary directions. In particular, ideal refraction is possible only if the metasurface is bianisotropic (weak spatial dispersion), and ideal reflection without polarization transformation requires spatial dispersion with a specific, strongly nonlocal response to the fields.