Backaction in metasurface etalons

We consider the response of etalons created by a combination of a conventional mirror and a metasurface composed of a periodic lattice of metal scatterers with a resonant response. This geometry has been used previously for hybridization of localized plasmons with Fabry-Perot resonances and for perfect absorption, in so-called Salisbury screens. The particular aspect we address is if one can assume an environment-independent reflectivity for the metasurface when calculating the reflectivity of the composite system, as in a standard Fabry-Perot analysis, or whether the fact that the metasurface interacts with its own mirror image renormalizes its response. Using lattice sum theory, we take into account all possible retarded dipole-dipole interactions of scatterers in the metasurface amongst each other and through the mirror. We show that while a layer-by-layer Fabry-Perot formalism captures the main qualitative features of metasurface etalons, in fact the mirror modifies both the polarizability and reflectivity of the metasurface in a fashion that is akin to Drexhage's modification of the radiative properties of a single dipole.