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Optical properties of Fano-resonant metallic metasurfaces on a substrate

Three different periodic optical metasurfaces exhibiting Fano resonances are studied in mid-IR frequency range in the presence of a substrate. We develop a rigorous semi-analytical technique and calculate how the presence of a substrate affects optical properties of these structures. An analytical minimal model based on the truncated exact technique is introduced and is shown to provide a simple description of the observed behavior. We demonstrate that the presence of a substrate substantially alters the collective response of the structures suppressing Wood's anomalies and spatial dispersion of the resonances. Different types of Fano resonances are found to be affected differently by the optical contrast between the substrate and the superstrate. The dependence of the spectral position of the resonances on the substrate/superstrate permittivities is studied and the validity of the widely used effective medium approaches is re-examined.