  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.
