Validity of effective medium theory for metal-dielectric lamellar gratings

The effective medium theory (EMT) description of metal-dielectric lamellar gratings under transverse magnetic polarization is studied by the exact mode analysis method. It is demonstrated that, except a lower order eigenmode which can be approximated as the effective mode, there is a higher order eigenmode that cannot be described by the EMT. The resonant enhancement of the high order eigenmode induced by the coupling between the two kinds of eigenmodes leads to the failure of the EMT. In the presence of material absorption, the higher order eigenmode will be suppressed and thus the effective medium approximation becomes applicable. This result clarifies the fuzzy recognition about EMT.