Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings

We perform a mathematical analysis of the transmission properties of a metallic layer with narrow slits. Our analysis is inspired by recent measurements and numerical calculations that report an unexpected high transmission coefficient of such a structure in a subwavelength regime. We analyze the time harmonic Maxwell’s equations in the H-parallel case for a fixed incident wavelength. Denoting by ? the typical size of the grated structure, we analyze the limit n -> 0 and derive effective equations that take into account the role of plasmonic waves. We obtain a formula for the effective transmission coefficient