Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings

We investigate the transmission properties of a metallic layer with narrow slits. Recent measurements and numerical calculations concerning the light transmission through metallic subwavelength structures suggest that an unexpectedly high transmission coefficient is possible. We analyze the time harmonic Maxwell’s equations in the H-parallel case for a fixed incident wavelength. Denoting by η > 0 the typical size of the complex structure, effective equations describing the limit η → 0 are derived. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfaces of the channels. When these waves are in resonance with the thickness of the layer, the result can be perfect transmission through the layer. MSC: 78M40, 35P25, 35J05 key-words: plasmonic wave, Helmholtz equation, scattering, resonance, homogenization, effective tensor