Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes

We analyze subwavelength cylindrical holes in an optically thick metallic film with the metal described by a plasmonic model. We find that the dispersion diagram exhibits three distinct features that have a profound impact on the transmission of incident light through cylindrical holes. First, such holes always support propagating modes near the surface plasmon frequency, regardless of how small the holes are. Second, the fundamental plasmonic mode (HE11) is located completely below the surface plasmon frequency and gives rise to a passband in the transmission spectrum. Third, when the radius of the holes is small, there exists a stop band, just above the surface plasmon frequency, where a normally incident plane wave does not transmit. Based on the dispersion analysis, we design both a single hole and a hole array in which propagating modes play a dominant role in the transport properties of incident light. These structures exhibit a different region of operation that has not been probed yet experimentally, while featuring a high packing density and diffractionless behavior.