Effect of film thickness and dielectric environment on optical transmission through subwavelength holes

Abstract

We present a detailed theoretical study for the spectral position of transmission resonances appearing in isolated subwavelength apertures in metallic films. We provide analytical expressions for the resonant wavelength as a function of the film thickness and the dielectrics surrounding (and filling) the system that are valid for hole shapes supporting large-cutoff wavelengths and for both isolated and periodically arranged holes. Our results are quantitatively valid in the microwave and terahertz regimes, but they also have qualitative validity in the optical regime. Our results show that for unfilled holes, in the limiting case when the hole is in a very thin film (metal thickness much smaller than the wavelength), the transmission resonance is controlled by a length scale related to the vanishing of the effective admittance of vacuum, as seen from the hole. On the contrary, for metal thicknesses larger than half the wavelength, the transmission resonance is controlled by the cutoff of the fundamental waveguide mode inside the hole. When thin films and high-index dielectrics are combined, the spectral location of the maximum transmission can be strongly redshifted compared to the cutoff wavelength of the apertures, and transmission intensity is substantially enhanced. © 2012 American Physical Society.