Substrate effect on aperture resonances in a thin metal film

We present a simple theoretical model to study the effect of a substrate on the resonance of an aperture in a thin metal film. The transmitted energy through an aperture is shown to be governed by the coupling of aperture waveguide mode to the incoming and the outgoing electromagnetic waves into the substrate region. Aperture resonance in the energy transmission thus depends critically on the refractive index of a substrate. We explain the substrate effect on aperture resonance in terms of destructive interference among evanescent modes or impedance mismatch. Our model shows an excellent agreement with a rigorous FDTD calculation and is consistent with previous experimental observations.