Light transmission through a high index dielectric-filled sub-wavelength hole in a metal film

We investigate transmission of a normally incident, linearly polarized plane wave through a circular sub-wavelength hole in a metal film filled by a high index dielectric medium. We demonstrate for the first time that the transmission efficiency of such holes exhibits a Fabry-Pérot-like behaviour versus thickness of the metal film, similar to that exhibited by sub-wavelength slits in metal films illuminated by TM-polarized plane waves. We show that by reducing the imaginary part of the propagation constant of the hybrid HE₁₁ mode and by fortifying the Fabry-Pérot resonance, the high index dielectric filling can greatly enhance light transmission through a circular sub-wavelength hole.