Transmission of light through a single rectangular hole in a real metal

A theory is presented to describe the optical transmission through a rectangular hole in a real metal film. The previous theory of the transmission through a rectangular hole in a perfect electric conductor is extended to include the effects associated with having a real metal by adding surface-impedance boundary conditions and an effective index mode calculation. Both the peak and amplitude of the Fabry-Perot resonance of the fundamental mode agree quantitatively with experiments. Finite-difference time-domain calculations are used to verify the theoretical findings as well as to show the effects of including loss, which is not included in the theory. The localized nature of the transmission resonances is also revealed by analyzing the electric field maps associated with the enhanced transmission process.