A mode-matching solution to plane wave scattering by a plasmonic nanohole array consisting of a silver film perforated by an infinite square array of circular holes is presented. A complete orthonormal basis set consisting of waveguide modes satisfying an impedance boundary condition on the hole wall is derived. Impedance boundary conditions are satisfied on the upper and lower horizontal surfaces of the film and on the walls of the hole. Extraordinary optical transmission (EOT) is studied over optical wavelengths. Theory predicts a peak transmission value that is in better agreement with experiment than previous modal studies. The effect of film thickness on coupling between modes bound to the upper and lower surfaces is studied. The transmission profile for thinner films evinces two peaks at different wavelengths resulting from strong coupling between surface waves bound to the upper and lower surfaces. For thicker films, the surface waves decouple and a single peak is observed. The effect of hole radius on EOT is considered. It is demonstrated that transmission peaks occur for holes of a roughly constant electrical size. A relationship between the lattice constant and the transmission-to-area efficiency is quantified.
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