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-Pérot 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. DOI: 10.1103/PhysRevB.74.153411 PACS number͑s͒: 78.66.Bz, 42.25.Bs, 41.20.Jb, 42.79.Ag Observations of extraordinary optical transmission through arrays of subwavelength holes in metal films have spurred on intense research activity into understanding and utilizing this phenomenon. 1-10 Recent works have experimented with the effects on transmission that arise from changing the hole shape. [11][12][13] The main findings of those works is that elliptical or rectangular holes can dramatically influence the polarization, the resonance wavelength, and the intensity of the transmission. Random arrays of rectangular holes were used to demonstrate that a resonance exists in the transmission spectrum which is governed by the shape of the individual hole. 12 The peak wavelength of the resonance could be redshifted by decreasing the width of the short side of the hole. On the other hand, recent studies on isolated rectangular holes have shown the same effects of a resonance in transmission and a redshift that arises when reducing the width of the hole. 14 To explain how the shape-controlled resonance wavelength arises from a single hole, the influence of the hole shape on the cutoff wavelength of the modes within the hole was considered. 15 It was shown that the cutoff wavelength increases for a real metal due to increased coupling between evanescent fields on the long edges inside the hole. Later, the origin of the resonance was explained with a theory that incorporated the coupling between the mode inside the hole with the free-space regions on either side of the film. 16 The physical nature of this effect was attributed to a Fabry-Pérot resonance due to multiple reflections of the mode within the hole at the interfaces with the free-space regions. That theory did not capture the observed redshift phenomenon that arises when the width of the hole is reduced in a real metal because it considered only a perfect electric conductor.In this paper, a theory that describes quantitatively the transmission resonance for a rectangular hole in a metal film is presented. Here, the previous theory has been generalized to allow for a finite dielectric constant, and thereby captures the new physics associated with having a real ...