Ab initio analytical model of light transmission through a cylindrical subwavelength hole in an optically thick film

The rigorous analytical theory of light transmission through a cylindrical hole of arbitrary diameter in an optically thick film is developed. The approach is based on the introduction of fictitious surface currents at both hole openings and both film surfaces. The solution of Maxwell's equations obeying the boundary conditions at all interfaces is obtained in the form of the Fourier integral over the axial-wave-vector component. The exact integral equation which determines the field-amplitude Fourier transforms is derived. The general approach is simplified in the case of an elongated hole, where the film thickness considerably exceeds the hole diameter. It is emphasized that a specific pole corresponding to excitation of surface plasmon polaritons does not appear in the analysis. The theory is illustrated by the calculation of light transmission through a subwavelength hole in an Ag film.