Directivity of Light Transmission through a Single Subwavelength Aperture without Plasmon Resonance

摘要

We present at first a rigorous differential method to resolve Maxwell equations in cylindrical coordinates. Such a method permits the calculation of field amplitudes in both spatial and spectral space in case of subwavelength hole pierced in metallic films with finite conductivity. From the rigorous method, we present a perturbation theory based on the single scattering approximation. It provides analytical formulas in the inverse space of the field amplitude in the spectral space. They lead to an equivalence with the well known model of single magnetic dipole excited inside a pierced layer. Light emitted by this dipole is then radiated to the cladding following the Fresnel's coefficients of light transmission from the layer to the cladding. This approach is in concordance with numerical results obtained from the rigorous method. The theory predicts that the directivity of the radiated pattern increases for smaller values of the layer permittivity modulus, as well as for a metallic layer than for a dieffectric one, independently from surface plasmon excitation.