Closed-form near-field expressions for electromagnetic scattering by an electrically small circular aperture on a conducting screen

Closed-form expressions were derived for the near-zone scattered fields caused by an obliquely incident plane wave of arbitrary polarization on a sub-wavelength circular aperture on an infinite conducting screen with an infinitesimal thickness. The analysis is based on a quasi-static model of the governing fields in the aperture which was published in the mid 40's by Bethe and improved by Bouwkamp a few years later by incorporating additional terms. Starting with first-order analytical expressions for the magnetic surface current density in the aperture, the scattering problem was formulated using the vector potential F→, the equivalence principle, and the image theory resulting in surface integrals over the aperture which involve the free-space Green's function. Using valid approximations for the near-zone field formulation, closed-form analytical expressions were derived for the corresponding scattered fields along the axis of the aperture. Obtained results based on these closed-form expressions were compared with published data obtained using the spectral-domain method indicating a very good agreement.