Analytical expressions for the scattering by an electrically small circular aperture on an infinite conducting ground plane

Near-field analytical expressions for the plane-wave scattering from an electrically small circular aperture on an infinite conducting screen were derived based on the Bethe-Bouwkamp (BB) quasi-static model. The formulation of the problem implements the equivalence principle and image theory in order to express the scattered fields in the near zone in terms of the vector potential F→. The vector potential is defined as a surface integral of the first-order BB approximation of the magnetic current on the aperture multiplied by the governing free-space Green's function. The free-space Green's function was expanded using Taylor series, thus producing integrals that can be evaluated analytically for the case where the observation point resides on the axis of the aperture. Results for the scattered electric field along the axis of the aperture, using the obtained closed-form near-field expressions, were validated against recently published results in the literature.