A gegenbauer polynomial solution for the electromagnetic scattering by a subwavelength circular aperture in an infinite conducting screen

In this paper, we use magnetic vector potential formulation, along with equivalence principle and image theory, to solve the electromagnetic scattering of a polarized incident plane wave by a subwavelength circular aperture in a conducting screen. The underlined analytical formulation yields a closed-form solution that is accurate for any angle of incidence or polarization and valid for the near-, intermediate- and far-field regions of observation. The formulation is based on Bouwkamp’s diffraction model that uses dominant quasi-static magnetic current modes to represent the governing magnetic current distribution in the circular aperture for any incident wave. Taylor series expansion was implemented on the free-space Green’s function, and the individual Taylor terms were integrated analytically to produce closed-form expressions for the scattered fields in all regions. In doing so, the Gegenbauer polynomial expansion was applied in order to allow evaluation of the resulting integrals for any observation point in the lower half space. The results obtained from the proposed analytical approach were compared with data generated through a direct application of a numerical integration technique. The comparison illustrates the validity and accuracy of the proposed analytical formulation.