Electromagnetic scattering by a subwavelength circular hole in a perfect metal plate of finite thickness: matched asymptotic expansion

Abstract

We present an approach to the problem of electromagnetic scattering by a subwavelength circular hole in a perfect metal plate of finite thickness. The matched asymptotic expansion is employed to solve the scattered fields in the inner and outer regions with respect to the hole position. By use of the dual potentials and Fabrikant’s theory, the solutions are expressed as a combination of spherical functions. In particular, the scattering behavior is illustrated with the near-field quasistatic potentials as well as the far-field radiation patterns. The dipole strengths associated with the subwavelength hole are scaled by the angle of incidence in terms of the vertical electric field and/or horizontal magnetic field components. The effect of the plate thickness is manifest on the attenuation of the dipole strengths associated with the subwavelength hole. For a large thickness, the dipole strengths approach the values for an infinitely deep hole, while for a very small thickness, the results coincide with the Bethe theory.