Closed-form expressions for magnetic polarizabilities of circular apertures excited by nonuniform magnetic fields

Abstract The problem of electromagnetic penetration through an aperture in a perfectly electrically conducting plane is a classical problem in electromagnetic theory and applications. This work aims to investigate the behavior of an electrically small aperture when excited by nonuniform magnetic fields. Based on the Taylor expansion of the exact solution in integral form of the corresponding mixed boundary problem, we derive the equivalent magnetic dipole moment of a circular aperture. Closed-form expressions of dipole moments are derived. Also, for the special case of axisymmetric excitation where the dipole moment vanishes, we develop a quadrupole model to describe the aperture behavior. The effectiveness of the obtained expressions is verified by comparisons with accurate analytical solutions in special cases and the exact solutions in integral form.