Low-Frequency Characteristic Modes for Aperture Coupling Problems

In this paper, a recently suggested general procedure which leads to an eigenvalue equation for aperture problems is specialized to the range of frequencies for which the maximum linear dimension of the aperture l is much smaller than the wavelengths, known as the Rayleigh region. As kl asymptotically approaches zero, we arrive at a set of two eigenvalue equations which aided by the edge condition, constitutes an alternative set of equations for a derivation of the quasi-static distributions characterizing the aperture.