Abstract
The transmission of an electromagnetic field produced by a current loop of finite radius through a coaxial circular aperture in a perfectly conducting plate is evaluated through a rapidly convergent formulation in an exact form. By applying the equivalence principle, the problem is first formulated in the Hankel transform domain, obtaining a set of dual integral equations in which the equivalent surface magnetic current density defined on the aperture is not known. The set of dual integral equations is regularised in a second-kind Fredholm integral equation by applying the Abel integral-transform technique. The solution is achieved by expanding the unknown in a set of orthogonal basis functions that correctly reproduce the behaviour of the equivalent magnetic current at the edge of the aperture. Finally, under particular assumptions, a low-frequency solution is extracted in a closed form. Numerical results are reported to validate the accuracy and efficiency of the proposed formulations.
Highlights
The transmission of an electromagnetic (EM) field through an aperture in a planar conducting screen is a canonical problem that has attracted great attention in the EM community [1, 2]
In the low‐frequency region, Lord Rayleigh was the first to propose a solution to the problem [4]: procedure of the solution was based on a series expansion in ascending powers of the wavenumber of certain quantities, and it has been shown that it leads to a sequence of simple integral equations with a kernel of the electrostatic type [2]
We address the problem of the transmission of the magnetic field radiated by a finite source through a circular aperture in a planar perfectly conducting (PEC) plate
Summary
The transmission of an electromagnetic (EM) field through an aperture in a planar conducting screen is a canonical problem that has attracted great attention in the EM community [1, 2]. After applying the equivalence principle, operating in the Hankel transform domain, a set of dual integral equations is derived whose unknown is the equivalent magnetic surface current density on the aperture. In the low‐frequency limit (i.e. k0 → 0), elements Ymn in Equation (40) become: Y mn ð4n þ Such an integral, again of the Weber–Schafheitlin type [24], can be evaluated in a closed form using identity [26, Section. 6.574] (in any case, the integral in Equation (47) is the product of two orthogonal functions) and it results in Ymn = 0 for m ≠ n, whereas The latter integral can be expressed in a closed form by using the following identity [26, Section 6.626]:. For the integrals in Equations (53) and (54), using the expressions for Ið1; 1; 1Þ and Ið1; 0; 1Þ in Ason et al [28], we have "
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