General Issues of the Theory of Thin Impedance Vibrators and Narrow Slots in a Spatial-Frequency Representation

Let us formulate in the most general form the problem of excitation, scattering and radiation of electromagnetic fields by material bodies of finite size in the presence of the coupling holes between the two electrodynamic volumes. Let there be an arbitrary volume \(V_{1}\) bounded by a perfectly conducting, impedance, or partially impedance surface \(S_{1}\), some parts of which can be removed to infinity. The volume \(V_{1}\) is coupling with another arbitrary volume \(V_{2}\) through holes \(\Sigma _{n} \left( {n = 1,2 \ldots N} \right)\) cut in the common surface between the two volumes. The boundary wall between the coupling volumes \(V_{1}\) and \(V_{2}\) has an infinitely small thickness in the region of the coupling holes.