Vectorial Impedance Identity for the Natural Dependence of Harmonic Fields on Closed Boundaries

Abstract

The exact description of the harmonic electromagnetic field solution at scattering surfaces is shown to require, in general, two impedances to relate the tangential electric field to the tangential magnetic field. The consequences lead to the generation of two independent surface vectors that are orthogonal, of equal norm, and have a realizable direction. They are used to describe the surface by two scalar equations. For the first time, the details of this vectorial impedance identity, the derivation of those two vectors, and the two scalar inverse scattering surface equations are shown.