Solution to the Phenomenological Problem of a Magnetic Line Source Above a Plane Structure that SupportsN-Excited Modes

Abstract

The phenomenological theory of multimode surface wave excitation is applied to the problem of a line source above an infinite plane exciting surface. Mathematically, this involves solving the reduced wave equation subject to an Nth order differential boundary condition, constructed to allow for the excitation of surface and leaky wave modes. The results of this paper show that the response of any plane surface that is Characterizable by such a boundary condition exhibits certain characteristic phenomena. Namely, the far field is composed of a radiated field and excited modes and there exist sectors where the excited modes disappear. Also, it is possible for energy to be transported to infinity along the surface. These phenomena are familiar in the case of a dielectric slab. The solution is obtained by introducing a suitable auxiliary operator which is then inverted. This allows the determination of the radiated far field by elementary algebraic techniques. Then the result is transformed into a contour integral and the excited modes and high frequency approximation are discussed.