A time-harmonic space/spectral-domain solution of the electromagnetic fields radiated by an arbitrary distribution of electric and magnetic currents in a three-dimensional Cartesian half-space

The radiation of current elements in the vicinity of a layered medium is of great importance in understanding systems where electromagnetic interaction with an interface leads to significant desirable or undesirable effects. The discussion involves an expansion on previous theories, such as those presented by A. Sommerfeld (see "Partial Differential Equations in Physics", Academic Press, chap. 6,1964) and R.W.P. King and G.S. Smith (see "Antennas in Matter: Fundamentals", MIT Press, chap.11,1981) for the radiation of current elements near an interface. The formulation of this novel technique closely follows the methodology developed by King and Smith to determine the fields radiated by an infinitesimal horizontally-oriented electric dipole in a half-space. However, certain modifications are made that provide a more general approach. These alterations permit formulation of the fields radiated by an arbitrary distribution of electric and magnetic current sources (either in the media or on the interface) in a half-space. A flaw in King and Smith\´s boundary condition equations becomes apparent using this novel technique.