TE/TM decomposition of electromagnetic sources

Three methods are given by which bounded EM sources can be decomposed into two parts radiating transverse electric (TE) and transverse magnetic (TM) fields with respect to a given constant direction in space. The theory applies source equivalence and nonradiating source concepts, which lead to decomposition methods based on a recursive formula or two differential equations for the determination of the TE and TM components of the original source. Decompositions for a dipole in terms of point, line, and plane sources are studied in detail. The planar decomposition is seen to match to an earlier result given by Clemmow (1963). As an application of the point decomposition method, it is demonstrated that the general exact image expression for the Sommerfeld half-space problem, previously derived through heuristic reasoning, can be more straightforwardly obtained through the present decomposition method.