Dyadic eigenfunctions and natural modes for hybrid waves in planar media

A new formulation for studying electromagnetic wave propagation in an open, planarly layered medium is presented based on eigenfunctions of the Hertzian potential dyadic Green's function operator. Due to the complicated coupling of scalar components of potential at material interfaces, elevation of the usual vector eigenfunction problem to dyadic level is found to lead to a convenient, compact representation of wave propagation phenomena. Although we study the source-free problem here, the three columns of the eigenfunction dyadics represent (up to an excitation-dependent amplitude) the vector fields excited by a given three-dimensional source. The general theory of dyadic eigenfunctions is presented, including orthogonality and the possibility of associated functions (root functions) at modal degeneracies, and an example of propagation in a grounded dielectric slab environment is provided.