Extension of classical EM solution representations to nonhomogeneous isotropic media with sources

An attempt is made to present unified, cohesive, and complete derivations of the classical representations of solutions to Maxwell's equations. The traditional arguments are reviewed with an eye towards generality, as regards the assumptions about the nature of the medium and the source terms. In this manner very specific results are obtained categorizing the existence, universality, and utility of the various transverse/longitudinal wave decomposition schemes in the presence of nonuniform permittivity and permeability, and arbitrary charge/current configurations. This makes it possible to differentiate between intrinsic physics and boundary conditions as the cause of mode 'disenfranchisement' in particular cases. Familiar physical examples are cited to demonstrate and delimit the conclusions.<>