Vector Potentials and Scalarization for Nonhomogeneous Isotropic Mediums

We show that the electromagnetic field in an isotropic (dielectric–magnetic) medium that is arbitrarily nonhomogeneous can be represented in terms of two vector potentials that are solutions of a system of two second-order partial differential equations. Furthermore, we derive conditions that permit the reduction of the two vector potentials to a pair of collinear single components and we establish a connection to an alternative solution formalism in terms of scalar Hertz potentials. The reduction involves both the vector potentials and their sources.