Scalar potential formulation for a uniaxial inhomogeneous medium

Abstract

Summary form only given. Vector potentials are frequently utilized in the electromagnetic analysis of problems involving simple (i.e., linear, homogeneous, and isotropic) media. In recent decades, various scalar and vector potential formulations have been investigated for the analysis of anisotropic and bianisotropic media. This interest has been greatly influenced by the significant developments in material fabrication capability and the phenomena associated with complex media. Uniaxial anisotropic media are particularly interesting from an application viewpoint due to the relative ease of manufacturing this type of material. The goals of this paper are to first briefly review a scalar potential formulation for a magnetically and electrically uniaxial anisotropic medium. It is assumed the medium is, in general, inhomogeneous along the longitudinal axis (i.e., the zaxis). Next, expected and unexpected depolarizing dyad contributions are identified in the scalar potential development. It is discussed, from a physical viewpoint, why the unexpected depolarizing dyad should not exist. Based on this insight, the final goal is to mathematically demonstrate the unexpected depolarizing dyad is actually removable, thus leading to a physically and mathematically consistent theory.