Scalar Potential Depolarizing Dyad Artifact for a Uniaxial Medium

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A scalar potential formulation for a uniaxial anisotropic medium is succinctly derived through the exclusive use of Helmholtz's theorem and subsequent identification of operator orthogonality. The resulting formulation is shown to be identical to prior published research, with the notable exception that certain scalar potential fields not considered in previous work are rigorously demonstrated to be unimportant in the field recovery process, thus ensuring uniqueness. In addition, it is revealed that both a physically expected and unexpected depolarizing dyad contribution appears in the development. Using a Green's function spectral domain analysis and subsequent careful application of Leibnitz's rule it is shown that, for an unbounded homogeneous uniaxial medium, the unexpected depolarizing dyad term is canceled, leading to a mathematically and physically consistent and correct theory.


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Progress in Electromagnetics Research