Scalar potential formulation for a bianisotropic gyrotropic inhomogeneous medium and associated boundary conditions

Summary form only given. Scalar and vector potentials have been recently investigated for use in the electromagnetic analysis of problems involving complex media such as anisotropic and bianisotropic materials. This interest is strongly influenced by the phenomenal advances made in material fabrication capability and the phenomena exclusively associated with complex media. Bianisotropic gyrotropic materials are extremely interesting, both theoretically and experimentally, due to their exotic and non-reciprocal properties.The goals of this paper are to first derive a scalar potential formulation for a magnetically and electrically gyrotropic bianisotropic medium (which is the most general media amenable to a scalar potential formulation). It is assumed the medium is, in general, inhomogeneous along the longitudinal axis (i.e., the taxis). The formulation is solely based upon the two-dimensional form of Helmholtz´s theorem and the identification of operator orthogonality. This approach comprises an important contribution of this work since it differs from others in that field uniqueness is guaranteed. Next, expected and unexpected depolarizing dyads encountered in the derivation are identified and it is shown that the unexpected dyads are removable via complex plane analysis. This constitutes another important contribution here since it provides the rigorously correct methodology for carefully handling complex media via a scalar potential approach. Finally, scalar potential boundary conditions for various geometries (such as material interfaces and perfect conductors) are derived which are based on identification of operator orthogonality. Identification of various boundary conditions in the scalar potential domain is a critical contribution of this work since it allows considerable simplification when compared to implementation of boundary conditions in the electromagnetic field domain. Future work is also discussed, including application to waveguide structures.