Semantics of dyadic and mixed potential field representation for 3-D current distributions in planar stratified media

Abstract

The full spectral electric dyadic Green's function for three dimensional current distributions in planar stratified media can be obtained straight from Maxwell's equations. By following a physical reasoning analogous with the free space case but using general derivative relations for multilayered Green's functions, we derive a "basic" mixed potential form with a simple vector potential kernel but multiple scalar potential kernels, and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel. Mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential, or choice of gauge condition. The nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and/or vector potentials are believed to be clarified by the proposed approach. A discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations.