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

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2 Author(s)
M. Vrancken ; Dept. of Electr. Eng., Katholieke Univ. Leuven, Belgium ; G. A. E. Vandenbosch

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.

Published in:

IEEE Transactions on Antennas and Propagation  (Volume:51 ,  Issue: 10 )