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Abstract: It is known that with restrictions on the type of the constitutive equations,Maxwell-s equations in non-uniform media can sometimes be reduced to two 2ndorder differential equations for 2 scalar quantities only. These results havepreviously been obtained in two quite different ways. Either by a``scalarization of the sources-, where the relevant scalar quantities areessentially vector potential components and where the derivation was limited toisotropic media; or alternatively by using the ``scalar Hertz potentials-, andthis method has been applied to more general media. In this paper it is shownthat both methods are equivalent for gyrotropic media. We show that thescalarization can be obtained by a combination of transformations betweenelectric and magnetic sources and gauge transformations. It is shown that themethod based on the vector potential, which previously used a non-traditionaldefinition of the vector potentials, can also be obtained using the traditionaldefinition provided a proper gauge condition is applied and this method is thenextended from isotropic to gyrotropic media. It is shown that the 2 basicscalar Hertz potentials occurring in the second method are invariant under thesource scalarization transformations of the first method and therefore are thenatural potentials for obtaining scalarization. Finally it is shown that bothmethods are also equivalent with a much older third method based on Hertzvectors.



Autor: Patrick De Visschere

Fuente: https://arxiv.org/







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