分层旋向性介质中的电磁源变换和标量化
Electromagnetic source transformations and scalarization in stratified gyrotropic media
摘要：
由于对本构方程类型的限制，非均匀介质中的Maxwell方程有时可以化为两个仅含两个标量的二阶微分方程。这些结果以前是用两种完全不同的方法得到的。或者通过“源的标量化”，其中相关的标量基本上是矢量势分量，并且推导仅限于各向同性介质;或者通过使用"标量赫兹势“，并且这种方法已被应用于更一般的介质。本文证明了这两种方法在旋向性介质中是等价的。我们表明，标量化可以通过组合的电力和磁场源和规范变换之间的转换。结果表明，基于矢量势的方法，以前使用的非传统的定义的矢量势，也可以得到使用传统的定义提供了一个适当的规范条件，然后将这种方法从各向同性的回转介质。结果表明，第二种方法中出现的2个基本标量赫兹势在第一种方法的源标量化变换下是不变的，因此是获得标量化的自然势。最后，它表明，这两种方法也相当于一个更古老的第三种方法的基础上赫兹矢量。
英文摘要：
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 2nd order differential equations for 2 scalar quantities only. These results have previously been obtained in two quite different ways. Either by a ``scalarization of the sources'', where the relevant scalar quantities are essentially vector potential components and where the derivation was limited to isotropic media; or alternatively by using the ``scalar Hertz potentials'', and this method has been applied to more general media. In this paper it is shown that both methods are equivalent for gyrotropic media. We show that the scalarization can be obtained by a combination of transformations between electric and magnetic sources and gauge transformations. It is shown that the method based on the vector potential, which previously used a non-traditional definition of the vector potentials, can also be obtained using the traditional definition provided a proper gauge condition is applied and this method is then extended from isotropic to gyrotropic media. It is shown that the 2 basic scalar Hertz potentials occurring in the second method are invariant under the source scalarization transformations of the first method and therefore are the natural potentials for obtaining scalarization. Finally it is shown that both methods are also equivalent with a much older third method based on Hertz vectors.
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