Generalized Q-media and Field Decomposition in Differential-form Approach

Abstract

Differential-form formalism in four dimensions gives the simplest possible representation to the Maxwell equations. The constitutive equation for the general linear (bi-anisotropic) medium is a relation between the two electromagnetic two-forms through a medium dyadic of the Hodge type. In a previous paper a class of bi-anisotropic media labeled as that of Q-media was studied in four-dimensional formalism. It was shown to correspond to a known class of media in the classical three-dimensional formalism allowing one to solve the Green dyadic in analytical form. The present paper is a continuation where the similar problem is solved for a class of bi-anisotropic media, previously labeled as that of generalized Q-media. It is shown that the simple four-dimensional definition of this class of media corresponds to a three-dimensional definition of a class of bi-anisotropic media which has been previously labeled as that of decomposable media. To see this explicitly, it is shown that fields of a plane wave are decomposed in two sets each satisfying a certain polarization condition.