Decomposable medium conditions in four-dimensional representation

TL;DR

This paper generalizes the TE/TM decomposition in electromagnetic media using four-dimensional differential forms, identifying new classes of media where such decomposition is possible and analyzing their properties.

Contribution

It introduces a generalized framework for medium conditions enabling TE/TM decomposition, including new classes of decomposable media and their mathematical characterizations.

Findings

Identified three subclasses of media allowing TE/TM decomposition.

Generalized known classes like Q-media and P-media within this framework.

Proposed a new class called special decomposable media (SDCM).

Abstract

The well-known TE/TM decomposition of time-harmonic electromagnetic fields in uniaxial anisotropic media is generalized in terms of four-dimensional differential-form formalism by requiring that the field two-form satisfies an orthogonality condition with respect to two given bivectors. Conditions for the electromagnetic medium in which such a decomposition is possible are derived and found to define three subclasses of media. It is shown that the previously known classes of generalized Q-media and generalized P-media are particular cases of the proposed decomposable media (DCM) associated to a quadratic equation for the medium dyadic. As a novel solution, another class of special decomposable media (SDCM) is defined by a linear dyadic equation. The paper further discusses the properties of medium dyadics and plane-wave propagation in all the identified cases of DCM and SDCM.