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A Spacetime Algebra Approach to Moving Bi-isotropic Media

Matos, S.A. ; Paiva, C. R. ; Barbosa, A.

A Spacetime Algebra Approach to Moving Bi-isotropic Media, Proc IEEE AP-S/URSI International Symp., Charleston, United States, Vol. -, pp. - - -, June, 2009.

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Abstract
Geometric algebra is a coordinate-free formalism, mainly known by physicists. The application of this formalism to study the electromagnetics of complex media as well as other problems addressed in electrical engineering constitutes a novel area of research. In particular, spacetime algebra (the geometric algebra of Minkowski spacetime) reveals a new geometric perspective of electromagnetics, that is unattainable with the usual tensor methods. The vacuum form reduction is one of these new techniques which enables to study, in a fictitious spacetime, a moving isotropic medium as in vacuum. Until now, this technique has only been used for isotropic media. In this communication, we will show how general bi-isotropic media can be easily handled with
spacetime algebra. Furthermore, the relativistic effects of moving Tellegen materials (non-reciprocal bi-isotropic media) are studied using the vacuum form reduction. This new approach brings a fresh viewpoint to the optics of Tellegen media. In spite of some claims that the “Post constraint” would be violated by Tellegen media, it can be shown that «the Post constraint as a general dogma should be buried with all due honors». In fact, there is a transformation which, for a sample of Tellegen material in free space, redefines fields so that the Tellegen material will look like a reciprocal
isotropic medium. However, the surrounding free space will then look as a nonreciprocal Tellegen medium. Therefore, although the nonreciprocal effect vanishes through this transformation when it is applied to an unbounded homogenous Tellegen medium, the
same is not true for heterogeneous regions containing Tellegen samples or to nonuniform Tellegen media. An equivalent reciprocal isotropic description of a Tellegen medium emerges as a geometric consequence of the Maxwell equations in Minkowski spacetime. In this paper we show, specifically, that a moving Tellegen medium, in the lab frame, is different from a moving isotropic medium – in the sense that both the refractive index surfaces and the electromagnetic fields are affected by the Tellegen parameter, in a way that could not be addressed as an equivalent moving reciprocal isotropic medium. Accordingly, this result highlights another physical manifestation of the irreducibility character of nonreciprocity due to Tellegen media.