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A geometric algebra approach to bianisotropy

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

A geometric algebra approach to bianisotropy, Proc NATO Advanced Research Workshop: Metamaterials for Secure Information and Communication Technologies - ARW, Marrakesh, Morocco, Vol. 1, pp. 86 - 86, May, 2008.

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The development of metamaterials technology has greatly increased the availability of complex media. We can now argue that the new relevant question is more about what classes of
materials can satisfy a given property than the other way around, i.e., what are the electromagnetic properties of a given well-specified material. Systematic analyses of complex (namely,
bianisotropic) media are thus a very important tool. Furthermore, a coordinate-free approach is the best way to address, in the most general form, the electromagnetic characteristics of a broad class of unbounded media – as in the case of bianisotropic materials. The most used coordinate-free formalism is the tensor (or dyadic) approach – apart from some efforts to make differential forms a
more commonly used technique. In this paper we show how a coordinate-free analysis of bianisotropy can be more easily handled through the new insight that only the unique approach to
linear and multilinear functions provided by Clifford’s geometric algebra can bring. We present three new contributions: i) we show how geometric algebra simplifies and gives a new geometric
insight for general bianisotropic media; ii) we develop what we think is the most general approach for plane wave propagation in reciprocal bianisotropic media (including all possible eigenwaves
and their corresponding electromagnetic fields); iii) we present, as an example of application, new results for the specific case of pseudochiral omega media, including a general discussion of the
optic axes as well as the polarization and energy velocity of the eigenwaves.