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Electromagnetics of Complex Media using Geometric Algebra

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

Electromagnetics of Complex Media using Geometric Algebra, Proc Encuentro Ibérico de Electromagnetismo Computacional - EIEC , Cádiz, Spain, Vol. -, pp. - - -, October, 2008.

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Abstract
The development of metamaterials technology has greatly increased the availability of complex media. 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 anisotropic and bianisotropic media. 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. A new trend on the analysis of plane wave propagation in bianisotropic and anisotropic media is currently under investigation. We believe that linear algebra provided by Clifford’s geometric algebra is a far better framework to understand (and work on) complex media. Several authors already proved that geometric algebra is particularly useful when applied to special relativity or to relativistic quantum mechanics and general relativity. However, only recently it has been shown how geometric algebra provides a better mathematical framework for anisotropy than tensors and dyadics [1]. Some preliminary results using this approach for the analysis of general anisotropy and reciprocal bianisotropy have been presented [2-3]. With the new algebraic techniques brought by geometric algebra, greater analytical simplicity is achieved when compared with tensor analysis. Furthermore, this new mathematical tool provides a new geometrical insight, which cannot be foreseen in other more conventional formalisms.