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Anisotropy without tensors: a novel approach using geometric algebra

Matos, S.A. ; Ribeiro, M. ; Paiva, C. R.

Optics Express Vol. 15, Nº 23, pp. 15175 - 15186, November, 2007.

ISSN (print): 1094-4087
ISSN (online): 1094-4087

Journal Impact Factor: 3,488 (in 2014)

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Abstract
The most widespread approach to anisotropic media is dyadic
analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinatefree meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: using geometric algebra we introduce a direct geometrical interpretation without the intervention of any coordinate system. By applying this new approach to biaxial crystals we show the effectiveness and insight that geometric algebra can bring to the optics of anisotropic media.