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Optic axes of general anisotropic media: a geometric algebra perspective

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

Optic axes of general anisotropic media: a geometric algebra perspective, Proc Conf. on Telecommunications - ConfTele, Santa Maria da Feira, Portugal, Vol. -, pp. - - -, May, 2009.

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For simple electric (magnetic) anisotropy, a single
mapping between the permittivity (permeability) value and the
direction of space describes the medium properties. The wellknown
classification of anisotropic crystals (uniaxial or biaxial)
depends only on a single constitutive function. The
generalization of this taxonomy for simultaneously electric and
magnetic anisotropy is presented using the formalism of
geometric algebra. For this case, the permittivity and
permeability functions lose their direct interpretation on the
classification scheme. We found a new constitutive function that
describes the type of general anisotropy. The mathematical and
geometric background, provided by the geometric algebra
formalism, is the keystone to derive these results in its most
general form. The binding between geometric algebra and
linear functions is proved to be a more elegant and insightful
way of working with anisotropy than the usual tensors or even
differential forms methods.