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A geometric algebra approach to the reflection and transmission of electromagnetic waves at interfaces between isotropic and general anisotropic media

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

A geometric algebra approach to the reflection and transmission of electromagnetic waves at interfaces between isotropic and general anisotropic media, Proc Metamorphose International Congress on Advanced Electromagnetic Materials in Microwaves and Optics - METAMATERIALS, London, United Kingdom, Vol. -, pp. - - -, September, 2009.

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Abstract
Using a mathematical framework, based on Clifford (geometric) algebra Cl3, we develop a coordinate-free approach to interfaces between isotropic and general anisotropic media. The anisotropy is characterized by two linear operators: the dielectric permittivity ε: Cl3 -> Cl3 and the magnetic permeability μ: Cl3 -> Cl3. Two different approaches are adopted and compared: (i) using a simple geometric approach that is applicable only when the two operators commute, i.e., if εμ=με; (ii) using a general approach, applicable even when εμ≠με, which leads to the more analytical formulation based on the solutions of the Booker quartic equation.