Isotropic-uniaxial interfaces for anisotropic media with biaxial electric and magnetic functions: A new approach with geometric algebra

The problem of interfaces between isotropic and uniaxial/pseudo-isotropic media has been addressed using a geometric algebra framework. In fact, only in this framework is it possible to classify the behavior of general anisotropic media in a clear and insightful way. Media characterized by both biaxial electric and magnetic functions, globally behaving as uniaxial or pseudo-isotropic, have then been analyzed. Furthermore, the transmitted wavenumber components have been explicitly obtained revealing that, unlike those of simple uniaxial crystals, they exhibit an explicit dependence with the azimuth angle. The conditions for total reflection were also found to depend on this azimuth angle. Additionally, since all the eigenwaves of general uniaxial/pseudo-isotropic media are extraordinary, it is not possible to obtain a transmitted angle that is equal to the incident angle for any of the wavenumbers. This can be easily achieved at an isotropic - (simple) uniaxial crystal interface by choosing the refractive index of the isotropic media to equal that of the ordinary wave of the (nonmagnetic) uniaxial crystal.