Alternative methods for ray tracing in uniaxial media. Application to negative refraction

In previous papers [C. Bellver-Cebreros, M. Rodriguez-Danta, Eikonal equation, alternative expression of Fresnel's equation and Möhr's construction in optical anisotropic media, Opt. Commun. 189 (2001) 193; C. Bellver-Cebreros, M. Rodriguez-Danta, Internal conical refraction in biaxial media and graphical plane constructions deduced from Möhr's method, Opt. Commun. 212 (2002) 199; C. Bellver-Cebreros, M. Rodriguez-Danta, Refracción cónica externa en medios biáxicos a partir de la construcción de Möhr, Ópt. Pura Appli. 36 (2003) 33], the authors have developed a method based on the local properties of dielectric permittivity tensor and on Möhr's plane graphical construction in order to study the behaviour of locally plane light waves in anisotropic media. In this paper, this alternative methodology is compared with the traditional one, by emphasizing the simplicity of the former when studying ray propagation through uniaxial media (comparison is possible since, in this case, traditional construction becomes also plane). An original and simple graphical method is proposed in order to determine the direction of propagation given by the wave vector from the knowledge of the extraordinary ray direction (given by Poynting vector). Some properties of light rays in these media not described in the literature are obtained. Finally, two applications are considered: a description of optical birefringence under normal incidence and the study of negative refraction in uniaxial media.