On the Fermat's principle in a semi-transparent sphere of uniaxial cristal

Laboratoire d'Études Thermiques, UMR 6608, CNRS-ENSMA, 86960 Futuroscope Cedex, France

Corresponding author: hamou.sadat@univ-poitiers.fr

Received: 6 June 2006
Revised: 13 October 2006
Accepted: 24 November 2006
Published online: 24 January 2007

Abstract

The determination of the optical trajectories on which the radiative energy is transported has been achieved by solving the anisotropic Fermat's principle in a sphere of uniaxial semi-transparent material when the dielectric perpendicular and parallel permittivities are space dependant; first established for the general case of an optical axis function of the location inside the medium, it has completely been solved for the particular case of a constant optical axis with a constant anisotropy factor when the perpendicular permittivity is a function of the radius; the calculation shows a lack of the spherical symmetry due to the presence of the optical axis which induces non planar trajectories contrarily to the isotropic case.