FERMATS PRINCIPLE, THE GENERAL EIKONAL EQUATION, AND SPACE GEOMETRY IN A STATIC ANISOTROPIC MEDIUM

Fermat's principle and the optical metric are generalized to the case of an anisotropic medium. The metric tensor of a three-dimensional Rie mannian manifold is related to the dielectric tensor of the medium. Th e general eikonal equation in a static anisotropic medium is derived. The expressions for the curvature tensor and the curvature scalar that characterize the geometrical structure of a three-dimensional manifol d are given. For an isotropic medium the derived expressions for the c urvature tensor and curvature scalar reduce to the previous results. ( C) 1997 Optical Society of America.