Wd. Shen et al., FERMATS PRINCIPLE, THE GENERAL EIKONAL EQUATION, AND SPACE GEOMETRY IN A STATIC ANISOTROPIC MEDIUM, Journal of the Optical Society of America. A, Optics, image science,and vision., 14(10), 1997, pp. 2850-2854
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.