Abstract

Fermat's principle and the optical metric are generalized to the case of an anisotropic medium. The metric tensor of a three-dimensional Riemannian manifold is related to the dielectric tensor of the medium. The 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 manifold are given. For an isotropic medium the derived expressions for the curvature tensor and curvature scalar reduce to the previous results.

© 1997 Optical Society of America

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Equations (43)

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Metrics

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