The geodesic equation, with dielectric tensor as its metric tensor, can be interpreted as the generalized ray equation, and it was employed for the numerical ray-tracing in optically anisotropic inhomogeneous media. Another form of generalized ray equation is derived from the Fermat’s principle under the assumption that transverse coordinates of rays are expressed as a function of optical axis. The new form of the generalized ray equation is applied to obtain closed-form solutions for ray-tracing in the media. The ray trajectories in specific types of medium are calculated by the closed-form solutions and their results are compared with those obtained by a numerical solution of the geodesic equation. It is shown that the results agree well for numerous types of anisotropic inhomogeneous media.

© 2013 Optical Society of America

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