Abstract

By generalization of the methods presented in Part I of the study [ J. Opt. Soc. Am. A 12, 600 ( 1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

© 1995 Optical Society of America

Differential geometrical methods in the study of optical transmission (scalar theory). I. Static transmission case

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