Abstract
Abbas A. RangwalaUniversity of MumbaiDepartment of PhysicsMumbai 400 098, IndiaAshok M. GhodgaonkarRamdulal TewariUniversity of MumbaiWestern Regional Instrumentation CenterMumbai 400 098, IndiaAbstract. Starting from the variational form of Fermat’s principle, weidentify the optical Lagrangian and obtain the standard form of the rayequations in inhomogeneous optical media. Specializing to cylindricallysymmetric media, we define the paraxial ray approximation through theexact first integral of the ray equation. This enables us not only to relatethe constants of integration to the boundary conditions at the entry pointof the ray into the medium, but more importantly furnishes a systematicway of introducing corrections to the paraxial approximation. We alsoexhibit power-law refractive index profiles, which result in periodic raytrajectories.
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