title: Refractive-index distributions generating as light rays a given family of curves lying on a surface.
abstract: In the framework of geometrical optics, we consider the inverse problem consisting in obtaining refractive-index distributions n=n(u,v) of a two-dimensional transparent inhomogeneous isotropic medium from a known family f(u,v)=c of monochromatic light rays, lying on a given regular surface. Using some basic concepts of differential geometry, we establish a first-order linear partial differential equation relating the assigned family of light rays with all possible refractive-index profiles compatible with this family. In particular, we study the refractive-index distribution producing, as light rays, a given family of geodesic lines on some remarkable surfaces. We give appropriate examples to explain the theory.
authors.affiliation: Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale, n. 72 09124 Cagliari, Italy.
authors.forename: Francesco
authors.initials: F
authors.lastname: Borghero
authors.forename: Thomas
authors.initials: T
authors.lastname: Kotoulas