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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 2 — Feb. 1, 2011
  • pp: 278–283

Refractive-index distributions generating as light rays a given family of curves lying on a surface

Francesco Borghero and Thomas Kotoulas  »View Author Affiliations

JOSA A, Vol. 28, Issue 2, pp. 278-283 (2011)

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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.

© 2011 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)

Original Manuscript: October 11, 2010
Manuscript Accepted: November 13, 2010
Published: February 1, 2011

Francesco Borghero and Thomas Kotoulas, "Refractive-index distributions generating as light rays a given family of curves lying on a surface," J. Opt. Soc. Am. A 28, 278-283 (2011)

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