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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1373–1379

Closed-form analytical solutions for ray tracing in optically anisotropic inhomogeneous media

Yohei Nishidate  »View Author Affiliations

JOSA A, Vol. 30, Issue 7, pp. 1373-1379 (2013)

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Closed-form analytical solutions are obtained for ray tracing in several types of optically anisotropic inhomogeneous media whose optical properties are characterized by a matrix form of the inhomogeneous dielectric tensor in principal coordinates. The first solution is for anisotropic axial media, the second solution is for meridional rays in epsilon-negative metamaterial, and the third solution is an approximate one for rectangular lenses fabricated by molding procedures. The validation of numerical ray-tracing procedures for optically anisotropic inhomogeneous media was widely ignored since the solution was not available, and thus the present solutions are also useful for the validation. Furthermore, as examples of validation, ray trajectories are calculated by the closed-form solutions, and their results are compared with those obtained by a numerical solution of the geodesic equation which can be interpreted as a generalized ray equation.

© 2013 Optical Society of America

OCIS Codes
(000.2690) General : General physics
(080.2720) Geometric optics : Mathematical methods (general)
(160.1190) Materials : Anisotropic optical materials
(260.1440) Physical optics : Birefringence
(080.5692) Geometric optics : Ray trajectories in inhomogeneous media
(260.2710) Physical optics : Inhomogeneous optical media

Original Manuscript: April 2, 2013
Revised Manuscript: May 27, 2013
Manuscript Accepted: May 28, 2013
Published: June 19, 2013

Yohei Nishidate, "Closed-form analytical solutions for ray tracing in optically anisotropic inhomogeneous media," J. Opt. Soc. Am. A 30, 1373-1379 (2013)

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