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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 7 — Apr. 4, 2005
  • pp: 2549–2555

Analysis of the refraction of the extraordinary ray in a plane-parallel uniaxial plate with an arbitrary orientation of the optical axis.

M. Avendaño-Alejo  »View Author Affiliations

Optics Express, Vol. 13, Issue 7, pp. 2549-2555 (2005)

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Ray tracing formulas in a plane-parallel uniaxial plate bounded by an isotropic medium are analyzed when the crystal axis lies in the incident plane, and when its orientation is arbitrary. We present the behavior of the critical angle for the extraordinary ray as a function of the crystal axis position with respect to the normal to the refracting surface. We give the conditions in order to obtain the incidence angle at which the ordinary and extraordinary ray have the same refraction angle into the uniaxial crystal for particular positions of the optical crystal axis, also we give a condition for normal incidence in order to maximize or minimize the separation between the ordinary and extraordinary ray as a function of the optical crystal axis.

© 2005 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(160.1190) Materials : Anisotropic optical materials

ToC Category:
Research Papers

Original Manuscript: February 2, 2005
Revised Manuscript: March 18, 2005
Published: April 4, 2005

M. Avendaño-Alejo, "Analysis of the refraction of the extraordinary ray in a plane-parallel uniaxial plate with an arbitrary orientation of the optical axis," Opt. Express 13, 2549-2555 (2005)

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  1. M. C. Simon, �??Ray tracing formulas for monoaxial optical components,�?? Appl. Opt. 22, 354-360, (1983). [CrossRef] [PubMed]
  2. M. C. Simon, �??Image formation through monoaxial plane-parallel plates,�?? Appl. Opt. 27, 4176-4182, (1988). [CrossRef] [PubMed]
  3. J. Lekner, �??Reflection and refraction by uniaxial crystals,�?? J. Phys. Condes. Matter 3, 6122-6133, (1991). [CrossRef]
  4. E. Cojocaru, �??Direction cosines and vectorial relations for extraordinary-wave propagation in uniaxial media,�?? Appl. Opt. 36, 302�??306, (1997). [CrossRef] [PubMed]
  5. Q.-T. Liang, �??Simple ray tracing formulas for uniaxial optical crystal,�?? Appl. Opt. 29, 1008�??1010 (1990). [CrossRef] [PubMed]
  6. W.-Q. Zhang, �??General ray-tracing formulas for crystal,�?? Appl. Opt. 31, 7328�??7331, (1992). [CrossRef] [PubMed]
  7. G. Beyerle and I. S. McDermind, �??Ray-tracing formulas for refraction and internal reflection in uniaxial crystal,�?? Appl. Opt. 37, 7947�??7953 (1998). [CrossRef]
  8. M. Avendaño-Alejo, O. Stavroudis, A. R. Boyain, �??Huygens�?? Principle and Rays in Uniaxial Anisotropic Media I. Crystal Axis Normal to Refracting Surface,�?? J. Opt. Soc. Am. A. 19, 1668-1673, (2002). [CrossRef]
  9. M. Avendaño-Alejo, O. Stavroudis, �??Huygens�?? Principle and Rays in Uniaxial Anisotropic Media II. Crystal Axis with Arbitrary Orientation,�?? J. Opt. Soc. Am. A. 19, 1674-1679, (2002). [CrossRef]
  10. M. Avendaño-Alejo, M. Rosete-Aguilar, �??Paraxial Theory of birefringent lenses,�?? J. Opt. Soc. Am. A. 22, No. 5, (2005). [CrossRef]
  11. David Park, Classical Dynamics and its Quantum Analogues, second edition, (Springer Verlag, New York, 1990), pp. 18.
  12. J. P. Mathieu, Optics Parts 1 and 2, (Pergamon Press, New York, 1975), pp. 94.
  13. M. Avendaño-Alejo, M. Rosete-Aguilar, �??Optical path difference in a plane parallel uniaxial plate,�?? unpublished.
  14. A. A. Muryĭand and V. I. Stroganov, �??Conditions for bringing the ordinary and extraordinary rays into coincidence in a plane-parallel plate fabricated from am optical uniaxial crystal,�?? J. Opt. Technol. 71, 283-285, (2004). [CrossRef]

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