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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 5 — May. 1, 2005
  • pp: 881–891

Paraxial theory for birefringent lenses

Maximino Avendaño-Alejo and Martha Rosete-Aguilar  »View Author Affiliations

JOSA A, Vol. 22, Issue 5, pp. 881-891 (2005)

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The generalized ray tracing for the extraordinary ray through uniaxial crystals developed by Avendaño-Alejo and Stavroudis [J. Opt. Soc. Am. A 19, 1674 (2002) ] has been applied to derive paraxial refracting equations. Paraxial equations are derived for three cases where the incident, ordinary, and extraordinary rays lie in the incident plane: (a) the crystal axis is parallel to the optical axis, (b) the crystal axis is orthogonal to the optical axis and lies in the plane of incidence, and (c) the crystal axis is orthogonal to both the optical axis and the incident plane. The paraxial ray-tracing equations for the extraordinary ray are represented by matrix operators. The elements of the matrix system give all the information of the focal points and of the principal points. Gaussian formulas are derived, and some examples are presented.

© 2005 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence

Original Manuscript: September 3, 2004
Manuscript Accepted: November 16, 2004
Published: May 1, 2005

Maximino Avendaño-Alejo and Martha Rosete-Aguilar, "Paraxial theory for birefringent lenses," J. Opt. Soc. Am. A 22, 881-891 (2005)

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  1. O. N. Stavroudis, “Ray tracing formulas for uniaxial crystals,” J. Opt. Soc. Am. 52, 187–191 (1962). [CrossRef]
  2. Q. T. Liang, “Simple ray tracing formulas for uniaxial optical crystals,” Appl. Opt. 29, 1008–1010 (1990). [CrossRef] [PubMed]
  3. Z. Shao, C. Yi, “Behavior of extraordinary rays in uniaxial crystals,” Appl. Opt. 33, 1209–1212 (1994). [CrossRef] [PubMed]
  4. E. Cojocaru, “Direction cosines and vectorial relations for extraordinary wave propagation in uniaxial media,” Appl. Opt. 36, 302–306 (1997). [CrossRef] [PubMed]
  5. G. Beyerle, I. S. McDermid, “Ray-tracing formulas for refraction and internal reflection in uniaxial crystals,” Appl. Opt. 37, 7947–7953 (1998). [CrossRef]
  6. H. Kikuta, K. Iwata, “First-order aberration of a double-focus lens made of a uniaxial crystal,” J. Opt. Soc. Am. A 9, 814–819 (1992). [CrossRef]
  7. M. C. Simon, R. M. Echarri, “Ray tracing formulas for monoaxial optical components: vectorial formulation,” Appl. Opt. 25, 1935–1939 (1986). [CrossRef]
  8. J. P. Lesso, A. J. Duncan, W. Sibbett, M. J. Padgett, “Aberrations introduced by a lens made from a birefringent material,” Appl. Opt. 39, 592–598 (2000). [CrossRef]
  9. 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]
  10. 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]
  11. E. Hecht, A. Zajac, Optics (Addison-Wesley, London, 1974), Chap. 6.

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