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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 10, Iss. 11 — Nov. 1, 1993
  • pp: 2371–2382

Polarization ray tracing in anisotropic optically active media. I. Algorithms

Stephen C. McClain, Lloyd W. Hillman, and Russell A. Chipman  »View Author Affiliations

JOSA A, Vol. 10, Issue 11, pp. 2371-2382 (1993)

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Procedures for performing polarization ray tracing through birefringent media are presented in a form compatible with the standard methods of geometrical ray tracing. The birefringent materials treated include the following: anisotropic optically active materials such as quartz, non-optically active uniaxial materials such as calcite, and isotropic optically active materials such as mercury sulfide and organic liquids. Refraction and reflection algorithms are presented that compute both ray directions and wave directions. Methods for computing polarization modes, refractive indices, optical path lengths, and Fresnel transmission and reflection coefficients are also specified. A numerical example of these algorithms is given for analyzing the field of view of a quartz rotator.

© 1993 Optical Society of America

Original Manuscript: March 18, 1992
Revised Manuscript: June 14, 1993
Manuscript Accepted: June 15, 1993
Published: November 1, 1993

Stephen C. McClain, Lloyd W. Hillman, and Russell A. Chipman, "Polarization ray tracing in anisotropic optically active media. I. Algorithms," J. Opt. Soc. Am. A 10, 2371-2382 (1993)

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  1. W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), pp. 71, 87–108.
  2. B. H. Billings, “Monochromatic depolarizer,”J. Opt. Soc. Am. 38, 819–829 (1948). [CrossRef] [PubMed]
  3. J. D. McGuire, R. A. Chipman, “Analysis of spatial pseudo-depolarizers in imaging systems,” Opt. Eng. 29, 1478–1484 (1990). [CrossRef]
  4. A. M. Title, W. J. Rosenberg, “Improvements in birefringent filters. 5: Field of view effects,” Appl. Opt. 18, 3443–3456 (1979). [CrossRef] [PubMed]
  5. J. E. Greivenkamp, “Color dependent optical prefilter for suppression of aliasing artifacts,” Appl. Opt. 29, 676–684 (1990). [CrossRef] [PubMed]
  6. J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978).
  7. O. N. Stavroudis, “Ray-tracing formulas for uniaxial crystals,”J. Opt. Soc. Am. 52, 187–191 (1962). [CrossRef]
  8. W. Swindell, “Extraordinary-ray and -wave tracing in uniaxial crystals,” Appl. Opt. 14, 2298–2301 (1975). [CrossRef] [PubMed]
  9. M. Simon, “Ray tracing formulas for monoaxial optical components,” Appl. Opt. 22, 354–360 (1983). [CrossRef] [PubMed]
  10. J. D. Trolinger, R. A. Chipman, D. K. Wilson, “Polarization ray tracing in birefringent media,” Opt. Eng. 30, 461–466 (1991). [CrossRef]
  11. Q.-T. Liang, “Simple ray tracing formulas for uniaxial optical crystals,” Appl. Opt. 29, 1008–1010 (1990). [CrossRef] [PubMed]
  12. E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 86–89 (1989). [CrossRef]
  13. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  14. R. A. Chipman, “Polarization ray tracing,” in Recent Trends in Optical Design; Computer Lens Design Workshop, C. Londono, R. E. Fischer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.766, 61–68 (1987). [CrossRef]
  15. T. J. Bruegge, “Analysis of polarization in optical systems,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 165–176 (1989). [CrossRef]
  16. S. C. McClain, L. W. Hillman, R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. II. Theory and physics,” J. Opt. Soc. Am. A 10, 2383–2393 (1993). [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  18. E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).
  19. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 69–102.
  20. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937). [CrossRef]
  21. D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), p. 6–248.
  22. R. C. Weast, ed., CRC Handbook of Chemistry and Physics, 66th ed. (CRC, Boca Raton, Fla., 1985), p. E-409.
  23. G. Szvivessy, C. Muenster, “Lattice optics of active crystals,” Ann. Phys. (Leipzig), 20, 703–736 (1934).
  24. E. E. Wahlstrom, Optical Crystallography, 3rd ed. (Wiley, New York, 1960), pp. 155–156.
  25. F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), p. 552.
  26. M. C. Simon, “Internal total reflection in monoaxial crystals,” Appl. Opt. 26, 3878–3883 (1987). [CrossRef] [PubMed]
  27. M. C. Simon, R. M. Echarri, “Inhibited reflection in uniaxial crystals,” Opt. Lett. 14, 257–259 (1989). [CrossRef] [PubMed]
  28. G. W. Stewart, Introduction to Matrix Computations (Academic, New York, 1973), pp. 317–320.
  29. G. H. Golub, C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md.1983), pp. 293–295.
  30. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), pp. 45, 60–72.
  31. W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986), p. 52.
  32. W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990), pp. 288–297.
  33. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 19–38.
  34. J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formulation and example,” J. Opt. Soc. Am. A 7, 1614–1626 (1990). [CrossRef]
  35. S. C. McClain, R. A. Chipman, L. W. Hillman, “Aberrations of a horizontal–vertical depolarizer,” Appl. Opt. 31, 2326–2331 (1992). [CrossRef] [PubMed]
  36. R. V. Shack, Optical Sciences Center, University of Arizona, Tuscon, Ariz. 85721 (personal communication, 1991).
  37. H. A. Macleod, “Microstructure of optical thin films,” in Optical Thin Films, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.325, 21–28 (1982). [CrossRef]

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