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Applied Optics

Applied Optics


  • Vol. 41, Iss. 19 — Jul. 1, 2002
  • pp: 3936–3940

Method for determining the optical axis and (n e , n o ) of a birefringent crystal

Der-Chin Su and Cheng-Chih Hsu  »View Author Affiliations

Applied Optics, Vol. 41, Issue 19, pp. 3936-3940 (2002)

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There is a phase difference between s and p polarizations when a circularly polarized heterodyne light beam is reflected from a birefringent crystal. It can be measured accurately with a common-path heterodyne interferometric technique. We have derived an equation that describes the relationship between the phase differences and n e , n o , and α. Two groups of solutions for (n e , n o ) can be obtained from this equation by the phase measurements performed at three incident angles under moderate conditions. Each group consists of three pairs of solutions for (n e , n o ). Finally, by justifying with physical conditions, we obtained the correct solution for (n e , n o ). Azimuth angle α of the birefringent crystal optical axis can also be determined. And the feasibility of this method is demonstrated.

© 2002 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(260.1440) Physical optics : Birefringence

Original Manuscript: June 22, 2001
Revised Manuscript: December 4, 2001
Published: July 1, 2002

Der-Chin Su and Cheng-Chih Hsu, "Method for determining the optical axis and (ne, no) of a birefringent crystal," Appl. Opt. 41, 3936-3940 (2002)

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  1. X. Wang, J. Yao, “Transmitted and tuning characteristics of birefringent filters,” Appl. Opt. 31, 4505–4508 (1992). [CrossRef] [PubMed]
  2. J. F. Valley, J. W. Wu, C. L. Valencia, “Heterodyne measurement of poling transient effects in electro-optic polymer thin films,” Appl. Phys. Lett. 57, 1084–1086 (1990). [CrossRef]
  3. I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998). [CrossRef]
  4. R. S. Weis, T. K. Gaylord, “Magnetooptic multilayered memory structure with a birefringent superstrate: a rigorous analysis,” Appl. Opt. 28, 1926–1930 (1989). [CrossRef] [PubMed]
  5. R. P. Shukla, G. M. Perera, M. C. George, P. Venkateswarlu, “Measurement of birefringence of optical materials using a wedged plate interferometer,” Opt. Commun. 78, 7–12 (1990). [CrossRef]
  6. M. H. Chiu, C. D. Chen, D. C. Su, “Method for determining the fast axis and phase retardation of a wave plate,” J. Opt. Soc. Am. A 13, 1924–1929 (1996). [CrossRef]
  7. Y. C. Huang, C. Chou, M. Chang, “Direct measurement of refractive indices of a linear birefringent retardation plate,” Opt. Commun. 133, 11–16 (1997). [CrossRef]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam1989), pp. 269–363.
  9. M. Schubert, B. Rheinlander, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996). [CrossRef]
  10. J. D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Kramer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998). [CrossRef]
  11. G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997). [CrossRef]
  12. G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997). [CrossRef]
  13. G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997). [CrossRef]
  14. J. Y. Lee, D. C. Su, “A method for measuring Brewster’s angle by circularly polarized heterodyne interferometry,” J. Opt. 29, 349–353 (1998). [CrossRef]
  15. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1991), pp. 232–239.
  16. R. M. A. Azzam, N. M. Bashara, “Application of generalized ellipsometry to anisotropic crystals,” J. Opt. Soc. Am. 64, 128–133 (1974). [CrossRef]
  17. R. L. Burden, J. D. Faires, Numerical Analysis, 5th ed. (PWS-Kent, Boston, Mass., 1993), pp. 553–560.
  18. E. D. Palik, ed., Handbook of Optical Constants of Solids III (Academic, New York, 1998), p. 708.
  19. Ref. 18, p. 729.
  20. M. H. Chiu, J. Y. Lee, D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999). [CrossRef]

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