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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 11 — Nov. 1, 1999
  • pp: 2763–2766

Reflection by uniaxial crystals: polarizing angle and Brewster angle

John Lekner  »View Author Affiliations

JOSA A, Vol. 16, Issue 11, pp. 2763-2766 (1999)

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The polarizing angle θpol is the angle of incidence at which an incident wave of arbitrary polarization becomes linearly polarized on reflection. In terms of the reflection amplitudes it is given by rpprss-rpsrsp=0. We show that it may be obtained by the solution of a quartic equation. This equation is closely related to the quartic that defines the Brewster angle θpp at which rpp is zero, previously obtained. The angles θpol and θpp are compared and contrasted. A method of identifying the physical root or roots of each quartic is given. Index matching enhances the difference between θpol and θpp.

© 1999 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(160.1190) Materials : Anisotropic optical materials
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(260.5430) Physical optics : Polarization

Original Manuscript: February 18, 1999
Revised Manuscript: July 22, 1999
Manuscript Accepted: July 22, 1999
Published: November 1, 1999

John Lekner, "Reflection by uniaxial crystals: polarizing angle and Brewster angle," J. Opt. Soc. Am. A 16, 2763-2766 (1999)

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  1. M. Malus, “Sur une propriété de la lumière réfléchie,” Mém. Phys. Chim. Soc. d’Arcueil 2, 143–158 (1809).
  2. D. Brewster, “On the laws which regulate the polarisation of light by reflexion from transparent bodies,” Philos. Trans. R. Soc. London 105, 125–130, 158–159 (1815). [CrossRef]
  3. W. Swindell, ed., Polarized Light (Halsted, New York, 1975).
  4. G. Green, “On the reflexion and refraction of sound,” Trans. Cambridge Philos. Soc. 6, 403–412 (1838).
  5. J. Lekner, Theory of Reflection (Nijhoff/Kluwer, Dordrecht, 1987).
  6. J. Lekner, “Nonreflecting stratifications,” Can. J. Phys. 68, 738–742 (1990). [CrossRef]
  7. M. Elshazly-Zaghloul, R. M. A. Azzam, “Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties,” J. Opt. Soc. Am. 72, 657–661 (1982);erratum, J. Opt. Soc. Am. A6, 607 (1989). [CrossRef]
  8. J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys. Condens. Matter 3, 6121–6133 (1991). [CrossRef]
  9. J. Lekner, “Bounds and zeros in reflection and refraction by uniaxial crystals,” J. Phys. Condens. Matter 4, 9459–9468 (1992). [CrossRef]
  10. J. Lekner, “Brewster angles in reflection by uniaxial crystals,” J. Opt. Soc. Am. A 10, 2059–2064 (1993). [CrossRef]
  11. S. Bassiri, C. H. Papas, N. Engheta, “Electromagnetic wave propagation through a dielectric–chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988). [CrossRef]
  12. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Norwood, Mass., 1994), Sec. 3.5.4.
  13. J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996), Sec. 3.3. [CrossRef]
  14. J. Lekner, “Reflection ellipsometry of uniaxial crystals,” J. Opt. Soc. Am. A 14, 1359–1362 (1997). [CrossRef]

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