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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 θ<sub>pol</sub> 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 <i>r</i><sub><i>pp</i></sub><i>r</i><sub><i>ss</i></sub>−<i>r</i><sub><i>ps</i></sub><i>r</i><sub><i>sp</i></sub>=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 θ<sub><i>pp</i></sub> at which <i>r</i><sub><i>pp</i></sub> is zero, previously obtained. The angles θ<sub>pol</sub> and θ<sub><i>pp</i></sub> are compared and contrasted. A method of identifying the physical root or roots of each quartic is given. Index matching enhances the difference between θ<sub>pol</sub> and θ<sub><i>pp</i></sub>.

© 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

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

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