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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 3 — Mar. 1, 2011
  • pp: 475–482

Geometric phase: two triangles on the Poincaré sphere

Piotr Kurzynowski, Władysław A. Woźniak, and Małgorzata Szarycz  »View Author Affiliations

JOSA A, Vol. 28, Issue 3, pp. 475-482 (2011)

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The method of obtaining the dynamic and geometric part of the phase introduced by a birefringent medium in two kinds of interferometric experiments is presented. The mathematical formulas for the phases obtained using Jones formalism are visualized with the specific triangles on the Poincaré sphere. Generally, these triangles are similar to those used in the Pancharatnam’s original construction developed by Courtial to calculate the Pancharatnam geometric phase for the light passing through a single birefringent plate. In these graphical constructions following Courtial’s idea, we used the points representing both of the birefringent medium’s eigenvectors. This allowed the most intuitive explanation of the mechanism of dividing the whole phase shift introduced by the birefringent plate into two different parts: dynamical and geometrical. The considered constructions were used as a description of two simple experiments with a birefringent medium in a Mach–Zehnder interferometer and a polariscopic setup. The experimental verifications of our theoretical predictions should convince the reader of the correctness of the assumed model.

© 2011 Optical Society of America

OCIS Codes
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(260.1440) Physical optics : Birefringence
(260.3160) Physical optics : Interference
(260.5430) Physical optics : Polarization
(350.1370) Other areas of optics : Berry's phase

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 9, 2010
Revised Manuscript: December 21, 2010
Manuscript Accepted: January 5, 2011
Published: March 1, 2011

Piotr Kurzynowski, Władysław A. Woźniak, and Małgorzata Szarycz, "Geometric phase: two triangles on the Poincaré sphere," J. Opt. Soc. Am. A 28, 475-482 (2011)

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