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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 9 — Sep. 1, 2010
  • pp: 1972–1976

Geometric interpretation of the Pancharatnam connection and non-cyclic polarization changes

Thomas van Dijk, Hugo F. Schouten, and Taco D. Visser  »View Author Affiliations


JOSA A, Vol. 27, Issue 9, pp. 1972-1976 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001972


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Abstract

If the state of polarization of a monochromatic light beam is changed in a cyclical manner, the beam acquires—in addition to the usual dynamic phase—a geometric phase. This geometric or Pancharatnam–Berry phase equals half the solid angle of the contour traced out on the Poincaré sphere. We show that such a geometric interpretation also exists for the Pancharatnam connection, the criterion according to which two beams with different polarization states are said to be in phase. This interpretation offers what is to our knowledge a new and intuitive method to calculate the geometric phase that accompanies non-cyclic polarization changes.

© 2010 Optical Society of America

OCIS Codes
(260.5430) Physical optics : Polarization
(350.1370) Other areas of optics : Berry's phase
(260.6042) Physical optics : Singular optics

ToC Category:
Physical Optics

History
Original Manuscript: April 12, 2010
Revised Manuscript: June 15, 2010
Manuscript Accepted: July 1, 2010
Published: August 12, 2010

Citation
Thomas van Dijk, Hugo F. Schouten, and Taco D. Visser, "Geometric interpretation of the Pancharatnam connection and non-cyclic polarization changes," J. Opt. Soc. Am. A 27, 1972-1976 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-9-1972


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References

  1. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984). [CrossRef]
  2. M. V. Berry, “Anticipations of the geometric phase,” Phys. Today 43(12), 34–40 (1990). [CrossRef]
  3. S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Indian Acad. Sci., Sect. A 44, 247–262 (1956).
  4. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).
  5. M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987). [CrossRef]
  6. R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 281, 1–64 (1997). [CrossRef]
  7. P. Hariharan, “The geometric phase,” in Progress in Optics, E.Wolf, ed., Vol. 48 (Elsevier, 2005), pp. 149–193. [CrossRef]
  8. R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988). [CrossRef] [PubMed]
  9. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27, 1141–1143 (2002). [CrossRef]
  10. G. Biener, Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Manipulation of polarization-dependent multivortices with quasi-periodic subwavelength structures,” Opt. Lett. 31, 1594–1596 (2006). [CrossRef] [PubMed]
  11. J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988). [CrossRef] [PubMed]
  12. T. F. Jordan, “Berry phases for partial cycles,” Phys. Rev. A 38, 1590–1592 (1988). [CrossRef] [PubMed]
  13. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–493 (1941). [CrossRef]
  14. F. Eriksson, “On the measure of solid angles,” Math. Mag. 63, 184–187 (1990). [CrossRef]
  15. L. E. J. Brouwer, “Über Abbildung von Mannigfaltigkeiten,” Math. Ann. LXXI, 97–115 (1912).
  16. T. H. Chyba, L. J. Wang, L. Mandel, and R. Simon, “Measurement of the Pancharatnam phase for a light beam,” Opt. Lett. 13, 562–564 (1988). [CrossRef] [PubMed]
  17. H. Schmitzer, S. Klein, and W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993). [CrossRef] [PubMed]
  18. R. Bhandari, “Observation of Dirac singularities with light polarization. I,” Phys. Lett. A 171, 262–266 (1992). [CrossRef]
  19. R. Bhandari, “Observation of Dirac singularities with light polarization. II,” Phys. Lett. A 171, 267–270 (1992). [CrossRef]
  20. T. van Dijk, H. F. Schouten, W. Ubachs, and T. D. Visser, “The Pancharatnam–Berry phase for non-cyclic polarization changes,” Opt. Express 18, 10796–10804 (2010). [CrossRef] [PubMed]

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