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

T. van Dijk; H. Schouten; T.D. Visser

doi:10.1364/JOSAA.27.001972

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

T. van Dijk, H. Schouten, T.D. Visser

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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.

Original language	English
Pages (from-to)	1972-1976
Number of pages	5
Journal	Journal of the Optical Society of America. A: Optics, image science, and vision.
Volume	27
Issue number	9
DOIs	https://doi.org/10.1364/JOSAA.27.001972
Publication status	Published - 2010

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title = "Geometric interpretation of the Pancharatnam connection and non-cyclic polarization changes",

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 Poincar{\'e} 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. {\textcopyright} 2010 Optical Society of America.",

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AB - 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.

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DO - 10.1364/JOSAA.27.001972

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JO - Journal of the Optical Society of America. A: Optics, image science, and vision.

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