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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. 31, Iss. 6 — Jun. 1, 2014
  • pp: 1141–1157

Classical light beams and geometric phases

N. Mukunda, S. Chaturvedi, and R. Simon  »View Author Affiliations


JOSA A, Vol. 31, Issue 6, pp. 1141-1157 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001141


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Abstract

We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell’s equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell’s equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.

© 2014 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: December 17, 2013
Revised Manuscript: March 11, 2014
Manuscript Accepted: March 12, 2014
Published: May 2, 2014

Citation
N. Mukunda, S. Chaturvedi, and R. Simon, "Classical light beams and geometric phases," J. Opt. Soc. Am. A 31, 1141-1157 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-6-1141


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References

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  37. See, for instance, Ref. [16].
  38. The definition of this group is given later, in Eq. (4.9).
  39. The group SO(3) is defined in the axis-angle description later in Eq. (4.2).
  40. The relationship between SU(2) and SO(3) is described, using axis-angle variables, later in Eq. (4.11) below.
  41. It may be useful to recall that for a spherical triangle on S2, the corresponding solid angle (subtended at the center of the sphere) is the “spherical excess,” i.e., the amount by which the sum of the three internal angles exceeds π. This excess occurs because S2 possesses positive curvature.
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