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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. 4 — Apr. 1, 2010
  • pp: 918–927

Signal representation on the angular Poincaré sphere, based on second-order moments

Martin J. Bastiaans and Tatiana Alieva  »View Author Affiliations


JOSA A, Vol. 27, Issue 4, pp. 918-927 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000918


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Abstract

Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensional optical signal is proposed, which is associated with the angular Poincaré sphere. Vortex-free (or zero-twist) optical beams arise on the equator of this sphere, while beams with a maximum vorticity (or maximum twist) are located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for the degree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beam propagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, a system that does not operate between conjugate planes is needed, with the gyrator as the prime representative of such a system. A direct way is derived to find an optical system (consisting of a lens, a magnifier, a rotator, and a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form.

© 2010 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.2468) Geometric optics : First-order optics
(140.3295) Lasers and laser optics : Laser beam characterization
(080.4865) Geometric optics : Optical vortices
(080.5084) Geometric optics : Phase space methods of analysis

History
Original Manuscript: December 17, 2009
Manuscript Accepted: February 15, 2010
Published: March 31, 2010

Citation
Martin J. Bastiaans and Tatiana Alieva, "Signal representation on the angular Poincaré sphere, based on second-order moments," J. Opt. Soc. Am. A 27, 918-927 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-4-918

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