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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

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1665–1671

Speckle beams with nonzero vorticity and Poincaré–Cartan invariant

Arthur Yu. Savchenko and Boris Ya. Zel’dovich  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1665-1671 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001665


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Abstract

The vorticity of a monochromatic speckle beam is introduced as an expectation value of the local difference of densities of right and left vortices, or wave-front dislocations. Gaussian statistics allows for the complete description of a speckle beam on the basis of the correlation function E(r1)E*(r2) only, and this function depends on the coordinate R=(r1+r2)/2 explicitly for statistically inhomogeneous beams. An analytic expression is found both for the vorticity and for the sum of the right and the left vortex densities. The vorticity is shown to be nonzero for inhomogeneous beams only. The Poincaré–Cartan invariant of Hamilton’s classical mechanics or of geometrical optics is shown to be the topologically invariant integral of vorticity. An example is given of a beam with finite vorticity, which has Gaussian intensity profiles in both angular and spatial distributions. The conditions on the parameters that describe such a beam are found; these conditions follow from the positive character of probability.

© 1999 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics

History
Original Manuscript: November 16, 1998
Revised Manuscript: January 25, 1999
Manuscript Accepted: January 25, 1999
Published: July 1, 1999

Citation
Arthur Yu. Savchenko and Boris Ya. Zel’dovich, "Speckle beams with nonzero vorticity and Poincaré–Cartan invariant," J. Opt. Soc. Am. A 16, 1665-1671 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1665


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References

  1. J. F. Nye, R. G. Kyte, D. C. Threlfall, “Proposal for measuring the movement of a large ice sheet by observing radio echoes,” J. Glaciol. 2, 319–325 (1972).
  2. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974). [CrossRef]
  3. N. B. Baranova, B. Ya. Zel’dovich, “Dislocations of the wave-front surface and zeroes of the amplitude,” JETP 53, 925–929 (1981).
  4. K. T. Gahagan, G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15, 524–534 (1998). [CrossRef]
  5. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).
  6. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, “Experimental investigation of density of wavefront dislocations of speckle-inhomogeneous light fields,” JETP 56, 983–988 (1982).
  7. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983). [CrossRef]
  8. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985), Chap. 3.
  9. I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994). [CrossRef]
  10. N. R. Heckenberg, R. McDuff, C. P. Smith, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef] [PubMed]
  11. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, “Optics of light beams with screw dislocation,” Opt. Commun. 103, 422–428 (1993). [CrossRef]
  12. E. Wolf, L. Mandel, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  13. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  14. B. Ya. Zel’dovich, A. V. Mamaev, V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, Boca Raton, 1995); V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1989).
  15. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass.1980)
  16. V. S. Liberman, B. Ya. Zel’dovich, “Spin-orbit interaction of a photon in a inhomogeneous medium,” Phys. Rev. A 46, 5199–5207 (1992). [CrossRef] [PubMed]
  17. M. A. Bolshtyansky, A. Yu. Savchenko, B. Ya. Zel’dovich, “Use of skew rays in multimode fibers to generate speckle field with nonzero vorticity,” Opt. Lett. 24, 433–435 (1999). [CrossRef]

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