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Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 8 — Apr. 15, 2007
  • pp: 891–893

Experimental umbilic diabolos in random optical fields

Marat S. Soskin, Roman I. Egorov, and Isaac Freund  »View Author Affiliations

Optics Letters, Vol. 32, Issue 8, pp. 891-893 (2007)

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The intensity of a random optical field consists of bright speckle spots (maxima) separated from dark areas (minima and optical vortices) by saddle points. We show that hidden in this complicated landscape are umbilic points—singular points at which the eigenvalues Λ ± of the Hessian matrix that measure the curvature of the landscape become degenerate. Although not observed previously in random optical fields, umbilic points are the most numerous of all special points, outnumbering maxima, minima, saddle points, and vortices. We show experimentally that the directions of principal curvature, the eigenvectors Ψ ± , rotate about intensity umbilic points with positive or negative half-integer winding number, in accord with theory, and that Λ + and Λ generate a double cone known as a diabolo. At optical vortices the curvature of the amplitude is singular, and we show from both theory and experiment that for this landscape Ψ ± rotate about vortex centers with a positive integer winding number. Diabolos can be classified as elliptic or hyperbolic, and we present initial results for the measured fractions of these two different types of umbilic diabolos.

© 2007 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(290.0290) Scattering : Scattering
(290.5880) Scattering : Scattering, rough surfaces
(350.0350) Other areas of optics : Other areas of optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: December 12, 2006
Revised Manuscript: December 24, 2006
Manuscript Accepted: January 9, 2007
Published: March 19, 2007

Marat S. Soskin, Roman I. Egorov, and Isaac Freund, "Experimental umbilic diabolos in random optical fields," Opt. Lett. 32, 891-893 (2007)

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  1. J. W. Goodman, Statistical Optics (Wiley, 1985).
  2. M. V. Berry, Adv. Phys. 25, 1 (1976). Umbilic points on the geometrical optics wavefront that generate far-field caustics are discussed there. [CrossRef]
  3. M. V. Berry and J. H. Hannay, J. Phys. A 10, 1809 (1977). [CrossRef]
  4. A. S. Thorndike, C. R. Cooley, and J. F. Nye, J. Phys. A 11, 1455 (1978). [CrossRef]
  5. J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999). Umbilic points on the geometrical optics wavefront that generate near field caustics are discussed there.
  6. M. V. Berry and M. Wilkinson, Proc. R. Soc. London, Ser. A 392, 15 (1984). [CrossRef]
  7. M. V. Berry, M. R. Jeffrey, and J. G. Lunney, Proc. R. Soc. London, Ser. A 462, 1629 (2006). [CrossRef]
  8. M. V. Berry and M. R. Jeffrey, J. Opt. A, Pure Appl. Opt. 8, 363 (2006). [CrossRef]
  9. R. I. Egorov, M. S. Soskin, and I. Freund, Opt. Lett. 31, 2048 (2006). [CrossRef] [PubMed]
  10. I. Freund, M. S. Soskin, R. I. Egorov, and V. Denisenko, Opt. Lett. 31, 2381 (2006). [CrossRef] [PubMed]
  11. I. Freund, "Optical diabolos: configurations, nucleations, transformations, and reactions," Opt. Commun. (to be published).
  12. A. L. Sobolewski and W. Domcke, Europhys. News 37, 20 (2006). [CrossRef]
  13. I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 036227 (1996). [CrossRef]
  14. L. F. Canto, P. Ring, Y. Sun, J. O. Rasmussen, S. Y. Chu, and M. A. Stoyer, Phys. Rev. C 47, 2836 (1993). [CrossRef]
  15. H. J. Hutchinson, J. F. Nye, and P. S. Salmon, J. Struct. Mech. 11, 371 (1983). [CrossRef]
  16. I. Freund, Opt. Lett. 26, 1996 (2001). [CrossRef]
  17. I. Freund and N. Shvartsman, Phys. Rev. A 50, 5164 (1994). [CrossRef] [PubMed]
  18. I. Freund, Waves Random Media 8, 119 (1998).
  19. I. Freund, Phys. Rev. E 52, 2348 (1995). [CrossRef]
  20. M. R. Dennis, Opt. Commun. 213, 201 (2002). [CrossRef]

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