Illustrations of optical vortices in three dimensions

K. O'Holleran; M. R. Dennis; M. J. Padgett

doi:10.2971/jeos.2006.06008

Journal of the European Optical Society - Rapid publications, Vol 1 (2006)

Illustrations of optical vortices in three dimensions

K. O'Holleran, M. R. Dennis, M. J. Padgett

Abstract

Optical vortices (phase singularities) arise from interference and are threads of darkness embedded within light fields. Although usually visualised in terms of their points of intersection with an observation plane, appreciation of their true form requires a view in three dimensions. Through numerical simulation we re-examine three situations where optical vortex lines evolve as an additional parameter is varied. Our specific examples are: the addition of a fourth plane wave of varying amplitude into a superposition of three plane waves, the increase of height of a non-integer spiral phase step, and finally the perturbation that creates, and then dissolves, a vortex link in a specific combination of Laguerre-Gauss modes.

Full Text: PDF

Citation Details

Cite this article

References

J. F. Nye and M. V. Berry, "Dislocations in wave trains" Proc. R. Soc. Lond. A 336, 165-190 (1974).

J. F. Nye, Natural focusing and fine structure of light (Institute of Physics Publishing, 1999).

J. W. Goodman, Statistical Optics (Wiley, 1985).

L. Allen and M. J. Padgett, "The Poynting vector in Laguerre- Gaussian beams and the interpretation of their angular momentum density" Opt. Commun. 184, 67-71 (2000).

M. V. Berry and M. R. Dennis," Knotted and linked phase singularities in monochromatic waves" Proc. R. Soc. Lond. A 457, 2251-2263 (2001).

D. Rozas, C. T. Law, and G. A. Swartzlander, "Propagation dynamics of optical vortices" J. Opt. Soc. Am. B 14, 3054-3065 (1997).

M. V. Berry, "Much ado about nothing: optical dislocation lines (phase singularities, zeros, vortices. . . )", in Proc. Int. Conf. on Singular Optics, M. S. Soskin, ed. (SPIE, 1998), vol. 3487, pp. 1-5

J. F. Nye, "Local solutions for the interaction of wave dislocations" J. Opt. A: Pure Appl. Opt. 6, S251-S254 (2004).

J. Ruostekoski and Z. Dutton, "Engineering vortex rings and systems for controlled studies of vortex interactions in Bose-Einstein condensates" Phys. Rev. A 72 063626 (2005).

Persistence of Vision Pty. Ltd, Persistence of Vision Raytracer (Version 3.6, 2004), http://www.povray.org

K. O'Holleran, M. J. Padgett, and M. R. Dennis, "Topology of optical vortex lines formed by the interference of three, four, and five plane waves" Opt. Express 14, 3039-3044 (2006).

M. V. Berry and M. R. Dennis, "Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 dimensions" J. Phys. A:Math. Gen. 34, 8877-8888 (2001).

M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps" J. Opt. A: Pure Appl. Opt. 6, 259-268 (2004).

J. Leach, E. Yao, and M. J. Padgett, "Observation of the vortex structure of a non-integer vortex beam" New J. Phys. 6, 71 (2004).

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light" New J. Phys. 7, 55 (2005).

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Knotted threads of darkness" Nature 432, 165 (2005).

J. F. Nye, "From Airy rings to the elliptic umbilic diffraction catastrophe" J. Opt. A: Pure Appl. Opt. 5, 503-510 (2003).

J. F. Nye, "Evolution of the hyperbolic umbilic diffraction catastrophe from Airy rings" J. Opt. A: Pure Appl. Opt. 8, 304-314 (2006).