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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 2 — Jan. 21, 2008
  • pp: 993–1006

Light beams with fractional orbital angular momentum and their vortex structure

Jörg B. Götte, Kevin O’Holleran, Daryl Preece, Florian Flossmann, Sonja Franke-Arnold, Stephen M. Barnett, and Miles J. Padgett  »View Author Affiliations

Optics Express, Vol. 16, Issue 2, pp. 993-1006 (2008)

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Light emerging from a spiral phase plate with a non-integer phase step has a complicated vortex structure and is unstable on propagation. We generate light carrying fractional orbital angular momentum (OAM) not with a phase step but by a synthesis of Laguerre-Gaussian modes. By limiting the number of different Gouy phases in the superposition we produce a light beam which is well characterised in terms of its propagation. We believe that their structural stability makes these beams ideal for quantum information processes utilising fractional OAM states.

© 2008 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(230.6120) Optical devices : Spatial light modulators
(270.0270) Quantum optics : Quantum optics
(350.5030) Other areas of optics : Phase
(050.4865) Diffraction and gratings : Optical vortices
(260.6042) Physical optics : Singular optics

ToC Category:
Physical Optics

Original Manuscript: October 11, 2007
Revised Manuscript: December 21, 2007
Manuscript Accepted: December 23, 2007
Published: January 11, 2008

Jörg B. Götte, Kevin O’Holleran, Daryl Preece, Florian Flossmann, Sonja Franke-Arnold, Stephen M. Barnett, and Miles J. Padgett, "Light beams with fractional orbital angular momentum and their vortex structure," Opt. Express 16, 993-1006 (2008)

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  1. M. V. Berry, "Much ado about nothing: optical distortion lines (phase singularities, zeros, and vortices)," in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE 3487, 1-5 (1998). http://spie.org/x648.xml?product id=317693. [CrossRef]
  2. M. V. Berry and M. R. Dennis, "Knotted and linked phase singularities in monochromatic waves," Proc. Royal Society of London, Series A 457(2013), 2251-2263 (2001). http://www.journals.royalsoc.ac.uk/content/yv6lqeufbq2phg9l. [CrossRef]
  3. J. Leach, M. R. Dennis, and M. J. Padgett, "Laser beams: Knotted threads of darkness," Nature 432(165) (2004). http://www.nature.com/nature/journal/v432/n7014/abs/432165a.html. [CrossRef] [PubMed]
  4. J. Leach, M. R. Dennis, J. Courtial, and M. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005). http://www.iop.org/EJ/abstract/1367-2630/7/1/055/. [CrossRef]
  5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes," Phys. Rev. A 45, 8185-8190 (1992). http://link.aps.org/abstract/PRA/v45/p8185. [CrossRef] [PubMed]
  6. 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). [CrossRef]
  7. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefrontnext term laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994). [CrossRef]
  8. V. Y. Bazhenov, M. V. Vastnetsov, and M. S. Soskin, "Laser-beams with screw dislocations in their wave-fronts," JETP Lett. 52, 429-431 (1990).
  9. M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps," J. Opt. A 6, 259-269 (2004). http://www.iop.org/EJ/abstract/1464-4258/6/2/018. [CrossRef]
  10. 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). http://www.iop.org/EJ/abstract/1367-2630/6/1/071/. [CrossRef]
  11. K. O’Holleran, M. R. Dennis, and M. J. Padgett, "Illustrations of optical vortices in three dimensions," Journal of European Optical Society - Rapid Publications 1, 06008 (2006). https://www.jeos.org/index.php/jeos rp/article/view/06008. [CrossRef]
  12. J. Gotte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, "Quantum formulation of fractional orbital angular momentum," J. Mod. Opt. 54, 1723-1738 (2007). http://www.informaworld.com/smpp/content∼content=a779773614. [CrossRef]
  13. S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhaus, and J. P. Woerdman, "How to observe high- dimensional two-photon entanglement with only two detectors," Phys. Rev. Lett. 92, 217901 (2004). http://link.aps.org/abstract/PRL/v92/e217901. [CrossRef] [PubMed]
  14. G. F. Calvo, A. Picon, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007). http://link.aps.org/abstract/PRA/v75/e012319. [CrossRef]
  15. A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, "Nonlocality of high-dimensional two-photon orbital angular momentum states," Phys. Rev. A 72, 052114 (2005). http://link.aps.org/abstract/PRA/v72/e052114. [CrossRef]
  16. S. M. Barnett and D. T. Pegg, "Quantum theory of rotation angles," Phys. Rev. A 41, 3427-3435 (1990). http://link.aps.org/abstract/PRA/v41/p3427. [CrossRef] [PubMed]
  17. J. Courtial, "Self-imaging beams and the Guoy [sic] effect," Opt. Commun. 151, 1-4 (1998). [CrossRef]
  18. R. Zambrini, L. C. Thomson, S. M. Barnett, and M. Padgett, "Momentum paradox in a vortex core," J. Modern Opt. 52(8), 1135-1144 (2005). http://www.informaworld.com/smpp/content∼conten a713736931. [CrossRef]
  19. C. Alonzo, P. J. Rodrigo and J. Gluckstad, "Helico-conical optical beams: a product of helical and conical phase fronts," Opt. Express. 13, 1749-1760 (2005). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-5-1749>. [CrossRef] [PubMed]

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