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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 24596–24608

Orbital angular momentum in optical waves propagating through distributed turbulence

Darryl J. Sanchez and Denis W. Oesch  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24596-24608 (2011)
http://dx.doi.org/10.1364/OE.19.024596


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Abstract

This is the second of two papers demonstrating that photons with orbital angular momentum can be created in optical waves propagating through distributed turbulence. In the companion paper, it is shown that propagation through atmospheric turbulence can create non-trivial angular momentum. Here, we extend the result and demonstrate that this momentum is, at least in part, orbital angular momentum. Specifically, we demonstrate that branch points (in the language of the adaptive optic community) indicate the presence of photons with non-zero OAM. Furthermore, the conditions required to create photons with non-zero orbital angular momentum are ubiquitous. The repercussions of this statement are wide ranging and these are cursorily enumerated.

© 2011 OSA

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(010.1285) Atmospheric and oceanic optics : Atmospheric correction

ToC Category:
Atmospheric and Oceanic Optics

Citation
Darryl J. Sanchez and Denis W. Oesch, "Orbital angular momentum in optical waves propagating through distributed turbulence," Opt. Express 19, 24596-24608 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24596


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References

  1. D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Applied Optics31, 2865–2882 (1992). [CrossRef] [PubMed]
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Physical Review A45, 8185–8189 (1992). [CrossRef] [PubMed]
  3. J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Optics Express14, 11919–11924 (2006). [CrossRef] [PubMed]
  4. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A15, 2759–2768 (1998). [CrossRef]
  5. D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch points - measuring the number and velocity of atmospheric turbulence layers,” Optics Express18, 22377–22392 (2010). [CrossRef] [PubMed]
  6. D. J. Sanchez and D. W. Oesch, “The localization of angular momentum in optical waves propagating through atmospheric turbulence,” Optics Express (2011). Accepted for publication. [PubMed]
  7. D. J. Sanchez, D. W. Oesch, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - the creation and evolution of branch points,” SPIE7466, 0501–0512 (2009).
  8. D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - persistent pairs,” Optics Express (2011). Submitted for publication.
  9. D. W. Oesch, C. M. Tewksbury-Christle, D. J. Sanchez, and P. R. Kelly, “The aggregate behavior of branch points - characterization in wave optical simulation,” Optics Express (2011). Submitted for publication.
  10. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE Press, Bellingham, Wa, USA, 2007), 2nd ed.
  11. J. W. Goodman, Statistical Optics (John Wiley & Sons, New York, New York, 2000), Wiley Classics Library ed.
  12. See for instance Ref. [11] page 394.
  13. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, USA, 1975), 2nd ed.
  14. R. A. Beth, “Mechanical detection of the angular momentum of light,” Physical Review50, 115–125 (1936). [CrossRef]
  15. This analysis is true for any type of wavefront sensor. The Shack-Hartmann is presented here because it is well known. In our lab, we use a self-referencing interferometer.
  16. This is in keeping with the notation in Fried’s seminal paper, Ref. [4].
  17. First pointed out by Terry Brennan, the Optical Science Corporation, in a private conversation.
  18. D. W. Oesch, C. M. Tewksbury-Christle, D. J. Sanchez, and P. R. Kelly, “The aggregate behavior of branch points - modeling parameters,” Optical Society of America - Frontiers in Optics proceedings (2011). Accepted for publication.
  19. D. J. Sanchez, D. W. Oesch, C. M. Tewksbury-Christle, and P. R. Kelly, “Branch points in deep turbulence and its relevance to adaptive optics – an overview of the ASALT laboratory’s deep turbulence research,” in “2010 DEPS Annual Conference,”, D. Herrick, ed. (Directed Energy Professional Society, 2010).
  20. D. J. Sanchez, D. W. Oesch, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - a proposal for an atmospheric turbulence layer sensor,” SPIE7816, 0601–0616 (2010).
  21. D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” SPIE7816, 0501–0513 (2010).
  22. D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” SPIE7466, 0601–0610 (2009).
  23. This result holds in general to include diffraction, not merely for the these simplifying assumptions Specifically, if the assumption were relaxed to allow diffraction, each small region after propagation would have non-zero components that extend to infinity. But other than in the local region, these components are trivial and would at most cause the location of the null to move slightly.
  24. D. W. Oesch and D. J. Sanchez, “Studying the optical field in and through the failure of the Rytov approximation,” Optics Express (2011). In preparation.
  25. D. J. Sanchez and D. W. Oesch, “The effect of orbital angular momentum in the Rytov approximation,” In preparation.
  26. D. J. Sanchez, D. W. Oesch, and S. M. Gregory, “Orbital angular momentum in waves propagating through galactic clouds and dust,” In preparation.
  27. We have taken great care in our research to make a distinction between the persistant topological features of the propagating wave from transient phenonena. The persistent topological features--pairs of zeros in amplitude with opposite winding number--we call branch points; all other ciculations, we label as noise. Prior to our work, this distinction was vague. As a point in fact, in the earlest days of adaptive optics all 2π circulations were lumped into what was then called the “slope discrepancy” or “null” space, and even today in the phase reconstruction process, standard wavefront sensors lump all 2π circulations into a single group so that they may be summarily discarded, hence Fried’s [4] terminology “hidden phase”.

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