Abstract

Knowledge of the behavior of stochastic optical fields can aid the understanding of the scintillation of light propagating through a turbulent medium. For this purpose, we perform a numerical investigation of the evolution of the scintillation index and the optical vortex density in a speckle field after removing its continuous phase. We find that both the scintillation index and the vortex density initially drop and then increase again to reach an equilibrium level. It is also found that the initial rate of decrease in both cases is 1 order of magnitude faster than the eventual rate of increase. Their detail shapes are however different. Therefore different empirical functions are used to fit the shapes of these curves.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
    [CrossRef]
  2. W. Wang, T. Yokozeki, R. Ishijima, and M. Takeda, “Optical vortex metrology based on the core structures of phase singularities in Laguerre–Gauss transform of a speckle pattern,” Opt. Express 14, 10195–10206 (2006).
    [CrossRef] [PubMed]
  3. J. Lin and X.-C. Yuan, “Application of orbital angular momentum in optical measurement,” Proc. SPIE 74300, 74300G (2009).
    [CrossRef]
  4. J. Masajada, M. Leniec, S. Drobczyński, H. Thienpont, and B. Kress, “Micro-step localization using double charge optical vortex interferometer,” Opt. Express 17, 16144–16159 (2009).
    [CrossRef] [PubMed]
  5. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
    [CrossRef] [PubMed]
  6. K. T. Gahagan and J. G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  7. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).
  8. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901-1 (2005).
    [CrossRef]
  9. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47, 2414–2429 (2008).
    [CrossRef] [PubMed]
  10. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [CrossRef] [PubMed]
  11. J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. W. Boyd, A. K. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express 17, 8287–8293 (2009).
    [CrossRef] [PubMed]
  12. G. Foo, D. M. Palacios, and J. Grover A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
    [CrossRef]
  13. M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25, 1279–1286 (2008).
    [CrossRef]
  14. I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
    [CrossRef]
  15. N. Shvartsman and I. Freund, “Vortices in random wave fields: nearest neighbor anticorrelations,” Phys. Rev. Lett. 72, 1008–1011 (1994).
    [CrossRef] [PubMed]
  16. M. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A, Pure Appl. Opt. 6, S202–S208 (2004).
    [CrossRef]
  17. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Knotted threads of darkness,” Nature 432, 165–165 (2004).
    [CrossRef] [PubMed]
  18. M. V. Berry and M. R. Dennis, “Topological events on wave dislocation lines: birth and death of loops, and reconnection,” J. Phys. A: Math. Theor. 40, 65–74 (2007).
    [CrossRef]
  19. K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Topology of light’s darkness,” Phys. Rev. Lett. 102, 143902 (2009).
    [CrossRef] [PubMed]
  20. G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
    [CrossRef]
  21. E. Ochoa and J. W. Goodman, “Statistical properties of ray directions in a monochromatic speckle pattern,” J. Opt. Soc. Am. 73, 943–949 (1983).
    [CrossRef]
  22. I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
    [CrossRef]
  23. M. Berry, “Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves,” J. Phys. A 11, 27–37 (1978).
    [CrossRef]
  24. K. A. O’Donnell, “Speckle statistics of doubly scattered light,” J. Opt. Soc. Am. 72, 1459–1463 (1982).
    [CrossRef]
  25. I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
    [CrossRef]
  26. M. R. Dennis, “Topological singularities in wave fields,” Ph.D. dissertation (University of Bristol, 2001).
  27. W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
    [CrossRef] [PubMed]
  28. S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
    [CrossRef] [PubMed]
  29. G. H. Sendra, H. J. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
    [CrossRef]
  30. M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80, 013824 (2009).
    [CrossRef]
  31. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  32. J. M. Martin and S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990).
    [CrossRef]
  33. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  34. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [CrossRef]
  35. A. J. Devaney and G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973).
    [CrossRef]
  36. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).
  37. L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16, 1417–1429 (1999).
    [CrossRef]

2009 (7)

J. Lin and X.-C. Yuan, “Application of orbital angular momentum in optical measurement,” Proc. SPIE 74300, 74300G (2009).
[CrossRef]

K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Topology of light’s darkness,” Phys. Rev. Lett. 102, 143902 (2009).
[CrossRef] [PubMed]

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[CrossRef]

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80, 013824 (2009).
[CrossRef]

J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. W. Boyd, A. K. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express 17, 8287–8293 (2009).
[CrossRef] [PubMed]

J. Masajada, M. Leniec, S. Drobczyński, H. Thienpont, and B. Kress, “Micro-step localization using double charge optical vortex interferometer,” Opt. Express 17, 16144–16159 (2009).
[CrossRef] [PubMed]

G. H. Sendra, H. J. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

2008 (2)

2007 (2)

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

M. V. Berry and M. R. Dennis, “Topological events on wave dislocation lines: birth and death of loops, and reconnection,” J. Phys. A: Math. Theor. 40, 65–74 (2007).
[CrossRef]

2006 (1)

2005 (4)

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901-1 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and J. Grover A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

2004 (3)

M. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A, Pure Appl. Opt. 6, S202–S208 (2004).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Knotted threads of darkness,” Nature 432, 165–165 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

2001 (2)

M. R. Dennis, “Topological singularities in wave fields,” Ph.D. dissertation (University of Bristol, 2001).

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
[CrossRef]

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

1996 (1)

1995 (2)

I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

1994 (2)

N. Shvartsman and I. Freund, “Vortices in random wave fields: nearest neighbor anticorrelations,” Phys. Rev. Lett. 72, 1008–1011 (1994).
[CrossRef] [PubMed]

I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
[CrossRef]

1993 (1)

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

1990 (1)

1988 (1)

1983 (1)

1982 (1)

1978 (1)

M. Berry, “Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves,” J. Phys. A 11, 27–37 (1978).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

1973 (1)

A. J. Devaney and G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973).
[CrossRef]

Al-Habash, M. A.

Andrews, L. C.

Anguita, J. A.

Arizaga, R.

G. H. Sendra, H. J. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[CrossRef]

Barnett, S. M.

J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. W. Boyd, A. K. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express 17, 8287–8293 (2009).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Berry, M.

M. Berry, “Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves,” J. Phys. A 11, 27–37 (1978).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Dennis, “Topological events on wave dislocation lines: birth and death of loops, and reconnection,” J. Phys. A: Math. Theor. 40, 65–74 (2007).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Boyd, R. W.

Chen, M.

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80, 013824 (2009).
[CrossRef]

M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25, 1279–1286 (2008).
[CrossRef]

Courtial, J.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Knotted threads of darkness,” Nature 432, 165–165 (2004).
[CrossRef] [PubMed]

Dennis, M.

M. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A, Pure Appl. Opt. 6, S202–S208 (2004).
[CrossRef]

Dennis, M. R.

K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Topology of light’s darkness,” Phys. Rev. Lett. 102, 143902 (2009).
[CrossRef] [PubMed]

M. V. Berry and M. R. Dennis, “Topological events on wave dislocation lines: birth and death of loops, and reconnection,” J. Phys. A: Math. Theor. 40, 65–74 (2007).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Knotted threads of darkness,” Nature 432, 165–165 (2004).
[CrossRef] [PubMed]

M. R. Dennis, “Topological singularities in wave fields,” Ph.D. dissertation (University of Bristol, 2001).

Devaney, A. J.

A. J. Devaney and G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973).
[CrossRef]

Drobczynski, S.

Flatté, S. M.

Foo, G.

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. W. Boyd, A. K. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express 17, 8287–8293 (2009).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Freilikher, V.

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Freund, I.

I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[CrossRef]

I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
[CrossRef]

N. Shvartsman and I. Freund, “Vortices in random wave fields: nearest neighbor anticorrelations,” Phys. Rev. Lett. 72, 1008–1011 (1994).
[CrossRef] [PubMed]

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Fried, D. L.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

Gahagan, K. T.

Genack, A. Z.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Gibson, G.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Goodman, J. W.

Grover A. Swartzlander, J.

Hanson, S. G.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

Hopen, C. Y.

Hu, B.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Ishijima, R.

Jack, B.

Jha, A. K.

Kress, B.

Leach, J.

Leniec, M.

Lin, J.

J. Lin and X.-C. Yuan, “Application of orbital angular momentum in optical measurement,” Proc. SPIE 74300, 74300G (2009).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Martin, J. M.

Masajada, J.

Miyamoto, Y.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Neifeld, M. A.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

O’Donnell, K. A.

O’Holleran, K.

K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Topology of light’s darkness,” Phys. Rev. Lett. 102, 143902 (2009).
[CrossRef] [PubMed]

Ochoa, E.

Padgett, M. J.

K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Topology of light’s darkness,” Phys. Rev. Lett. 102, 143902 (2009).
[CrossRef] [PubMed]

J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. W. Boyd, A. K. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express 17, 8287–8293 (2009).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Knotted threads of darkness,” Nature 432, 165–165 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Palacios, D. M.

Pas’ko, V.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901-1 (2005).
[CrossRef]

Phillips, R. L.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Rabal, H.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[CrossRef]

Rabal, H. J.

Ritsch-Marte, M.

Romero, J.

Roux, F. S.

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80, 013824 (2009).
[CrossRef]

M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25, 1279–1286 (2008).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

Sebbah, P.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Sendra, G.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[CrossRef]

Sendra, G. H.

Sherman, G. C.

A. J. Devaney and G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973).
[CrossRef]

Shvartsman, N.

N. Shvartsman and I. Freund, “Vortices in random wave fields: nearest neighbor anticorrelations,” Phys. Rev. Lett. 72, 1008–1011 (1994).
[CrossRef] [PubMed]

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Swartzlander, J. G. A.

Takeda, M.

W. Wang, T. Yokozeki, R. Ishijima, and M. Takeda, “Optical vortex metrology based on the core structures of phase singularities in Laguerre–Gauss transform of a speckle pattern,” Opt. Express 14, 10195–10206 (2006).
[CrossRef] [PubMed]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Thienpont, H.

Trivi, M.

G. H. Sendra, H. J. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[CrossRef]

Vasic, B. V.

Vasnetsov, M.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Wang, W.

W. Wang, T. Yokozeki, R. Ishijima, and M. Takeda, “Optical vortex metrology based on the core structures of phase singularities in Laguerre–Gauss transform of a speckle pattern,” Opt. Express 14, 10195–10206 (2006).
[CrossRef] [PubMed]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Yokozeki, T.

Yuan, X. -C.

J. Lin and X.-C. Yuan, “Application of orbital angular momentum in optical measurement,” Proc. SPIE 74300, 74300G (2009).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Opt. A, Pure Appl. Opt. (1)

M. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A, Pure Appl. Opt. 6, S202–S208 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

J. Phys. A (1)

M. Berry, “Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves,” J. Phys. A 11, 27–37 (1978).
[CrossRef]

J. Phys. A: Math. Theor. (1)

M. V. Berry and M. R. Dennis, “Topological events on wave dislocation lines: birth and death of loops, and reconnection,” J. Phys. A: Math. Theor. 40, 65–74 (2007).
[CrossRef]

Nature (2)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Knotted threads of darkness,” Nature 432, 165–165 (2004).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Opt. Commun. (2)

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[CrossRef]

Opt. Eng. (Bellingham) (1)

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Eng. (Bellingham) 12, 5448–5456 (2004).

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80, 013824 (2009).
[CrossRef]

Phys. Rev. E (1)

I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[CrossRef]

Phys. Rev. Lett. (6)

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, “Speckle evolution of diffusive and localized waves,” Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Topology of light’s darkness,” Phys. Rev. Lett. 102, 143902 (2009).
[CrossRef] [PubMed]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901-1 (2005).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

N. Shvartsman and I. Freund, “Vortices in random wave fields: nearest neighbor anticorrelations,” Phys. Rev. Lett. 72, 1008–1011 (1994).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Proc. SPIE (1)

J. Lin and X.-C. Yuan, “Application of orbital angular momentum in optical measurement,” Proc. SPIE 74300, 74300G (2009).
[CrossRef]

SIAM Rev. (1)

A. J. Devaney and G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

M. R. Dennis, “Topological singularities in wave fields,” Ph.D. dissertation (University of Bristol, 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Anatomy of a speckle field: (a) amplitude of the speckle field (square root of the intensity), (b) total phase of the speckle field, (c) least-squares continuous phase, and (d) the singular part of the phase of a speckle field.

Fig. 2
Fig. 2

Normalized optical vortex density for a phase corrected speckle field, shown as a function of (a) linear normalized propagation distance, as well as (b) logarithmic normalized propagation distance. The diamonds represent numerical data, averaged over more than a hundred different simulations. The error bars represent standard deviations. A solid curve is fitted through these data points as discussed in the text.

Fig. 3
Fig. 3

Scintillation index for a phase corrected speckle field, shown as a function of (a) linear normalized propagation distance, as well as (b) logarithmic normalized propagation distance. The diamonds represent numerical data, averaged over more than a hundred different simulations. The error bars represent standard deviations. A solid curve is fitted through these data points as discussed in the text.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ψ ( x ) = α ( a ) exp ( i 2 π a x ) d 2 a ,
α ( a ) = χ ̃ ( a ) exp ( | a | 2 W 2 ) ,
ψ ( x ) = | ψ ( x ) | exp [ i θ c ( x ) + i n ν n ϕ ( x x n ) ] ,
F { T 2 θ ( x ) } = | a | 2 F { θ ( x ) } .
θ LS ( x ) = F 1 { F { T 2 θ ( x ) } | a | 2 } .
θ LS ( x ) = F 1 { F { Δ T 2 θ ( x ) } 2 [ 2 cos ( 2 π δ x ) cos ( 2 π δ y ) ] } ,
σ I = I 2 I 2 1.
V ( z ) = A 0 + A 1   exp ( K 0 z 2 k 1 z ) A 2   exp ( k 2 z ) ,
σ ( z ) = B 0 B 1   exp [ G   ln ( z z d ) 2 ] ,
2 V ( z ) z 2 + [ κ ( z ) + k 2 ] V ( z ) z + k 2 κ ( z ) [ V ( z ) A 0 ] = 0 ,
κ ( z ) = 2 K 0 z + k 1 2 K 0 2 K 0 z + k 1 k 2 .

Metrics