Abstract

The propagation of vortex beams through weak-to-strong atmospheric turbulence is simulated and analyzed. It is demonstrated that the topological charge of such a beam is a robust quantity that could be used as an information carrier in optical communications. The advantages and limitations of such an approach are discussed.

© 2008 Optical Society of America

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References

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  1. M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, Vol. XLII, E.Wolf, ed. (Elsevier, North-Holland, 2001), pp. 219-276.
    [CrossRef]
  2. C. Paterson, "Atmospheric turbulence and orbital angular momentum of single photons for optical communication," Phys. Rev. Lett. 94, 153901 (2005).
    [CrossRef] [PubMed]
  3. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
    [CrossRef] [PubMed]
  4. L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (IOP, 2004).
  5. W. M. Lee, X.-C. Yuan, and W. C. Cheong, "Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation," Opt. Lett. 29, 1796-1798 (2004).
    [CrossRef] [PubMed]
  6. A. Vinotte and L. Berg, "Femtosecond optical vortices in air," Phys. Rev. Lett. 95, 193901 (2005).
    [CrossRef]
  7. Z. Bouchal, "Resistance of nondiffracting vortex beam against amplitude and phase perturbations," Opt. Commun. 210, 155-164 (2002).
    [CrossRef]
  8. M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, "Self-reconstruction of an optical vortex," JETP Lett. 71, 130-133 (2000).
    [CrossRef]
  9. Y. Zhang and C. Tao, "Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulent atmosphere," Chin. Opt. Lett. 2, 559-561 (2004).
  10. Y. Zhang, M. Tang, and C. Tao, "Partially coherent vortex beam propagation in a turbulent atmosphere," Chin. Opt. Lett. 3, 559-561 (2005).
  11. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London, Ser. A 336, 165-190 (1974).
    [CrossRef]
  12. J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP, 1999).
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  14. 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).
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  15. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
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  16. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).
  17. M. Chen, F. S. Roux, and J. C. Olivier, "Detection of phase singularities with a Shack-Hartman wavefront sensor," J. Opt. Soc. Am. A 24, 1994-2002 (2007).
    [CrossRef]

2007 (1)

2005 (3)

Y. Zhang, M. Tang, and C. Tao, "Partially coherent vortex beam propagation in a turbulent atmosphere," Chin. Opt. Lett. 3, 559-561 (2005).

A. Vinotte and L. Berg, "Femtosecond optical vortices in air," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

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

2004 (3)

2002 (1)

Z. Bouchal, "Resistance of nondiffracting vortex beam against amplitude and phase perturbations," Opt. Commun. 210, 155-164 (2002).
[CrossRef]

2001 (2)

M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, Vol. XLII, E.Wolf, ed. (Elsevier, North-Holland, 2001), pp. 219-276.
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

2000 (1)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, "Self-reconstruction of an optical vortex," JETP Lett. 71, 130-133 (2000).
[CrossRef]

1999 (1)

J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP, 1999).

1998 (1)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

1997 (2)

1988 (1)

1974 (1)

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

Allen, L.

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Beijersbergen, M. W.

Berg, L.

A. Vinotte and L. Berg, "Femtosecond optical vortices in air," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

Berry, M. V.

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

Bouchal, Z.

Z. Bouchal, "Resistance of nondiffracting vortex beam against amplitude and phase perturbations," Opt. Commun. 210, 155-164 (2002).
[CrossRef]

Chen, M.

Cheong, W. C.

Dholakia, K.

Flatté, S. M.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

Karman, G. P.

Lee, W. M.

Marienko, I. G.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, "Self-reconstruction of an optical vortex," JETP Lett. 71, 130-133 (2000).
[CrossRef]

Martin, J. M.

Nye, J. F.

J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP, 1999).

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

Olivier, J. C.

Padgett, M. J.

Paterson, C.

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

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Roux, F. S.

Simpson, N. B.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, Vol. XLII, E.Wolf, ed. (Elsevier, North-Holland, 2001), pp. 219-276.
[CrossRef]

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, "Self-reconstruction of an optical vortex," JETP Lett. 71, 130-133 (2000).
[CrossRef]

Tang, M.

Tao, C.

van Duijl, A.

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, Vol. XLII, E.Wolf, ed. (Elsevier, North-Holland, 2001), pp. 219-276.
[CrossRef]

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, "Self-reconstruction of an optical vortex," JETP Lett. 71, 130-133 (2000).
[CrossRef]

Vinotte, A.

A. Vinotte and L. Berg, "Femtosecond optical vortices in air," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

Woerdman, J. P.

Yuan, X.-C.

Zhang, Y.

Appl. Opt. (1)

Chin. Opt. Lett. (2)

J. Opt. Soc. Am. A (1)

JETP Lett. (1)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, "Self-reconstruction of an optical vortex," JETP Lett. 71, 130-133 (2000).
[CrossRef]

Opt. Commun. (1)

Z. Bouchal, "Resistance of nondiffracting vortex beam against amplitude and phase perturbations," Opt. Commun. 210, 155-164 (2002).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (2)

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

A. Vinotte and L. Berg, "Femtosecond optical vortices in air," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

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]

Other (5)

J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP, 1999).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, Vol. XLII, E.Wolf, ed. (Elsevier, North-Holland, 2001), pp. 219-276.
[CrossRef]

L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (IOP, 2004).

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Figures (8)

Fig. 1
Fig. 1

Simulation of the transverse profile of a Laguerre–Gaussian (LG). beam of order m = 1 , n = 1 . (a) Combined phase-intensity plot. The gray scale indicates the intensity profile of the field, while the red and green lines are lines of constant phase: green represents Im { U m n } = 0 ; red represents Re { U m n } = 0 . The intersection of the lines represents a phase singularity. The window size is 10 cm square, and w 0 = 2 cm . (b) Detailed phase plot of the LG beam. The phase increases continuously by 2 π as one progresses around the circle.

Fig. 2
Fig. 2

Simulation of the average topological charge for (a) LG beam of order m = 1 , n = 1 , and (b) LG beam of order m = 5 , n = 5 , propagating in moderate C n 2 = 10 15 m 2 3 atmospheric turbulence. Here w 0 = 2 cm , λ = 1.55 μ m , and the detector radius is 4 cm . The shaded region illustrates the standard deviation of the topological charge.

Fig. 3
Fig. 3

Simulation of the transverse profile of a LG beam of order m = 1 , n = 1 , at a distance of d = 4 km from the source. All other beam and turbulence parameters are as in Fig. 2. The image size is 50 cm square. It can be seen that the vortex has wandered outside the detector region (blue circle); no charge is detected.

Fig. 4
Fig. 4

Simulation of the average toplogical charge for a LG beam of order m = 1 , n = 1 , for various turbulence strengths. (a) C n 2 = 10 14 m 2 3 , (b) C n 2 = 10 15 m 2 3 , (c) C n 2 = 10 16 m 2 3 , (d) C n 2 = 10 17 m 2 3 . All other parameters are as in Fig. 2.

Fig. 5
Fig. 5

Simulation of the average toplogical charge for LG beams of order (a) m = 5 , n = 5 , and (b) m = 10 , n = 1 , in strong turbulence C n 2 = 10 14 m 2 3 . All other parameters are as in Fig. 2.

Fig. 6
Fig. 6

Simulation of the average topological charge for LG beams with variable aperture detectors. (a) m = 1 , n = 1 , C n 2 = 10 14 m 2 3 ; (b) m = 1 , n = 1 , C n 2 = 10 15 m 2 3 ; (c) m = 5 , n = 5 , C n 2 = 10 14 m 2 3 ; (d) m = 5 , n = 5 , C n 2 = 10 15 m 2 3 . The quantity r 0 = 4 cm ; all other parameters are as in Fig. 2.

Fig. 7
Fig. 7

Simulation of vortex pair production (intersection of red and green circles) in a LG beam of order m = 1 , n = 1 , with a variable aperture detector at a propagation distance of 6.5 km . All other parameters are as in Fig. 2. (a) Pair production (indicated by yellow arrow) results in no net change in topological charge. (b) Pair production (indicated by yellow arrow) results in one member of the pair lying outside the aperture; the detected topological charge is 2. The image size is 80 cm square.

Fig. 8
Fig. 8

Simulation of the average topological charge for a LG beam of order m = 10 , n = 1 , in strong turbulence, C n 2 = 10 13 m 2 3 : (a) with a fixed detector radius 4 cm and (b) with a variable detector radius. All other parameters are as in Fig. 2.

Equations (7)

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U ( r ) = A ( r ) exp [ i ϕ ( r ) ] .
t 1 2 π C ϕ ( r ) d l ,
ϕ n ( κ ) = 0.033 C n 2 κ 11 3 ,
U m n ( r , θ ) = A m n ( 2 r w 0 ) m L n ( m ) ( 2 r 2 w 0 2 ) exp [ i m θ r 2 w 0 2 ] ,
t ¯ 1 N n = 1 N t n ,
Δ t ( 1 N n = 1 N t n 2 t ¯ 2 ) 1 2 ,
r ap ( d ) = r 0 w 0 + w 0 1 + 4 d 2 ( k 2 w 0 4 ) ,

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