Abstract

We investigate the atmospheric turbulence effects on orbital angular momentum (OAM) spectra of different kinds of vortex beams, including Laguerre–Gaussian (LG) beams and Bessel beams, numerically. We generate the holograms of atmospheric turbulence with different structure constants of the refractive index. The OAM spectra of distorted single-mode or multiplexed LG beams and Bessel beams are analyzed. Compared with the OAM spectra of the two kinds of vortex beams, the spectrum of the Bessel beams is more dispersive. The results illustrate that Bessel beams suffer more from turbulent atmosphere than LG beams.

© 2016 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
  13. V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
    [Crossref]
  14. E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
    [Crossref]
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    [Crossref]
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    [Crossref]
  17. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [Crossref]
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    [Crossref]

2015 (3)

2013 (1)

2012 (2)

I. P. Lukin, “Variance of fluctuations of the orbital angular momentum of Bessel beam in turbulent atmosphere,” Proc. SPIE 8696, 869607 (2012).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

2010 (1)

K. Cheng, H. R. Zhang, and B. D. Lv, “Coherence vortex properties of partially coherent vortex beams,” Acta Phys. Sin. 59, 246–255 (2010).

2009 (1)

2008 (1)

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
[Crossref]

2006 (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (2006).
[Crossref]

2005 (1)

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

1998 (1)

V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
[Crossref]

1994 (1)

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

1992 (1)

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,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

1987 (1)

1965 (1)

1948 (1)

T. V. Karman, “Progress in the statistical theory of turbulence,” Proc. Natl. Acad. Sci. USA 34, 530–539 (1948).
[Crossref]

Ahmed, N.

Allen, L.

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,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Beijersbergen, M. W.

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,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Birch, P.

Boyd, R. W.

Brahler, B.

V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
[Crossref]

Chandrasekaran, N.

Chatwin, C.

Cheng, K.

K. Cheng, H. R. Zhang, and B. D. Lv, “Coherence vortex properties of partially coherent vortex beams,” Acta Phys. Sin. 59, 246–255 (2010).

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (2006).
[Crossref]

Dolinar, S.

Durnin, J.

Erkmen, B. I.

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Fried, D. L.

Gao, C.

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
[Crossref]

Gao, M.

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
[Crossref]

Gavel, D. T.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (2006).
[Crossref]

Goedecke, G. H.

V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
[Crossref]

Huang, H.

Ituen, I.

Johansson, E. M.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

Karman, T. V.

T. V. Karman, “Progress in the statistical theory of turbulence,” Proc. Natl. Acad. Sci. USA 34, 530–539 (1948).
[Crossref]

Lane, R. G.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (2006).
[Crossref]

Lavery, M. P. J.

Li, F.

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
[Crossref]

Liu, Y. D.

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
[Crossref]

Lukin, I. P.

I. P. Lukin, “Variance of fluctuations of the orbital angular momentum of Bessel beam in turbulent atmosphere,” Proc. SPIE 8696, 869607 (2012).
[Crossref]

Lv, B. D.

K. Cheng, H. R. Zhang, and B. D. Lv, “Coherence vortex properties of partially coherent vortex beams,” Acta Phys. Sin. 59, 246–255 (2010).

McKechnie, T. S.

T. S. McKechnie, General Theory of Light Propagation and Imaging through the Atmosphere (Springer, 2016).

Mellert, V.

V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
[Crossref]

Neifeld, M.

Ostashev, V. E.

V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
[Crossref]

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]

Ren, Y.

Shapiro, J. H.

Spreeuw, R. J. C.

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,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Steinhoff, N. K.

Tur, M.

Tyler, G. A.

Wang, J.

L. Zhu and J. Wang, “Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode,” Opt. Lett. 40, 5463–5466 (2015).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Willner, A. E.

Woerdman, J. P.

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,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Xie, G.

Yan, Y.

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Young, R.

Yu, S.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Zhang, H. R.

K. Cheng, H. R. Zhang, and B. D. Lv, “Coherence vortex properties of partially coherent vortex beams,” Acta Phys. Sin. 59, 246–255 (2010).

Zhu, L.

Acta Phys. Sin. (1)

K. Cheng, H. R. Zhang, and B. D. Lv, “Coherence vortex properties of partially coherent vortex beams,” Acta Phys. Sin. 59, 246–255 (2010).

J. Acoust. Soc. Am. (1)

V. E. Ostashev, B. Brahler, V. Mellert, and G. H. Goedecke, “Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities,” J. Acoust. Soc. Am. 104, 727–737 (1998).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Opt. Commun. (1)

Y. D. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

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,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Phys. Rev. Lett. (1)

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

Proc. Natl. Acad. Sci. USA (1)

T. V. Karman, “Progress in the statistical theory of turbulence,” Proc. Natl. Acad. Sci. USA 34, 530–539 (1948).
[Crossref]

Proc. SPIE (2)

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

I. P. Lukin, “Variance of fluctuations of the orbital angular momentum of Bessel beam in turbulent atmosphere,” Proc. SPIE 8696, 869607 (2012).
[Crossref]

Waves Random Media (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (2006).
[Crossref]

Other (1)

T. S. McKechnie, General Theory of Light Propagation and Imaging through the Atmosphere (Springer, 2016).

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Figures (5)

Fig. 1.
Fig. 1.

Intensity and phase distribution before and after propagating through the atmospheric turbulence at the distance of 1 km with different Cn2. (a) Case of LG beams. (b) Case of Bessel beams. In the map of the phase distribution, black denotes 0 and white denotes 2π.

Fig. 2.
Fig. 2.

OAM spectra of single-mode LG beam and Bessel beam with topological charge of +3 before and behind turbulence. (a) Case of before propagating through turbulence. (b), (c), and (d) Cases of after propagating through turbulence at the distance of 1 km and with Cn2 of 1×1013, 1×1014, and 1×1015  m2/3, respectively.

Fig. 3.
Fig. 3.

Intensity and phase distribution of multiplexed vortex beams before and after propagating through the atmospheric turbulence at the distance of 1 km with different Cn2. The multiplexed beams consist of four channels, whose topological charges are 6, 2, +3, and +7, respectively. (a) Case of multiplexed LG beams. (b) Case of multiplexed Bessel beams. In the map of the phase distribution, black denotes 0 and white denotes 2π.

Fig. 4.
Fig. 4.

OAM spectra of multiplexed LG beams and Bessel beams with topological charge of 6, 2, +3, and +7 before and behind turbulence. (a) Case of before propagating through turbulence. (b), (c), and (d) Cases of after propagating a distance of 1 km through turbulence with Cn2 of 1×1013, 1×1014, and 1×1015  m2/3, respectively.

Fig. 5.
Fig. 5.

(a) Curves show the relationship between the desired channel proportion of the two vortex beams and the propagating distance. (b) Desired channel proportions of LG beams with different radial index when they propagate through weak turbulence (Cn2=1×1015  m2/3) at the distance of 1 km.

Equations (5)

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φn(κ)=0.033Cn2·(κ2+k02)11/6exp(κ2/km2),
φϕ(κ)=2πk2zφn(κ).
ϕ(x,y)=F[C·(2πNΔx)·φϕ(κ)],
ϕL(x,y)=P=1Mn=11m=11cn,m,Pexp[i2π(fxnx+fymy)],
r0=(0.423k2Cn2z)3/5.

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