Abstract

We develop a novel model of the probability density of the orbital angular momentum (OAM) modes for Hankel-Bessel beams in paraxial turbulence channel based on the Rytov approximation. The results show that there are multi-peaks of the mode probability density along the radial direction. The peak position of the mode probability density moves to beam center with the increasing of non-Kolmogorov turbulence-parameters and the generalized refractive-index structure parameters and with the decreasing of OAM quantum number, propagation distance and wavelength of the beams. Additionally, larger OAM quantum number and smaller non-Kolmogorov turbulence-parameter can be selected in order to obtain larger mode probability density. The probability density of the OAM mode crosstalk is increasing with the decreasing of the quantum number deviation and the wavelength. Because of the focusing properties of Hankel-Bessel beams in turbulence channel, compared with the Laguerre-Gaussian beams, Hankel-Bessel beams are a good light source for weakening turbulence spreading of the beams and mitigating the effects of turbulence on the probability density of the OAM mode.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
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    [Crossref]
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    [Crossref]
  10. S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).
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  13. X. Sheng, Y. Zhang, F. Zhao, L. Zhang, and Y. Zhu, “Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states,” Opt. Lett. 37(13), 2607–2609 (2012).
    [Crossref] [PubMed]
  14. F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

2013 (1)

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

2012 (5)

2011 (3)

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

2010 (1)

F. E. S. Vetelino and R. J. Morgana, “Model validation of turbulence effects on orbital angular momentum of single photons for optical communication,” Proc. SPIE 7685, 76850R (2010).
[Crossref]

2009 (1)

2008 (1)

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Anguita, J. A.

Boyd, R. W.

Ding, J.

Gong, L. Y.

Jia, J.

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Jiang, Y.

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

Kotlyar, V. V.

Kovalev, A. A.

Lavery, M. P. J.

Leach, J.

Li, F.

F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

Malik, M.

Mirhosseini, M.

Morgana, R. J.

F. E. S. Vetelino and R. J. Morgana, “Model validation of turbulence effects on orbital angular momentum of single photons for optical communication,” Proc. SPIE 7685, 76850R (2010).
[Crossref]

Neifeld, M. A.

O’Sullivan, M. N.

Ou, J.

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

Padgett, M.

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Robertson, D. J.

Rodenburg, B.

Sheng, X.

X. Sheng, Y. Zhang, F. Zhao, L. Zhang, and Y. Zhu, “Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states,” Opt. Lett. 37(13), 2607–2609 (2012).
[Crossref] [PubMed]

X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
[Crossref]

Soifer, V. A.

Tang, H.

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

Tyler, G. A.

Vasic, B. V.

Vetelino, F. E. S.

F. E. S. Vetelino and R. J. Morgana, “Model validation of turbulence effects on orbital angular momentum of single photons for optical communication,” Proc. SPIE 7685, 76850R (2010).
[Crossref]

Wang, J.

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Wang, S.

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

Wang, X.

X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
[Crossref]

Wang, Y.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

Wang, Z.

X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
[Crossref]

Xu, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

Zhang, J.

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

Zhang, L.

Zhang, Y.

X. Sheng, Y. Zhang, F. Zhao, L. Zhang, and Y. Zhu, “Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states,” Opt. Lett. 37(13), 2607–2609 (2012).
[Crossref] [PubMed]

X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
[Crossref]

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

Zhao, F.

Zhao, S. M.

Zheng, B. Y.

Zhu, Y.

X. Sheng, Y. Zhang, F. Zhao, L. Zhang, and Y. Zhu, “Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states,” Opt. Lett. 37(13), 2607–2609 (2012).
[Crossref] [PubMed]

X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
[Crossref]

Acta Phys. Sin. (1)

F. Li, H. Tang, Y. Jiang, and J. Ou, “Spiral spectrum of Laguerre-Gaussian beams propagating in turbulent atmosphere,” Acta Phys. Sin. 60(1), 014204 (2011).

Appl. Opt. (1)

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

Opt. Commun. (2)

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Y. Jiang, S. Wang, J. Zhang, J. Ou, and H. Tang, “Spiral spectrum of Laguerre-Gaussian beams propagation in non-Kolmogorov turbulence,” Opt. Commun. 303, 38–41 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

X. Sheng, Y. Zhang, X. Wang, Z. Wang, and Y. Zhu, “The effects of non-Kolmogorov turbulence on the orbital angular momentum of photon-beam propagation in a slant channel,” Opt. Quantum Electron. 43(6–10), 121–127 (2012).
[Crossref]

Optik (1)

J. Wang, J. Jia, J. Xu, Y. Wang, and Y. Zhang, “The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere,” Optik 122(11), 996–999 (2011).
[Crossref]

Phys. Rev. Lett. (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

F. E. S. Vetelino and R. J. Morgana, “Model validation of turbulence effects on orbital angular momentum of single photons for optical communication,” Proc. SPIE 7685, 76850R (2010).
[Crossref]

Other (1)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 6th ed. (Academic, 2000).

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Figures (5)

Fig. 1
Fig. 1

The mode probability densities | β l 0 (r,z) | 2 and the crosstalk probability densities | β l (r,z) | 2 of the HB beams and LG beams against r for l0.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2

The mode probability densities | β l 0 (r,z) | 2 and the crosstalk probability densities | β l (r,z) | 2 of the HB beams and LG beams against r for α.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3

The mode probability densities | β l 0 (r,z) | 2 and the crosstalk probability densities | β l (r,z) | 2 of the HB beams and LG beams against r for C n 2 .

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4

The mode probability densities | β l 0 (r,z) | 2 and the crosstalk probability densities | β l (r,z) | 2 of the HB beams and LG beams against r for z.

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5

The mode probability densities | β l 0 (r,z) | 2 and the crosstalk probability densities | β l (r,z) | 2 of the HB beams and LG beams against r for the wavelength λ.

Download Full Size | PPT Slide | PDF

Equations (7)

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

HB( r,φ,z )=H B l 0 ( r,φ,z )exp[ ψ 1 ( r,φ,z ) ]
H B para, l 0 ( r,φ,z )= i 3 l 0 +1 l 0 ! A 0 π 2kz exp[ i( kz− π l 0 4 − π 4 )+i l 0 φ ] J l 0 /2 [ k r 2 /4z ]
H B para ( r,φ,z )= ∑ l β l ( r,z )exp( ilφ )
β l ( r,z )= 1 2π ∫ 0 2π H B para ( r,φ,z ) exp[ −ilφ ]dφ
∫ 0 2π exp[−in φ 1 +ηcos( φ 1 − φ 2 )] d φ 1 =2πexp(−in φ 2 ) I n (η)
| β l (r,z) | 2 = π 2kz ( l 0 ! A 0 ) 2 | J l 0 /2 [ k r 2 /4z ] | 2 exp[ −2 r 2 / ρ 0 2 ] I l− l 0 ( 2 r 2 / ρ 0 2 )
ρ 0 = { 2Γ[ ( 3−α )/2 ]( α−1 ) π 1/2 k 2 Γ( 1−α/2 ) C n 2 z } 1/( α−2 )  , 3<α<4.

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