Abstract

We investigate the atmospheric turbulence effects on the propagation of vortex modes carried by Lommel beam. The analytic expression of the received signal and crosstalk mode intensity is derived based on the weak-to-strong non-Kolmogorov turbulence theory. The simulation results show that turbulence with small non-Kolmogorov spectrum parameter, small inner-scale factor and large outer-scale factor is more likely to induce modal crosstalk. With the increment of turbulence strength, the crosstalk spreads from adjacent modes to peripheral modes. The received signal intensity can be improved by use of Lommel beam with small asymmetry parameter, low orbital angular momentum quantum number and long wavelength. The results are helpful to the design of orbital angular momentum based free-space optical communication link.

© 2017 Optical Society of America

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References

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2016 (3)

A. Belafhal, L. Ez-zariy, and Z. Hricha, “A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. 184, 1–7 (2016).
[Crossref]

L. Ez-zariy, F. Boufalah, L. Dalil-Essakali, and A. Belafhal, “Effects of a turbulent atmosphere on an aperture Lommel-Gaussian beam,” Optik (Stuttg.) 127(23), 11534–11543 (2016).
[Crossref]

A. Trichili, A. B. Salem, A. Dudley, M. Zghal, and A. Forbes, “Encoding information using Laguerre Gaussian modes over free space turbulence media,” Opt. Lett. 41(13), 3086–3089 (2016).
[Crossref] [PubMed]

2015 (6)

A. A. Kovalev and V. V. Kotlyar, “Lommel modes,” Opt. Commun. 338, 117–122 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

S. C. Mi, T. J. Wang, G. S. Jin, and C. Wang, “High-capacity quantum secure direct communication with orbital angular momentum of photons,” IEEE Photonics J. 7(5), 7600108 (2015).
[Crossref]

Y. Huang, A. Zeng, Z. Gao, and B. Zhang, “Beam wander of partially coherent array beams through non-Kolmogorov turbulence,” Opt. Lett. 40(8), 1619–1622 (2015).
[Crossref] [PubMed]

Q. Zhao, L. Gong, and Y. M. Li, “Shaping diffraction-free Lommel beams with digital binary amplitude masks,” Appl. Opt. 54(25), 7553–7558 (2015).
[Crossref] [PubMed]

P. Birch, I. Ituen, R. Young, and C. Chatwin, “Long-distance Bessel beam propagation through Kolmogorov turbulence,” J. Opt. Soc. Am. A 32(11), 2066–2073 (2015).
[Crossref] [PubMed]

2014 (4)

P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22(7), 7598–7606 (2014).
[Crossref] [PubMed]

Y. Zhu, X. Liu, J. Gao, Y. Zhang, and F. Zhao, “Probability density of the orbital angular momentum mode of Hankel-Bessel beams in an atmospheric turbulence,” Opt. Express 22(7), 7765–7772 (2014).
[Crossref] [PubMed]

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

2013 (1)

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).
[Crossref]

2012 (3)

2008 (3)

2004 (1)

C. Y. Yong, A. J. Masino, F. E. Thomas, and C. J. Subich, “The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory,” Waves Random Media 14(1), 75–96 (2004).
[Crossref]

1999 (1)

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Aksenov, V. P.

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).
[Crossref]

Alfano, R. R.

Anguita, J. A.

Aruga, T.

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Bai, X.

Bao, C.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Belafhal, A.

A. Belafhal, L. Ez-zariy, and Z. Hricha, “A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. 184, 1–7 (2016).
[Crossref]

L. Ez-zariy, F. Boufalah, L. Dalil-Essakali, and A. Belafhal, “Effects of a turbulent atmosphere on an aperture Lommel-Gaussian beam,” Optik (Stuttg.) 127(23), 11534–11543 (2016).
[Crossref]

Birch, P.

Boufalah, F.

L. Ez-zariy, F. Boufalah, L. Dalil-Essakali, and A. Belafhal, “Effects of a turbulent atmosphere on an aperture Lommel-Gaussian beam,” Optik (Stuttg.) 127(23), 11534–11543 (2016).
[Crossref]

Cao, X.

Cao, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Chatwin, C.

Cui, L.

Dalil-Essakali, L.

L. Ez-zariy, F. Boufalah, L. Dalil-Essakali, and A. Belafhal, “Effects of a turbulent atmosphere on an aperture Lommel-Gaussian beam,” Optik (Stuttg.) 127(23), 11534–11543 (2016).
[Crossref]

Deng, P.

P. Deng, X. H. Yuan, and D. X. Huang, “Scintillation of a laser beam propagation through non- Kolmogorov strong turbulence,” Opt. Commun. 285(6), 880–887 (2012).
[Crossref]

Ding, J.

Dudley, A.

Ez-zariy, L.

A. Belafhal, L. Ez-zariy, and Z. Hricha, “A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. 184, 1–7 (2016).
[Crossref]

L. Ez-zariy, F. Boufalah, L. Dalil-Essakali, and A. Belafhal, “Effects of a turbulent atmosphere on an aperture Lommel-Gaussian beam,” Optik (Stuttg.) 127(23), 11534–11543 (2016).
[Crossref]

Forbes, A.

Gan, X.

Gao, J.

Gao, Z.

Golbraikh, E.

Gong, L.

Gong, L. Y.

He, Y. T.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Hricha, Z.

A. Belafhal, L. Ez-zariy, and Z. Hricha, “A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. 184, 1–7 (2016).
[Crossref]

Huang, D. X.

P. Deng, X. H. Yuan, and D. X. Huang, “Scintillation of a laser beam propagation through non- Kolmogorov strong turbulence,” Opt. Commun. 285(6), 880–887 (2012).
[Crossref]

Huang, H.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Huang, Y.

Ituen, I.

Jiang, Y. S.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Jin, G. S.

S. C. Mi, T. J. Wang, G. S. Jin, and C. Wang, “High-capacity quantum secure direct communication with orbital angular momentum of photons,” IEEE Photonics J. 7(5), 7600108 (2015).
[Crossref]

Kolosov, V. V.

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).
[Crossref]

Kopeika, N. S.

Kotlyar, V. V.

A. A. Kovalev and V. V. Kotlyar, “Lommel modes,” Opt. Commun. 338, 117–122 (2015).
[Crossref]

Kovalev, A. A.

A. A. Kovalev and V. V. Kotlyar, “Lommel modes,” Opt. Commun. 338, 117–122 (2015).
[Crossref]

Lavery, M. P. J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Leach, J.

Li, L.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Li, P.

Li, R.

Li, S. W.

Li, Y. M.

Liao, J. L.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Liu, S.

Liu, X.

Liu, Z. J.

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

Masino, A. J.

C. Y. Yong, A. J. Masino, F. E. Thomas, and C. J. Subich, “The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory,” Waves Random Media 14(1), 75–96 (2004).
[Crossref]

Mi, S. C.

S. C. Mi, T. J. Wang, G. S. Jin, and C. Wang, “High-capacity quantum secure direct communication with orbital angular momentum of photons,” IEEE Photonics J. 7(5), 7600108 (2015).
[Crossref]

Molisch, A. F.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Neifeld, M. A.

Ou, J.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Peng, T.

Pogutsa, C. E.

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).
[Crossref]

Qin, Z. Y.

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

Ramachandran, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Ren, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Salem, A. B.

Subich, C. J.

C. Y. Yong, A. J. Masino, F. E. Thomas, and C. J. Subich, “The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory,” Waves Random Media 14(1), 75–96 (2004).
[Crossref]

Sztul, H. I.

Takabe, M.

Tang, H.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Tao, R. M.

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

Thomas, F. E.

C. Y. Yong, A. J. Masino, F. E. Thomas, and C. J. Subich, “The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory,” Waves Random Media 14(1), 75–96 (2004).
[Crossref]

Trichili, A.

Tur, M.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Vasic, B. V.

Wang, C.

S. C. Mi, T. J. Wang, G. S. Jin, and C. Wang, “High-capacity quantum secure direct communication with orbital angular momentum of photons,” IEEE Photonics J. 7(5), 7600108 (2015).
[Crossref]

Wang, J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Wang, S. H.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Wang, T. J.

S. C. Mi, T. J. Wang, G. S. Jin, and C. Wang, “High-capacity quantum secure direct communication with orbital angular momentum of photons,” IEEE Photonics J. 7(5), 7600108 (2015).
[Crossref]

Willner, A. E.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Xie, G.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22(7), 7598–7606 (2014).
[Crossref] [PubMed]

Xu, X. J.

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

Xue, B.

Xue, W.

Yan, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Yong, C. Y.

C. Y. Yong, A. J. Masino, F. E. Thomas, and C. J. Subich, “The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory,” Waves Random Media 14(1), 75–96 (2004).
[Crossref]

Yoshikado, S.

Young, R.

Yuan, X. H.

P. Deng, X. H. Yuan, and D. X. Huang, “Scintillation of a laser beam propagation through non- Kolmogorov strong turbulence,” Opt. Commun. 285(6), 880–887 (2012).
[Crossref]

Zeng, A.

Zghal, M.

Zhang, B.

Zhang, J. H.

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Zhang, Y.

Zhao, F.

Zhao, J.

Zhao, Q.

Zhao, S. M.

Zhao, Z.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Zheng, B. Y.

Zheng, S.

Zhou, F.

Zhou, P.

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

Zhu, Y.

Zilberman, A.

Adv. Opt. Photonics (1)

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Appl. Opt. (4)

IEEE Photonics J. (1)

S. C. Mi, T. J. Wang, G. S. Jin, and C. Wang, “High-capacity quantum secure direct communication with orbital angular momentum of photons,” IEEE Photonics J. 7(5), 7600108 (2015).
[Crossref]

J. Opt. (1)

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15(4), 044007 (2013).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transf. (1)

A. Belafhal, L. Ez-zariy, and Z. Hricha, “A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. 184, 1–7 (2016).
[Crossref]

Opt. Commun. (3)

A. A. Kovalev and V. V. Kotlyar, “Lommel modes,” Opt. Commun. 338, 117–122 (2015).
[Crossref]

J. Ou, Y. S. Jiang, J. H. Zhang, H. Tang, Y. T. He, S. H. Wang, and J. L. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

P. Deng, X. H. Yuan, and D. X. Huang, “Scintillation of a laser beam propagation through non- Kolmogorov strong turbulence,” Opt. Commun. 285(6), 880–887 (2012).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

Z. Y. Qin, R. M. Tao, P. Zhou, X. J. Xu, and Z. J. Liu, “Propagation of partially coherent Bessel-Gaussian beams carrying optical vortices in non-Kolmogorov turbulence,” Opt. Laser Technol. 56, 182–188 (2014).
[Crossref]

Opt. Lett. (2)

Optik (Stuttg.) (1)

L. Ez-zariy, F. Boufalah, L. Dalil-Essakali, and A. Belafhal, “Effects of a turbulent atmosphere on an aperture Lommel-Gaussian beam,” Optik (Stuttg.) 127(23), 11534–11543 (2016).
[Crossref]

Waves Random Media (1)

C. Y. Yong, A. J. Masino, F. E. Thomas, and C. J. Subich, “The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory,” Waves Random Media 14(1), 75–96 (2004).
[Crossref]

Other (1)

L. C. Andrews, R. L. Philips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

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Figures (7)

Fig. 1
Fig. 1 The transverse intensity pattern of Lommel beam with different asymmetry parameters at the source plane.
Fig. 2
Fig. 2 The received mode intensity distribution of Lommel beam and Laguerre-Gaussian beam in (a, d) weak, (b, e) moderate and (c, f) strong turbulence. (a)-(c): Lommel beam; (d)-(f): Laguerre-Gaussian beam.
Fig. 3
Fig. 3 The received (a) signal intensity P s and (b) crosstalk intensity P c under different propagation distances and turbulence strengths.
Fig. 4
Fig. 4 In (a, b) weak and (c, d) strong turbulence, the received signal intensity P s and crosstalk intensity P c versus the OAM quantum number and the modulus of beam asymmetry parameter.
Fig. 5
Fig. 5 The received (a) signal intensity P s and (b) crosstalk intensity P c under different beam wavelengths and turbulence strengths.
Fig. 6
Fig. 6 The received (a) signal intensity P s and (b) crosstalk intensity P c under different values of non-Kolmogorov spectrum parameter and turbulence strengths.
Fig. 7
Fig. 7 In (a, b) weak and (c, d) strong turbulence, the received signal intensity P s and crosstalk intensity P c versus the turbulence’s inner-scale factor and outer-scale factor.

Equations (14)

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E 0 ( r,φ,z )= c n 0 exp( iz k 2 k ρ 2 ) u n 0 [c k ρ rexp( iφ ), k ρ r],
E 0 ( r,φ,z )=exp(ikz) p=0 ( c 2 ) p exp[i( n 0 +2p )φ] J n 0 +2p ( k ρ r) .
E(r,φ,z)= E 0 (r,φ,z)exp[ψ(r,φ,z)]= 1 2π n= β n exp(inφ) ,
β n = 1 2π 0 2π E(r,φ,z) exp(inφ)dφ.
| β n | 2 = 1 2π 0 2π 0 2π E 0 (r,φ,z) E 0 * (r, φ ,z) exp[ψ(r,φ,z)+ ψ * (r, φ ,z)] exp[in(φ φ )]d φ dφ.
exp[ψ(r,φ,z)+ ψ * (r,φ',z)] =exp [ 1 3 π 2 k 2 z[2 r 2 2 r 2 cos(φφ')] 0 κ 3 Φ neff (κ)dκ ], =exp[ 2 r 2 2 r 2 cos( φ φ ) ρ 0 2 ]
| β n | 2 = 1 2π p =0 p=0 ( 1 ) p+ p 0 2π 0 2π c 2p+2 p exp[ i2( p- p )φ ] J n 0 +2p ( k ρ r ) J n 0 +2 p ( k ρ r ) ×exp[ 2 r 2 ρ 0 2 ]exp[ 2 r 2 cos( φ φ ) ρ 0 2 i( n n 0 2 p )( φ φ ) ]d φ dφ, =2π p=0 c 4p [ J n 0 +2p ( k ρ r)] 2 exp[ 2 r 2 ρ 0 2 ] I n n 0 -2p ( 2 r 2 ρ 0 2 )
| β Δn | 2 =2π p=0 c 4p [ J n 0 +2p ( k ρ r)] 2 exp[ 2 r 2 ρ 0 2 ] I Δn2p ( 2 r 2 ρ 0 2 ).
P Δn = 0 D/2 | β Δn | 2 rdr Δn= 0 D/2 | β Δn | 2 rdr .
Φ neff (κ)=A(α) C n 2 κ α [f( κ,α, l 0 )g( κ, L 0 ) G X (κ,α)+ G Y (κ,α)] A(α)= Γ(α1) 4 π 2 cos( π 2 α ) ,
f( κ,α, l 0 )=exp( κ 2 κ l 2 ),g( κ, L 0 )=1exp( κ 2 κ L 2 ). G x (κ,α)=exp[ κ 2 κ x 2 ], G y (κ,α)= κ α [ κ 2 + κ y 2 ] α/2
c(α)= [ 2π 3 A(α)Γ( 5α 2 ) ] 1/( α5 ) ,β( α )=4Γ( 1 α 2 )sin πα 4 Γ 2 ( α/2 ) Γ( α ) , η x = 1 1+ f x (α) σ R 4/(α2) [ 7.35β( α ) Γ( 3α/2 ) ] 2/( 6α ) , f x (α)= [ 1.02r( α )I( α ) ] 2/( α6 ) , η y = [ 0.06375( α2 )β( α ) ] 2/( 2α ) [ 1+ f y (α) σ R 4/(α2) ], f y (α)= ( ln2 0.51 ) 2/(2α) , σ R 2 =β( α )A( α ) C n 2 π 2 k 3α/2 z α/2 ,I( α )= ( α1 ) 6α α2 Γ 2 ( α3 ) Γ( 2α6 ) , r( α )= 1 α2 2 ( 3α )( α10 ) α2 [ Γ( 1α/2 ) Γ( α/2 ) ] α6 α2 Γ( 6α α2 ) [ β( α ) ] 82α α2 .
Φ neff (κ)=A(α) C n 2 κ α { exp( κ 2 κ lx 2 )exp( κ 2 κ Llx 2 )+ κ α [ κ 2 + κ y 2 ] α/2 }, 1 κ lx 2 = 1 κ l 2 + 1 κ x 2 , 1 κ Llx 2 = 1 κ L 2 + 1 κ l 2 + 1 κ x 2 .
ρ 0 = [ 1 3 π 2 k 2 z 0 κ 3 Φ neff (κ)dκ ] 1 2 ={ Γ(α1) C n 2 k 2 z 48 cos( πα 2 ) [ 2Γ( 2 α 2 )( κ lx 4α κ Llx 4α )+ κ l 4 κ y α F 2 1 ( α 2 ,2;3, κ l 2 κ y 2 ) ] } 1 2 .

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