Abstract

We analyze OAM modal crosstalk of a Lommel-Gaussian beam induced by anisotropic oceanic turbulence. The theoretical model is constructed to illustrate the impacts of turbulence and beam parameters on the received crosstalk probability. Turbulence conditions with a larger inner-scale factor, larger anisotropic factor, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and smaller temperature-salinity contribution ratio usually cause smaller crosstalk. Due to its better immunity to turbulence interference, a Lommel-Gaussian beam with a small asymmetry factor, low OAM quantum number, optimum waist width, and long wavelength in the transmission window is preferable for application. The results are useful to improve OAM communication performances in oceanic turbulence.

© 2017 Optical Society of America

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Intensity of vortex modes carried by Lommel beam in weak-to-strong non-Kolmogorov turbulence

Lin Yu, Beibei Hu, and Yixin Zhang
Opt. Express 25(16) 19538-19547 (2017)

References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2017 (1)

2016 (7)

M. J. Cheng, L. X. Guo, J. T. Li, and Y. X. Zhang, “Channel capacity of the OAM-based free- space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8(1), 7901411 (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]

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Y. Q. Wu, Y. X. Zhang, Y. Zhu, and Z. D. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Y. Li, Y. Zhang, Y. Zhu, and M. Chen, “Effects of anisotropic turbulence on average polarizability of Gaussian Schell-model quantized beams through ocean link,” Appl. Opt. 55(19), 5234–5239 (2016).
[Crossref] [PubMed]

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]

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

2015 (5)

Y. Dong, L. Guo, C. Liang, F. Wang, and Y. Cai, “Statistical properties of a partially coherent cylindrical vector beam in oceanic turbulence,” J. Opt. Soc. Am. A 32(5), 894–901 (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]

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

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

2014 (3)

2013 (2)

W. Wen, K. H. Song, Y. M. Dong, and M. Yao, “Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation,” Opt. Laser Technol. 48, 28–34 (2013).
[Crossref]

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

2012 (1)

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

2010 (1)

2006 (1)

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

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]

2004 (1)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

2002 (1)

2000 (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27(1), 82–98 (2000).
[Crossref]

Ahmed, N.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Andrews, L. C.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Arbabi, A.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Arbabi, E.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Ashrafi, S.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Baykal, Y.

Belafhal, A.

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]

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]

Cai, Y.

Cao, Y.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Chen, M.

Cheng, M. J.

M. J. Cheng, L. X. Guo, J. T. Li, and Y. X. Zhang, “Channel capacity of the OAM-based free- space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8(1), 7901411 (2016).
[Crossref]

Crabbs, R.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

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]

Davidson, F. M.

Davis, C. C.

Dogariu, A.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Dong, Y.

Dong, Y. M.

W. Wen, K. H. Song, Y. M. Dong, and M. Yao, “Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation,” Opt. Laser Technol. 48, 28–34 (2013).
[Crossref]

Dudley, A.

Ez-zariy, 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]

Faraon, A.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Farwell, N.

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

Fletcher, A. S.

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

Forbes, A.

Gong, L.

Guo, L.

Guo, L. X.

M. J. Cheng, L. X. Guo, J. T. Li, and Y. X. Zhang, “Channel capacity of the OAM-based free- space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8(1), 7901411 (2016).
[Crossref]

Hamilton, S. A.

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

Hu, B. B.

Hu, Z. D.

Y. Q. Wu, Y. X. Zhang, Y. Zhu, and Z. D. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Ji, X.

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Kamali, S. M.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Korotkova, O.

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Kotlyar, V. V.

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

A. A. Kovalev and V. V. Kotlyar, “Family of three-dimensional asymmetric nonparaxial Lommel modes,” Proc. SPIE 9448, 944828 (2014).

Kovalev, A. A.

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

A. A. Kovalev and V. V. Kotlyar, “Family of three-dimensional asymmetric nonparaxial Lommel modes,” Proc. SPIE 9448, 944828 (2014).

Leclerc, T.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Li, J. T.

M. J. Cheng, L. X. Guo, J. T. Li, and Y. X. Zhang, “Channel capacity of the OAM-based free- space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8(1), 7901411 (2016).
[Crossref]

Li, L.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Li, Y.

Li, Y. M.

Liang, C.

Liu, C.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Liu, L. R.

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

Lu, L.

Lu, W.

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

Moores, J. D.

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

Nelson, W.

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27(1), 82–98 (2000).
[Crossref]

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27(1), 82–98 (2000).
[Crossref]

Palastro, J. P.

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]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Pires, H. D.

Ren, Y.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Ricklin, J. C.

Salem, A. B.

Salem, M.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Shen, B.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Shi, Y.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Song, K. H.

W. Wen, K. H. Song, Y. M. Dong, and M. Yao, “Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation,” Opt. Laser Technol. 48, 28–34 (2013).
[Crossref]

Sprangle, P.

Sun, J. F.

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

Trichili, A.

Tur, M.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

van Exter, M. P.

Wang, F.

Wang, W.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Wang, X.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Wang, Z.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Wen, W.

W. Wen, K. H. Song, Y. M. Dong, and M. Yao, “Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation,” Opt. Laser Technol. 48, 28–34 (2013).
[Crossref]

Willner, A. E.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Willner, A. J.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Wolf, E.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Woudenberg, J.

Wu, Y. Q.

Y. Q. Wu, Y. X. Zhang, Y. Zhu, and Z. D. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Xie, G.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Xu, J.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Xu, Z.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Yan, Y.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Yao, M.

W. Wen, K. H. Song, Y. M. Dong, and M. Yao, “Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation,” Opt. Laser Technol. 48, 28–34 (2013).
[Crossref]

Yi, L.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Yu, L.

Zghal, M.

Zhang, L.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Zhang, X.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Zhang, Y.

Zhang, Y. X.

L. Yu, B. B. Hu, and Y. X. Zhang, “Intensity of vortex modes carried by Lommel beam in weak-to-strong non-Kolmogorov turbulence,” Opt. Express 25(16), 19538–19547 (2017).
[Crossref]

M. J. Cheng, L. X. Guo, J. T. Li, and Y. X. Zhang, “Channel capacity of the OAM-based free- space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8(1), 7901411 (2016).
[Crossref]

Y. Q. Wu, Y. X. Zhang, Y. Zhu, and Z. D. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Zhao, Q.

Zhao, Z.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Zhu, Y.

Y. Q. Wu, Y. X. Zhang, Y. Zhu, and Z. D. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Y. Li, Y. Zhang, Y. Zhu, and M. Chen, “Effects of anisotropic turbulence on average polarizability of Gaussian Schell-model quantized beams through ocean link,” Appl. Opt. 55(19), 5234–5239 (2016).
[Crossref] [PubMed]

Appl. Opt. (2)

IEEE Access (1)

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

IEEE Commun. Mag. (1)

A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

IEEE Photonics J. (1)

M. J. Cheng, L. X. Guo, J. T. Li, and Y. X. Zhang, “Channel capacity of the OAM-based free- space optical communication links with Bessel-Gauss beams in turbulent ocean,” IEEE Photonics J. 8(1), 7901411 (2016).
[Crossref]

Int. J. Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27(1), 82–98 (2000).
[Crossref]

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

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

J. Opt. Soc. Am. A (3)

Laser Phys. (1)

Y. Q. Wu, Y. X. Zhang, Y. Zhu, and Z. D. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Opt. Commun. (2)

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

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

Opt. Express (2)

Opt. Laser Technol. (1)

W. Wen, K. H. Song, Y. M. Dong, and M. Yao, “Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation,” Opt. Laser Technol. 48, 28–34 (2013).
[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]

Phys. Rev. Lett. (2)

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

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Proc. SPIE (2)

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

A. A. Kovalev and V. V. Kotlyar, “Family of three-dimensional asymmetric nonparaxial Lommel modes,” Proc. SPIE 9448, 944828 (2014).

Sci. Rep. (1)

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref] [PubMed]

Waves Random Media (1)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Other (2)

S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE, 2005).

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Figures (6)

Fig. 1
Fig. 1 The transverse intensity pattern of Lommel-Gaussian beam under different beam parameters. Compared with the parameters in (a) c = 0.1 , n 0 = 1 , λ = 532 nm , w 0 = 10 mm , β = 0 .001 , the different parameters in (b) - (f) are: (b) n 0 = 4 , (c) λ = 850 nm , (d) w 0 = 2 mm , (e) c = 0.9 , (f) c = 0.9 i , (g) c = 0.9 exp ( i π / 4 ) and (h) c = 0.9 exp ( i 3 π / 4 ) .
Fig. 2
Fig. 2 (a) The crosstalk probability of Lommel-Gaussian beam under different propagation distances and anisotropic factors of turbulence. (b) A comparison of crosstalk probability of Lommel-Gaussian beam with those of Bessel-Gaussian and Laguerre-Gaussian beam.
Fig. 3
Fig. 3 The crosstalk probability of Lommel-Gaussian beam under different dissipation rates of the mean-squared temperature and kinetic energy per unit mass of fluid.
Fig. 4
Fig. 4 The crosstalk probability of Lommel-Gaussian beam under different temperature-salinity contribution ratios and turbulence inner-scale factors.
Fig. 5
Fig. 5 The crosstalk probability of Lommel-Gaussian beam under different OAM quantum numbers and asymmetry factors’ modulus.
Fig. 6
Fig. 6 The crosstalk probability of Lommel-Gaussian beam under different beam waist widths and wavelengths.

Equations (13)

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E 0 ( r , φ , z ) = q 1 ( z ) c n 0 exp [ i k z i z k ρ 2 2 k q ( z ) r 2 w 0 2 1 q ( z ) ] U n 0 [ c k ρ r exp ( i φ ) q ( z ) , k ρ r q ( z ) ] , = 1 q ( z ) exp [ i k z i z k ρ 2 2 k q ( z ) r 2 w 0 2 1 q ( z ) ] p = 0 ( c 2 ) p exp [ i ( n 0 + 2 p ) φ ] J n 0 + 2 p [ k ρ r q ( z ) ]
q ( z ) = 1 + i z z 0 = 1 + i 2 z k w 0 2 .
W ( r , φ , φ , z ) = E 0 ( r , φ , z ) E 0 * ( r , φ , z ) exp [ 1 2 D s ( r , r , z ) ] ,
D s ( r , r , z ) = 8 π 2 k 2 z 0 1 0 κ Φ ( κ ) [ 1 J 0 ( κ ξ | r r | ) ] d κ d ξ = 2 | r r | 2 ρ c 2 ,
Φ ( κ ) = Φ ( κ ρ , κ z ) = 0.388 × 10 8 χ ε 1 / 3 ζ 2 κ ζ 11 / 3 [ 1 + 2.35 ( κ ζ η ) 2 / 3 ] f ( κ ζ ) , f ( κ ζ ) = exp [ A 1 f ( κ ζ ) ] 2 γ 1 exp [ A 2 f ( κ ζ ) ] + γ 2 exp [ A 3 f ( κ ζ ) ] , f ( κ ζ ) = 8 .284 ( κ ζ η ) 4 / 3 + 12.978 ( κ ζ η ) 2 ,
ρ c 2 = 1 3 π 2 k 2 z ζ 4 0 κ ζ 3 Φ ( κ ζ ) d κ ζ = 1.276 × 10 8 k 2 ε 1 / 3 ζ 2 χ z [ 0 κ ζ 2 / 3 f ( κ ζ ) d κ ζ + 2.35 η 2 / 3 0 f ( κ ζ ) d κ ζ ] .
ρ c 2 = 8.705 × 10 8 k 2 ( ε η ) 1 / 3 ζ 2 χ z ( 1 2.605 γ 1 + 7.007 γ 2 ) .
W ( r , φ , φ , z ) = 1 2 π n = | ϖ n | 2 exp [ i n ( φ φ ) ] ,
| ϖ n | 2 = 1 2 π 0 2 π 0 2 π W ( r , φ , φ , z ) exp [ i n ( φ φ ) ] d φ d φ = 1 2 π 1 | q ( z ) | 2 exp { r 2 w 0 2 [ 1 q ( z ) + 1 q * ( z ) ] } p = 0 p = 0 ( 1 ) p + p c 2 p ( c * ) 2 p J n 0 + 2 p [ k ρ r q ( z ) ] J n 0 + 2 p [ k ρ r q * ( z ) ] . × 0 2 π 0 2 π exp [ i ( n 0 + 2 p ) φ i ( n 0 + 2 p ) φ ] exp [ 2 r 2 2 r 2 cos ( φ φ ) ρ c 2 ] exp [ i n ( φ φ ) ] d φ d φ
0 2 π exp [ i n φ + τ cos ( φ φ ) ] d φ = 2 π exp ( i n φ ) I n ( τ ) ,
| ϖ n | 2 = 2 π | q ( z ) | 2 exp [ 2 r 2 ( 1 w 0 2 | q ( z ) | 2 + 1 ρ c 2 ) ] p = 0 | c | 4 p | J n 0 + 2 p ( k ρ r q ( z ) ) | 2 I n n 0 2 p ( 2 r 2 ρ c 2 ) ,
S Δ n = 2 π | q ( z ) | 2 p = 0 | c | 4 p 0 R exp [ 2 r 2 ( 1 w 0 2 | q ( z ) | 2 + 1 ρ c 2 ) ] | J n 0 + 2 p ( k ρ r q ( z ) ) | 2 I Δ n 2 p ( 2 r 2 ρ c 2 ) r d r ,
P = 1 S Δ n = 0 Δ n = S Δ n .

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