Abstract

Applying the angular spectrum theory, we derive the expression of a new Hermite-Gaussian (HG) vortex beam. Based on the new Hermite-Gaussian (HG) vortex beam, we establish the model of the received probability density of orbital angular momentum (OAM) modes of this beam propagating through a turbulent ocean of anisotropy. By numerical simulation, we investigate the influence of oceanic turbulence and beam parameters on the received probability density of signal OAM modes and crosstalk OAM modes of the HG vortex beam. The results show that the influence of oceanic turbulence of anisotropy on the received probability of signal OAM modes is smaller than isotropic oceanic turbulence under the same condition, and the effect of salinity fluctuation on the received probability of the signal OAM modes is larger than the effect of temperature fluctuation. In the strong dissipation of kinetic energy per unit mass of fluid and the weak dissipation rate of temperature variance, we can decrease the effects of turbulence on the received probability of signal OAM modes by selecting a long wavelength and a larger transverse size of the HG vortex beam in the source’s plane. In long distance propagation, the HG vortex beam is superior to the Laguerre-Gaussian beam for resisting the destruction of oceanic turbulence.

© 2017 Optical Society of America

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Propagation of an optical vortex carried by a partially coherent Laguerre–Gaussian beam in turbulent ocean

Mingjian Cheng, Lixin Guo, Jiangting Li, Qingqing Huang, Qi Cheng, and Dan Zhang
Appl. Opt. 55(17) 4642-4648 (2016)

References

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  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(11), 8185–8189 (1992).
    [Crossref] [PubMed]
  2. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
    [Crossref] [PubMed]
  3. Y. Baykal, “Intensity fluctuations of multimode laser beams in underwater medium,” J. Opt. Soc. Am. A 32(4), 593–598 (2015).
    [Crossref] [PubMed]
  4. Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
    [Crossref]
  5. V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27(1), 82–98 (2000).
    [Crossref]
  6. M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55(17), 4642–4648 (2016).
    [Crossref] [PubMed]
  7. M. Cheng, L. Guo, J. Li, and Y. Zhang, “Channel capacity of the OAM based free-space optical communication links with Bessel–Gauss beams in turbulent ocean,” IEEE Photonics J. 8, 7901411 (2016).
  8. J. Xu and D. Zhao, “Propagation of a stochastic electromagnetic vortex beam in the oceanic turbulence,” Opt. Laser Technol. 57, 189–193 (2014).
    [Crossref]
  9. Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22(15), 17723–17734 (2014).
    [Crossref] [PubMed]
  10. D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence,” Appl. Opt. 54(35), 10510–10516 (2015).
    [Crossref] [PubMed]
  11. B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
    [Crossref]
  12. M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
    [Crossref]
  13. M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
    [Crossref]
  14. V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994).
    [Crossref]
  15. V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347–355 (1995).
    [Crossref]
  16. Y. Zhu, M. Chen, Y. Zhang, and Y. Li, “Propagation of the OAM mode carried by partially coherent modified Bessel-Gaussian beams in an anisotropic non-Kolmogorov marine atmosphere,” J. Opt. Soc. Am. A 33(12), 2277–2283 (2016).
    [Crossref] [PubMed]
  17. I. Toselli, “Introducing the concept of anisotropy at different scales for modeling optical turbulence,” J. Opt. Soc. Am. A 31(8), 1868–1875 (2014).
    [Crossref] [PubMed]
  18. 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]
  19. Y. Wu, Y. Zhang, Y. Zhu, and Z. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
    [Crossref]
  20. W. Lu, L. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
    [Crossref]
  21. F. Pampaloni and J. Enderlein, “Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer,” arXiv:physics/0410021 (2004)
  22. O. Korotkova, Random Light Beams Theory and Applications (CRC, 2014).
  23. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, Series and Products, 6th Ed. (Academic, 2000).
  24. V. A. Sennikov, P. A. Konyaev, and V. P. Lukin, “Computer simulation of scalar vortex and annular beams LG0L in time-varying random inhomogeneous media,” Proc. SPIE 10035, 10035–10237 (2016).
  25. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (Washington: SPIE, 2005).
  26. 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]

2016 (7)

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

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

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

V. A. Sennikov, P. A. Konyaev, and V. P. Lukin, “Computer simulation of scalar vortex and annular beams LG0L in time-varying random inhomogeneous media,” Proc. SPIE 10035, 10035–10237 (2016).

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55(17), 4642–4648 (2016).
[Crossref] [PubMed]

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]

Y. Zhu, M. Chen, Y. Zhang, and Y. Li, “Propagation of the OAM mode carried by partially coherent modified Bessel-Gaussian beams in an anisotropic non-Kolmogorov marine atmosphere,” J. Opt. Soc. Am. A 33(12), 2277–2283 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (3)

2012 (1)

2006 (3)

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

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[Crossref]

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (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]

2000 (1)

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

1999 (1)

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

1995 (1)

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347–355 (1995).
[Crossref]

1994 (1)

V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (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(11), 8185–8189 (1992).
[Crossref] [PubMed]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Barchers, J. D.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Baykal, Y.

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Belen’kii, M. S.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[Crossref]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Brown, J. M.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Chen, M.

Cheng, M.

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

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55(17), 4642–4648 (2016).
[Crossref] [PubMed]

Cheng, Q.

Cuellar, E.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[Crossref]

Dikovskaya, N.

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Duan, Z.

Fugate, R. Q.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Galperin, B.

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Gao, Z.

Guo, L.

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55(17), 4642–4648 (2016).
[Crossref] [PubMed]

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

Hu, Z.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

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

Huang, Q.

Huang, Y.

Hughes, K. A.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[Crossref]

Karis, S. J.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Konyaev, P. A.

V. A. Sennikov, P. A. Konyaev, and V. P. Lukin, “Computer simulation of scalar vortex and annular beams LG0L in time-varying random inhomogeneous media,” Proc. SPIE 10035, 10035–10237 (2016).

Li, J.

M. Cheng, L. Guo, J. Li, Q. Huang, Q. Cheng, and D. Zhang, “Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean,” Appl. Opt. 55(17), 4642–4648 (2016).
[Crossref] [PubMed]

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

Li, Y.

Liu, D.

Liu, L.

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

Lu, W.

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

Lukin, V. P.

V. A. Sennikov, P. A. Konyaev, and V. P. Lukin, “Computer simulation of scalar vortex and annular beams LG0L in time-varying random inhomogeneous media,” Proc. SPIE 10035, 10035–10237 (2016).

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347–355 (1995).
[Crossref]

V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994).
[Crossref]

Nikishov, V. I.

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

Osmon, C. L.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

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]

Read, P. L.

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Rye, V. A.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[Crossref]

Sennikov, V. A.

V. A. Sennikov, P. A. Konyaev, and V. P. Lukin, “Computer simulation of scalar vortex and annular beams LG0L in time-varying random inhomogeneous media,” Proc. SPIE 10035, 10035–10237 (2016).

Sheng, X.

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Sukoriansky, S.

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Sun, J. F.

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

Toselli, I.

Wang, Y.

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wordsworth, R.

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Wu, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

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

Xu, J.

J. Xu and D. Zhao, “Propagation of a stochastic electromagnetic vortex beam in the oceanic turbulence,” Opt. Laser Technol. 57, 189–193 (2014).
[Crossref]

Yamazaki, Y. H.

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Yin, H.

Zhang, B.

Zhang, D.

Zhang, L.

Zhang, Y.

Y. Wu, Y. Zhang, Y. Zhu, and Z. 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]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

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

Y. Zhu, M. Chen, Y. Zhang, and Y. Li, “Propagation of the OAM mode carried by partially coherent modified Bessel-Gaussian beams in an anisotropic non-Kolmogorov marine atmosphere,” J. Opt. Soc. Am. A 33(12), 2277–2283 (2016).
[Crossref] [PubMed]

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]

Zhao, D.

J. Xu and D. Zhao, “Propagation of a stochastic electromagnetic vortex beam in the oceanic turbulence,” Opt. Laser Technol. 57, 189–193 (2014).
[Crossref]

Zhao, F.

Zhao, G.

Zhu, Y.

Appl. Opt. (3)

IEEE Photonics J. (1)

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

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

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent 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. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour 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. Wu, Y. Zhang, Y. Zhu, and Z. Hu, “Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean,” Laser Phys. 26(9), 095001 (2016).
[Crossref]

Nonlinear Process. Geophys. (1)

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, and R. Wordsworth, “Anisotropic turbulence and zonal jets in rotating flows with a β-effect,” Nonlinear Process. Geophys. 13(1), 83–98 (2006).
[Crossref]

Opt. Commun. (1)

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

J. Xu and D. Zhao, “Propagation of a stochastic electromagnetic vortex beam in the oceanic turbulence,” Opt. Laser Technol. 57, 189–193 (2014).
[Crossref]

Opt. Lett. (1)

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

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 (5)

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[Crossref]

V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994).
[Crossref]

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347–355 (1995).
[Crossref]

V. A. Sennikov, P. A. Konyaev, and V. P. Lukin, “Computer simulation of scalar vortex and annular beams LG0L in time-varying random inhomogeneous media,” Proc. SPIE 10035, 10035–10237 (2016).

Other (4)

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

F. Pampaloni and J. Enderlein, “Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer,” arXiv:physics/0410021 (2004)

O. Korotkova, Random Light Beams Theory and Applications (CRC, 2014).

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

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Figures (7)

Fig. 1
Fig. 1 Intensity profiles of HG vortex beams in the absence of turbulence (a) n = 2 , m = 2 , (b) n = 2 , m = 4 ,(c) n = 2 , m = 6 . When z = 0 in the plane, the intensity of the HG vortex beam decreases with deviating from the optical axis center. In addition, the intensity forms annular shapes along the optical axis center with increasing quantum number m .
Fig. 2
Fig. 2 Probability of signal OAM modes of the HG vortex beam propagation through oceanic turbulence for several values of parameter n (a) m = 2 , (b) m = 4 respectively.
Fig. 3
Fig. 3 Probability of crosstalk OAM modes of the HG vortex beam propagation through oceanic turbulence versus propagation distance z for different modes Δ l .
Fig. 4
Fig. 4 Probability of signal OAM modes of the HG vortex beam propagation through oceanic turbulence versus propagation distance z for different anisotropic factor ζ .
Fig. 5
Fig. 5 Probability of signal OAM modes of the HG vortex beam propagation through oceanic turbulence versus wavelength λ for different inner scale η .
Fig. 6
Fig. 6 Probability of signal OAM modes of the HG vortex beam propagation through oceanic turbulence versus the dissipation rate of temperature variance χ t for different the source’s transverse size w 0 .
Fig. 7
Fig. 7 Probability of signal OAM modes of the HG vortex beam propagation through oceanic turbulence versus the rate of dissipation of kinetic energy per unit mass of fluid ε for different the ratio of temperature and salinity contributions to the refractive index spectrum ϖ .

Equations (37)

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ϕ ( κ , ζ ) = 0.388 C m 2 ζ 2 κ 11 / 3 [ 1 + 2.35 ( κ η ) 2 / 3 ] f ( κ , ζ , ϖ ) ,
u ( x , y , z ; ω ) = exp ( i k z ) 4 π 2 a ( k x , k y ; ω ) exp [ i ( k x x + k y y ) ] exp [ i z 2 k ( k x 2 + k y 2 ) ] d k x d k y ,
Δ θ ( z ; ω ) Δ ω ( z ; ω ) min .
Δ θ ( z ; ω ) = 1 4 π 2 ( k x 2 + k y 2 ) | a ( k x , k y ; ω ) | 2 d k x d k y = 1 4 π 2 k x 2 | a ( k x , k y ; ω ) | 2 d k x k y 2 | a ( k x , k y ; ω ) | 2 d k y ,
Δ ω ( z ; ω ) = 1 4 π 2 ( | a ( k x , k y ; ω ) k x | 2 + | a ( k x , k y ; ω ) k y | 2 ) d k x d k y , = 1 4 π 2 | a ( k x , k y ; ω ) k x | 2 d k x | a ( k x , k y ; ω ) k y | 2 d k y
1 4 π 2 k x 2 | a ( k x , k y ; ω ) | 2 d k x | a ( k x , k y ; ω ) k x | 2 d k min .
| f ( x ) | 2 d x | g ( x ) | 2 d x | f * ( x ) g ( x ) d x | 2 ,
a ( k x , k y ; ω ) = exp [ w 0 2 4 ( k x 2 + k y 2 ) ] .
a ( k x , k y ; ω ) = k x n k y n exp [ w 0 2 4 ( k x 2 + k y 2 ) ] .
a ( k x , k y ; ω ) = k x n k y n ( k x i k y ) m exp [ w 0 2 4 ( k x 2 + k y 2 ) ] ,
u ( x , y , z ; ω ) = exp ( i k z ) 4 π 2 k x n k y n ( k x i k y ) m exp [ ϒ ( k x , k y ) ] d k x d k y ,
exp [ ϒ ( k x , k y ) ] = exp [ w 0 2 4 ( 1 + i z ζ ) ( k x 2 + k y 2 ) ] exp [ i ( k x x + k y y ) ] ,
n exp [ i ( k x x + k y y ) ] x n = ( i k x ) n exp [ i ( k x x + k y y ) ] ,
n exp [ i ( k x x + k y y ) ] y n = ( i k y ) n exp [ i ( k x x + k y y ) ] ,
( x i y ) m exp [ i ( k x x + k y y ) ] = i m ( k x i k y ) m exp [ i ( k x x + k y y ) ] .
u ( x , y , z ; ω ) = exp ( i k z ) 4 π 2 2 n x n y n ( x i y ) m exp [ ϒ ( k x , k y ) ] d k x d k y .
u ( x , y , z ; ω ) = exp ( i k z ) 4 π 2 2 n x n y n γ a m exp [ ϒ ( k x , k y ) ] d k x d k y ,
1 2 π exp ( i a x b 2 2 x 2 ) d x = 1 b 2 π exp [ a 2 2 b 2 ] ,
u m ( x , y , z ; ω ) = exp ( i k z ) 1 [ w 0 2 ( 1 + i z ζ ) ] m + 1 2 n x n y n γ b m exp [ γ a γ b w 0 2 ( 1 + i z ζ ) ] .
u m ( x , y , z ; ω ) = exp ( i m φ ) exp ( i k z ) [ w 0 2 ( 1 + i z ζ ) ] m + 1 u = 0 m / 2 ( m / 2 ) ! ( m / 2 u ) ! u ! H V n m 2 u ( x ) H V n 2 u ( y ) ,
u m ( x , y , z ; ω ) = 1 [ w 0 2 ( 1 + i z ζ ) ] n + 1 H n ( x / w 0 2 ( 1 + i z ζ ) ) × H n ( y w 0 2 ( 1 + i z ζ ) ) exp [ i k z x 2 + y 2 w 0 2 ( 1 + i z ζ ) ] ,
u m ( x , y , z ; ω ) = exp ( i m φ ) exp ( i k z ) [ w 0 2 ( 1 + i z ζ ) ] m + 1 ( r ) m exp [ r 2 w 0 2 ( 1 + i z ζ ) ] L m 0 [ r 2 w 0 2 ( 1 + i z ζ ) ] ,
p ( l | u ) = l | a l ( r , z ) | 2 ,
p ( l / m ) = p ( l | u ) = m | a l ( r , z ) | 2 ,
a l ( r , z ) = 1 2 π 0 2 π u ( r , φ , z ) exp ( i l φ ) d φ .
u ( r , φ , z ) = u m ( r , φ , z ) exp [ i ψ ( r , φ ) ] ,
| a l ( r , z ) | 2 s , a t = ( 1 2 π ) 2 0 2 π 0 2 π u m ( r , φ , z ) u m * ( r , φ , z ) s exp [ i l ( φ φ ) ] × exp [ i ψ ( r , φ ) i ψ ( r , φ ) ] a t d φ d φ ,
u m ( r , φ , z ) u m * ( r , φ , z ) s = exp [ i m ( φ φ ) ] 1 [ w 0 4 ( 1 + z ζ 2 ) ] m + 1 u = 0 m u = 0 m m ! ( m u ) ! u ! × m ! ( m u ) ! u ! H V n 2 m 2 u ( x 1 ) H V n 2 u ( y 1 ) H V n 2 m 2 u ( x 2 ) H V n 2 u ( y 2 ) , = exp [ i m ( φ φ ) ] Γ ( r , φ , φ , z )
Γ ( r , φ , φ , z ) = 1 [ w 0 4 ( 1 + z ζ 2 ) ] m + 1 u = 0 m u = 0 m m ! ( m u ) ! u ! m ! ( m u ) ! u ! . × H V n 2 m 2 u ( x 1 ) H V n 2 u ( y 1 ) H V n 2 m 2 u ( x 2 ) H V n 2 u ( y 2 )
p ( l / m ) = ( 1 2 π ) 2 0 0 2 π 0 2 π Γ ( r , φ , φ , z ) exp [ i ( l m ) ( φ φ ) ] , × exp [ i ψ ( r , φ ) i ψ * ( r , φ ) ] a t r d r d φ d φ
exp [ i ψ ( r , φ ) i ψ * ( r , φ ) ] a t = exp { 1 2 [ ψ ( r , φ ) ψ * ( r , φ ) ] 2 a t } ,
[ ψ ( r , φ ) ψ * ( r , φ ) ] 2 a t = 2 | ( r 1 r ) 2 | 5 / 3 / ρ o c ζ 5 / 3 .
exp [ i ψ ( r , φ ) i ψ * ( r , φ ) ] a t = exp { 2 5 / 6 [ 1 cos ( φ φ ) ] 5 / 6 r 5 / 3 ρ o c ζ 5 / 3 } ,
ρ o c ς = [ π 2 k 2 z 3 ζ 4 0 κ 3 ϕ ( κ , ζ ) d κ ] 3 / 5 .
ρ o c ς = ζ 6 / 5 | ϖ | 6 / 5 [ 1.802 × 10 7 k 2 z ( ε η ) 1 / 3 χ T ( 0.483 ϖ 2 0.835 ϖ + 3.380 ) ] 3 / 5 ,
P ( l / m ) = p ( l / m ) / h = p ( h / m ) ,
p ( l / m ) = ( 1 2 π ) 2 0 0 2 π 0 2 π Γ ( r , φ , φ , z ) exp [ i ( l m ) ( φ φ ) ] , × exp { 2 5 / 6 [ 1 cos ( φ φ ) ] 5 / 6 r 5 / 3 / ρ o c ς 5 / 3 } r d r d φ d φ

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