Abstract

For practical wireless communication links, one of the critical challenges is the random fluctuation of turbulence that will impair link performance. Here a transmission model of partially coherent elegant Laguerre–Gaussian (ELG) beams in oceanic turbulence is established. An analytical formula for channel capacity of a partially coherent ELG beam propagating through a turbulent ocean is derived. The effects of oceanic turbulence on the evolution of channel capacity performance are studied quantitatively in a series of numerical simulations. Research results show that decreasing the rate of dissipation of mean-square temperature and ratio of temperature to salinity, as well as increasing the dissipation rate of turbulent kinetic energy per unit mass of fluid of a turbulent ocean can significantly improve communication channel capacity. Furthermore, choosing optimum beam source parameters is favorable to mitigate the influence of oceanic turbulence. Results also show that in the underwater turbulence, the partially coherent ELG beams are more affected by turbulence as compared to the fully coherent ELG beams. These study results may provide potential help in designing the free-space optical vortex communication systems.

© 2019 Optical Society of America

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2018 (4)

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital angular momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Y. Xu, Y. Zhu, and Y. Zhang, “Crosstalk probability of the bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in marine-atmosphere turbulence,” Opt. Commun. 427, 493–496 (2018).
[Crossref]

Y. Li, Y. Zhang, and Y. Zhu, “Influence of oceanic turbulence on propagation of the Gaussian pulsed X wave carrying orbital angular momentum,” Opt. Commun. 428, 57–62 (2018).
[Crossref]

Y. Xu, H. Shi, and Y. Zhang, “Effects of anisotropic oceanic turbulence on the power of the bandwidth-limited OAM mode of partially coherent modified Bessel correlated vortex beams,” J. Opt. Soc. Am. A 35, 1839–1845 (2018).
[Crossref]

2017 (6)

G. Vallone, “Role of beam waist in Laguerre-Gauss expansion of vortex beams,” Opt. Lett. 42, 1097–1100 (2017).
[Crossref]

T. Yang, Y. Xu, H. Tian, D. Di, Q. Du, B. Zhang, and Y. Dan, “Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere,” J. Opt. Soc. Am. A 34, 713–720 (2017).
[Crossref]

Y. Li, L. Yu, and Y. Zhang, “Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean,” Opt. Express 25, 12203–12215 (2017).
[Crossref]

Y. Li and Y. Zhang, “OAM mode of the Hankel-Bessel vortex beam in weak to strong turbulent link of marine-atmosphere,” Laser Phys. 27, 045201 (2017).
[Crossref]

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” Commun. Surveys Tuts. 19, 57–96 (2017).
[Crossref]

2016 (4)

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 Photon. J. 8, 7901411 (2016).
[Crossref]

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, 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, 4642–4648 (2016).
[Crossref]

M. Cheng, L. Guo, J. Li, and Q. Huang, “Propagation properties of an optical vortex carried by a Bessel-Gaussian beam in anisotropic turbulence,” J. Opt. Soc. Am. A 33, 1442–1450 (2016).
[Crossref]

2015 (3)

2014 (6)

Y. Ata and Y. Baykal, “Scintillations of optical plane and spherical waves in underwater turbulence,” J. Opt. Soc. Am. A 31, 1552–1556 (2014).
[Crossref]

Y. Huang, B. Zhang, Z. Gao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
[Crossref]

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

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

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

2012 (2)

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

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50, 760–766 (2012).
[Crossref]

2011 (3)

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102, 937–944 (2011).
[Crossref]

H. Xu, Z. Cui, and J. Qu, “Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence,” Opt. Express 19, 21163–21173 (2011).
[Crossref]

O. Korotkova and N. Farwell, “Effect of oceanic turbulence on polarization of stochastic beams,” Opt. Commun. 284, 1740–1746 (2011).
[Crossref]

2010 (2)

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res. 103, 33–56 (2010).
[Crossref]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

2009 (2)

2005 (2)

L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13, 873–881 (2005).
[Crossref]

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

2004 (2)

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, 82–98 (2000).
[Crossref]

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

1988 (1)

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

1963 (1)

S. Q. Duntley, “Light in the sea,” J. Opt. Soc. Am. A 53, 214–233 (1963).
[Crossref]

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, and J. Wang, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

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

Andrews, L. C.

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Ata, Y.

Barnett, S.

Baykal, Y.

Y. Ata and Y. Baykal, “Scintillations of optical plane and spherical waves in underwater turbulence,” J. Opt. Soc. Am. A 31, 1552–1556 (2014).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res. 103, 33–56 (2010).
[Crossref]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Boyd, R. W.

Cai, Y.

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res. 103, 33–56 (2010).
[Crossref]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17, 22366–22379 (2009).
[Crossref]

Carrasco, S.

Cheng, M.

Cheng, Q.

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Cui, Z.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50, 760–766 (2012).
[Crossref]

H. Xu, Z. Cui, and J. Qu, “Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence,” Opt. Express 19, 21163–21173 (2011).
[Crossref]

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102, 937–944 (2011).
[Crossref]

Dan, Y.

Di, D.

Ding, C.

C. Ding, L. Liao, H. Wang, Y. Zhang, and L. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

Dolinar, S.

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

Du, Q.

Duan, Z.

Duntley, S. Q.

S. Q. Duntley, “Light in the sea,” J. Opt. Soc. Am. A 53, 214–233 (1963).
[Crossref]

Enderlein, J.

Eyyuboglu, H. T.

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res. 103, 33–56 (2010).
[Crossref]

Farwell, N.

O. Korotkova and N. Farwell, “Effect of oceanic turbulence on polarization of stochastic beams,” Opt. Commun. 284, 1740–1746 (2011).
[Crossref]

Fazal, I. M.

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

Fickler, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Fink, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Franke-Arnold, S.

Friberg, A. T.

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

Gao, Z.

Gibson, G.

Gradshteyn, I. S.

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

Guo, L.

Handsteiner, J.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

He, Q.

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Hu, Z.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital angular momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

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]

Huang, H.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, and J. Wang, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

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

Huang, Q.

Huang, Y.

Ivan, J. S.

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” Commun. Surveys Tuts. 19, 57–96 (2017).
[Crossref]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” Commun. Surveys Tuts. 19, 57–96 (2017).
[Crossref]

Korotkova, O.

O. Korotkova and N. Farwell, “Effect of oceanic turbulence on polarization of stochastic beams,” Opt. Commun. 284, 1740–1746 (2011).
[Crossref]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17, 22366–22379 (2009).
[Crossref]

Krenn, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Li, J.

Li, Y.

Y. Li, Y. Zhang, and Y. Zhu, “Influence of oceanic turbulence on propagation of the Gaussian pulsed X wave carrying orbital angular momentum,” Opt. Commun. 428, 57–62 (2018).
[Crossref]

Y. Li, L. Yu, and Y. Zhang, “Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean,” Opt. Express 25, 12203–12215 (2017).
[Crossref]

Y. Li and Y. Zhang, “OAM mode of the Hankel-Bessel vortex beam in weak to strong turbulent link of marine-atmosphere,” Laser Phys. 27, 045201 (2017).
[Crossref]

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. Xu, Y. Li, and X. Zhao, “Intensity and effective beam width of partially coherent Laguerre-Gaussian beams through a turbulent atmosphere,” J. Opt. Soc. Am. A 32, 1623–1630 (2015).
[Crossref]

Liao, L.

C. Ding, L. Liao, H. Wang, Y. Zhang, and L. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Liu, L.

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

Luo, H.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50, 760–766 (2012).
[Crossref]

Madhu, V.

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

Malik, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optic, 1st ed. (Cambridge University, 1995).

Massari, M.

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, 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, 82–98 (2000).
[Crossref]

Padgett, M.

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Pampaloni, F.

Pan, L.

C. Ding, L. Liao, H. Wang, Y. Zhang, and L. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

Pas’ko, V.

Paterson, C.

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

Philips, R. L.

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Qu, J.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50, 760–766 (2012).
[Crossref]

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102, 937–944 (2011).
[Crossref]

H. Xu, Z. Cui, and J. Qu, “Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence,” Opt. Express 19, 21163–21173 (2011).
[Crossref]

Ren, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, and J. Wang, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

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

Romanato, F.

Ruffato, G.

Ryzhik, I. M.

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

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Scheidl, T.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).

Shi, H.

Shi, J.

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102, 937–944 (2011).
[Crossref]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Tian, H.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Torner, L.

Torres, J.

Tur, M.

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

Turunen, J.

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

Tyler, G. A.

Ursin, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Vallone, G.

Vasnetsov, M.

Wang, F.

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res. 103, 33–56 (2010).
[Crossref]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17, 22366–22379 (2009).
[Crossref]

Wang, H.

C. Ding, L. Liao, H. Wang, Y. Zhang, and L. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Wang, J.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital angular momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, and J. Wang, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

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

Wei, M.

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital angular momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Willner, A. E.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optic, 1st ed. (Cambridge University, 1995).

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]

Xie, G.

Xu, H.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50, 760–766 (2012).
[Crossref]

H. Xu, Z. Cui, and J. Qu, “Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence,” Opt. Express 19, 21163–21173 (2011).
[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]

Xu, Y.

Yan, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, and J. Wang, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

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

Yang, J.-Y.

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

Yang, T.

Yu, L.

Yue, Y.

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

Zeilinger, A.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Zhang, B.

Zhang, D.

Zhang, Y.

Y. Xu, H. Shi, and Y. Zhang, “Effects of anisotropic oceanic turbulence on the power of the bandwidth-limited OAM mode of partially coherent modified Bessel correlated vortex beams,” J. Opt. Soc. Am. A 35, 1839–1845 (2018).
[Crossref]

Y. Li, Y. Zhang, and Y. Zhu, “Influence of oceanic turbulence on propagation of the Gaussian pulsed X wave carrying orbital angular momentum,” Opt. Commun. 428, 57–62 (2018).
[Crossref]

Y. Xu, Y. Zhu, and Y. Zhang, “Crosstalk probability of the bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in marine-atmosphere turbulence,” Opt. Commun. 427, 493–496 (2018).
[Crossref]

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital angular momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Y. Li and Y. Zhang, “OAM mode of the Hankel-Bessel vortex beam in weak to strong turbulent link of marine-atmosphere,” Laser Phys. 27, 045201 (2017).
[Crossref]

Y. Li, L. Yu, and Y. Zhang, “Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean,” Opt. Express 25, 12203–12215 (2017).
[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 Photon. J. 8, 7901411 (2016).
[Crossref]

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]

C. Ding, L. Liao, H. Wang, Y. Zhang, and L. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

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, X.

Zhong, Y.

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102, 937–944 (2011).
[Crossref]

Zhu, Y.

Y. Xu, Y. Zhu, and Y. Zhang, “Crosstalk probability of the bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in marine-atmosphere turbulence,” Opt. Commun. 427, 493–496 (2018).
[Crossref]

Y. Li, Y. Zhang, and Y. Zhu, “Influence of oceanic turbulence on propagation of the Gaussian pulsed X wave carrying orbital angular momentum,” Opt. Commun. 428, 57–62 (2018).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (1)

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102, 937–944 (2011).
[Crossref]

Commun. Surveys Tuts. (1)

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” Commun. Surveys Tuts. 19, 57–96 (2017).
[Crossref]

IEEE Photon. 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 Photon. J. 8, 7901411 (2016).
[Crossref]

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, 82–98 (2000).
[Crossref]

J. Opt. (1)

C. Ding, L. Liao, H. Wang, Y. Zhang, and L. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

J. Opt. Soc. Am. A (7)

Laser Phys. (1)

Y. Li and Y. Zhang, “OAM mode of the Hankel-Bessel vortex beam in weak to strong turbulent link of marine-atmosphere,” Laser Phys. 27, 045201 (2017).
[Crossref]

Nat. Photonics (1)

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

New J. Phys. (1)

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

Opt. Commun. (6)

Y. Xu, Y. Zhu, and Y. Zhang, “Crosstalk probability of the bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in marine-atmosphere turbulence,” Opt. Commun. 427, 493–496 (2018).
[Crossref]

O. Korotkova and N. Farwell, “Effect of oceanic turbulence on polarization of stochastic beams,” Opt. Commun. 284, 1740–1746 (2011).
[Crossref]

M. Wei, J. Wang, Y. Zhang, and Z. Hu, “Orbital angular momentum photons for optical communication in non-Kolmogorov atmospheric turbulence,” Opt. Commun. 416, 89–93 (2018).
[Crossref]

Y. Li, Y. Zhang, and Y. Zhu, “Influence of oceanic turbulence on propagation of the Gaussian pulsed X wave carrying orbital angular momentum,” Opt. Commun. 428, 57–62 (2018).
[Crossref]

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]

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

Opt. Express (6)

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. Lasers Eng. (1)

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50, 760–766 (2012).
[Crossref]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

Y. Zhang, L. Liu, F. Wang, Y. Cai, C. Ding, and L. Pan, “Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation,” Opt. Quantum Electron. 46, 365–379 (2014).
[Crossref]

Phys. Rev. A (1)

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

Phys. Rev. Lett. (3)

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

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Prog. Electromagn. Res. (1)

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res. 103, 33–56 (2010).
[Crossref]

Other (4)

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

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optic, 1st ed. (Cambridge University, 1995).

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of the oceanic turbulence on propagation of the ELG beams.
Fig. 2.
Fig. 2. Normalized (top) 3D amplitude and (middle) transverse intensity distributions and (bottom) phase for ELG beams propagating through turbulent ocean with the radial mode number p=1 and the OAM mode number l=1,2,3,4 at z=30  m.
Fig. 3.
Fig. 3. Received power for transmitted OAM modes of partially coherent ELG beams in oceanic turbulence against l for l0.
Fig. 4.
Fig. 4. Effects of OAM mode number and propagation distance on channel capacity for partially coherent ELG beams in oceanic turbulence. (a) OAM mode number N and (b) transmission distance z.
Fig. 5.
Fig. 5. Channel capacity of partially ELG beams at a fixed distance z=30  m against OAM mode number for different values of parameters λ, χT, ε, and ω, respectively. (a) optical wavelength λ, (b) rate of dissipation of mean-square temperature χT, (c) rate of dissipation of turbulent kinetic energy ε, and (d) ratio of temperature to salinity ω.
Fig. 6.
Fig. 6. Effects of source beam waist and spatial coherence length on channel capacity for partially ELG beams in oceanic turbulence. (a) Beam waist ω0 and (b) source spatial coherence length ρs.

Equations (17)

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

Epl(r,θ,ζ)=rlωp+l+1(ζ)Lpl[r2ω02(1+iζ)]×exp[r2ω02(1+iζ)+ikzilθiψpl],
u(r,θ,ζ)=Ep0l0(r,θ,ζ)exp[ψ(r,θ,ζ)+iψs(r,θ)],
W(r,r,θ,θ,ζ)=u(r,θ,ζ)u*(r,θ,ζ)s,oe,
W(r,r,θ,θ,ζ)=Ep0l0(r,θ,ζ)Ep0l0*(r,θ,ζ)×exp[ψ(r,θ,ζ)+ψ*(r,θ,ζ)]oe×exp[iψs(r,θ)iψs(r,θ)]s.
exp[iψs(r,θ)iψs(r,θ)]s=exp{1ρs2[r2+r22rrcos(θθ)]},
exp[ψ(r,θ,ζ)+ψ*(r,θ,ζ)]oeexp{1ρ02[r2+r22rrcos(θθ)]},
ρ0=[1.28×108k2zχTη1/3ε1/3×(6.78+47.57ω217.67ω1)]1/2,
W(r,r,θ,θ,ζ)=Ep0l0(r,θ,ζ)Ep0l0*(r,θ,ζ)×exp[r2+r22rrcos(θθ)ρ˜02],
ρ˜02=ρs2+ρ02.
u(r,θ,ζ)=12πl=l=+Rl(r,ζ)exp(ilθ),
Rl(r,ζ)=12π02πu(r,θ,ζ)exp(ilθ)dθ.
|Rl(r,ζ)|2=12π02π02πW(r,r,ζ)×exp[il(θθ)]dθdθ.
02πexp(ilθ)dθ={2π(l=0)0(l0),
02πexp[ilθ+acos(θθ)]dθ=2πexp(ilθ)Il(a),
Il=0R|Rl(r,ζ)|2rdr=2πω2(p0+l0+1)(ζ)0Rr2l0+1|Lp0l0[r2ω02(1+iζ)]|2×exp[2r2ω2(ζ)]exp(2r2ρ˜02)Ill0(2r2ρ˜02)dr.
P(l|l0)=Il/m=m=+Im.
C=maxP(l0)[H(l0)H(l0|l)]=log2(N)+1Nl=l=+l0=MMP(l|l0)×[log2P(l|l0)log2l0=MMP(l|l0)],

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