Abstract

In the paper, we experimentally demonstrate the propagation property of Laguerre-Gaussian (LG) beams carrying fractional orbital angular momentum (FOAM) in an underwater environment. The effects of topological charge (TC), temperature gradient, and salinity on the transmission of the LG-FOAM beam in underwater turbulence are analyzed, and the optimum interval of TC for FOAM communication and their help for the improvement of system capacity are discussed. The results show that both the salinity and the temperature gradient have serious impacts on the beam, and meanwhile, the temperature gradient plays a heavier influence. Although the detection probability of one FOAM mode at the receiver side is lower than that nearest integer OAM mode, in the case of that topological charges used are limited, the interval-based mode-multiplexed communication using FOAM can increase the channel capacity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  16. J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
    [Crossref]
  17. Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).
  18. J. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008).
    [Crossref]
  19. L. Wei, L. R. 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]
  20. V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” J. Opt. A: Pure Appl. Opt. 27(1), 82–98 (2000).
    [Crossref]

2019 (2)

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

X. Wang, Z. Yang, and S. Zhao, “Influence of oceanic turbulence on propagation of Airy vortex beam carrying orbital angular momentum,” Optik 176, 49–55 (2019).
[Crossref]

2016 (4)

Y. Ren, L. Li, Z. Wang, S. 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]

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

J. Baghdady, K. Miller, K. Morgan, M. Byrd, S. Osler, R. Ragusa, W. Li, B. Cochenour, and E. Johnson, “Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing,” Opt. Express 24(9), 9794–9805 (2016).
[Crossref]

M. Cheng, “Propagation of an optical vortex carried by a partially coherent laguerre-gaussian beam in turbulent ocean,” Appl. Opt. 55(17), 4642 (2016).
[Crossref]

2014 (1)

2012 (1)

2011 (2)

M. Alison Yao, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

A. Munafo, E. Simetti, A. Turetta, A. Caiti, and G. Casalino, “Autonomous underwater vehicle teams for adaptive ocean sampling: a data-driven approach,” Ocean Dyn. 61(11), 1981–1994 (2011).
[Crossref]

2008 (2)

2007 (1)

J. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[Crossref]

2006 (1)

L. Wei, L. R. 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]

2005 (1)

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

2004 (2)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

J. Leach, Y. Eric, and J. M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6(1), 71 (2004).
[Crossref]

2000 (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” J. Opt. A: Pure Appl. Opt. 27(1), 82–98 (2000).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Ahmed, N.

Y. Ren, L. Li, Z. Wang, S. 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]

Aiello, A.

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Arbabi, A.

Y. Ren, L. Li, Z. Wang, S. 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]

Arbabi, E.

Y. Ren, L. Li, Z. Wang, S. 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]

Ashrafi, S.

Y. Ren, L. Li, Z. Wang, S. 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]

Baghdady, J.

Barnett, S.

Barnett, S. M.

J. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

Byrd, M.

Caiti, A.

A. Munafo, E. Simetti, A. Turetta, A. Caiti, and G. Casalino, “Autonomous underwater vehicle teams for adaptive ocean sampling: a data-driven approach,” Ocean Dyn. 61(11), 1981–1994 (2011).
[Crossref]

Cao, Y.

Y. Ren, L. Li, Z. Wang, S. 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]

Casalino, G.

A. Munafo, E. Simetti, A. Turetta, A. Caiti, and G. Casalino, “Autonomous underwater vehicle teams for adaptive ocean sampling: a data-driven approach,” Ocean Dyn. 61(11), 1981–1994 (2011).
[Crossref]

Chen, H.

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

Chen, L.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

Cheng, M.

Cheng, W.

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

Cochenour, B.

Ding, J.

Eliel, E.

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

Eric, Y.

J. Leach, Y. Eric, and J. M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6(1), 71 (2004).
[Crossref]

Faraon, A.

Y. Ren, L. Li, Z. Wang, S. 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]

Flossmann, F.

Franke-Arnold, S.

J. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008).
[Crossref]

J. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[Crossref]

Gao, Z.

Gong, L.

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

Gong, L. Y.

Götte, J.

J. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008).
[Crossref]

J. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[Crossref]

Gruska, J.

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

Gui, C.

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).

Hanson, F.

Huang, Y.

Johnson, E.

Kamali, S.

Y. Ren, L. Li, Z. Wang, S. 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]

Leach, J.

Li, L.

Y. Ren, L. Li, Z. Wang, S. 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]

Li, S.

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).

Li, W.

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

J. Baghdady, K. Miller, K. Morgan, M. Byrd, S. Osler, R. Ragusa, W. Li, B. Cochenour, and E. Johnson, “Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing,” Opt. Express 24(9), 9794–9805 (2016).
[Crossref]

Liu, C.

Y. Ren, L. Li, Z. Wang, S. 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]

Liu, L. R.

L. Wei, L. R. 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]

Ma, X.

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

Miller, K.

Morgan, K.

Munafo, A.

A. Munafo, E. Simetti, A. Turetta, A. Caiti, and G. Casalino, “Autonomous underwater vehicle teams for adaptive ocean sampling: a data-driven approach,” Ocean Dyn. 61(11), 1981–1994 (2011).
[Crossref]

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” J. Opt. A: Pure Appl. Opt. 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,” J. Opt. A: Pure Appl. Opt. 27(1), 82–98 (2000).
[Crossref]

O’Holleran, K.

Oemrawsingh, S.

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

Osler, S.

Padgett, J. M.

J. Leach, Y. Eric, and J. M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6(1), 71 (2004).
[Crossref]

Padgett, M. J.

Preece, D.

Radic, S.

Ragusa, R.

Ren, Y.

Y. Ren, L. Li, Z. Wang, S. 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]

Simetti, E.

A. Munafo, E. Simetti, A. Turetta, A. Caiti, and G. Casalino, “Autonomous underwater vehicle teams for adaptive ocean sampling: a data-driven approach,” Ocean Dyn. 61(11), 1981–1994 (2011).
[Crossref]

Spreeuw, R. J.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Sun, J. F.

L. Wei, L. R. 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]

Tur, M.

Y. Ren, L. Li, Z. Wang, S. 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]

Turetta, A.

A. Munafo, E. Simetti, A. Turetta, A. Caiti, and G. Casalino, “Autonomous underwater vehicle teams for adaptive ocean sampling: a data-driven approach,” Ocean Dyn. 61(11), 1981–1994 (2011).
[Crossref]

Voigt, D.

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

Wang, J.

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).

Wang, L.

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

Wang, X.

X. Wang, Z. Yang, and S. Zhao, “Influence of oceanic turbulence on propagation of Airy vortex beam carrying orbital angular momentum,” Optik 176, 49–55 (2019).
[Crossref]

Wang, Z.

Y. Ren, L. Li, Z. Wang, S. 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]

Wei, L.

L. Wei, L. R. 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]

Willner, A. E.

Y. Ren, L. Li, Z. Wang, S. 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]

Willner, A. J.

Y. Ren, L. Li, Z. Wang, S. 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]

Woerdman, J.

S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. Eliel, and J. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Xie, G.

Y. Ren, L. Li, Z. Wang, S. 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]

Xu, Z.

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).

Yan, Y.

Y. Ren, L. Li, Z. Wang, S. 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]

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X. Wang, Z. Yang, and S. Zhao, “Influence of oceanic turbulence on propagation of Airy vortex beam carrying orbital angular momentum,” Optik 176, 49–55 (2019).
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Zambrini, R.

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S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
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Zhou, J.

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).

Adv. Opt. Photonics (1)

M. Alison Yao, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108(11), 111108 (2016).
[Crossref]

J. Mod. Opt. (1)

J. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[Crossref]

J. Opt. A: Pure Appl. Opt. (3)

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J. Leach, Y. Eric, and J. M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6(1), 71 (2004).
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Ocean Dyn. (1)

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Opt. Express (4)

Optik (1)

X. Wang, Z. Yang, and S. Zhao, “Influence of oceanic turbulence on propagation of Airy vortex beam carrying orbital angular momentum,” Optik 176, 49–55 (2019).
[Crossref]

Phys. Rev. A: At., Mol., Opt. Phys. (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
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Phys. Rev. Lett. (1)

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[Crossref]

Sci. Rep. (2)

Y. Ren, L. Li, Z. Wang, S. 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]

S. M. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, H. Chen, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 2025 (2019).
[Crossref]

Other (1)

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” Advanced Photonics for Communication. San Diego, California, USA, JT3A-1, (2014).

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Figures (5)

Fig. 1.
Fig. 1. The experimental setup for the propagation property of LG-FOAM in the an underwater environment. NDF, neutral density filter; Pol., polarizer; HWP, half-wave plate; SLM, spatial light modulator.
Fig. 2.
Fig. 2. Power spectrum of FOAM beam with $\ell =+2.5$ under various underwater conditions.
Fig. 3.
Fig. 3. The propagation property of LG-FOAM beams against salinity and temperature gradient in the underwater environment.
Fig. 4.
Fig. 4. The detection probability against different $\Delta$ values for different salinity and temperature gradient. The topological charge of FOAM at the transmitter is 2, and the interval value at the receiver is ${\Delta }$ =0,0.05,0.1,0.15,0.20
Fig. 5.
Fig. 5. The channel capacity of a multiplexed communication system with a limited topological charges, say, ${0<\ell <5}$, versus salinity and temperature gradient.

Equations (8)

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u M ( r , φ , z ) = m C m [ M ( α ) ] u m ( r , φ , z ) ,
C m [ M ( α ) ] = exp ( i μ α ) i exp [ i ( M m ) θ 0 ] 2 π ( M m ) [ exp ( i ( M m ) α ) ] [ 1 exp ( i μ 2 π ) ] .
u R ( r , φ , z ) = M C M u M ( r , φ , z ) ,
C M = u M ( r , φ , z ) | u R ( r , φ , z ) = | u M ( r , φ , z ) u R ( r , φ , z ) | z = z d r d r d φ .
P ( M ) = | C M | 2 .
E M = 0 2 π 0 r A | u ( r , φ , z ) | z = z d | 2 r d r d φ
u ( r , φ , z ) = u M ( r , φ , z ) u R ( r , φ , z ) ,
P M = E M M M E M + E M .

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