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. 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]

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]

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]

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]

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. 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]

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]

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]

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. 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]

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]

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]

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]

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. 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]

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]

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]

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]

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. 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]

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. 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]

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]

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).

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]

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, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).

[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]

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]

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).

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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).

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]

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]

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]

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]

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. 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]

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]

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]

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).

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]

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]

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

[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]

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. 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]

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]

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]

S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).

[Crossref]

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]

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).

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

[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. 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]

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]

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]

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]

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]

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]

S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).

[Crossref]

Y. Huang, B. Zhang, Z. Gao, G. Zhao, and G. Z. Duan, “Evolution behavior of gaussian schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22(15), 17723–17734 (2014).

[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]

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]

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]

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]

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]

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).