Abstract

By proposing a statistical averaging control function of the light intensity longitudinal profile and deriving the second moment of random complex weighting factors of Bessel-Gaussian beams, we derive the transmittance of a random frozen photons beam and analyze the freezing evolution characteristics of a random frozen photons beam as the parameters of the beam and channel of a turbulent ocean. It is concluded that the freezing characteristics of transmittance can be effectively improved by choosing beam parameters, such as, a larger number of superposition sub beams, a larger beam waist and a smaller quantum number of orbital angular momentum of the vortex mode. However, channel parameters, such as “equivalent temperature structure constant”, dissipation rate of the mean-squared temperature, dissipation rate of kinetic energy per unit mass of fluid, and the ratio of temperature and salinity can only affect the transmittance of a random frozen photons beam without changing the transmittance freezing characteristics. In addition, the influences of the inner and outer scales of turbulence on the transmittance freezing characteristics can be ignored.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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2020 (1)

2019 (13)

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
[Crossref]

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

Y. Li, Y. Han, Z. Cui, and Y. Hui, “Performance analysis of the OAM based optical wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. 21(3), 035702 (2019).
[Crossref]

C. Sun, X. Lv, B. Ma, J. Zhang, D. Deng, and W. Hong, “Statistical properties of partially coherent radially and azimuthally polarized rotating elliptical Gaussian beams in oceanic turbulence with anisotropy,” Opt. Express 27(8), A245–A256 (2019).
[Crossref]

S. Deng, Y. Zhu, and Y. Zhang, “Received probability of vortex modes carried by localized wave of Bessel-Gaussian amplitude envelope in turbulent seawater,” JMSE 7(7), 203 (2019).
[Crossref]

W. Zhang, L. Wang, W. Wang, and S. Zhao, “Propagation property of Laguerre-Gaussian beams carrying fractional orbital angular momentum in an underwater channel,” OSA Continuum 2(11), 3281–3287 (2019).
[Crossref]

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

Q. Liang, Y. Zhu, and Y. Zhang, “Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence,” Results Phys. 14, 102511 (2019).
[Crossref]

Y. Li, Z. Cui, Y. Han, and Y. Hui, “Channel capacity of orbital-angular-momentum based wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. Soc. Am. A 36(4), 471–477 (2019).
[Crossref]

D. Yang, Y. Zhang, and H. Shi, “Capacity of turbulent ocean links with carrier Bessel–Gaussian localized vortex waves,” Appl. Opt. 58(34), 9484–9490 (2019).
[Crossref]

M. P. Fewell and A. V. Trojan, “Absorption of light by water in the region of high transparency: recommended values for photon-transport calculations,” Appl. Opt. 58(9), 2408–2421 (2019).
[Crossref]

Y. Li, Y. Zhang, and Y. Zhu, “Oceanic spectrum of unstable stratification turbulence with outer scale and scintillation index of Gaussian-beam wave,” Opt. Express 27(5), 7656–7672 (2019).
[Crossref]

2018 (1)

F. Ye, J. Zhang, J. Xie, and D. Deng, “Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence,” Opt. Commun. 426, 456–462 (2018).
[Crossref]

2017 (4)

2016 (3)

2015 (1)

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through Bessel-Gauss-beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

2014 (2)

T. A. Vieira, M. Zamboni-Rached, and M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of Frozen Waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

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]

2012 (2)

2010 (1)

2006 (1)

Alkhazragi, O.

Ambrósio, L. A.

Backman, V.

Cheng, M.

Cheng, Q.

Cheng, W.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

Cui, Z.

Y. Li, Y. Han, Z. Cui, and Y. Hui, “Performance analysis of the OAM based optical wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. 21(3), 035702 (2019).
[Crossref]

Y. Li, Z. Cui, Y. Han, and Y. Hui, “Channel capacity of orbital-angular-momentum based wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. Soc. Am. A 36(4), 471–477 (2019).
[Crossref]

Deng, D.

C. Sun, X. Lv, B. Ma, J. Zhang, D. Deng, and W. Hong, “Statistical properties of partially coherent radially and azimuthally polarized rotating elliptical Gaussian beams in oceanic turbulence with anisotropy,” Opt. Express 27(8), A245–A256 (2019).
[Crossref]

F. Ye, J. Zhang, J. Xie, and D. Deng, “Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence,” Opt. Commun. 426, 456–462 (2018).
[Crossref]

Deng, S.

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

S. Deng, Y. Zhu, and Y. Zhang, “Received probability of vortex modes carried by localized wave of Bessel-Gaussian amplitude envelope in turbulent seawater,” JMSE 7(7), 203 (2019).
[Crossref]

Ding, W.

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

Dorrah, A. H.

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, T. A Vieira, M. R. R. Gesualdi, and M. Mojahedi, “Experimental demonstration of attenuation resistant frozen waves,” Laser Sources And Applications III 9893, 989311 (2016).
[Crossref]

Duan, Z.

Fewell, M. P.

Gao, Z.

Gesualdi, M. R. R.

A. H. Dorrah, M. Zamboni-Rached, T. A Vieira, M. R. R. Gesualdi, and M. Mojahedi, “Experimental demonstration of attenuation resistant frozen waves,” Laser Sources And Applications III 9893, 989311 (2016).
[Crossref]

T. A. Vieira, M. Zamboni-Rached, and M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of Frozen Waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37(11), 2034–2036 (2012).
[Crossref]

Gong, L.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, (Mathematics of Computation: 2007).

Gruska, J.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

Guo, L.

Guo, Y.

Han, Y.

Y. Li, Y. Han, Z. Cui, and Y. Hui, “Performance analysis of the OAM based optical wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. 21(3), 035702 (2019).
[Crossref]

Y. Li, Z. Cui, Y. Han, and Y. Hui, “Channel capacity of orbital-angular-momentum based wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. Soc. Am. A 36(4), 471–477 (2019).
[Crossref]

Hernández-Figueroa, H. E.

Hong, W.

Hu, L.

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

Huang, Q.

Huang, Y.

Hui, Y.

Y. Li, Y. Han, Z. Cui, and Y. Hui, “Performance analysis of the OAM based optical wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. 21(3), 035702 (2019).
[Crossref]

Y. Li, Z. Cui, Y. Han, and Y. Hui, “Channel capacity of orbital-angular-momentum based wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. Soc. Am. A 36(4), 471–477 (2019).
[Crossref]

Jones, B. H.

Kang, C.

Kong, M.

Korotkova, O.

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

Li, J.

Li, W.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

Li, Y.

Liang, Q.

Q. Liang, Y. Zhu, and Y. Zhang, “Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence,” Results Phys. 14, 102511 (2019).
[Crossref]

Liu, D.

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
[Crossref]

D. Liu, H. Yin, G. Wang, and Y. Wang, “Propagation of partially coherent Lorentz–Gauss vortex beam through oceanic turbulence,” Appl. Opt. 56(31), 8785–8792 (2017).
[Crossref]

Lv, X.

Ma, B.

Mojahedi, M.

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, T. A Vieira, M. R. R. Gesualdi, and M. Mojahedi, “Experimental demonstration of attenuation resistant frozen waves,” Laser Sources And Applications III 9893, 989311 (2016).
[Crossref]

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through Bessel-Gauss-beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

Ng, T. K.

Ooi, B. S.

Ouhssain, M.

Radosevich, A. J.

Rogers, J. D.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, (Mathematics of Computation: 2007).

Shan, L.

Shen, C.

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

Shi, H.

Sun, C.

Sun, X.

Trojan, A. V.

Vieira, T. A

A. H. Dorrah, M. Zamboni-Rached, T. A Vieira, M. R. R. Gesualdi, and M. Mojahedi, “Experimental demonstration of attenuation resistant frozen waves,” Laser Sources And Applications III 9893, 989311 (2016).
[Crossref]

Vieira, T. A.

T. A. Vieira, M. Zamboni-Rached, and M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of Frozen Waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37(11), 2034–2036 (2012).
[Crossref]

Wang, G.

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
[Crossref]

D. Liu, H. Yin, G. Wang, and Y. Wang, “Propagation of partially coherent Lorentz–Gauss vortex beam through oceanic turbulence,” Appl. Opt. 56(31), 8785–8792 (2017).
[Crossref]

Wang, L.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

W. Zhang, L. Wang, W. Wang, and S. Zhao, “Propagation property of Laguerre-Gaussian beams carrying fractional orbital angular momentum in an underwater channel,” OSA Continuum 2(11), 3281–3287 (2019).
[Crossref]

Wang, W.

Wang, Y.

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
[Crossref]

D. Liu, H. Yin, G. Wang, and Y. Wang, “Propagation of partially coherent Lorentz–Gauss vortex beam through oceanic turbulence,” Appl. Opt. 56(31), 8785–8792 (2017).
[Crossref]

Weng, Y.

Xie, J.

F. Ye, J. Zhang, J. Xie, and D. Deng, “Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence,” Opt. Commun. 426, 456–462 (2018).
[Crossref]

Yang, D.

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

D. Yang, Y. Zhang, and H. Shi, “Capacity of turbulent ocean links with carrier Bessel–Gaussian localized vortex waves,” Appl. Opt. 58(34), 9484–9490 (2019).
[Crossref]

Ye, F.

F. Ye, J. Zhang, J. Xie, and D. Deng, “Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence,” Opt. Commun. 426, 456–462 (2018).
[Crossref]

Yi, J.

Yi, X.

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

Yin, H.

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
[Crossref]

D. Liu, H. Yin, G. Wang, and Y. Wang, “Propagation of partially coherent Lorentz–Gauss vortex beam through oceanic turbulence,” Appl. Opt. 56(31), 8785–8792 (2017).
[Crossref]

Yu, L.

Yue, P.

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

Zamboni-Rached, M.

A. H. Dorrah, M. Zamboni-Rached, T. A Vieira, M. R. R. Gesualdi, and M. Mojahedi, “Experimental demonstration of attenuation resistant frozen waves,” Laser Sources And Applications III 9893, 989311 (2016).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through Bessel-Gauss-beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

T. A. Vieira, M. Zamboni-Rached, and M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of Frozen Waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37(11), 2034–2036 (2012).
[Crossref]

M. Zamboni-Rached, L. A. Ambrósio, and H. E. Hernández-Figueroa, “Diffraction–attenuation resistant beams: their higher order versions and finite-aperture generations,” Appl. Opt. 49(30), 5861 (2010).
[Crossref]

M. Zamboni-Rached, “Diffraction-Attenuation resistant beams in absorbing media,” Opt. Express 14(5), 1804–1809 (2006).
[Crossref]

Zhang, B.

Zhang, D.

Zhang, J.

C. Sun, X. Lv, B. Ma, J. Zhang, D. Deng, and W. Hong, “Statistical properties of partially coherent radially and azimuthally polarized rotating elliptical Gaussian beams in oceanic turbulence with anisotropy,” Opt. Express 27(8), A245–A256 (2019).
[Crossref]

F. Ye, J. Zhang, J. Xie, and D. Deng, “Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence,” Opt. Commun. 426, 456–462 (2018).
[Crossref]

Zhang, W.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

W. Zhang, L. Wang, W. Wang, and S. Zhao, “Propagation property of Laguerre-Gaussian beams carrying fractional orbital angular momentum in an underwater channel,” OSA Continuum 2(11), 3281–3287 (2019).
[Crossref]

Zhang, Y.

S. Deng, Y. Zhu, and Y. Zhang, “Received probability of vortex modes carried by localized wave of Bessel-Gaussian amplitude envelope in turbulent seawater,” JMSE 7(7), 203 (2019).
[Crossref]

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

Q. Liang, Y. Zhu, and Y. Zhang, “Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence,” Results Phys. 14, 102511 (2019).
[Crossref]

D. Yang, Y. Zhang, and H. Shi, “Capacity of turbulent ocean links with carrier Bessel–Gaussian localized vortex waves,” Appl. Opt. 58(34), 9484–9490 (2019).
[Crossref]

Y. Li, Y. Zhang, and Y. Zhu, “Oceanic spectrum of unstable stratification turbulence with outer scale and scintillation index of Gaussian-beam wave,” Opt. Express 27(5), 7656–7672 (2019).
[Crossref]

Y. Zhang, L. Shan, Y. Li, and L. Yu, “Effects of moderate to strong turbulence on the Hankel-Bessel-Gaussian pulse beam with orbital angular momentum in the marine atmosphere,” Opt. Express 25(26), 33469–33479 (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(11), 12203–12215 (2017).
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L. Yu and Y. Zhang, “Analysis of modal crosstalk for communication in turbulent ocean using Lommel-Gaussian beam,” Opt. Express 25(19), 22565–22574 (2017).
[Crossref]

Zhao, G.

Zhao, S.

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

W. Zhang, L. Wang, W. Wang, and S. Zhao, “Propagation property of Laguerre-Gaussian beams carrying fractional orbital angular momentum in an underwater channel,” OSA Continuum 2(11), 3281–3287 (2019).
[Crossref]

Zheng, R.

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

Zheng, Y.

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

Zhong, H.

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
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Zhu, Y.

S. Deng, Y. Zhu, and Y. Zhang, “Received probability of vortex modes carried by localized wave of Bessel-Gaussian amplitude envelope in turbulent seawater,” JMSE 7(7), 203 (2019).
[Crossref]

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Q. Liang, Y. Zhu, and Y. Zhang, “Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence,” Results Phys. 14, 102511 (2019).
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Appl. Opt. (5)

J. Lightwave Technol. (1)

J. Opt. (1)

Y. Li, Y. Han, Z. Cui, and Y. Hui, “Performance analysis of the OAM based optical wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence,” J. Opt. 21(3), 035702 (2019).
[Crossref]

J. Opt. Soc. Am. A (1)

JMSE (1)

S. Deng, Y. Zhu, and Y. Zhang, “Received probability of vortex modes carried by localized wave of Bessel-Gaussian amplitude envelope in turbulent seawater,” JMSE 7(7), 203 (2019).
[Crossref]

Laser Sources And Applications III (1)

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[Crossref]

Opt. Commun. (4)

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[Crossref]

X. Yi, R. Zheng, P. Yue, W. Ding, and C. Shen, “Propagation properties of OAM modes carried by partially coherent lg beams in turbulent ocean based on an oceanic power-law spectrum,” Opt. Commun. 443, 238–244 (2019).
[Crossref]

F. Ye, J. Zhang, J. Xie, and D. Deng, “Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence,” Opt. Commun. 426, 456–462 (2018).
[Crossref]

D. Liu, G. Wang, H. Yin, H. Zhong, and Y. Wang, “Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence,” Opt. Commun. 437, 346–354 (2019).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

OSA Continuum (1)

Phys. Rev. A (1)

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through Bessel-Gauss-beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

Results Phys. (2)

Q. Liang, Y. Zhu, and Y. Zhang, “Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence,” Results Phys. 14, 102511 (2019).
[Crossref]

S. Deng, D. Yang, Y. Zheng, L. Hu, and Y. Zhang, “Transmittance of finite-energy frozen beams in oceanic turbulence,” Results Phys. 15, 102802 (2019).
[Crossref]

Sci. Rep. (1)

S. Zhao, W. Zhang, L. Wang, W. Li, L. Gong, W. Cheng, and J. Gruska, “Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment,” Sci. Rep. 9(1), 1–8 (2019).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Transmittance ${T_I}$ of a random frozen photons beam transmitting in a turbulent ocean versus the propagation z and radial coordinate r for the different superimposing numbers M.
Fig. 2.
Fig. 2. Transmittance ${T_I}$ of a random frozen photons beam transmitting in a turbulent ocean versus the propagation z and radial coordinate r for the different beam waists ${w_0}$ in (a), (b), (c), (d) and for different OAM quantum numbers ${l_0}$ in (c), (e), (f).
Fig. 3.
Fig. 3. Transmittance ${T_I}$ of a random frozen photons beam in a turbulent ocean versus the propagation distance z and radial coordinate r for different equivalent “temperature structure” constants in (a), (b), (c) and versus the dissipation rate of the mean-squared temperature ${\chi _T}$ and the rate of dissipation of kinetic energy per unit mass of fluid $\varepsilon$ at $z\textrm{ = 30}$ and 330  m in (d).
Fig. 4.
Fig. 4. Light transmittance ${T_I}$ of a random frozen photons beam transmitting in a turbulent ocean versus the propagation z and radial coordinate r for the different ratio of temperature and salinity $\varpi $ .
Fig. 5.
Fig. 5. Light transmittance ${T_I}$ of a random frozen photons beam transmitting in a turbulent ocean versus the propagation z and radial coordinate r for the different inner scales ${\eta _0}$ and outer scales ${\eta _c}$ of turbulence.

Equations (25)

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u l 0 ( r , θ , z ) = E 0 B l 0 1 + i z / z z R z R exp [ i k ( r 2 2 R z  +  z 2 R z ) r 2 w z 2  + i l 0 θ ] × m = M M A m J l 0 ( α m r 1 + i z / z z R z R ) exp [ i β m ( z R z 1 ) z α m 2 k 2 w z 2 z 2 ]
α m = | 2 k | 1 β m R / β m R k R k R
u l 0 ( r , θ , z ) = E 0 B l 0 1 + i z / z z R z R exp [ i k ( r 2 2 R z  +  z 2 R z ) r 2 w z 2  + i Ψ ( r , θ , z )  + i l 0 θ ] × m = M M A ~ m J l 0 ( α m 1 + i z / z z R z R r ) exp [ ( n ¯ I n ¯ R i ) ( z R z 1 ) ( Q + 2 π m L ) z α m 2 z 2 k 2 w z 2 ]
| u l 0 ( r = r 0 , θ , z ) | 2 | F ( z ) | 2 ,
u l 0 ( r , θ , z ) E 0 B l 0 1 + i z / z z R z R exp [ i k ( r 2 2 R z  +  z 2 R z ) r 2 w 0 2 ( 1 z 2 z R 2 )  + i Ψ ( r , θ , z ) + i Q z + i l 0 θ ] × m = M M A ~ m J l 0 ( α m 1 + i z / z z R z R r ) exp [ ( Q + 2 π m L ) n ¯ I n ¯ R z α m 2 z 2 k 2 w 0 2 ] exp ( i 2 π m L z ) .
| F ( z ) | 2 E 0 2 w 0 2 ( k R 2 + k I 2 ) w 0 2 ( k R 2 + k I 2 ) + 4 z ( k R + z / w 0 2 ) exp [ i Ψ ( r 0 , θ , z ) i Ψ ( r 0 , θ , z ) ] × n = N N m = M M A ~ n A ~ m exp { 8 k I ( k R 2 k I 2 ) z w 0 4 ( k R 2 + k I 2 ) 2 ( z 2 + r 0 2 2 ) 2 r 0 2 w 0 2 [ 1 4 z 2 ( k R 2 k I 2 ) w 0 4 ( k R 2 + k I 2 ) 2 ] } × exp [ ( α m 2 + α n 2 ) ( k R 2 k I 2 ) + i 2 k R k I ( α n 2 α m 2 ) w 0 2 ( k R 2 + k I 2 ) 2 z 2 ] × exp [ i2 π ( m n ) z / L 2 ( Q + ( m n ) π / L ) n ¯ I z / n ¯ R ]
{ 8 k I ( k R 2 k I 2 ) z w 0 4 ( k R 2 + k I 2 ) 2 ( z 2 + r 0 2 2 ) 2 k I z ( z 2 | z R | 2 ) 0 4 z w 0 2 ( k R 2 + k I 2 ) ( k R + z w 0 2 ) 2 z | z R | + z 2 | z R | 2 0
| F ( z ) | 2 E 0 2 exp { 2 r 0 2 w 0 2 [ 1 4 z 2 ( k R 2 k I 2 ) w 0 4 ( k R 2 + k I 2 ) 2 ] } exp [ i Ψ ( r 0 , θ , z ) i Ψ ( r 0 , θ , z ) ] × n = N N m = M M A ~ n A ~ m exp [ ( α m 2 + α n 2 ) ( k R 2 k I 2 ) + i 2 k R k I ( α n 2 α m 2 ) w 0 2 ( k R 2 + k I 2 ) 2 z 2 ] × exp [ i2 π ( m n ) z / L 2 ( Q + ( m + n ) π / L ) z n ¯ I / n ¯ R ]
exp [ i Ψ ( r 0 , θ , z ) i Ψ ( r 0 , θ , z ) ] = exp ( r 0 2 / ρ oc 2 )
ρ o c  =  [ π 2 k 2 z 0 κ 3 Φ n ( κ ) d κ ] 1 / 2
Φ n ( κ ) = 1.69 C m 2 γ [ 1 + C 1 ( κ η ) 2 / 3 ] π ϖ 2 ( κ 2 + κ 0 2 ) 11 / 6 [ ϖ 2 exp ( κ 2 η 2 / R T 2 ) + d r 1 exp ( κ 2 η 2 / R S 2 ) ( 1 + d r 1 ) ϖ exp ( κ 2 η 2 / R T S 2 ) ] , 0 < κ < ,
d r = | ϖ | R F { 1 / ( 1 ( 1 1 / | ϖ | ) ) | ϖ | 1 1.85 | ϖ | 0.85 0.5 | ϖ | 1 , 0.15 | ϖ | | ϖ | 0.5
q
U ( μ + 1 2 ; μ 1 3 ; κ 0 2 κ H 2 ) = 1 κ 0 2 μ 8 / 3 Γ ( μ + 1 / 2 ) 0 κ 2 μ exp ( κ 2 / κ H 2 ) ( κ 0 2 + κ 2 ) 11 / 6 d κ ,
ρ o c = ( 169 ω 2 200 c 2 ( n ¯ r 2 + n ¯ i 2 ) π z γ C m 2 { κ 0 1 / 3 [ U ( 2 ; 7 6 ; κ 0 2 η 2 R T 2 ) + 1 d r ϖ 2 U ( 2 ; 7 6 ; κ 0 2 η 2 R S 2 ) 1 + d r ϖ d r U ( 2 ; 7 6 ; κ 0 2 η 2 R T S 2 ) ] + C 1 η 2 / 3 κ 0 Γ ( 7 3 ) [ U ( 7 3 ; 3 2 ; κ 0 2 η 2 R T 2 ) + 1 d r ϖ 2 U ( 7 3 ; 3 2 ; κ 0 2 η 2 R S 2 ) 1 + d r ϖ d r U ( 7 3 ; 3 2 ; κ 0 2 η 2 R T S 2 ) ] } ) 1 2 .
| F ( z ) | 2 E 0 2 exp { 2 r 0 2 w 0 2 [ 1 4 z 2 ( k R 2 k I 2 ) w 0 4 ( k R 2 + k I 2 ) 2 r 0 2 ρ o c 2 ] } n = N N m = M M A ~ n A ~ m exp [ i 2 π L ( m n ) z ] × exp [ 2 ( Q + m + n L π ) n ¯ I n ¯ R z ( α m 2 + α n 2 ) ( k R 2 k I 2 ) + i 2 k r k i ( α n 2 α m 2 ) w 0 2 ( k R 2 + k I 2 ) 2 z 2 ]
β m R β ¯ R  =  m = M M β m R 2 M + 1 = Q ,
β m I Q n ¯ I / n ¯ R = β 0 I , α m | 2 k | 1 β 0 I / k R = α 0 .
n = N N m = M M A ~ m A ~ n [ i 2 π L ( m n ) z ] | F ( z ) | 2 E 0 2 exp { 2 r 0 2 w 0 2 [ 1 4 z 2 ( k R 2 k I 2 ) w 0 4 ( k R 2 + k I 2 ) 2 ] + r 0 2 ρ o c 2 + 2 Q n ¯ I n ¯ R z + 2 α 0 2 ( k R 2 k I 2 ) w 0 2 ( k R 2 + k I 2 ) 2 z 2 }
A ~ m A ~ n = 1 L E 0 2 0 L | F ( z ) | 2 exp { [ 2 ( k R 2 k I 2 ) w 0 2 ( k R 2 + k I 2 ) 2 ( α 0 2 4 r 0 2 w 0 4 ) ] z 2 + 2 Q n ¯ I n ¯ R z + r 0 2 / ρ o c 2 i2 π ( m n ) z / L + 2 r 0 2 / w 0 2 } d z
A ~ m A ~ n = 1 L E 0 2 0 L | F ( z ) | 2 p = 0 [ 2 ( k R 2 k I 2 ) w 0 2 ( k R 2 + k I 2 ) 2 ( α 0 2 4 r 0 2 w 0 4 ) ] p ( z ) 2 p p ! × exp { [ 2 Q n ¯ I n ¯ R + r 0 2 ρ 0 2 i 2 π ( m n ) L ] z + 2 r 0 2 w 0 2 } d z
I ( r , θ , z ) = E 0 2 B l 0 2 1 + ( z / z z R z R ) 2 exp [ r 2 ρ o c 2 2 r 2 w z 2 ] n = N N m = M M A ~ n A ~ m J l 0 ( α m r 1 + i z / z z R z R ) J l 0 ( α n r 1 i z / z z R z R ) × exp { [ i 2 π L ( m n ) ( z R z 1 ) z + 2 n ¯ I n ¯ R ( Q + m + n L π ) ] ( z R z 1 ) z α m 2 + α n 2 k 2 w z 2 z 2 }
x h exp ( a x b ) d x = exp ( a x b ) b [ ( γ 1 ) ! q = 0 γ 1 ( 1 ) ( q + 1 γ ) x b q q ! a γ q ] , ( a 0 , γ = h + 1 b = 1 , 2 , ) ,
A ~ m A ~ n = F 0 L E 0 2 p = 0 [ 2 ( k R 2 k I 2 ) w 0 2 ( k R 2 + k I 2 ) 2 ( α 0 2 4 r 0 2 w 0 4 ) ] p ( 2 p ) ! p ! × exp { [ 2 Q n ¯ I n ¯ R + r 0 2 ρ 0 2 i 2 π ( m n ) L ] L } q = 0 2 p ( 1 ) ( q 2 p ) L q q ! a 2 p + 1 q
I ( r , θ , z ) = F 0 B l 0 2 L [ 1 + ( z / z z R z R ) 2 ] exp [ r 2 ρ o c 2 2 r 2 w z 2 ] × n = N N m = M M J l 0 ( α m r 1 + i z / z z R z R ) J l 0 ( α n r 1 i z / z z R z R ) p = 0 [ 2 ( k R 2 k I 2 ) w 0 2 ( k R 2 + k I 2 ) 2 ( α 0 2 4 r 0 2 w 0 4 ) ] p ( 2 p ) ! p ! × exp [ ( 2 Q n ¯ I n ¯ R + r 0 2 ρ 0 2 i 2 π ( m n ) L ) L ] q = 0 2 p ( 1 ) ( q 2 p ) L q q ! a 2 p + 1 q × exp { [ i 2 π L ( m n ) ( z R z 1 ) z + 2 n ¯ I n ¯ R ( Q + m + n L π ) ] ( z R z 1 ) z α m 2 + α n 2 k 2 w z 2 z 2 }

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