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Recently, the laser beam propagation in the oceanic turbulence has become a hot research topic. In addition to the characteristics of free diffraction and self-reconstruction, the high-order Bessel-Gaussian beam is a kind of typical vortex beam because of the existence of a spiral phase factor with orbital angular momentum. Researchers have investigated the self-reconstruction property of the high-order Bessel-Gaussian beams in the free space, also carried out intensive researches on the transmission characteristics of high-order Bessel-Gaussian beam in the ABCD optical system and in the atmospheric turbulence. However, to the best of our knowledge, to date there has been no investigation on the propagation of this laser beam in the oceanic turbulence. In this paper, we will study the propagation characteristics of the random electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence, and discuss the variation of the normalized spectrum intensity, the spectral degree of polarization, and the spectral degree of coherence. By using the extended Huygens-Fresnel diffraction integral formula, the general expression for the cross spectral density matrix of the stochastic electromagnetic high-order Bessel-Gaussian beams propagating in the oceanic turbulence is obtained, and the statistical properties of the random electromagnetic high-order Bessel-Gaussian beams propagating in the seawater are investigated by numerical calculation. The numerical results show that the oceanic turbulence can affect the normalized spectral intensity distribution of the random electromagnetic beam. With the increase of the transmission distance, the center of the zero-order Bessel-Gaussian beam becomes depressed, and the center of the higher-order Bessel-Gaussian beam will become flat and then depressed. As the transmission distance increases far enough, regardless of the zero-order or higher-order, the intensity distribution will eventually evolve into the quasi Gaussian shaped distribution. The variation of the degree of polarization of each point on the x axis is related to the coherence length (xx，yy) and the oceanic turbulence parameters. The spectral coherence of the origin and any point on the x axis also changes with the increase of x, and the rate of dissipation of mean-square temperature T has influence on the spectral coherence. This research is of great value for applying the high-order Bessel-Gaussian beam to the optical communication, optical imaging and underwater exploration in the ocean.
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Keywords:
- oceanic turbulence /
- stochastic electromagnetic beam /
- high order Bessel-Gaussian beam /
- propagation
[1] Korotkova O, Farwell N 2011 Opt. Commun. 284 1740
[2] Shchepakina E, Farwell N, Korotkova O 2011 Appl. Phys. B 105 415
[3] Farwell N, Korotkova O 2012 Opt. Commun. 285 872
[4] Fu W Y, Zhang H M 2013 Opt. Commun. 304 11
[5] Fu W Y, Zhang H M, Zheng X R 2015 Chin. J. Lasers 42 s113002 (in Chinese) [付文羽, 张汉谋, 郑兴荣 2015 中国激光 42 s113002]
[6] Tang M M, Zhao D M 2013 Appl. Phys. B 111 665
[7] Xu J, Tang M M, Zhao D M 2014 Opt. Commun. 331 1
[8] Xu J, Zhao D M 2014 Opt. Laser Technol. 57 189
[9] Tang M M, Zhao D M 2014 Opt. Commun. 312 89
[10] Zhu W T, Tang M M, Zhao D M 2016 Optik 127 3775
[11] Lu L, Ji X L, Li X Q, Deng J P, Chen H, Yang T 2014 Optik 125 7154
[12] Yang T, Ji X L, Li X Q 2015 Acta Phys. Sin. 64 024206 (in Chinese) [杨婷, 季小玲, 李晓庆 2015 64 024206]
[13] Huang Y P, Huang P, Wang F, Zhao G, Zeng A 2015 Opt. Commun. 336 146
[14] Liu D J, Wang Y C, Wang G Q, Yin H M, Wang J R 2016 Opt. Laser Technol. 82 76
[15] Liu D J, Chen L, Wang Y C, Wang G Q, Yin H M 2016 Optik 127 6961
[16] Liu D J, Wang Y R, Yin H M 2015 Appl. Opt. 54 10510
[17] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. Sin.: Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011 中国科学: 物理学 力学 天文学 41 1131]
[18] Chen B S, Chen Z Y, Pu J X 2008 Opt. Laser Technol. 40 820
[19] Chen Z Y, Cui S W, Zhang L, Sun C Z, Xiong M S, Pu J X 2014 Opt. Express 22 18278
[20] Zhao C L, Wang L G, Lu X H, Chen H 2007 Opt. Laser Technol. 39 1199
[21] Eyyuboglu H T 2007 Appl. Phys. B 88 259
[22] Nikishov V V, Nikishov V I 2000 Int. J. Fluid Mech. Res. 27 82
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[1] Korotkova O, Farwell N 2011 Opt. Commun. 284 1740
[2] Shchepakina E, Farwell N, Korotkova O 2011 Appl. Phys. B 105 415
[3] Farwell N, Korotkova O 2012 Opt. Commun. 285 872
[4] Fu W Y, Zhang H M 2013 Opt. Commun. 304 11
[5] Fu W Y, Zhang H M, Zheng X R 2015 Chin. J. Lasers 42 s113002 (in Chinese) [付文羽, 张汉谋, 郑兴荣 2015 中国激光 42 s113002]
[6] Tang M M, Zhao D M 2013 Appl. Phys. B 111 665
[7] Xu J, Tang M M, Zhao D M 2014 Opt. Commun. 331 1
[8] Xu J, Zhao D M 2014 Opt. Laser Technol. 57 189
[9] Tang M M, Zhao D M 2014 Opt. Commun. 312 89
[10] Zhu W T, Tang M M, Zhao D M 2016 Optik 127 3775
[11] Lu L, Ji X L, Li X Q, Deng J P, Chen H, Yang T 2014 Optik 125 7154
[12] Yang T, Ji X L, Li X Q 2015 Acta Phys. Sin. 64 024206 (in Chinese) [杨婷, 季小玲, 李晓庆 2015 64 024206]
[13] Huang Y P, Huang P, Wang F, Zhao G, Zeng A 2015 Opt. Commun. 336 146
[14] Liu D J, Wang Y C, Wang G Q, Yin H M, Wang J R 2016 Opt. Laser Technol. 82 76
[15] Liu D J, Chen L, Wang Y C, Wang G Q, Yin H M 2016 Optik 127 6961
[16] Liu D J, Wang Y R, Yin H M 2015 Appl. Opt. 54 10510
[17] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. Sin.: Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011 中国科学: 物理学 力学 天文学 41 1131]
[18] Chen B S, Chen Z Y, Pu J X 2008 Opt. Laser Technol. 40 820
[19] Chen Z Y, Cui S W, Zhang L, Sun C Z, Xiong M S, Pu J X 2014 Opt. Express 22 18278
[20] Zhao C L, Wang L G, Lu X H, Chen H 2007 Opt. Laser Technol. 39 1199
[21] Eyyuboglu H T 2007 Appl. Phys. B 88 259
[22] Nikishov V V, Nikishov V I 2000 Int. J. Fluid Mech. Res. 27 82
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