[1] Wei Y, Yu Y H, Hei X B et al. Application of vortex beam and photon counting in underwater optical communication[J]. Laser & Optoelectronics Progress, 59, 1301001(2022).

[2] Tang J W, Zhu P Z, Liu B Y et al. Polarized light scattering of particulate matter in detection of oceanographic profiling LiDAR[J]. Acta Optica Sinica, 42, 1200001(2022).

[3] Wang M J, Zhang J L, Wang Z Y et al. Scattering of Laguerre-Gaussian vortex beams by underwater suspended spherical algal particle swarms[J]. Acta Optica Sinica, 42, 1829001(2022).

[4] Liu D J, Wang G Q, Yin H et al. Propagation properties of a partially coherent anomalous hollow vortex beam in underwater oceanic turbulence[J]. Optics Communications, 437, 346-354(2019).

[5] Liu X Y, Zhou G Q, Shen Y T. Effect of oceanic turbulence with anisotropy on the propagation of multi-sinc Schell-model beams[J]. Results in Physics, 36, 105447(2022).

[6] Ata Y, Baykal Y. Scintillations of optical plane and spherical waves in underwater turbulence[J]. Journal of the Optical Society of America A, 31, 1552-1556(2014).

[7] Wang Z Q, Zhang P F, Qiao C H et al. Scintillation index of Gaussian waves in weak turbulent ocean[J]. Optics Communications, 380, 79-86(2016).

[8] Farwell N, Korotkova O. Intensity and coherence properties of light in oceanic turbulence[J]. Optics Communications, 285, 872-875(2012).

[9] Zhang J L, Kou L L, Yang Y et al. Monte-Carlo-based optical wireless underwater channel modeling with oceanic turbulence[J]. Optics Communications, 475, 126214(2020).

[10] Liu N, Ke J Y, Yang S H et al. Simulation and analysis on underwater transmission characteristics of Gaussian pulse lasers with carrier modulation[J]. Acta Optica Sinica, 38, 0401003(2018).

[11] Li K, Yang S H, Liao Y Q et al. Underwater ranging with intensity modulated 532 nm laser source[J]. Acta Physica Sinica, 70, 084203(2021).

[12] Coullet P, Gil L, Rocca F. Optical vortices[J]. Optics Communications, 73, 403-408(1989).

[13] Ma Z Y, Chen K, Zhang M M et al. Propagation characteristics of Laguerre-Gaussian power-exponent-phase-vortex beams[J]. Acta Optica Sinica, 42, 0526001(2022).

[14] Wang L Y, Ma J T, Xiao M et al. Application of optical orbital angular momentum to rotation measurements[J]. Results in Optics, 5, 100158(2021).

[15] Jiang Y X, Li Z H. Monte Carlo simulation of Mueller matrix of randomly rough surfaces[J]. Optics Communications, 474, 126113(2020).

[16] Freund I. Joseph W. Goodman: speckle phenomena in optics: theory and applications[J]. Journal of Statistical Physics, 130, 413-414(2008).

[17] Ogilvy J A, Merklinger H M. Theory of wave scattering from random rough surfaces[J]. The Journal of the Acoustical Society of America, 90, 3382(1991).

[18] Liu M. Distribution properties of intensity and phase of speckle fields produced by vortex beam[J]. Acta Optica Sinica, 34, 1126001(2014).

[19] Liu M, Song H S, Chen X Y et al. Intensity distribution and phase vortices of speckle fields generated by multi-aperture random scattering screens[J]. Chinese Physics Letters, 27, 034202(2010).

[20] Holmes J F, Lee M H, Kerr J R. Effect of the log-amplitude covariance function on the statistics of speckle propagation through the turbulent atmosphere[J]. Journal of the Optical Society of America A, 70, 355-360(1980).

[21] Cui C, Wang Z, Zhan X K et al. Measurement of the adjustable slight roughness emulated by a spatial light modulator employing the vortex beam speckle pattern[J]. Applied Optics, 59, 3630-3635(2020).

[22] Li Y Q, Wu Z S. Statistical characteristics of a Gaussian beam reflected by a retro-reflector in atmospheric turbulence[J]. Optik, 158, 1361-1369(2018).

[23] Li Y Q, Wang L G, Wu Z S. Numerical simulation for echo characteristics of laser beams reflected by retro-reflectors in atmospheric turbulence[J]. Optik, 179, 244-251(2019).

[24] Li Y Q, Wang L G, Gong L et al. Speckle characteristics of vortex beams scattered from rough targets in turbulent atmosphere[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 257, 107342(2020).

[25] Li Y L, Mei H P, Ren Y C et al. Simulation of spatial coherence of laser echo light field from random rough surface in turbulent atmosphere[J]. Acta Physica Sinica, 71, 140201(2022).

[26] Zhang K N, Liu Y X, Pu J X. Scintillation index of vortex beams propagating in oceanic turbulence[J]. Chinese Journal of Lasers, 46, 0705001(2019).

[27] Lu T F, Liu Y X, Pu J X. Experimental study on scintillation index of vortex beam propagation in underwater turbulence[J]. Acta Photonica Sinica, 48, 1214004(2019).

[28] Pan S X, Zhao S M, Wang L et al. Experimental investigation of underwater propagation characteristics of orbital angular momentum[J]. Acta Optica Sinica, 38, 0606004(2018).

[29] Allen L, Beijersbergen M W, Spreeuw R J et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 45, 8185-8189(1992).

[30] Li X Q, Zhao Q, Ji X L. Confirmation of the quadratic approximation of Rytov phase structure function and the approximation of complex Gaussian-function expansion of hard-edge apertures[J]. Acta Optica Sinica, 31, 1201002(2011).

[31] Pan Y Q, Zhao M L, Zhang M M et al. Propagation properties of rotationally-symmetric power-exponent-phase vortex beam through oceanic turbulence[J]. Optics & Laser Technology, 159, 109024(2023).

[32] Wang L G, Gao M, Li Y Q et al. Intensity fluctuations of reflected wave from a diffuse target with a hard edge in atmospheric turbulence[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 195, 141-146(2017).

[33] Xiang N J, Wu Z S, Guo Q F et al. Backscatter amplification effect for a reflected partially coherent Gaussian beam in turbulent medium[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 163, 1-6(2015).

[34] Cheng M J, Guo L X, Li J T et al. Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean[J]. Applied Optics, 55, 4642-4648(2016).

[35] Gradshteyn I S, Ryzhik I M[M]. Table of integrals, series, and products(2007).

[36] Wang L G, Wu Z S, Wang M J. Second-order statistics for wave reflected by a plane mirror with a finite aperture[J]. Acta Optica Sinica, 33, 1101001(2013).