| [1] | 
				
					GÖKÇE M C, BAYKAL Y. Scintillation analysis of multiple-input single-output underwater optical links[J]. Applied Optics, 2016, 55(22): 6130-6136. doi:  10.1364/AO.55.006130
					 | 
			
		
				| [2] | 
				
					ISHIMARU A. Wave Propagation and Scattering in Random Media[M]. New York: Academic Press, 1978.
					 | 
			
		
				| [3] | 
				
					HOU W L. A simple underwater imaging model[J]. Optics Letters, 2009, 34(17): 2688-2690. doi:  10.1364/OL.34.002688
					 | 
			
		
				| [4] | 
				
					LUO B, WU G H, YIN L F, et al. Propagation of optical coherence lattices in oceanic turbulence[J]. Optics Communications, 2018, 425: 80-84. doi:  10.1016/j.optcom.2018.04.076
					 | 
			
		
				| [5] | 
				
					ATA Y, BAYKAL Y. Effect of anisotropy on bit error rate for an asymmetrical Gaussian beam in a turbulent ocean[J]. Applied Optics, 2018, 57(9): 2258-2262. doi:  10.1364/AO.57.002258
					 | 
			
		
				| [6] | 
				
					JOHNSON L J, GREEN R J, LEESON M S. Underwater optical wireless communications: depth dependent variations in attenuation[J]. Applied Optics, 2013, 52(33): 7867-7873. doi:  10.1364/AO.52.007867
					 | 
			
		
				| [7] | 
				
					CHENG M J, GUO L X, LI J T, et al. Channel capacity of the OAM-based free-space optical communication links with Bessel-Gauss beams in turbulent ocean[J]. IEEE Photonics Journal, 2016, 8(1): 7901411.
					 | 
			
		
				| [8] | 
				
					ZHAO SH M, WANG L, ZOU L, et al. Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing[J]. Optics Communications, 2016, 376: 92-98. doi:  10.1016/j.optcom.2016.04.075
					 | 
			
		
				| [9] | 
				
					WANG ZH Q, ZHANG P F, QIAO C H, et al. Scintillation index of Gaussian waves in weak turbulent ocean[J]. Optics Communications, 2016, 380: 79-86. doi:  10.1016/j.optcom.2016.05.089
					 | 
			
		
				| [10] | 
				
					LU T F, ZHANG K N, WU Z J, et al. Propagation properties of elliptical vortex beams in turbulent ocean[J]. Chinese Optics, 2020, 13(2): 323-332. (in Chinese) doi:  10.3788/co.20201302.0323
					 | 
			
		
				| [11] | 
				
					LI Y, ZHANG Y X, ZHU Y. Oceanic spectrum of unstable stratification turbulence with outer scale and scintillation index of Gaussian-beam wave[J]. Optics Express, 2019, 27(5): 7656-7672. doi:  10.1364/OE.27.007656
					 | 
			
		
				| [12] | 
				
					EYYUBOĞLU H T. Apertured averaged scintillation of fully and partially coherent Gaussian, annular Gaussian, flat toped and dark hollow beams[J]. Optics Communications, 2015, 339: 141-147. doi:  10.1016/j.optcom.2014.11.070
					 | 
			
		
				| [13] | 
				
					BAYKAL Y. Higher order mode laser beam scintillations in oceanic medium[J]. Waves in Random and Complex Media, 2016, 26(1): 21-29. doi:  10.1080/17455030.2015.1099760
					 | 
			
		
				| [14] | 
				
					BAYKAL Y. Scintillation index in strong oceanic turbulence[J]. Optics Communications, 2016, 375: 15-18. doi:  10.1016/j.optcom.2016.05.002
					 | 
			
		
				| [15] | 
				
					GERÇEKCIOĞLU H. Bit error rate of focused Gaussian beams in weak oceanic turbulence[J]. Journal of the Optical Society of America A, 2014, 31(9): 1963-1968. doi:  10.1364/JOSAA.31.001963
					 | 
			
		
				| [16] | 
				
					ATA Y, BAYKAL Y. Scintillations of optical plane and spherical waves in underwater turbulence[J]. Journal of the Optical Society of America A, 2014, 31(7): 1552-1556. doi:  10.1364/JOSAA.31.001552
					 | 
			
		
				| [17] | 
				
					YI X, LI Z, LIU Z J. Underwater optical communication performance for laser beam propagation through weak oceanic turbulence[J]. Applied Optics, 2015, 54(6): 1273-1278. doi:  10.1364/AO.54.001273
					 | 
			
		
				| [18] | 
				
					YOUSEFI M, KASHANI F D, GOLMOHAMMADY S, et al. Scintillation and bit error rate analysis of a phase-locked partially coherent flat-topped array laser beam in oceanic turbulence[J]. Journal of the Optical Society of America A, 2017, 34(12): 2126-2137. doi:  10.1364/JOSAA.34.002126
					 | 
			
		
				| [19] | 
				
					CUI Z M, YUE P, Yi X, et al. Scintillation of a partially coherent beam with pointing errors resulting from a slightly skewed underwater platform in oceanic turbulence[J]. Applied Optics, 2019, 58(16): 4443-4449. doi:  10.1364/AO.58.004443
					 | 
			
		
				| [20] | 
				
					BRAMBILLA M, BATTIPEDE F, LUGIATO L A, et al. Transverse laser patterns. I. Phase singularity crystals[J]. Physical Review A, 1991, 43(9): 5090-5113. doi:  10.1103/PhysRevA.43.5090
					 | 
			
		
				| [21] | 
				
					BEIJERSBERGEN M W, ALLEN L, VAN DER VEEN H E L O, et al. Astigmatic laser mode converters and transfer of orbital angular momentum[J]. Optics Communications, 1993, 96(1-3): 123-132. doi:  10.1016/0030-4018(93)90535-D
					 | 
			
		
				| [22] | 
				
					TAO S H, YUAN X C, LIN J, et al. Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams[J]. Journal of Applied Physics, 2006, 100(4): 043105. doi:  10.1063/1.2260823
					 | 
			
		
				| [23] | 
				
					FRIESE M E J, RUBINSZTEIN-DUNLOP H, GOLD J, et al. Optically driven micromachine elements[J]. Applied Physics Letters, 2001, 78(4): 547-549. doi:  10.1063/1.1339995
					 | 
			
		
				| [24] | 
				
					GIBSON G, COURTIAL J, PADGETT M J, et al. Free-space information transfer using light beams carrying orbital angular momentum[J]. Optics Express, 2004, 12(22): 5448-5456. doi:  10.1364/OPEX.12.005448
					 | 
			
		
				| [25] | 
				
					XU J, ZHAO D M. Propagation of a stochastic electromagnetic vortex beam in the oceanic turbulence[J]. Optics &Laser Technology, 2014, 57: 189-193.
					 | 
			
		
				| [26] | 
				
					LIU ZH L, CHEN J L, ZHAO D M. Experimental study of propagation properties of vortex beams in oceanic turbulence[J]. Applied Optics, 2017, 56(12): 3577-3582. doi:  10.1364/AO.56.003577
					 | 
			
		
				| [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, 2019, 48(12): 1214004. (in Chinese) doi:  10.3788/gzxb20194812.1214004
					 | 
			
		
				| [28] | 
				
					EYYUBOĞLU H T. Estimation of aperture averaged scintillations in weak turbulence regime for annular, sinusoidal and hyperbolic Gaussian beams using random phase screen[J]. Optics &Laser Technology, 2013, 52: 96-102.
					 |