[1] [1] SHIRAI T, DOGARIU A, WOLF E. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence[J]. J Opt Soc Am A, 2003, 20(6):1094-1102. DOI: 10.1364/JOSAA.20.001094.

[2] [2] PADGETT M, BOWMAN R. Tweezers with a twist[J]. Nat Photonics, 2011, 5:343-348. DOI: https://doi.org/10.1038/nphoton.2011.81.

[3] [3] D’AMBROSIO V, NAGALI E, WALBORN S P, et al. Complete experimental toolbox for alignment-free quantum communication[J]. Nat Commun, 2012, 3:961. DOI: https://doi.org/10.1038/ncomms1951.

[4] [4] BASTIAANS M J. Application of the Wigner distribution function to partially coherent light[J]. J Opt Soc Am A, 1986, 3(8):1227-1238. DOI: https://doi.org/10.1364/JOSAA.3.001227.

[5] [5] YUAN Y, CAI Y, QU J, et al. M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere[J]. Opt Express, 2009, 17(20):17344-17356. DOI: https://doi.org/10.1364/OE.17.017344.

[6] [6] YUAN Y, CAI Y, EYYUBOLU H T, et al. Propagation factor of partially coherent flat-topped beam array in free space and turbulent atmosphere[J]. Opt Laser Eng, 2012, 50(5):752-759. DOI: https://doi.org/10.1016/j.optlaseng.2011.12.003.

[7] [7] XU Y, TIAN H, DAN Y, et al. Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence[J]. J Mod Optics, 2017, 64(8):844-854. DOI: 10.1080/09500340.2016.1262073.

[8] [8] SONG Z, LIU Z, ZHOU K, et al. Propagation factor of electromagnetic concentric rings Schell-model beams in non-Kolmogorov turbulence[J]. Chin Phys B, 2017, 26(2):024201. DOI: 10.1088/1674-1056/26/2/024201.

[9] [9] ZHONG Y, CUI Z, SHI J, et al. Propagation properties of partially coherent Laguerre-Gaussian beams in turbulent atmosphere[J]. Opt Lasser Technol, 2011, 43(4):741-747. DOI: 10.1016/j.optlastec.2010.07.015.

[10] [10] ZHU K, LI S, TANG Y, et al. Study on the propagation parameters of Bessel-Gaussian beams carrying optical vortices through atmospheric turbulence[J]. J Opt Soc Am A, 2012, 29(3):251-257. DOI: https://doi.org/10.1364/JOSAA.29.000251.

[11] [11] JI G, JI X. Effective radius of curvature of Hermite-Gaussian array beams[J]. Opt Lasser Technol, 2010, 42(6):1054-1058. DOI: 10.1016/j.optlastec.2010.01.030.

[12] [12] JI X, EYYUBOGLU H T, BAYKAL Y. Influence of turbulence on the effective radius of curvature of radial Gaussian array beams[J]. Opt Express, 2010, 18(7):6922-6928. DOI: 10.1364/OE.18.006922.

[13] [13] EYYUBOGLU H T, JI X.Radius of curvature of Bessel and modified Bessel Gaussian beams[J]. Opt Commun, 2013, 298:30-33. DOI: https://doi.org/10.1016/j.optcom.2013.02.039.

[14] [14] HUANG Y, HUANG P, WANG F, et al. The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite-Gaussian linear array beams[J]. Opt Commun, 2015, 336:146-152. DOI: https://doi.org/10.1016/j.optcom.2014.09.055.

[15] [15] HUANG X, BAI Y, FU X. Propagation Factors of Partially Coherent Model Beams in Oceanic Turbulence[J]. IEEE Photonics Journal, 2017, 9(5):1-11. DOI: 10.1109/JPHOT.2017.2747601.

[16] [16] ALEXEY A K, VICTOR V K. Family of three-dimensional asymmetric nonparaxial Lommel modes[J]. Proc SPIE, 2015, 9448:944828.

[17] [17] ZAHID M, ZUBAIRY M S. Directionality of partially coherent Bessel-Gauss beams[J]. Opt Commun, 1989, 70(5):361-364. DOI: https://doi.org/10.1016/0030-4018(89)90131-4.

[18] [18] DAN Y, ZHANG B. Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere[J]. Opt Express, 2008, 16(20):15563-15575. DOI: 10.1364/OE.16.015563.

[19] [19] LI J, WANG W, DUAN M, et al. Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams[J]. Opt Express, 2016, 24(18):20413-20423. DOI: https://doi.org/10.1364/OE.24.020413.

[20] [20] DU S, YUAN Y, LIANG C, et al. Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere[J]. Opt Laser Technol, 2013, 50:14-19. DOI: https://doi.org/10.1016/j.optlastec.2013.01.027.

[21] [21] WEN W, WANG Z, QIAO C. Beam propagation quality factor of Airy laser beam in oceanic turbulence[J]. Optik, 2022, 252:168428. DOI: https://doi.org/10.1016/j.ijleo.2021.168428.

[22] [22] ZHANG B, XU Y, WANG X, et al. Propagation factor and beam wander of electromagnetic Gaussian Schell-model array beams in non-Kolmogorov turbulence[J]. OSA Continuum, 2019, 2:162-174. DOI: 10.1364/OSAC.2.000162.

[23] [23] BORGHI R, SANTARSIERO M. M2 factor of Bessel-Gauss beams[J]. Opt Lett, 1997, 22(5):262-264. DOI: https://doi.org/10.1364/OL.22.000262.