[1] BRAUNBEK W, LAUKIEN G. Features of refraction by a semi-plane[J]. Optik, 1952, 9: 174-179.
[2] BERRY M, DENNIS M, SOSKIN M. The plurality of optical singula-rities[J]. Journal of Optics, 2004, A6(5): S155-S156.
[3] DESYATNIKOV A S, TORNER L, KIVSHAR Y S. Optical vortices and vortex solitons[J]. Progress in Optics, 2005, 47: 291-391.
[4] KAUSHAL H, KADDOUM G. Optical communication in space: Cha-llenges and mitigation techniques[J]. IEEE Communications Surveys & Tutorials, 2017, 19(1): 57-96.
[5] 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
[6] DU J, WANG J. High-dimensional structured light coding/decoding for free-space optical communications free of obstructions[J]. Optics Letters, 2015, 40(21): 4827-4830. doi: 10.1364/OL.40.004827
[7] FANTE R L. Electromagnetic beam propagation in turbulent media[J]. IEEE Proceedings, 1975, 63(12): 1669-1692. doi: 10.1109/PROC.1975.10035
[8] KIM I I, WOODBRIDGE E L, CHAN V J, et al. Scintillation mea-surements performed during the limited-visibility lasercom experiment[J]. Proceedings of the SPIE, 1998, 3266: 209-220. doi: 10.1117/12.308709
[9] YANG Y J, DONG Y, ZHAO Ch L, et al. Generation and propagation of an anomalous vortex beam[J]. Optics Letters, 2013, 38(24): 5418-5421. doi: 10.1364/OL.38.005418
[10] YUAN Y P, YANG Y J. Propagation of anomalous vortex beams through an annular apertured paraxial ABCD optical system[J]. Optical and Quantum Electronics, 2015, 47(7): 2289-2297. doi: 10.1007/s11082-014-0105-y
[11] XU Y G, WANG S J. Characteristic study of anomalous vortex beam through a paraxial optical system[J]. Optics Communications, 2014, 331: 32-38. doi: 10.1016/j.optcom.2014.05.054
[12] TOSELLI I. Introducing the concept of anisotropy at different scales for modeling optical turbulence[J]. Journal of the Optical Society of America, 2014, A31(8): 1868-1875.
[13] XU Y G, DAN Y Q. Statistical properties of electromagnetic anomalous vortex beam with orbital angular momentum in atmospheric turbulence[J]. Optik, 2019, 179: 654-664. doi: 10.1016/j.ijleo.2018.10.194
[14] GBUR G, TYSON R K. Vortex beam propagation through atmospheric turbulence and topological charge conservation[J]. Journal of the Optical Society of America, 2008, A25(1): 225-230.
[15] ZENG J, CHEN Y H, LIU X L, et al. Research progress of partially coherent vortex beams[J]. Acta Optica Sinica, 2019, 39(1): 0126004(in Chinese). doi: 10.3788/AOS201939.0126004
[16] WANG Y, LI Ch Q, WANG T F, et al. The effects of polarization changes of stochastic electromagnetic beams on heterodyne detection in turbulence[J]. Laser Physics Letters, 2016, 13(11): 116006. doi: 10.1088/1612-2011/13/11/116006
[17] SHCHEPAKINA E, KOROTKOVA O. Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence[J]. Optics Express, 2010, 18(10): 10650-10658. doi: 10.1364/OE.18.010650
[18] WANG F, CAI Y, EYYUBOGLU H T, et al. Partially coherent elegant Hermite-Gaussian beam in turbulent atmosphere[J]. Applied Physics, 2011, B103(2): 461-469. doi: 10.1007/s00340-010-4219-z
[19] XU Y G, TIAN H H, FENG H, et al. Propagation factors of standard and elegant Laguerre Gaussian beams in non-Kolmogorov turbulence[J]. Optik, 2016, 127(22): 10999-11008. doi: 10.1016/j.ijleo.2016.09.019
[20] XU H F, LUO H, CUI Zh F, et al. Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence[J]. Optics and Lasers in Engineering, 2012, 50(5): 760-766. doi: 10.1016/j.optlaseng.2011.12.002
[21] XU Y G, DAN Y Q, YU J Y, et al. Propagation properties of partially coherent dark hollow beam in inhomogeneous atmospheric turbulence[J]. Journal of Modern Optics, 2016, 63(21): 2186-2197. doi: 10.1080/09500340.2016.1187308
[22] XU Y G, TIAN H H, YANG T, et al. Propagation characteristics of partially coherent flat-topped beams propagating through inhomogeneous atmospheric turbulence[J]. Applied Optics, 2017, 56(10): 2691-2696. doi: 10.1364/AO.56.002691
[23] SHIRAI T, DOGARIU A, WOLF E. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence[J]. Journal of the Optical Society of America, 2003, A20(6): 1094-1102.
[24] YUAN Y Sh, CAI Y J, QU J, et al. M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere[J]. Optics Express, 2009, 17(20): 17344-17356. doi: 10.1364/OE.17.017344
[25] CARTER W H. Spot size and divergence for Hermite Gaussian beams of any order[J]. Applied Optics, 1980, 19(7): 1027-1029. doi: 10.1364/AO.19.001027
[26] CHENG P P, QU J, ZHOU Zh X, et al. Beam wander of array beams propagating through anisotropic turbulent atmosphere[J]. Chinese Journal of Quantum Electronics, 2019, 36(3): 270-277(in Chinese).
[27] XU Y G, TIAN H H, DAN Y Q, et al. Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence[J]. Journal of Modern Optics, 2017, 64(8): 844-854. doi: 10.1080/09500340.2016.1262073
[28] TIAN H H, XU Y G, YANG T, et al. Beam wander of partially coherent anomalous elliptical hollow Gaussian beam propagating through non-Kolmogorov turbulence[J]. Laser & Optoelectronics Progress, 2017, 54(5): 050103(in Chinese).
[29] YU J Y, ZHU X L, WANG F, et al. Experimental study of reducing beam wander by modulating the coherence structure of structured light beams[J]. Optics Letters, 2019, 44(17): 4371-4374. doi: 10.1364/OL.44.004371