[1] YOUNG C Y, GILCHREST Y V, MACON B R. Turbulenceinduced beam spreading of higherorder mode optical waves［J］. Optical Engineering, 2002, 41(5): 1097103.

[2] EYYUBOLU H T. Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence［J］. Optics & Laser Technology , 2008, 40(1): 15666.

[3] BAYKAL Y. Formulation of correlations for generaltype beams in atmospheric turbulence［J］. JOSA A, 2006, 23(4): 88993.

[4] DAN Y, ZHANG B. Beam propagation factor of partially coherent flattopped beams in a turbulent atmosphere［J］. Optics Express, 2008, 16(20): 1556374.

[5] DAN Y, ZHANG B. Second moments of partially coherent beams in atmospheric turbulence［J］. Optics Letters, 2009, 34(5): 5635.

[6] YANG A, ZHANG E, JI X, et al. Propagation properties of partially coherent HermitecoshGaussian beams through atmospheric turbulence［J］. Optics & Laser Technology, 2009, 41(6): 714722.

[7] JI X, CHEN X, L B. Spreading and directionality of partially coherent HermiteGaussian beams propagating through atmospheric turbulence［J］. JOSA A, 2008, 25(1): 2128.

[8] CHEN Xiaowen, TANG Mingyue, JI Xiaoling. The influence of atmospheric turbulence on the spatial correlation property of partially coherent HermiteGaussian beam［J］. Acta Physica Sinica, 2008, 57(4): 26072613.

[9] QIAO Na, DAN Youquan, ZHANG Bin. Propagation properties of elegant hermitegaussian beams in atmospheric turbulence［J］. Acta Optica Sinica, 2010, 30(6): 15427.

[10] YUAN Y, CAI Y, QU J, et al. Propagation factors of HermiteGaussian beams in turbulent atmosphere［J］. Optics & Laser Technology, 2010, 42(8): 13441348.

[11] HUANG Y, ZHANG B, DAN Y, et al. Changes of propagation characteristic parameters for partially coherent HermiteGaussian beams in a turbulent atmosphere［J］. Optics and Lasers in Engineering, 2011, 49(4): 514520.

[12] JI X, LI X. Effective radius of curvature of partially coherent HermiteGaussian beams propagating through atmospheric turbulence［J］. Journal of Optics, 2010, 12(3): 15.

[13] SIEGMAN A E. Lasers［M］. California: University Science Books, 1986: 642803.

[14] ZHANG S, YI L. Twodimensional HermiteGaussian solutions in strongly nonlocal nonlinear medium with rectangular boundaries［J］. Optics Communications, 2009, 282(8): 16548.

[16] GORI F. Flattened Gaussian beams［J］. Optics Communications, 1994, 107(56): 33541.

[17] DAYTON D, PIERSON B, SPIELBUSCH B, et al. Atmospheric structure function measurements with a ShackHartmann wavefront sensor［J］. Opitcs Letters, 1992, 17(24): 17379.

[18] RAO C, JIANG W, LING N. Spatial and temporal characterization of phase fluctuations in nonKolmogorov atmospheric turbulence［J］.Journal of Modern Optics, 2000, 47(6): 111126.

[19] TOSELLI I, ANDREWS L C, PHILLIPS R L, et al. Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence［C］. SPIE, 2007, 6457: 65510E.

[20] WU G, GUO H, YU S, et al. Spreading and direction of GaussianSchell model beam through a nonKolmogorov turbulence［J］. Optics Letters, 2010, 35(5): 715717.