[1] [1] J. Serna, R. Martínez-Herrero, P. M. Mejías. Parametric characterization of general partially coherent beams propagating through ABCD optical systems［J］. J. Opt. Soc. Am. A, 1991, 8(7): 1094～1098

[2] [2] H. Weber. Propagation of higher-order intensity moments in quadratic-index media［J］. Opt. & Quantum Electron., 1992, 24(9): 1027～1049

[3] [3] R. Simon, N. Mukunda, E. C. G. Sudarshan. Partially coherent beams and a generalized ABCD-law［J］. Opt. Commun., 1988, 65(5): 322～328

[4] [4] L. C. Andrews, R. L. Phillips. Laser Beam Propagation Through Random Media［M］. Washington: SPIE Press, 1998

[5] [5] G. Gbur, E. Wolf. Spreading of partially coherent beams in random media［J］. J. Opt. Soc. Am. A, 2002, 19(8): 1592～1598

[6] [6] A. Dogariu, S. Amarande. Propagation of partially coherent beams: turbulence-induced degradation ［J］. Opt. Lett., 2003, 28(1): 10～12

[7] [7] Y. J. Cai, S. L. He, Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere［J］. Appl. Phys. Lett., 2006, 89(4): 041117

[8] [8] Y. B. Zhu, D. M. Zhao, X. Y. Du. Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere ［J］. Opt. Express, 2008, 16(22): 18437～18442

[9] [9] J. X. Pu, O. Korotkova. Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere［J］. Opt. Commun., 2009, 282(9): 1691～1698

[10] [10] X. L. Ji, H. T. Eyyubolu, Y. Baykal. Influence of turbulence on the effective radius of curvature of radial Gaussian array beams［J］. Opt. Express, 2010, 18(7): 6922～6928

[11] [11] G. H. Wu, H. Guo, S. Yu et al.. Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence ［J］. Opt. Lett., 2010, 35(5): 715～717

[12] [12] G. Q. Zhou. Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere［J］. Opt. Express, 2011, 19(5): 3945～3951

[13] [13] X. X. Chu. Evolution of an Airy beam in turbulence ［J］. Opt. Lett., 2011, 36(14): 2701～2703

[14] [14] X. X. Chu, C. H. Qiao, X. X. Feng et al.. Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model［J］. Appl. Opt., 2011, 50(21): 3871～3878

[15] [15] Y. Dan, B. Zhang. Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere ［J］. Opt. Express, 2008, 16(20): 15563～15575

[16] [16] R. Martinez-Herrero, P. M. Mejias. Second-order spatial characterization of hard-edge diffracted beams［J］. Opt. Lett., 1993, 18(19): 1669～1671

[17] [17] G. Q. Zhou. Generalized M2 factors of truncated partially coherent Lorentz and Lorentz-Gauss beams [J]. J. Opt., 2010, 12(1): 015701

[18] [18] Z. D. Lu, H. L. Jiang, X. Y. Du et al.. Generalized M2 factor of truncated partially coherent controllable dark-hollow beams［J］. J. Mod. Opt., 2008, 55(13): 2381～2390

[19] [19] X. L. Chu, B. Zhang, Q. Wen. Generalized M2 factor of a partially coherent beam propagating through a circular hardedged aperture［J］. Appl. Opt., 2003, 42(21): 4280～4284

[20] [20] Li Xiaoqing, Ji Xiaoling. Generalized M2G factor of truncated partially coherent Hermite-Gaussian beam［J］. Acta Physica Sinica, 2011, 60(9): 094206

[21] [21] P. A. Belanger, Y. Champagne, C. Pare. Beam propagation factor of diffracted laser beams ［J］. Opt. Commun., 1994, 105(3-4): 233～242

[22] [22] C. Pare, P. A. Belanger. Propagation law and quasi-invariance properties of the truncated second-order moment of a diffracted laser beam［J］. Opt. Commun., 1996, 123(4-6): 679～693

[23] [23] B. D. Lü, S. R. Luo. Asymptotic approach to the truncated cosh-Gaussian beams［J］. Opt. & Quantum Electron., 2001, 33(1): 107～113

[24] [24] S. Amarande, A. Giesen, H. Hügel. Propagation analysis of self-convergent beam width and characterization of hard-edged diffracted beams［J］. Appl. Opt., 2000, 39(22): 3914～3924

[25] [25] X. Q. Li, X. L. Ji. Complex Gaussian functions expansion method applied to truncated Gaussian beams［J］. J. Mod. Opt., 2011, 58(12): 1060～1064

[26] [26] Li Xiaoqing, Zhao Qi, Ji Xiaoling. 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, 2011, 31(12): 1201002

[27] [27] Zhao Yanzhong, Sun Huayan, Zhang Laixian et al.. Backwards propagation characteristics of distorted reflected beams with cat-eye effect［J］. Chinese J. Lasers, 2011, 38(7): 0702015

[28] [28] J. J. Wen, M. A. Breazeal. Diffraction beam field expressed as the superposition of Gaussian beams ［J］. J. Acoust. Soc. Am., 1988, 83(5): 1752～1756

[29] [29] A. W. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform［J］. J. Opt. Soc. Am. A, 1993, 10(10): 2181～2186

[30] [30] Ji Xiaoling. Propagation equation of the effective radius of curvature of general beams［J］. Acta Optica Sinica, 2010, 30(10): 2845～2848

[31] [31] L. Mandel, E. Wolf. Optical Coherence and Quantum Optics［M］. Cambridge: Cambridge University Press, 1995

[32] [32] A. E. Siegman. Lasers［M］. California: University Science Books,1986

[33] [33] A. E. Siegman. New developments in laser resonators［C］. SPIE, 1990, 1224: 2～14