[1] [1] SOSKIN M S, VASNETSOV M V. Singular optics［J］. Progress in Optics, 2001, 42(7):219-276.

[2] [2] FLOSSMANN F, SCHWARZ U T, MAIER M. Propagation dynamics of optical vortices in Laguerre–Gaussian beams［J］. Optics Communications, 2005, 250(4-6): 218-230.

[3] [3] ORLOV S, REGELSKIS K, SMIL GEVICIUS V, et al. Propagation of Bessel beams carrying optical vortices［J］. Optics Communications, 2002, 209(1): 155-165.

[4] [4] PYRAGAITE V, STABINIS A. Free-space propagation of overlapping light vortex beams［J］. Optics Communications, 2002, 213(4-6): 187-191.

[5] [5] MALEEV I D, SWARTZLANDER JR G A. Composite optical vortices［J］. JOSA B, 2003, 20(6): 1169-1176.

[6] [6] REN Xiang-gui, L Bai-da. Evolution of phase singularities of higher-order bessel beam diffracted by aperture［J］. Acta Photonica Sinica, 2009, 38(2): 259-263.

[7] [7] MASAJADA J. Half-plane diffraction in the case of Gaussian beams containing an optical vortex［J］. Optics Communications, 2000, 175(4-6): 289-294.

[8] [8] LIU Pu-sheng, L Bai-da. Propagation of gaussian background vortex beams diffracted at a half-plane screen［J］. Optics and Laser Technology, 2008, 40(2): 227-234.

[9] [9] XING Yan, L Bai-da. Propergation of partially polarized, partially coherent gaussian-schell model electromagnetic beams through an aperture lens［J］. Acta Photonica Sinica, 2009, 38(11): 2942-2947.

[10] [10] LIU Hai-gang, L Bai-da. Focusing properties of non-uniformly polarized beams through an astigmatic lens with annular aperture［J］. Acta Photonica Sinica, 2009, 38(7): 1602-1607.

[11] [11] KUMAR A, VAITY P, SINGH R P. Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm［J］. Optics Communications, 2010, 283(21): 4141-4145.

[12] [12] MALEEV I D, PALACIOS D M, MARATHAY A S, et al. Spatial correlation vortices in partially coherent light: theory［J］. JOSA B, 2004, 21(11): 1895-1900.

[13] [13] LI Y. Light beams with flat-topped profiles［J］. Optics Letters, 2002, 27(12): 1007-1009.

[14] [14] FREUND I, SHVARTSMAN N. Wave-field phase singularities: the sign principle［J］ Physical Review Letters, 1994, 50(6): 5164-5172.