[1] Leach J, Dennis M R, Courtial J, et al.. Laser beams: Knotted threads of darkness[J]. Nature, 2004, 432(7014): 165.
[2] Cai X L, Wang J W, Strain M J, et al.. Integrated compact optical vortex beam emitters[J]. Science, 2012, 338(6105): 363-366.
[3] McMorran B J, Agrawal A, Anderson I M, et al.. Electron vortex beams with high quanta of orbital angular momentum[J]. Science, 2011, 331(6014): 192-195.
[4] Yuanjie Y, Mingzhou C, Michael M, et al.. Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity[J]. New Journal of Physics, 2013, 15(11): 113053.
[5] Yang Y, Dong Y, Zhao C, et al.. Autocorrelation properties of fully coherent beam with and without orbital angular momentum[J]. Opt Express, 2014, 22(3): 2925-2932.
[6] Yang Y, Dong Y, Zhao C, et al.. Generation and propagation of an anomalous vortex beam[J]. Opt Lett, 2013, 38(24): 5418-5421.
[8] Liu Jian, Yang Yanfang, He Ying, et al.. Flattop beam creation based on strong focusing of circularly polarized vortex beams[J]. Acta Optica Sinica, 2014, 34(5): 0526003.
[9] Sun Cunzhi, Chen Ziyang, Pu Jixiong. Experimental study of tightly focused vortex beams through turbid media[J]. Acta Optica Sinica, 2014, 34(6): 0601002.
[10] Li Yinmei, Gong Lei, Li Di, et al.. Progress in optical tweezers technology[J]. Chinese J Lasers, 2015, 42(1): 0101001.
[11] Zhang Jiefang, Zhao Bi, Hu Wencheng, et al.. Interaction propagation of optical vortex solitons in inhomogeneous nonlinear waveguides[J]. Acta Optica Sinica, 2013, 33(4): 0419001.
[12] Wang W, Hanson S G, Miyamoto Y, et al.. Experimental investigatio、n of local properties and statistics of optical vortices in random wave fields[J]. Physical Review Letters, 2005, 94(10): 103902.
[13] Wang W, Yokozeki T, Ishijima R, et al.. Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern[J]. Opt. Express, 2006, 14(22): 10195-10206.
[14] Wang W, Yokozeki T, Ishijima R, et al.. Optical vortex metrology for nanometric speckle displacement measurement[J]. Opt Express, 2006, 14(1): 120-127.
[15] Wang W, Qiao Y, Ishijima R, et al.. Constellation of phase singularities in a speckle- like pattern for optical vortex metrology applied to biological kinematic analysis[J]. Opt. Express, 2008, 16(18): 13908-13917.
[16] Li X, Tai Y, Nie Z. Digital speckle correlation method based on phase vortices[J]. Optical Engineering, 2012, 51(7): 07004.
[17] Li X, Tai Y, Zhang L, et al.. Characterization of dynamic random process using optical vortex metrology[J]. Appl Phys B, 2014, 116(4): 901-909.
[18] Petrov N V, Pavlov P V, Malov A N. Numerical simulation of optical vortex propagation and reflection by the methods of scalar diffraction theory[J]. Quantum Electron, 2013, 43(6): 582-587.
[19] Reddy S G, Kumar A, Prabhakar S, et al.. Experimental generation of ring-shaped beams with random sources[J]. Opt Lett, 2013, 38(21): 4441-4444.
[20] Reddy S G, Prabhakar S, Kumar A, et al.. Higher order optical vortices and formation of speckles[J]. Opt Lett, 2014, 39(15): 4364-4367.
[21] Kumar A, Banerji J, Singh R P. Intensity correlation properties of high-order optical vortices passing through a rotating ground-glass plate[J]. Opt Lett., 2010, 35(22): 3841-3843.
[22] Goodman J W, Speckle Phenomena in Optics: Theory and Applications[M]. Greenwood Village: Roberts & Co., 2007.