[1] [1] Nye J F, Berry M V. Dislocations in wave trains[J]. Proceedings of the Royal Society of London A: Mathematical and Physical Sciences, 1974, 336(1605): 165-190.

[2] [2] Yao A M, Padgett M J. Orbital angular momentum: origins, behavior andapplications[J]. Advances in Optics and Photonics, 2011, 3(2): 161-204.

[3] [3] Yin J P, Gao W J, Zhu Y F. Generation of dark hollow beams and their applications[J]. Progress in Optics, 2003, 45: 119-204.

[4] [4] Ostrovsky A S, Rickenstorffparrao C, Arrizon V. Generation of the perfect optical vortex using a liquidcrystal spatial light modulator[J]. Optics Letters, 2013, 38(4): 534-536.

[5] [5] Huang S J, He C, Wang T Y. Generation of sidelobe-free optical vortices utilizing object-oriented computer generated holograms[J]. Journal of Optics, 2014, 16(3): 035402.

[6] [6] Wang Yadong, Gan Xuetao, Ju Pei, et al. Control of topological structure in high-order optical vortices by use of noncanonical helical phase[J]. Acta Physica Sinica, 2015, 64(3): 034204.

[7] [7] Deng D G, Fu X Y, Wei C Y, et al. Far-field intensity distribution and M2 factor of hollow Gaussian beams[J]. Applied Optics, 2005, 44(33): 7187-7190.

[8] [8] Cai Y J, Zhang L. Coherent and partially coherent dark hollow beams with rectangular symmetry and paraxial propagation properties[J]. Journal of the Optical Society of America B, 2006, 23(7): 1398-1407.

[9] [9] Sun Chuan, He Yanlin, Wu Fengtie. Bottle beam generation with a double ring lens by focusing parallel light[J]. Acta Optica Sinica, 2015, 35(12): 1208001.

[10] [10] Shi Jianzhen, Xu Shuwu, Ji Xianming, et al. Generation of the tunable rectangular hollow beams by using wave plates[J]. Acta Optica Sinica, 2015, 35(9): 0926001.

[11] [11] Petrov D V. Vortex-edge dislocation interaction in a linear medium[J]. Optics Communications, 2001, 188(5-6): 307-312.

[12] [12] Yan H W, Lü B D. Vortex-edge dislocation interaction in the presence of an astigmatic lens[J]. Optics Communications, 2009, 282(5): 717-726.

[13] [13] Yan H W, Lü B D, Gao Z H, et al. Interaction of two edge dislocations in free-space propagation[J]. Chinese Physics B, 2011, 20(1): 014201.

[14] [14] Chen H T, Gao Z H, Yang H J, et al. Interaction between a vortex and an edge dislocation nested in a cos-Gaussian beam passing through a tilted lens[J]. Journal of Modem Optics, 2012, 59(6): 579-586.

[15] [15] Feng Bo, Gan Xuetao, Liu Sheng, et al. Transformation of multi-edge-dislocations to screw-dislocations in optical field[J]. Acta Physica Sinica, 2011, 60(9): 094203.

[16] [16] Casperson L W, Hall D G, Tovar A A. Sinusoidal-Gaussian beams in complex optical systems[J].Journal of the Optical Society of America A, 1997, 14(12): 3341-3348.

[17] [17] Casperson L W, Tovar A A. Hermite-sinusoidal-Gaussian beams in complex optical systems[J]. Journal of the Optical Society of America A, 1998, 15(4): 954-961.

[18] [18] Tovar A A, Casperson L W. Production and propagation of Hermite-sinusoidal-Gaussian laser beams[J].Journal of the Optical Society of America A, 1998, 15(9): 2425-2432.

[19] [19] Zhang Bin, Ma Hong, Lü Baida. M2-factor and coherent-mode decomposition of sinh-Gaussian beams[J]. Acta Physica Sinica, 1999, 48(10): 1869-1874.

[20] [20] Eyyuboglu H T, Baykal Y. Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere[J]. Journal of the Optical Society of America A, 2005, 22(12): 2709-2718.

[21] [21] Eyyuboglu H T, Tanyer H. Hermite hyperbolic/sinusoidal Gaussian beams in ABCD systems[J]. Optik, 2007, 118(6): 289-295.

[22] [22] Ding P H, Qu J, Meng K, et al. The beam quality of nonparaxial Hermite-sine-Gaussian beam[J]. Optics Communications, 2008, 281(3): 395-400.

[23] [23] He Xuemei, Lü Baida. Dynamic evolution of composite coherence vortices by superimpositions of partially coherent hyperbolic-sine-Gaussian vortex beams in non-Kolmogorov atmospheric turbulence[J]. Acta Physica Sinica, 2012, 61(5): 054201

[24] [24] Tang H Q, Zhu K C. Generation of dark hollow beam by focusing a sine-Gaussian beam using a cylindrical lens and a focusing lens[J]. Optics & Laser Technology, 2013, 54(30): 68-71.

[25] [25] Zhu Kaicheng, Tang Huiqin, Zheng Xiaojuan, et al. Gyrator transform of generalized sinh-Gaussian beam and generation of dark hollow light beam with vortex[J]. Acta Physica Sinica, 2014, 63(10): 104210.

[26] [26] Zhu K C, Tang H Q, Tang Y, et al. Gyrator transform of generalized sine-Gaussian beams and conversion an edge-dislocation into a vortex[J]. Optics & Laser Technology, 2014, 64(7): 11-16.

[27] [27] Alda J, Bernabeu E. Characterization of aberrated laser beams[J].Journal of the Optical Society of America A, 1997, 14(10): 2737-2747.

[28] [28] Yan H W, Lü B D. Propagation of spectral Stokes singularities of stochastic electromagnetic beams through an astigmatic lens[J]. Journal of the Optical Society of America B, 2010, 27(3): 375-381.

[29] [29] Chen H T, Gao Z H, Yang H J, et al. Propagation of Riemann-Silberstein vortices through an astigmatic lens[J]. Journal of the Optical Society of America A, 2012, 29(11): 2406-2414.