[1] Swartzlander J G A, Law C T. Optical vortex solitons observed in Kerr nonlinear media[J]. Physical Review Letters, 1992, 69(17): 2503-2506.

[2] Tikhonenko V, Christou J, Luther-Daves B. Spiraling bright spatial solitons forms by the breakup of an optical vortex in a saturable self-focusing medium[J]. Journal of the Optical Society of America B, 1995, 12(11): 2046-2052.

[3] Chen Z G, Shih M F, Segev M, et al.. Steady-state vortex-screening solitons formed in biased photorefractive media[J]. Optics Letters, 1997, 22(23): 1751-1753.

[4] Firth W J, Skryabin D V. Optical solitons carrying orbital angular momentum[J]. Physical Review Letters, 1997, 79(13): 2450-2453.

[5] Quiroga-Teixeiro M, Michinel H. Stable azimuthal stationary state in quintic nonlinear optical media[J]. Journal of the Optical Society of America B, 1997, 14(8): 2004-2009.

[6] Yang J K. Stability of vortex solitons in a 2D photorefractive optical lattice[C]. Nonlinear Guided Waves and Their Applications, Toronto, 2004: TuC10.

[7] Rosberg C R, Neshev D N, Sukhorukov A A, et al.. Observation of nonlinear self-trapping in triangular photonic lattices[J]. Optics Letters, 2007, 32(4): 397-399.

[8] Wang J D, Yang J K. Families of vortex solitons in periodic media[J]. Physical Review A, 2008, 77(3): 033834.

[9] Shen M, Zheng J J, Kong Q, et al.. Stabilization of counter-rotating vortex pairs in nonlocal media[J]. Physical Review A, 2012, 86(1): 013827.

[10] Desyatnikov A S, Mihalache D, Mazilu D, et al.. Stable counter-rotating vortex pairs in saturable media[J]. Physics Letters A, 2007, 364(3): 231-234.

[11] Efremidis N K, Sears S, Christodoulides D N, et al.. Discrete solitons in photorefractive optically induced photonic lattices[J]. Physical Review E, 2002, 66(4): 046602.

[12] Chen C R, Yeh C H, Shih M F. Propagation of a topologically half-charge vortex light beam in a self-focusing photorefractive medium[J]. Optics Express, 2014, 22(3): 3180-3185.

[13] Shih M F, Chen Z G, Mitchell M, et al.. Waveguides induced by photorefractive screening solitons[J]. Journal of the Optical Society of America B, 1997, 14(11): 3091-3101.

[14] Wesner M, Herden C, Pankrath R, et al.. Temporal development of photorefractive solitons up to the telecommunication wavelengths in strontium-barium niobate waveguides[J]. Physical Review E, 2001, 64(3): 036613.

[15] Terhalle B, Gries D, Richter T, et al.. Anisotropy-controlled topological stability of discrete vortex solitons in optically induced photonic lattices[J]. Optics Letters, 2010, 35(4): 604-606.

[16] Alexander T J, Sukhorukov A A, Kivshar Y S. Asymmetric vortex solitons in nonlinear periodic lattices[J]. Physical Review Letters, 2004, 93(6): 063901.

[17] Ferrando A, Zacarés M, García-March M , et al.. Vortex transmutation[J]. Physical Review Letters, 2005, 95(12): 123901.

[18] Malomed B A, Kevrekidis P G. Discrete vortex solitons[J]. Physical Review E, 2001, 64(2): 026601.

[19] Neshev D N, Alexander T J, Ostrovskaya E A, et al.. Observation of discrete vortex solitons in optically induced photonic lattices[J]. Physical Review Letters, 2004, 92(12): 123903.

[20] Fleischar J W, Bartal G, Cohen O, et al.. Observation of vortex-ring "discrete" solitons in 2D photonic lattices[J]. Physical Review Letters, 2004, 92(12): 123904.

[21] Alexander T J, Desyatnikov A S, Kivshar Y S. Multivortex solitons in triangular photonic lattices[J]. Optics Letters, 2007, 32(10): 1293-1295.

[22] Liang J, Xu B, Cai Z. Internal oscillation of necklace solitons in Bessel photonic lattice imprinted in defocusing and focusing materials[J]. Journal of the Optical Society of America B, 2011, 28(1): 93-99.

[23] 余文愫, 覃亚丽, 任宏亮, 等. 贝塞尔晶格中环状涡旋孤子的研究[J]. 光学学报, 2014, 34(7): 0719001.

    Yu Wensu, Qin Yali, Ren Hongliang, et al.. Research on ring-like vortex solitons in Bessel lattices[J]. Acta Optica Sinica, 2014, 34(7): 0719001.

[24] 鄢曼, 覃亚丽, 任宏亮, 等. 贝塞尔晶格中高斯光束的传输[J]. 激光与光电子学进展, 2015, 52(2): 021901.

    Yan Man, Qin Yali, Ren Hongliang, et al.. Propagation of the Gaussian beam in Bessel optical lattice[J]. Laser & Optoelectronics Progress, 2015, 52(2): 021901.

[25] Lobanov V E, Borovkova O V, Kartashov Y V, et al.. Stable bright and vortex solitons in photonic crystal fibers with inhomogeneous defocusing nonlinearity[J]. Optics Letters, 2012, 37(11): 1799-1801.

[26] Efremidis N K, Hizanidis K, Malomed B A, et al.. Three-dimensional vortex solitons in self-defocusing media[J]. Physical Review Letters, 2007, 98(11): 113901.

[27] 凌振芳, 郭儒, 刘思敏, 等. 光生伏打-光折变介质中光学涡旋孤子[J]. 物理学报, 1999, 49(3): 455-459.

    Ling Zhenfang, Guo Ru, Liu Simin, et al.. Optical vortex solitons in photovoltaic-photorefractive medium[J]. Acta Physica Sinica, 1999, 49(3): 455-459.

[28] 方桂娟, 林惠川, 蒲继雄. Besinc相干涡旋光束的产生与传输[J]. 中国激光, 2015, 42(7): 0713001.

    Fang Guijuan, Lin Huichuan, Pu Jixiong. Generation and propagation of Besinc-correlated partially coherent vortex beam[J]. Chinese J Lasers, 2015, 42(7): 0713001.

[29] Sakaguchi H, Malomed B A. Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice[J]. Europhysics Letters, 2005, 72(5): 698-704.