[1] DENNIS M R, O'HOLLERAN K, PADGETT M J. Singular optics: Optical vortices and polarization singularities[J]. Progress in Optics, 2009, 53: 293-363.
[2] RUCHI SENTHILKUMARAN P, PAL S K. Phase singularities to polarization singularities[J]. International Journal of Optics, 2020, 2020: 2812803.
[3] NYE J F, BERRY M V. Dislocations in wave trains[J]. Proceedings of the Royal Society of London A, 1974, 336(1605): 165-190.
[4] ALLEN L, BEIJERSBERGEN M W, SPREEUW R J C, et al. Orbi-tal angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 1992, 45(11): 8185-8189. doi: 10.1103/PhysRevA.45.8185
[5] BERRY M V. Optical vortices evolving from helicoidal integer and fractional phase steps[J]. Journal of Optics, 2004, A6(2): 259-268.
[6] LEACH J, YAO E, PADGETT M J. Observation of the vortex structure of a non-integer vortex beam[J]. New Journal of Physics, 2004, 6(1): 71.
[7] GBUR G. Fractional vortex Hilbert's hotel[J]. Optica, 2016, 3(3): 222-225. doi: 10.1364/OPTICA.3.000222
[8] 熊光昀, 唐奥, 兰斌, 等. 基于连续镜面变形镜本征模方法的复杂涡旋光场调控[J]. 光电工程, 2022, 49(11): 220066.XIONG G Y, TANG A, LAN B, et al. Vortex field manipulation based on deformation mirror with continuous surface[J]. Opto-Electron Engineering, 2022, 49(11): 220066.
[9] WANG Q, TU Ch H, LI Y N, et al. Polarization singularities: Progress, fundamental physics, and prospects[J]. APL Photonics, 2021, 6(4): 040901. doi: 10.1063/5.0045261
[10] BECKLEY A M, BROWN T G, ALONSO M A. Full poincaré beams[J]. Optics Express, 2010, 18(10): 10777-10785. doi: 10.1364/OE.18.010777
[11] SHVEDOV V, KARPINSKI P, SHENG Y, et al. Visualizing pola-rization singularities in Bessel-Poincaré beams[J]. Optics Express, 2015, 23(9): 12444-12453. doi: 10.1364/OE.23.012444
[12] GARCIA-GRACIA H, GUTIÉRREZ-VEGA J C. Polarization singularities in nondiffracting Mathieu-Poincaré beams[J]. Journal of Optics, 2016, 18(1): 014006. doi: 10.1088/2040-8978/18/1/014006
[13] YE D, PENG X Y, ZHOU M Ch, et al. Simulation of generation and dynamics of polarization singularities with circular Airy beams[J]. Journal of the Optical Society of America, 2017, A34(11): 1957-1960.
[14] SUN W Y, YE D. Simulated generation of fractional polarization singularities based on fractional vortex beam[J]. Optik, 2021, 242: 167201. doi: 10.1016/j.ijleo.2021.167201
[15] ZHAN Q W. Trapping metallic Rayleigh particles with radial polarization[J]. Optics Express, 2004, 12(15): 3377-3382. doi: 10.1364/OPEX.12.003377
[16] HNATOVSKY C, SHVEDOV V, KROLIKOWSKI W, et al. Revealing local field structure of focused ultrashort pulses[J]. Physical Review Letters, 2011, 106(12): 123901. doi: 10.1103/PhysRevLett.106.123901
[17] 谢有朋, 张珊, 雷霆, 等. 奇点光束复用光通信[J]. 光通信研究, 2018, 210(6): 11-20.XIE Y P, ZHANG Sh, LEI T, et al. Singular optical beams multiplexing optical communication[J]. Study on Optical Communications, 2018(6): 11-20(in Chinese).
[18] ZHANG G L, CAI M Q, HE X L, et al. Pseudo-topological property of Julia fractal vector optical fields[J]. Optics Express, 2019, 27(9): 13263-13279. doi: 10.1364/OE.27.013263
[19] LAROCQUE H, SUGIC D, MORTIMER D, et al. Reconstructing the topology of optical polarization knots[J]. Nature Physics, 2018, 14(11): 1079-1082. doi: 10.1038/s41567-018-0229-2
[20] OTTE E, ALPMANN C, DENZ C. Polarization singularity explosions in tailored light fields[J]. Laser & Photonics Reviews, 2018, 12(6): 1700200.
[21] 陈海涛, 李婷, 高曾辉. 非相干叠加光束携带C点偶极子的演化特性[J]. 激光技术, 2022, 46(5): 691-696.CHEN H T, LI T, GAO Z H. The evolution of C-dipole by incohe-rent superposition beams[J]. Laser Technology, 2022, 46(5): 691-696(in Chinese).
[22] ZHANG G L, TU Ch H, LI Y N, et al. Observation of polarization topological singular lines[J]. Photonics Research, 2019, 7(6): 705-710. doi: 10.1364/PRJ.7.000705
[23] GU B, HU Y Q, ZHANG X H, et al. Angular momentum separation in focused fractional vector beams for optical manipulation[J]. Optics Express, 2021, 29(10): 14705-14719. doi: 10.1364/OE.423357
[24] EFREMIDIS N K, CHEN Zh G, SEGEV M, et al. Airy beams and accelerating waves: An overview of recent advances[J]. Optica, 2019, 6(5): 686-701. doi: 10.1364/OPTICA.6.000686
[25] EFREMIDIS N K, CHRISTODOULIDES D N. Abruptly autofocusing waves[J]. Optics Letters, 2010, 35(23): 4045-4047. doi: 10.1364/OL.35.004045
[26] CHEN B, CHEN Ch D, PENG X, et al. Propagation of sharply autofocused ring Airy Gaussian vortex beams[J]. Optics Express, 2015, 23(15): 19288-19298. doi: 10.1364/OE.23.019288
[27] 高金金, 周正兰, 徐华锋, 等. 部分相干Airy涡旋光束在非Kolmogorov谱中的模态强度[J]. 激光技术, 2021, 45(4): 522-529.GAO J J, ZHOU Zh L, XU H F, et al. Modal intensity of partially coherent Airy vortex beams in non-Kolmogorov turbulence[J]. Laser Technology, 2021, 45(4): 522-529(in Chinese).
[28] 许森东. 艾里涡旋光束通过负折射率介质的传输特性[J]. 激光技术, 2022, 46(6): 850-854.XU S D. Study on propagation properties of vortex Airy beams through negative index medium[J]. Laser Technology, 2022, 46(6): 850-854(in Chinese).
[29] GOODMAN J W. Introduction to Fourier optics[M]. 4th ed. New York, USA: Robort & Company Publisher, 2017: 61-67.
[30] FREUND I, MOKHUN A I, SOSKIN M S, et al. Stokes singularity relations[J]. Optics Letters, 2002, 27(7): 545-547. doi: 10.1364/OL.27.000545