[1] PATERSON L, MACDONALD M P, ARLT J et al. Controlled rotation of optically trapped microscopic particles[J]. Science, 292, 912-914(2001).

[2] JACK B, LEACH J, ROMERO J et al. Holographic ghost imaging and the violation of a bell inequality[J]. Physical Review Letters, 103(2009).

[3] PATERSON C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication[J]. Physical Review Letters, 94, 153901(2005).

[4] WANG J, YANG J Y, FAZAL I M et al. Terabit free-space data transmission employing orbital angular momentum multiplexing[J]. Nature Photonics, 6, 488-496(2012).

[5] [5] 高春清, 付时尧. 涡旋光束[M]. 北京: 清华大学出版社, 2019: 1-9.GAOCH Q, FUSH Y. Vortex Beams[M]. Beijing: Tsinghua University Press, 2019: 1-9.(in Chinese)

[6] BAI Y H, LV H R, FU X et al. Vortex beam: generation and detection of orbital angular momentum[J]. Chinese Optics Letters, 20(2022).

[7] [7] 朱向阳, 邱松, 丁友, 等. 多径向节次拉盖尔-高斯光束旋转多普勒效应分析[J]. 光学学报, 2023, 43(7): 0726003. doi: 10.3788/AOS221762ZHUX Y, QIUS, DINGY, et al. Rotational Doppler effect analysis of multi-radial index Laguerre-Gaussian beam[J]. Acta Optica Sinica, 2023, 43(7): 0726003. (in Chinese). doi: 10.3788/AOS221762

[8] ALLEN L, BEIJERSBERGEN M, SPREEUW R et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, Atomic, Molecular, and Optical Physics, 45, 8185-8189(1992).

[9] STEPHEN M. Orbital angular momentum and nonparaxial light beams[J]. Optics Communications, 110, 670-678(1994).

[10] LEACH J, YAO E, PADGETT M J. Observation of the vortex structure of a non-integer vortex beam[J]. New Journal of Physics, 6, 71(2004).

[11] TAO S H, LEE W M, YUAN X C. Experimental study of holographic generation of fractional Bessel beams[J]. Applied Optics, 43, 122(2004).

[12] ZHANG N, DAVIS J A, MORENO I et al. Analysis of fractional vortex beams using a vortex grating spectrum analyzer[J]. Applied Optics, 49, 2456(2010).

[13] ZHOU J, ZHANG W H, CHEN L X. Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter[J]. Applied Physics Letters, 108, 111108(2016).

[14] LIU Z W, YAN S, LIU H G et al. Superhigh-resolution recognition of optical vortex modes assisted by a deep-learning method[J]. Physical Review Letters, 123, 183902(2019).

[15] DENG D, LIN M C, LI Y et al. Precision measurement of fractional orbital angular momentum[J]. Physical Review Applied, 12(2019).

[16] MAO Z X, YU H Y, XIA M et al. Broad bandwidth and highly efficient recognition of optical vortex modes achieved by the neural-network approach[J]. Physical Review Applied, 13(2020).

[17] ZHANG H, ZENG J, LU X Y et al. Review on fractional vortex beam[J]. Nanophotonics, 11, 241-273(2022).

[18] [18] 李晨昊, MAIERS A, 任浩然. 纳米光子学中的光学涡旋[J]. 中国光学（中英文）, 2021, 14(4): 792-811. doi: 10.37188/CO.2021-0066LICH H，MAIERS A，RENH R. Optical vortices in nanophotonics[J]. Chinese Optics, 2021, 14(4): 792-811. (in Chinese). doi: 10.37188/CO.2021-0066

[19] [19] 庄京秋, 熊晗, 虞天成, 等. 基于软边小孔的涡旋光轨道角动量检测研究[J]. 光学 精密工程, 2022, 30(12): 1394-1405. doi: 10.37188/OPE.20223012.1394ZHUANGJ Q, XIONGH, YUT CH, et al. Orbital angular momentum detection of vortex beam based on soft-edge aperture[J]. Opt. Precision Eng., 2022, 30(12): 1394-1405. (in Chinese). doi: 10.37188/OPE.20223012.1394

[20] [20] 徐鹏. 液晶空间光调制器光调制特性测量及其在光学图像处理中的应用研究[D]. 济南: 山东大学, 2005: 10-13.XUP. Measurement of Light Modulation Characteristics of Liquid Crystal Spatial Light Modulator and Its Application In Optical Image Processing[D]. Jinan: Shandong University, 2005: 10-13.(in Chinese)

[21] CHEN P, WEI B Y, JI W et al. Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings[J]. Photonics Research, 3, 133(2015).