[1] [1] Gbur G. Singular Optics[M]. US: WileyVCH Verlag GmbH & Co., 2015.

[2] [2] Bn M, Wolf E. Principles of Optics: Electromagic They of Propagation, Interference Diffraction of Light [M]. 7th ed. Britain: Pergamon Press, 1999.

[3] Wolter H. Concerning the path of light upon total reflection[J]. Journal of Optics A Pure & Applied Optics, 11, 090401(2009).

[4] [4] Braunbek W, Laukien G. Features of refraction by a semiplane[J]. Optik, 1952, 9: 174179.

[5] Coullet P, Gil L, Rocca F. Optical vortices[J]. Optics Communications, 73, 403-408(1989).

[6] Allen L, Beijersbergen M W, Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 45, 8185-8189(1992).

[7] Barnett S M, Allen L. Orbital angular momentum and nonparaxial light beams[J]. Optics Communications, 110, 670-678(1994).

[8] Zhang Y Q, Zeng X Y, Ma L, et al. Manipulation for superposition of orbital angular momentum states in surface plasmon polaritons[J]. Advanced Optical Materials, 7, 1900372(2019).

[9] Yang W, Qiu X, Chen L. Research progress in detection, imaging, sensing, and micromanipulation application of orbital angular momentum of beams[J]. Chinese Journal of Lasers, 47, 0500013(2020).

[10] Wang Jian, Liu Jun, Zhao Yifan. Research progress of structured light coding/decoding communications[J]. Acta Optica Sinica, 39, 0126013(2019).

[11] Gu Y L, Gbur G. Measurement of atmospheric turbulence strength by vortex beam[J]. Opt Commun, 283, 1209-1212(2010).

[12] Zhang W, Zhang D, Qiu X, et al. Quantum remote sensing of the angular rotation of structured objects[J]. Physical Review A, 100, 043832(2019).

[13] Lavery M P J, Peuntinger C, Günthneret K, et al. Free-space propagation of high-dimensional structured optical fields in an urban environment[J]. Science Advances, 3, e1700552(2017).

[14] Man Zhongsheng, Xi Zheng, Yuan Xiaocong, et al. Dual coaxial longitudinal polarization vortex structures[J]. Physical Review Letters, 124, 103901(2020).

[15] Shen Y, Wang X, Xie Z, et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities[J]. Light: Science & Applications, 8, 90(2019).

[16] Beijersbergen M W, Allen L, Veen H E L O, et al. Astigmatic laser mode converters and transfer of orbital angular momentum[J]. Optics Communications, 96, 123-132(1993).

[17] Liang G, Wang Q. Controllable conversion between Hermite Gaussian and Laguerre Gaussian modes due to cross phase[J]. Opt Express, 27, 10684-10691(2019).

[18] Wang C, Ren Y, Liu T, et al. Generation and measurement of high-order optical vortices by using the cross phase[J]. Applied Optics, 59, 4040(2020).

[19] Ren Y, Wang C, Liu T, et al. Polygonal shaping and multi-singularity manipulation of optical vortices via high-order cross-phase[J]. Opt Express, 28, 26257-26266(2020).

[20] Wang C, Ren Y, Liu T, et al. New kind of Hermite–Gaussian-like optical vortex generated by cross phase[J]. Chinese Optics Letters, 18, 100501(2020).

[21] Xin Jingtao, Li Kai, Zhang Wen, et al. Generation of vector beams by Sagnac interferometer and spiral phase plates[J]. Infrared and Laser Engineering, 46, 0217001(2017).

[22] Wang C, Liu T, Ren Y, et al. Generating optical vortex with large topological charges by spiral phase plates in cascaded and double-pass configuration[J]. Optik, 171, 404-412(2018).

[23] [23] Wang Chen, Liu Tong, Shao Qiongling, et al. Quadrupling topological ges of vtex using multipassed spiral phase plate[J]. Infrared Laser Engineering, 2018, 47(9): 0918008. （in Chinese）

[24] Wagemann E U, Tiziani H J, Reicherter M, et al. Optical particle trapping with computer-generated holograms written on a liquid-crystal display[J]. Optics Letters, 24, 608(1999).

[25] Ganic D, Hain M, Gu M, et al. Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%[J]. Optics Letters, 27, 1351(2002).

[26] Chen Lixiang, Zhang Yuanying. Research progress on preparation, manipulation, and remote sensing applications of high-order orbital angular momentum of photons[J]. Acta Physica Sinica, 64, 164210(2015).

[27] Takashima S, Kobayashi H, Iwashita K. Integer multiplier for the orbital angular momentum of light using a circular-sector transformation[J]. Physical Review A, 100, 063822(2019).

[28] Clark T W, Offer R F, Franke-Arnold S, et al. Comparison of beam generation techniques using a phase only spatial light modulator[J]. Opt Express, 24, 6249-6264(2016).

[29] [29] Weng X, Liu L, Sui G, et al. Realtime pixellevel polarization modulation using polarizedspatial light modulat based on phase vectization [J]. arXiv eprints, 2020: 2004.00446.

[30] He Y, Liu Z, Liu Y, et al. Higher-order laser mode converters with dielectric metasurfaces[J]. Optics Letters, 40, 5506(2015).

[31] [31] Yang Weidong, Qiu Xiaodong, Chen Lixiang. Research progress in detection, imaging, sensing, micromanipulation application of bital angular momentum of beams[J]. Chinese Journal of Lasers, 2020, 47(5): 0500013. (in Chinese)

[32] [32] Wang Chen, Liu Tong, Shao Qiongling, et al. Method research of optical vtex generation based on sagnac interferometer[J]. Acta Photonica Sinica, 2018, 47(3): 326002. (in Chinese)

[33] Ji Z, Liu W, Krylyuk S, et al. Photocurrent detection of the orbital angular momentum of light[J]. Science, 368, 763-767(2020).

[34] Liu Q, Pan J, Wan Z, et al. Generation methods for complex vortex structured light field[J]. Chinese Journal of Lasers, 47, 0500006(2020).

[35] Garetz B A, Arnold S. Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate[J]. Optics Communications, 31, 1-3(1979).

[36] Garetz B A. Angular Doppler effect[J]. J Opt Soc Am A, 71, 609-611(1981).

[37] [37] Bart S M, Zambrini R. bital Angular Momentum of Light [M]. New Yk: Springer, 2007: 277311.

[38] Padgett M. A new twist on the Doppler shift[J]. Physics Today, 67, 58-59(2014).

[39] Belmonte A, Torres J P. Optical Doppler shift with structured light[J]. Opt Lett, 36, 4437-4439(2011).

[40] Lavery M P, Speirits F C, Barnett S M, et al. Detection of a spinning object using light's orbital angular momentum[J]. Science, 341, 537-540(2013).

[41] Speirits F C, Lavery M P J, Padgett M J, et al. Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body[J]. Optica, 1, 1-4(2014).

[42] Rosales-Guzmán C, Hermosa N, Belmonte A, et al. Direction-sensitive transverse velocity measurement by phase-modulated structured light beams[J]. Optics Letters, 39, 5415-5418(2014).

[43] Phillips M P L D B, Speirits F C, Barnett S M, et al. Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles[J]. Physical Review, 90, 011801(2014).

[44] Fu S, Gao C, Wang T, et al. Non-diffractive Bessel-Gauss beams for the detection of rotating object free of obstructions[J]. Opt Express, 25, 20098-20108(2017).

[45] Zhang W, Gao J, Zhang D, et al. Free-space remote sensing of rotation at the photon-counting level[J]. Phys Rev A, 10, 044014(2018).

[46] Qiu S, Liu T, Li Z, et al. Influence of lateral misalignment on the optical rotational Doppler effect[J]. Appl Opt, 58, 2650-2655(2019).

[47] Qiu S, Liu T, Ren Y, et al. Detection of spinning objects at oblique light incidence using the optical rotational Doppler effect[J]. Optics Express, 27, 24781-24792(2019).

[48] Zhang Z, Cen L, Zhang J, et al. Rotation velocity detection with orbital angular momentum light spot completely deviated out of the rotation center[J]. Opt Express, 28, 6859-6867(2020).

[49] Anderson A Q, Strong E F, Heffernan B M, et al. Detection technique effect on rotational Doppler measurements[J]. Opt Lett, 45, 2636-2639(2020).

[50] [50] Yu T, Xia H, Fan Z, et al. Study on the influence of phase noise on coherent beam combined BesselGaussian beam[J]. Optics Communications, 2019, 436: 1420.

[51] Hodby E, Hopkins S A, Hechenblaikner G, et al. Experimental observation of a superfluid gyroscope in a dilute Bose-Einstein condensate[J]. Phys Rev Lett, 91, 090403(2003).

[52] Thanvanthri S, Kapale K T, Dowling J P. Ultra-stable matter-wave gyroscopy with counter-rotating vortex superpositions in Bose–Einstein condensates[J]. Journal of Modern Optics, 59, 1180-1185(2012).

[53] Moxley F I, Dowling J P, Dai W, et al. Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates[J]. Physical Review A, 93, 053603(2016).

[54] Lidzey D G, Bradley D D C, Skolnick M S, et al. Strong exciton–photon coupling in an organic semiconductor microcavity[J]. Nature, 395, 53-55(1998).

[55] Daskalakis K S, Maier S A, Kena-Cohen S. Spatial coherence and stability in a disordered organic polariton condensate[J]. Physical Review Letters, 115, 5301(2015).

[56] [56] Ren Yuan, Cheng Rui, Xie Lu, et al. Waveparticle vtex gyro: China, ZL201610318157.8[P]. 20160512.

[57] [57] Ren Yuan, Wang Gang, Xie Lu, et al. Vtex optical circulat: China, ZL201610319453. X [P]. 20160512.

[58] Chen Haijun, Ren Yuan, Wang Hua. The dynamics of a matter-wave soliton under the effect of a two-dimensional constant external force field[J]. Physica Scripta, 94, 115221(2019).

[59] [59] Wu H, Ren Y, Liu T, et al. Research on rotational dynamics acteristics of planar superimposed vtexes of exciton polariton condensates[J]. Acta Phys Sin, 2020, 69(23): 230303.

[60] [60] Moxley F I, Dowling J P, Dai W, et al. Sagnac interferometry with coherent vtex superposition states in excitonpolariton condensates[J]. Physical Review A, 2016, 93(5): 053603 .