[1] Gbur G. Singular Optics[M]. US: Wiley-VCH Verlag GmbH & Co., 2015.
[2] Born M, Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and 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, 2009, 11(9): 090401.
[4] Braunbek W, Laukien G. Features of refraction by a semi-plane[J]. Optik, 1952, 9: 174-179.
[5] Coullet P, Gil L, Rocca F. Optical vortices [J]. Optics Communications, 1989, 73(5): 403-408. doi:  10.1016/0030-4018(89)90180-6
[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, 1992, 45(11): 8185-8189. doi:  10.1103/PhysRevA.45.8185
[7] Barnett S M, Allen L. Orbital angular momentum and nonparaxial light beams [J]. Optics Communications, 1994, 110(5-6): 670-678. doi:  10.1016/0030-4018(94)90269-0
[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, 2019, 7(18): 1900372.
[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, 2020, 47(5): 0500013. (in Chinese)
[10] Wang Jian, Liu Jun, Zhao Yifan. Research progress of structured light coding/decoding communications [J]. Acta Optica Sinica, 2019, 39(1): 0126013. (in Chinese)
[11] Gu Y L, Gbur G. Measurement of atmospheric turbulence strength by vortex beam [J]. Opt Commun, 2010, 283(7): 1209-1212. doi:  10.1016/j.optcom.2009.11.049
[12] Zhang W, Zhang D, Qiu X, et al. Quantum remote sensing of the angular rotation of structured objects [J]. Physical Review A, 2019, 100(4): 043832. doi:  10.1103/PhysRevA.100.043832
[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, 2017, 3(10): e1700552. doi:  10.1126/sciadv.1700552
[14] Man Zhongsheng, Xi Zheng, Yuan Xiaocong, et al. Dual coaxial longitudinal polarization vortex structures [J]. Physical Review Letters, 2020, 124(10): 103901. doi:  10.1103/PhysRevLett.124.103901
[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, 2019, 8(1): 90.
[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, 1993, 96(1-3): 123-132. doi:  10.1016/0030-4018(93)90535-D
[17] Liang G, Wang Q. Controllable conversion between Hermite Gaussian and Laguerre Gaussian modes due to cross phase [J]. Opt Express, 2019, 27(8): 10684-10691. doi:  10.1364/OE.27.010684
[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, 2020, 59(13): 4040. doi:  10.1364/AO.389617
[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, 2020, 28(18): 26257-26266. doi:  10.1364/OE.397345
[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, 2020, 18(10): 100501. doi:  10.3788/COL202018.100501
[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, 2017, 46(2): 0217001. (in Chinese) doi:  10.3788/IRLA201746.0217001
[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, 2018, 171: 404-412.
[23] Wang Chen, Liu Tong, Shao Qiongling, et al. Quadrupling topological charges of vortex using multi-passed spiral phase plate[J]. Infrared and 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, 1999, 24(9): 608. doi:  10.1364/OL.24.000608
[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, 2002, 27(15): 1351. doi:  10.1364/OL.27.001351
[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, 2015, 64(16): 164210. (in Chinese)
[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, 2019, 100(6): 063822. doi:  10.1103/PhysRevA.100.063822
[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, 2016, 24(6): 6249-6264. doi:  10.1364/OE.24.006249
[29] Weng X, Liu L, Sui G, et al. Real-time pixel-level polarization modulation using polarized-spatial light modulator based on phase vectorization [J]. arXiv e-prints, 2020: 2004.00446.
[30] He Y, Liu Z, Liu Y, et al. Higher-order laser mode converters with dielectric metasurfaces [J]. Optics Letters, 2015, 40(23): 5506. doi:  10.1364/OL.40.005506
[31] Yang Weidong, Qiu Xiaodong, Chen Lixiang. Research progress in detection, imaging, sensing, and micromanipulation application of orbital angular momentum of beams[J]. Chinese Journal of Lasers, 2020, 47(5): 0500013. (in Chinese)
[32] Wang Chen, Liu Tong, Shao Qiongling, et al. Method research of optical vortex 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, 2020, 368(6492): 763-767. doi:  10.1126/science.aba9192
[34] Liu Q, Pan J, Wan Z, et al. Generation methods for complex vortex structured light field [J]. Chinese Journal of Lasers, 2020, 47(5): 0500006. (in Chinese)
[35] Garetz B A, Arnold S. Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate [J]. Optics Communications, 1979, 31(1): 1-3. doi:  10.1016/0030-4018(79)90230-X
[36] Garetz B A. Angular Doppler effect [J]. J Opt Soc Am A, 1981, 71(5): 609-611. doi:  10.1364/JOSA.71.000609
[37] Barnett S M, Zambrini R. Orbital Angular Momentum of Light [M]. New York: Springer, 2007: 277-311.
[38] Padgett M. A new twist on the Doppler shift [J]. Physics Today, 2014, 67(2): 58-59. doi:  10.1063/PT.3.2286
[39] Belmonte A, Torres J P. Optical Doppler shift with structured light [J]. Opt Lett, 2011, 36(22): 4437-4439. doi:  10.1364/OL.36.004437
[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, 2013, 341(6145): 537-540. doi:  10.1126/science.1239936
[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, 2014, 1(1): 1-4. doi:  10.1364/OPTICA.1.000001
[42] Rosales-Guzmán C, Hermosa N, Belmonte A, et al. Direction-sensitive transverse velocity measurement by phase-modulated structured light beams [J]. Optics Letters, 2014, 39(18): 5415-5418. doi:  10.1364/OL.39.005415
[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, 2014, 90(1): 011801.
[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, 2017, 25(17): 20098-20108. doi:  10.1364/OE.25.020098
[45] Zhang W, Gao J, Zhang D, et al. Free-space remote sensing of rotation at the photon-counting level [J]. Phys Rev A, 2018, 10(4): 044014. doi:  10.1103/PhysRevApplied.10.044014
[46] Qiu S, Liu T, Li Z, et al. Influence of lateral misalignment on the optical rotational Doppler effect [J]. Appl Opt, 2019, 58(10): 2650-2655. doi:  10.1364/AO.58.002650
[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, 2019, 27(17): 24781-24792. doi:  10.1364/OE.27.024781
[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, 2020, 28(5): 6859-6867. doi:  10.1364/OE.380324
[49] Anderson A Q, Strong E F, Heffernan B M, et al. Detection technique effect on rotational Doppler measurements [J]. Opt Lett, 2020, 45(9): 2636-2639. doi:  10.1364/OL.390425
[50] Yu T, Xia H, Fan Z, et al. Study on the influence of phase noise on coherent beam combined Bessel-Gaussian beam[J]. Optics Communications, 2019, 436: 14-20.
[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, 2003, 91(9): 090403. doi:  10.1103/PhysRevLett.91.090403
[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, 2012, 59(13): 1180-1185. doi:  10.1080/09500340.2012.702228
[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, 2016, 93(5): 053603. doi:  10.1103/PhysRevA.93.053603
[54] Lidzey D G, Bradley D D C, Skolnick M S, et al. Strong exciton–photon coupling in an organic semiconductor microcavity [J]. Nature, 1998, 395(6697): 53-55. doi:  10.1038/25692
[55] Daskalakis K S, Maier S A, Kena-Cohen S. Spatial coherence and stability in a disordered organic polariton condensate [J]. Physical Review Letters, 2015, 115(3): 5301.
[56] Ren Yuan, Cheng Rui, Xie Lu, et al. Wave-particle vortex gyro: China, ZL201610318157.8[P]. 2016-05-12.
[57] Ren Yuan, Wang Gang, Xie Lu, et al. Vortex optical circulator: China, ZL201610319453. X [P]. 2016-05-12.
[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, 2019, 94(11): 115221. doi:  10.1088/1402-4896/ab2945
[59] Wu H, Ren Y, Liu T, et al. Research on rotational dynamics characteristics of planar superimposed vortexes of exciton polariton condensates[J]. Acta Phys Sin, 2020, 69(23): 230303.
[60] 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, 2016, 93(5): 053603 .