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Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Yijie Shen, Xuejiao Wang, Zhenwei Xie and 5 more

Light: Science & Applications · 2019 · Review · CC BY-NC

doi:10.1038/s41377-019-0194-2

Abstract

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin–orbital interactions, Bose–Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

References 306

  1. 1.

    Coullet P, Gil L, Rocca F. Optical vortices. Opt. Commun. 1989;73:403-408.

    Not in our library10.1016/0030-4018(89)90180-6

  2. 2.

    Graham R, Haken H. Laserlight—first example of a second-order phase transition far away from thermal equilibrium. Z. Phys. 1970;237:31-46.

    Not in our library10.1007/bf01400474

  3. 3.

    Aranson IS, Kramer L. The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 2002;74:99-143.

    Not in our library10.1103/revmodphys.74.99

  4. 4.

    Coullet P, Gil L, Lega J. Defect-mediated turbulence. Phys. Rev. Lett. 1989;62:1619-1622.

    Not in our library10.1103/physrevlett.62.1619

  5. 5.

    Brambilla M, et al. Transverse laser patterns. I. Phase singularity crystals. Phys. Rev. A. 1991;43:5090-5113.

    Not in our library10.1103/physreva.43.5090

  6. 6.

    Brambilla M, et al. Transverse laser patterns. II. Variational principle for pattern selection, spatial multistability, and laser hydrodynamics. Phys. Rev. A. 1991;43:5114-5120.

    Not in our library10.1103/physreva.43.5114

  7. 7.

    Rosanov NN, Fedorov SV, Shatsev AN. Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling. Phys. Rev. Lett. 2005;95:053903.

    Not in our library10.1103/physrevlett.95.053903

  8. 8.

    Genevet P, et al. Bistable and addressable localized vortices in semiconductor lasers. Phys. Rev. Lett. 2010;104:223902.

    Not in our library10.1103/physrevlett.104.223902

  9. 9.

    Barland, S. et al. Observation of “true” optical vortices in a laser system. in Nonlinear Photonics and Novel Optical Phenomena (eds Chen, Z. G. & Morandotti, R.) 195–205 (Springer, New York, NY, 2012).

    Not in our library

  10. 10.

    Bazhenov VY, Soskin MS, Vasnetsov MV. Screw dislocations in light wavefronts. J. Mod. Opt. 1992;39:985-990.

    Not in our library10.1080/09500349214551011

  11. 11.

    Crasovan LC, Malomed BA, Mihalache D. Stable vortex solitons in the two-dimensional Ginzburg–Landau equation. Phys. Rev. E. 2000;63:016605.

    Not in our library10.1103/physreve.63.016605

  12. 12.

    Mihalache D, et al. Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials. Phys. Rev. A. 2010;82:023813.

    Not in our library10.1103/physreva.82.023813

  13. 13.

    Fedorov SV, et al. Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber. IEEE J. Quantum Electron. 2003;39:197-205.

    Not in our library10.1109/jqe.2002.807212

  14. 14.

    Paulau PV, et al. Vortex solitons in lasers with feedback. Opt. Express. 2010;18:8859-8866.

    Not in our library10.1364/oe.18.008859

  15. 15.

    Mihalache D, et al. Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation. Phys. Rev. Lett. 2006;97:073904.

    Not in our library10.1103/physrevlett.97.073904

  16. 16.

    Allen L, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A. 1992;45:8185-8189.

    Not in our library10.1103/physreva.45.8185

  17. 17.

    Beijersbergen MW, et al. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun. 1993;96:123-132.

    Not in our library10.1016/0030-4018(93)90535-d

  18. 18.

    Dennis MR, O’Holleran K, Padgett MJ. Singular optics: optical vortices and polarization singularities. Prog. Opt. 2009;53:293-363.

    Not in our library10.1016/s0079-6638(08)00205-9

  19. 19.

    He H, et al. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 1995;75:826-829.

    Not in our library10.1103/physrevlett.75.826

  20. 20.

    Gahagan KT, Swartzlander GA. Optical vortex trapping of particles. Opt. Lett. 1996;21:827-829.

    Not in our library10.1364/ol.21.000827

  21. 21.

    Simpson NB, Allen L, Padgett MJ. Optical tweezers and optical spanners with Laguerre–Gaussian modes. J. Mod. Opt. 1996;43:2485-2491.

    Not in our library10.1080/09500349608230675

  22. 22.

    Swartzlander GA, Law CT. Optical vortex solitons observed in Kerr nonlinear media. Phys. Rev. Lett. 1992;69:2503-2506.

    Not in our library10.1103/physrevlett.69.2503

  23. 23.

    Tikhonenko V, Christou J, Luther-Daves B. Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium. J. Opt. Soc. Am. B. 1995;12:2046-2052.

    Not in our library10.1364/josab.12.002046

  24. 24.

    Firth WJ, Skryabin DV. Optical solitons carrying orbital angular momentum. Phys. Rev. Lett. 1997;79:2450-2453.

    Not in our library10.1103/physrevlett.79.2450

  25. 25.

    Dholakia K, et al. Second-harmonic generation and the orbital angular momentum of light. Phys. Rev. A. 1996;54:R3742-R3745.

    Not in our library10.1103/physreva.54.r3742

  26. 26.

    Courtial J, et al. Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes. Phys. Rev. A. 1997;56:4193-4196.

    Not in our library10.1103/physreva.56.4193

  27. 27.

    Soskin MS, et al. Topological charge and angular momentum of light beams carrying optical vortices. Phys. Rev. A. 1997;56:4064-4075.

    Not in our library10.1103/physreva.56.4064

  28. 28.

    Courtial J, et al. Rotational frequency shift of a light beam. Phys. Rev. Lett. 1998;81:4828-4830.

    Not in our library10.1103/physrevlett.81.4828

  29. 29.

    Scheuer J, Orenstein M. Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities. Science. 1999;285:230-233.

    Not in our library10.1126/science.285.5425.230

  30. 30.

    Mair A, et al. Entanglement of the orbital angular momentum states of photons. Nature. 2001;412:313-316.

    Not in our library10.1038/35085529

  31. 31.

    Molina-Terriza G, Torres JP, Torner L. Twisted photons. Nat. Phys. 2007;3:305-310.

    Not in our library10.1038/nphys607

  32. 32.

    Paterson L, et al. Controlled rotation of optically trapped microscopic particles. Science. 2001;292:912-914.

    Not in our library10.1126/science.1058591

  33. 33.

    MacDonald MP, et al. Creation and manipulation of three-dimensional optically trapped structures. Science. 2002;296:1101-1103.

    Not in our library10.1126/science.1069571

  34. 34.

    Grier DG. A revolution in optical manipulation. Nature. 2003;424:810-816.

    Not in our library10.1038/nature01935

  35. 35.

    Harwit M. Photon orbital angular momentum in astrophysics. Astrophys. J. 2003;597:1266-1270.

    Not in our library10.1086/378623

  36. 36.

    Zhuang XW. Unraveling DNA condensation with optical tweezers. Science. 2004;305:188-190.

    Not in our library10.1126/science.1100603

  37. 37.

    Fürhapter S, et al. Spiral phase contrast imaging in microscopy. Opt. Express. 2005;13:689-694.

    Not in our library10.1364/opex.13.000689

  38. 38.

    Tamburini F, et al. Overcoming the Rayleigh criterion limit with optical vortices. Phys. Rev. Lett. 2006;97:163903.

    Not in our library10.1103/physrevlett.97.163903

  39. 39.

    Barreiro JT, Wei TC, Kwiat PG. Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 2008;4:282-286.

    Not in our library10.1038/nphys919

  40. 40.

    Hickmann JM, et al. Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum. Phys. Rev. Lett. 2010;105:053904.

    Not in our library10.1103/physrevlett.105.053904

  41. 41.

    Yu NF, et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science. 2011;334:333-337.

    Not in our library10.1126/science.1210713

  42. 42.

    Cai XL, et al. Integrated compact optical vortex beam emitters. Science. 2012;338:363-366.

    Not in our library10.1126/science.1226528

  43. 43.

    Wang J, et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat, Photonics. 2012;6:488-496.

    Not in our library10.1038/nphoton.2012.138

  44. 44.

    Bozinovic N, et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science. 2013;340:1545-1548.

    Not in our library10.1126/science.1237861

  45. 45.

    Fickler R, et al. Quantum entanglement of angular momentum states with quantum numbers up to 10,010. Proc. Natl Acad. Sci. USA. 2016;113:13642-13647.

    Not in our library10.1073/pnas.1616889113

  46. 46.

    Devlin RC, et al. Arbitrary spin-to–orbital angular momentum conversion of light. Science. 2017;358:896-901.

    Not in our library10.1126/science.aao5392

  47. 47.

    Stav T, et al. Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials. Science. 2018;361:1101-1104.

    Not in our library10.1126/science.aat9042

  48. 48.

    Kong FQ, et al. Controlling the orbital angular momentum of high harmonic vortices. Nat. Commun. 2017;8:14970.

    Not in our library10.1038/ncomms14970

  49. 49.

    Gauthier D, et al. Tunable orbital angular momentum in high-harmonic generation. Nat. Commun. 2017;8:14971.

    Not in our library10.1038/ncomms14971

  50. 50.

    Lee JCT, et al. Laguerre–Gauss and Hermite–Gauss soft X-ray states generated using diffractive optics. Nat. Photonics. 2019;13:205-209.

    Not in our library10.1038/s41566-018-0328-8

  51. 51.

    Xie ZW, et al. Ultra-broadband on-chip twisted light emitter for optical communications. Light Sci. Appl. 2018;7:18001.

    Not in our library10.1038/lsa.2018.1

  52. 52.

    Zambon NC, et al. Optically controlling the emission chirality of microlasers. Nat. Photonics. 2019;13:283-288.

    Not in our library10.1038/s41566-019-0380-z

  53. 53.

    Rego L, et al. Generation of extreme-ultraviolet beams with time-varying orbital angular momentum. Science. 2019;364:eaaw9486.

    Not in our library10.1126/science.aaw9486

  54. 54.

    Nye JF, Berry MV. Dislocations in wave trains. Proc. R Soc A Math. Phys. Eng. Sci. 1974;336:165-190.

    Not in our library10.1098/rspa.1974.0012

  55. 55.

    Penrose LS, Penrose R. Impossible objects: a special type of visual illusion. Br. J. Psychol. 1958;49:31-33.

    Not in our library10.1111/j.2044-8295.1958.tb00634.x

  56. 56.

    Bauer T, et al. Observation of optical polarization Möbius strips. Science. 2015;347:964-966.

    Not in our library10.1126/science.1260635

  57. 57.

    Leach J, Yao E, Padgett MJ. Observation of the vortex structure of a non-integer vortex beam. New J. Phys. 2004;6:71.

    Not in our library10.1088/1367-2630/6/1/071

  58. 58.

    Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J. Opt. A Pure Appl. Opt. 2004;6:259-268.

    Not in our library10.1088/1464-4258/6/2/018

  59. 59.

    Verbeeck J, Tian H, Schattschneider P. Production and application of electron vortex beams. Nature. 2010;467:301-304.

    Not in our library10.1038/nature09366

  60. 60.

    Clark CW, et al. Controlling neutron orbital angular momentum. Nature. 2015;525:504-506.

    Not in our library10.1038/nature15265

  61. 61.

    Wang XW, et al. Recent advances on optical vortex generation. Nanophotonics. 2018;7:1533-1556.

    Not in our library10.1515/nanoph-2018-0072

  62. 62.

    Zhu L, Wang J. A review of multiple optical vortices generation: methods and applications. Front. Optoelectron. 2019;12:52-68.

    Not in our library10.1007/s12200-019-0910-9

  63. 63.

    Chen MLM, Jiang LJ, Sha WEI. Orbital angular momentum generation and detection by geometric-phase based metasurfaces. Appl. Sci. 2018;8:362.

    Not in our library10.3390/app8030362

  64. 64.

    Barnett SM, Babiker M, Padgett MJ. Optical orbital angular momentum. Philos. Trans. R Soc. A Math. Phys. Eng. Sci. 2017;375:20150444.

    Not in our library10.1098/rsta.2015.0444

  65. 65.

    Padgett MJ. Orbital angular momentum 25 years on [Invited]. Opt. Express. 2017;25:11265-11274.

    Not in our library10.1364/oe.25.011265

  66. 66.

    Yao AM, Padgett MJ. Orbital angular momentum: origins, behavior and applications. Adv. Opti. Photonics. 2011;3:161-204.

    Not in our library10.1364/aop.3.000161

  67. 67.

    Milonni PW, Boyd RW. Momentum of light in a dielectric medium. Adv. Opt. Photonics. 2010;2:519-553.

    Not in our library10.1364/aop.2.000519

  68. 68.

    Nelson DF. Momentum, pseudomomentum, and wave momentum: toward resolving the Minkowski-Abraham controversy. Phys. Rev. A. 1991;44:3985-3996.

    Not in our library10.1103/physreva.44.3985

  69. 69.

    Bliokh KY, Bekshaev AY, Nori F. Optical momentum, spin, and angular momentum in dispersive media. Phys. Rev. Lett. 2017;119:073901.

    Not in our library10.1103/physrevlett.119.073901

  70. 70.

    Bliokh KY, Nori F. Transverse and longitudinal angular momenta of light. Phys. Rep. 2015;592:1-38.

    Not in our library10.1016/j.physrep.2015.06.003

  71. 71.

    Karimi E, Boyd RW. Classical entanglement? Science. 2015;350:1172-1173.

    Not in our library10.1126/science.aad7174

  72. 72.

    Chen YF, Lu TH, Huang KF. Observation of spatially coherent polarization vector fields and visualization of vector singularities. Phys. Rev. Lett. 2006;96:033901.

    Not in our library10.1103/physrevlett.96.033901

  73. 73.

    Chen YF, et al. Observation of vector vortex lattices in polarization states of an isotropic microcavity laser. Phys. Rev. Lett. 2003;90:053904.

    Not in our library10.1103/physrevlett.90.053904

  74. 74.

    Rosales-Guzmán C, Ndagano B, Forbes A. A review of complex vector light fields and their applications. J. Opt. 2018;20:123001.

    Not in our library10.1088/2040-8986/aaeb7d

  75. 75.

    Abramochkin E, Alieva T. Closed-form expression for mutual intensity evolution of Hermite–Laguerre–Gaussian Schell-model beams. Opt. Lett. 2017;42:4032-4035.

    Not in our library10.1364/ol.42.004032

  76. 76.

    Alieva T, Bastiaans MJ. Mode mapping in paraxial lossless optics. Opt. Lett. 2005;30:1461-1463.

    Not in our library10.1364/ol.30.001461

  77. 77.

    Abramochkin EG, Volostnikov VG. Generalized Hermite-Laguerre-Gauss beams. Phys. Wave Phenom. 2010;18:14-22.

    Not in our library10.3103/s1541308x10010036

  78. 78.

    Bandres MA, Gutiérrez-Vega JC. Ince–Gaussian beams. Opt. Lett. 2004;29:144-146.

    Not in our library10.1364/ol.29.000144

  79. 79.

    Bandres MA, Gutiérrez-Vega JC. Elliptical beams. Opt. Express. 2008;16:21087-21092.

    Not in our library10.1364/oe.16.021087

  80. 80.

    Bandres MA, Gutiérrez-Vega JC. Ince–Gaussian modes of the paraxial wave equation and stable resonators. J. Opt. Soc. Am. A. 2004;21:873-880.

    Not in our library10.1364/josaa.21.000873

  81. 81.

    Bentley JB, et al. Generation of helical Ince-Gaussian beams with a liquid-crystal display. Opt. Lett. 2006;31:649-651.

    Not in our library10.1364/ol.31.000649

  82. 82.

    Woerdemann M, Alpmann C, Denz C. Optical assembly of microparticles into highly ordered structures using Ince–Gaussian beams. Appl. Phys. Lett. 2011;98:111101.

    Not in our library10.1063/1.3561770

  83. 83.

    Shen YJ, et al. Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince-Gaussian and Hermite-Laguerre-Gaussian modes. J. Opt. Soc. Am. A. 2019;36:578-587.

    Not in our library10.1364/josaa.36.000578

  84. 84.

    Volke-Sepulveda K, et al. Orbital angular momentum of a high-order Bessel light beam. J. Opt. B Quantum Semiclassical Opt. 2002;4:S82-S89.

    Not in our library10.1088/1464-4266/4/2/373

  85. 85.

    Gutiérrez-Vega JC, Iturbe-Castillo MD, Chávez-Cerda S. Alternative formulation for invariant optical fields: Mathieu beams. Opt. Lett. 2000;25:1493-1495.

    Not in our library10.1364/ol.25.001493

  86. 86.

    Lóxpez-Mariscal C, et al. Orbital angular momentum transfer in helical Mathieu beams. Opt. Express. 2006;14:4182-4187.

    Not in our library10.1364/oe.14.004182

  87. 87.

    Chávez-Cerda S, et al. Holographic generation and orbital angular momentum of high-order Mathieu beams. J. Opt. B Quantum Semiclassical Opt. 2002;4:S52-S57.

    Not in our library10.1088/1464-4266/4/2/368

  88. 88.

    Alpmann C, et al. Mathieu beams as versatile light moulds for 3D micro particle assemblies. Opt. Express. 2010;18:26084-26091.

    Not in our library10.1364/oe.18.026084

  89. 89.

    Zhu L, Wang J. Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode. Opt. Lett. 2015;40:5463-5466.

    Not in our library10.1364/ol.40.005463

  90. 90.

    Bužek V, Quang T. Generalized coherent state for bosonic realization of SU(2)Lie algebra. J. Opt. Soc. Am. B. 1989;6:2447-2449.

    Not in our library10.1364/josab.6.002447

  91. 91.

    Lin YC, et al. Model of commensurate harmonic oscillators with SU(2) coupling interactions: Analogous observation in laser transverse modes. Phys. Rev. E. 2012;85:046217.

    Not in our library10.1103/physreve.85.046217

  92. 92.

    Tuan PH, et al. Realizing high-pulse-energy large-angular-momentum beams by astigmatic transformation of geometric modes in an Nd:YAG/Cr4+:YAG laser. IEEE J. Sel. Top. Quantum Electron. 2018;24:1600809.

    Not in our library10.1109/jstqe.2018.2798999

  93. 93.

    Tung JC, et al. Exploring vortex structures in orbital-angular-momentum beams generated from planar geometric modes with a mode converter. Opt. Express. 2016;24:22796-22805.

    Not in our library10.1364/oe.24.022796

  94. 94.

    Chen YF, et al. Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces. Phys. Rev. Lett. 2006;96:213902.

    Not in our library10.1103/physrevlett.96.213902

  95. 95.

    Lu TH, et al. Three-dimensional coherent optical waves localized on trochoidal parametric surfaces. Phys. Rev. Lett. 2008;101:233901.

    Not in our library10.1103/physrevlett.101.233901

  96. 96.

    Shen YJ, et al. Polygonal vortex beams. IEEE Photonics J. 2018;10:1503016.

    Not in our library

  97. 97.

    Shen YJ, Fu X, Gong ML. Truncated triangular diffraction lattices and orbital-angular-momentum detection of vortex SU(2) geometric modes. Opt. Express. 2018;26:25545-25557.

    Not in our library10.1364/oe.26.025545

  98. 98.

    Freund I. Optical Möbius strips in three-dimensional ellipse fields: I. Lines of circular polarization. Opt. Commun. 2010;283:1-15.

    Not in our library10.1016/j.optcom.2009.09.042

  99. 99.

    Freund I. Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization. Opt. Commun. 2010;283:16-28.

    Not in our library10.1016/j.optcom.2009.09.037

  100. 100.

    Galvez EJ, et al. Multitwist Möbius strips and twisted ribbons in the polarization of paraxial light beams. Sci. Rep. 2017;7:13653.

    Not in our library10.1038/s41598-017-13199-1

  101. 101.

    Veretenov NA, Fedorov SV, Rosanov NN. Topological vortex and knotted dissipative optical 3D solitons generated by 2D vortex solitons. Phys. Rev. Lett. 2017;119:263901.

    Not in our library10.1103/physrevlett.119.263901

  102. 102.

    Leach J, et al. Vortex knots in light. New J. Phys. 2005;7:55.

    Not in our library10.1088/1367-2630/7/1/055

  103. 103.

    Kleckner D, Irvine WTM. Creation and dynamics of knotted vortices. Nat. Phys. 2013;9:253-258.

    Not in our library10.1038/nphys2560

  104. 104.

    Dennis MR, et al. Isolated optical vortex knots. Nat. Phys. 2010;6:118-121.

    Not in our library10.1038/nphys1504

  105. 105.

    Tempone-Wiltshire SJ, Johnstone SP, Helmerson K. Optical vortex knots–one photon at a time. Sci. Rep. 2016;6:24463.

    Not in our library10.1038/srep24463

  106. 106.

    Cunzhi S, Pu JX, Chávez-Cerda S. Elegant Cartesian Laguerre–Hermite–Gaussian laser cavity modes. Opt. Lett. 2015;40:1105-1108.

    Not in our library10.1364/ol.40.001105

  107. 107.

    Ellenbogen T, et al. Nonlinear generation and manipulation of Airy beams. Nat. Photonics. 2009;3:395-398.

    Not in our library10.1038/nphoton.2009.95

  108. 108.

    Ring JD, et al. Auto-focusing and self-healing of Pearcey beams. Opt. Express. 2012;20:18955-18966.

    Not in our library10.1364/oe.20.018955

  109. 109.

    Bandres MA, Gutiérrez-Vega JC, Chávez-Cerda S. Parabolic nondiffracting optical wave fields. Opt. Lett. 2004;29:44-46.

    Not in our library10.1364/ol.29.000044

  110. 110.

    O’Holleran K, et al. Fractality of light’s darkness. Phys. Rev. Lett. 2008;100:053902.

    Not in our library10.1103/physrevlett.100.053902

  111. 111.

    Zhang LG, et al. Deflection of a reflected intense vortex laser beam. Phys. Rev. Lett. 2016;117:113904.

    Not in our library10.1103/physrevlett.117.113904

  112. 112.

    Omatsu T, Miyamoto K, Lee AJ. Wavelength-versatile optical vortex lasers. J. Opt. 2017;19:123002.

    Not in our library10.1088/2040-8986/aa9445

  113. 113.

    de Araujo LEE, Anderson ME. Measuring vortex charge with a triangular aperture. Opt. Lett. 2011;36:787-789.

    Not in our library10.1364/ol.36.000787

  114. 114.

    Mourka A, et al. Visualization of the birth of an optical vortex using diffraction from a triangular aperture. Opt. Express. 2011;19:5760-5771.

    Not in our library10.1364/oe.19.005760

  115. 115.

    Melo LA, et al. Direct measurement of the topological charge in elliptical beams using diffraction by a triangular aperture. Sci. Rep. 2018;8:6370.

    Not in our library10.1038/s41598-018-24928-5

  116. 116.

    Ghai DP, Senthilkumaran P, Sirohi RS. Single-slit diffraction of an optical beam with phase singularity. Opt. Lasers Eng. 2009;47:123-126.

    Not in our library10.1016/j.optlaseng.2008.07.019

  117. 117.

    Mesquita PHF, et al. Engineering a square truncated lattice with light’s orbital angular momentum. Opt. Express. 2011;19:20616-20621.

    Not in our library10.1364/oe.19.020616

  118. 118.

    Liu YX, et al. Propagation of an optical vortex beam through a diamond-shaped aperture. Opt. Laser Technol. 2013;45:473-479.

    Not in our library10.1016/j.optlastec.2012.06.007

  119. 119.

    Ambuj A, Vyas R, Singh S. Diffraction of orbital angular momentum carrying optical beams by a circular aperture. Opt. Lett. 2014;39:5475-5478.

    Not in our library10.1364/ol.39.005475

  120. 120.

    Taira Y, Zhang SK. Split in phase singularities of an optical vortex by off-axis diffraction through a simple circular aperture. Opt. Lett. 2017;42:1373-1376.

    Not in our library10.1364/ol.42.001373

  121. 121.

    Bahl M, Senthilkumaran P. Energy circulations in singular beams diffracted through an isosceles right triangular aperture. Phys. Rev. A. 2015;92:013831.

    Not in our library10.1103/physreva.92.013831

  122. 122.

    Chen RS, et al. Detecting the topological charge of optical vortex beams using a sectorial screen. Appl. Opt. 2017;56:4868-4872.

    Not in our library10.1364/ao.56.004868

  123. 123.

    Zhang WH, et al. Experimental demonstration of twisted light’s diffraction theory based on digital spiral imaging. Chin. Opt. Lett. 2016;14:110501.

    Not in our library10.3788/col201614.110501

  124. 124.

    Ram BSB, Sharma A, Senthilkumaran P. Diffraction of V-point singularities through triangular apertures. Opt. Express. 2017;25:10270-10275.

    Not in our library10.1364/oe.25.010270

  125. 125.

    Holleczek A, et al. Classical and quantum properties of cylindrically polarized states of light. Opt. Express. 2011;19:9714-9736.

    Not in our library10.1364/oe.19.009714

  126. 126.

    Milione G, et al. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 2011;107:053601.

    Not in our library10.1103/physrevlett.107.053601

  127. 127.

    Naidoo D, et al. Controlled generation of higher-order Poincaré sphere beams from a laser. Nat. Photonics. 2016;10:327-332.

    Not in our library10.1038/nphoton.2016.37

  128. 128.

    Yi XN, et al. Hybrid-order Poincaré sphere. Phys. Rev. A. 2015;91:023801.

    Not in our library10.1103/physreva.91.023801

  129. 129.

    Liu ZX, et al. Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere. Photonics Res. 2017;5:15-21.

    Not in our library10.1364/prj.5.000015

  130. 130.

    Wang RS, et al. Electrically driven generation of arbitrary vector vortex beams on the hybrid-order Poincaré sphere. Opt. Lett. 2018;43:3570-3573.

    Not in our library10.1364/ol.43.003570

  131. 131.

    Franke-Arnold S, et al. Uncertainty principle for angular position and angular momentum. New J. Phys. 2004;6:103.

    Not in our library10.1088/1367-2630/6/1/103

  132. 132.

    Leach J, et al. Quantum correlations in optical angle–orbital angular momentum variables. Science. 2010;329:662-665.

    Not in our library10.1126/science.1190523

  133. 133.

    Jha AK, et al. Fourier relationship between the angle and angular momentum of entangled photons. Phys. Rev. A. 2008;78:043810.

    Not in our library10.1103/physreva.78.043810

  134. 134.
  135. 135.

    Otte E, et al. Entanglement beating in free space through spin–orbit coupling. Light Sci. Appl. 2018;7:18009.

    Not in our library10.1038/lsa.2018.9

  136. 136.

    Bliokh KY, et al. Spin–orbit interactions of light. Nat. Photonics. 2015;9:796-808.

    Not in our library10.1038/nphoton.2015.201

  137. 137.

    Cardano F, Marrucci L. Spin–orbit photonics. Nat. Photonics. 2015;9:776-778.

    Not in our library10.1038/nphoton.2015.232

  138. 138.

    Shao ZK, et al. Spin-orbit interaction of light induced by transverse spin angular momentum engineering. Nat. Commun. 2018;9:926.

    Not in our library10.1038/s41467-018-03237-5

  139. 139.

    Magaña-Loaiza OS, et al. Hanbury brown and Twiss interferometry with twisted light. Sci. Adv. 2016;2:e1501143.

    Not in our library10.1126/sciadv.1501143

  140. 140.

    Mohanty A, et al. Quantum interference between transverse spatial waveguide modes. Nat. Commun. 2017;8:14010.

    Not in our library10.1038/ncomms14010

  141. 141.

    Zhang YW, et al. Engineering two-photon high-dimensional states through quantum interference. Sci. Adv. 2016;2:e1501165.

    Not in our library10.1126/sciadv.1501165

  142. 142.

    Yin XB, et al. Photonic spin Hall effect at metasurfaces. Science. 2013;339:1405-1407.

    Not in our library10.1126/science.1231758

  143. 143.

    Liu YC, et al. Photonic spin Hall effect in metasurfaces: a brief review. Nanophotonics. 2017;6:51-70.

    Not in our library10.1515/nanoph-2015-0155

  144. 144.

    Forbes A, Dudley A, McLaren M. Creation and detection of optical modes with spatial light modulators. Adv. Opt. Photonics. 2016;8:200-227.

    Not in our library10.1364/aop.8.000200

  145. 145.

    Berkhout GCG, et al. Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 2010;105:153601.

    Not in our library10.1103/physrevlett.105.153601

  146. 146.

    Wen YH, et al. Spiral transformation for high-resolution and efficient sorting of optical vortex modes. Phys. Rev. Lett. 2018;120:193904.

    Not in our library10.1103/physrevlett.120.193904

  147. 147.

    Liu GG, et al. Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate. Opt. Lett. 2018;43:823-826.

    Not in our library10.1364/ol.43.000823

  148. 148.

    Ndagano B, et al. Beam quality measure for vector beams. Opt. Lett. 2016;41:3407-3410.

    Not in our library10.1364/ol.41.003407

  149. 149.

    McLaren M, Konrad T, Forbes A. Measuring the nonseparability of vector vortex beams. Phys. Rev. A. 2015;92:023833.

    Not in our library10.1103/physreva.92.023833

  150. 150.

    Forbes A. Controlling light’s helicity at the source: orbital angular momentum states from lasers. Philos. Trans. R Soc. A Math. Phys. Eng. Sci. 2017;375:20150436.

    Not in our library10.1098/rsta.2015.0436

  151. 151.

    Qiao Z, et al. Generating high-charge optical vortices directly from laser up to 288th order. Laser Photonics Rev. 2018;12:1800019.

    Not in our library10.1002/lpor.201800019

  152. 152.

    Lee CY, et al. Generation of higher order vortex beams from a YVO4/Nd:YVO4 self-Raman laser via off-axis pumping with mode converter. IEEE J. Sel. Top Quantum Electron. 2015;21:1600305.

    Not in our library10.1109/jstqe.2015.2432022

  153. 153.

    Sueda K, et al. Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses. Opt. Express. 2004;12:3548-3553.

    Not in our library10.1364/opex.12.003548

  154. 154.

    Cardano F, et al. Polarization pattern of vector vortex beams generated by q-plates with different topological charges. Appl. Opt. 2012;51:C1-C6.

    Not in our library10.1364/ao.51.0000c1

  155. 155.

    Marrucci L. The q-plate and its future. J. Nanophotonics. 2013;7:078598.

    Not in our library10.1117/1.jnp.7.078598

  156. 156.

    Brasselet E. Tunable high-resolution macroscopic self-engineered geometric phase optical elements. Phys. Rev. Lett. 2018;121:033901.

    Not in our library10.1103/physrevlett.121.033901

  157. 157.

    Mock A, Sounas D, Alù A. Tunable orbital angular momentum radiation from angular-momentum-biased microcavities. Phys. Rev. Lett. 2018;121:103901.

    Not in our library10.1103/physrevlett.121.103901

  158. 158.

    Zhou N, et al. Generating and synthesizing ultrabroadband twisted light using a compact silicon chip. Opt. Lett. 2018;43:3140-3143.

    Not in our library10.1364/ol.43.003140

  159. 159.

    Horikawa MT, et al. Handedness control in a tunable midinfrared (6.0-12.5 μm) vortex laser. J. Opt. Soc. Am. B. 2015;32:2406-2410.

    Not in our library10.1364/josab.32.002406

  160. 160.

    Abulikemu A, et al. Widely-tunable vortex output from a singly resonant optical parametric oscillator. Opt. Express. 2015;23:18338-18344.

    Not in our library10.1364/oe.23.018338

  161. 161.

    Zhang WD, et al. Optical vortex generation with wavelength tunability based on an acoustically-induced fiber grating. Opt. Express. 2016;24:19278-19285.

    Not in our library10.1364/oe.24.019278

  162. 162.

    Lyubopytov VS, et al. Simultaneous wavelength and orbital angular momentum demultiplexing using tunable MEMS-based Fabry-Perot filter. Opt. Express. 2017;25:9634-9646.

    Not in our library10.1364/oe.25.009634

  163. 163.

    Liu QY, et al. Wavelength- and OAM-tunable vortex laser with a reflective volume Bragg grating. Opt. Express. 2017;25:23312-23319.

    Not in our library10.1364/oe.25.023312

  164. 164.

    Yao SZ, et al. Tunable orbital angular momentum generation using all-fiber fused coupler. IEEE Photonics Technol. Lett. 2018;30:99-102.

    Not in our library10.1109/lpt.2017.2776981

  165. 165.

    Shen YJ, et al. Wavelength-tunable Hermite–Gaussian modes and an orbital-angular-momentum-tunable vortex beam in a dual-off-axis pumped Yb:CALGO laser. Opt. Lett. 2018;43:291-294.

    Not in our library10.1364/ol.43.000291

  166. 166.

    Shen YJ, et al. Dual-wavelength vortex beam with high stability in a diode-pumped Yb:CaGdAlO4 laser. Laser Phys. Lett. 2018;15:055803.

    Not in our library10.1088/1612-202x/aaaa97

  167. 167.

    Wang S, et al. Generation of wavelength- and OAM-tunable vortex beam at low threshold. Opt. Express. 2018;26:18164-18170.

    Not in our library10.1364/oe.26.018164

  168. 168.

    Zhou N, Liu J, Wang J. Reconfigurable and tunable twisted light laser. Sci. Rep. 2018;8:11394.

    Not in our library10.1038/s41598-018-29868-8

  169. 169.

    Fadeyeva TA, et al. Spatially engineered polarization states and optical vortices in uniaxial crystals. Opt. Express. 2010;18:10848-10863.

    Not in our library10.1364/oe.18.010848

  170. 170.

    Rafayelyan M, Tkachenko G, Brasselet E. Reflective spin-orbit geometric phase from chiral anisotropic optical media. Phys. Rev. Lett. 2016;116:253902.

    Not in our library10.1103/physrevlett.116.253902

  171. 171.

    Kobashi J, Yoshida H, Ozaki M. Polychromatic optical vortex generation from patterned cholesteric liquid crystals. Phys. Rev. Lett. 2016;116:253903.

    Not in our library10.1103/physrevlett.116.253903

  172. 172.

    Piccirillo B, et al. Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate. Appl. Phys. Lett. 2010;97:241104.

    Not in our library10.1063/1.3527083

  173. 173.

    Toyoda K, et al. Using optical vortex to control the chirality of twisted metal nanostructures. Nano Lett. 2012;12:3645-3649.

    Not in our library10.1021/nl301347j

  174. 174.

    Yang L, et al. Direct laser writing of complex microtubes using femtosecond vortex beams. Appl. Phys. Lett. 2017;110:221103.

    Not in our library10.1063/1.4984744

  175. 175.

    Zürch M, et al. Strong-field physics with singular light beams. Nat. Phys. 2012;8:743-746.

    Not in our library10.1038/nphys2397

  176. 176.

    Ran LL, Guo ZY, Qu SL. Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser. Chin. Phys. B. 2012;21:104206.

    Not in our library10.1088/1674-1056/21/10/104206

  177. 177.

    Ishaaya AA, et al. Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser. IEEE J. Quantum Electron. 2003;39:74-82.

    Not in our library10.1109/jqe.2002.806164

  178. 178.

    Kim DJ, Kim JW, Clarkson WA. Q-switched Nd:YAG optical vortex lasers. Opt. Express. 2013;21:29449-29454.

    Not in our library10.1364/oe.21.029449

  179. 179.

    Zhao YG, et al. 1 mJ pulsed vortex laser at 1645 nm with well-defined helicity. Opt. Express. 2016;24:15596-15602.

    Not in our library10.1364/oe.24.015596

  180. 180.

    Chang CC, et al. Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations. Laser Phys. 2017;27:125805.

    Not in our library10.1088/1555-6611/aa92e2

  181. 181.

    He HS, et al. Low-threshold, nanosecond, high-repetition-rate vortex pulses with controllable helicity generated in Cr, Nd:YAG self-Q-switched microchip laser. Laser Phys. 2018;28:055802.

    Not in our library10.1088/1555-6611/aaad4c

  182. 182.

    Wang YB, et al. Generation of 1535-nm pulsed vortex beam in a diode-pumped Er, Yb:glass microchip laser. IEEE Photonics Technol. Lett. 2018;30:891-894.

    Not in our library10.1109/lpt.2018.2822838

  183. 183.

    Koyama M, et al. Power scaling of a picosecond vortex laser based on a stressed Yb-doped fiber amplifier. Opt. Express. 2011;19:994-999.

    Not in our library10.1364/oe.19.000994

  184. 184.

    Liang HC, et al. Compact efficient multi-GHz Kerr-lens mode-locked diode-pumped Nd:YVO4 laser. Opt. Express. 2008;16:21149-21154.

    Not in our library10.1364/oe.16.021149

  185. 185.

    Liang HC, et al. Picosecond optical vortex converted from multigigahertz self-mode-locked high-order Hermite-Gaussian Nd:GdVO4 lasers. Opt. Letters. 2009;34:3842-3844.

    Not in our library10.1364/ol.34.003842

  186. 186.

    Liang HC, et al. Total self-mode locking of multi-pass geometric modes in diode-pumped Nd:YVO4 lasers. Laser Phys. Lett. 2013;10:105804.

    Not in our library10.1088/1612-2011/10/10/105804

  187. 187.

    Tung JC, et al. Exploring the self-mode locking and vortex structures of nonplanar elliptical modes in selectively end-pumped Nd:YVO4 lasers: manifestation of large fractional orbital angular momentum. Opt. Express. 2017;25:22769-22779.

    Not in our library10.1364/oe.25.022769

  188. 188.

    Huang K, et al. Controlled generation of ultrafast vector vortex beams from a mode-locked fiber laser. Opt. Lett. 2018;43:3933-3936.

    Not in our library10.1364/ol.43.003933

  189. 189.

    Bolze T, Nuernberger P. Temporally shaped Laguerre–Gaussian femtosecond laser beams. Appl. Opt. 2018;57:3624-3628.

    Not in our library10.1364/ao.57.003624

  190. 190.

    Zhuang WZ, et al. High-power high-repetition-rate subpicosecond monolithic Yb:KGW laser with self-mode locking. Opt. Lett. 2013;38:2596-2599.

    Not in our library10.1364/ol.38.002596

  191. 191.

    Chang MT, et al. Exploring transverse pattern formation in a dual-polarization self-mode-locked monolithic Yb: KGW laser and generating a 25-GHz sub-picosecond vortex beam via gain competition. Opt. Express. 2016;24:8754-8762.

    Not in our library10.1364/oe.24.008754

  192. 192.

    Zhang ZM, et al. Generation of all-fiber femtosecond vortex laser based on NPR mode-locking and mechanical LPG. Chin. Opt. Lett. 2018;16:110501.

    Not in our library10.3788/col201816.110501

  193. 193.

    Wang S, et al. Direct emission of chirality controllable femtosecond LG01 vortex beam. Appl. Phys. Lett. 2018;112:201110.

    Not in our library10.1063/1.5028477

  194. 194.

    Wang S, et al. Direct generation of femtosecond vortex beam from a Yb:KYW oscillator featuring a defect-spot mirror. OSA Contin. 2019;2:523-530.

    Not in our library10.1364/osac.2.000523

  195. 195.

    Woerdemann M, et al. Advanced optical trapping by complex beam shaping. Laser Photonics Rev. 2013;7:839-854.

    Not in our library10.1002/lpor.201200058

  196. 196.

    Li XF, et al. Automultiscopic displays based on orbital angular momentum of light. J. Opt. 2016;18:085608.

    Not in our library10.1088/2040-8978/18/8/085608

  197. 197.

    Anguita JA, Herreros J, Djordjevic IB. Coherent multimode OAM superpositions for multidimensional modulation. IEEE Photonics J. 2014;6:7900811.

    Not in our library10.1109/jphot.2014.2309645

  198. 198.

    Padgett M, et al. An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes. Am. J. Phys. 1996;64:77-82.

    Not in our library10.1119/1.18283

  199. 199.

    Courtial J, Padgett MJ. Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes. Opt. Commun. 1999;159:13-18.

    Not in our library10.1016/s0030-4018(98)00599-9

  200. 200.

    O’Neil AT, Courtial J. Mode transformations in terms of the constituent Hermite–Gaussian or Laguerre–Gaussian modes and the variable-phase mode converter. Opt. Commun. 2000;181:35-45.

    Not in our library10.1016/s0030-4018(00)00736-7

  201. 201.

    Padgett MJ, Allen L. Orbital angular momentum exchange in cylindrical-lens mode converters. J. Opt. B Quantum Semiclassical Opt. 2002;4:S17-S19.

    Not in our library10.1088/1464-4266/4/2/362

  202. 202.

    Shen YJ, et al. Observation of spectral modulation coupled with broadband transverse-mode-locking in an Yb:CALGO frequency-degenerate cavity. Chin. Opt. Lett. 2019;17:031404.

    Not in our library10.3788/col201917.031404

  203. 203.

    Shen YJ, et al. Vortex lattices with transverse-mode-locking states switching in a large-aperture off-axis-pumped solid-state laser. J. Opt. Soc. Am. B. 2018;35:2940-2944.

    Not in our library10.1364/josab.35.002940

  204. 204.

    Shen YJ, et al. Periodic-trajectory-controlled, coherent-state-phase-switched, and wavelength-tunable SU(2) geometric modes in a frequency-degenerate resonator. Appl. Opt. 2018;57:9543-9549.

    Not in our library10.1364/ao.57.009543

  205. 205.

    Ngcobo S, et al. A digital laser for on-demand laser modes. Nat. Commun. 2013;4:2289.

    Not in our library10.1038/ncomms3289

  206. 206.

    Porfirev AP, Khonina SN. Simple method for efficient reconfigurable optical vortex beam splitting. Opt. Express. 2017;25:18722-18735.

    Not in our library10.1364/oe.25.018722

  207. 207.

    Ma HX, et al. Generation of circular optical vortex array. Ann. Phys. 2017;529:1700285.

    Not in our library10.1002/andp.201700285

  208. 208.

    Li L, et al. Generation of optical vortex array along arbitrary curvilinear arrangement. Opt. Express. 2018;26:9798-9812.

    Not in our library10.1364/oe.26.009798

  209. 209.

    Wan ZS, et al. Quadrant-separable multi-singularity vortices manipulation by coherent superposed mode with spatial-energy mismatch. Opt. Express. 2018;26:34940-34955.

    Not in our library10.1364/oe.26.034940

  210. 210.

    Hou TY, et al. Spatially-distributed orbital angular momentum beam array generation based on greedy algorithms and coherent combining technology. Opt. Express. 2018;26:14945-14958.

    Not in our library10.1364/oe.26.014945

  211. 211.

    Gbur G. Fractional vortex Hilbert’s hotel. Optica. 2016;3:222-225.

    Not in our library10.1364/optica.3.000222

  212. 212.

    Wang YYD, Gbur G. Hilbert’s Hotel in polarization singularities. Opt. Lett. 2017;42:5154-5157.

    Not in our library10.1364/ol.42.005154

  213. 213.

    Ferrando A, García-March MA. Analytical solution for multi-singular vortex Gaussian beams: the mathematical theory of scattering modes. J. Opt. 2016;18:064006.

    Not in our library10.1088/2040-8978/18/6/064006

  214. 214.

    Brasselet E. Tunable optical vortex arrays from a single nematic topological defect. Phys. Rev. Lett. 2012;108:087801.

    Not in our library10.1103/physrevlett.108.087801

  215. 215.

    Barboza R, et al. Harnessing optical vortex lattices in nematic liquid crystals. Phys. Rev. Lett. 2013;111:093902.

    Not in our library10.1103/physrevlett.111.093902

  216. 216.

    Ashkin A. Acceleration and trapping of particles by radiation pressure. Phys. Rev. Lett. 1970;24:156-159.

    Not in our library10.1103/physrevlett.24.156

  217. 217.

    Padgett M, Bowman R. Tweezers with a twist. Nat. Photonics. 2011;5:343-348.

    Not in our library10.1038/nphoton.2011.81

  218. 218.

    Chapin SC, Germain V, Dufresne ER. Automated trapping, assembly, and sorting with holographic optical tweezers. Opt. Express. 2006;14:13095-13100.

    Not in our library10.1364/oe.14.013095

  219. 219.

    Tao SH, et al. Fractional optical vortex beam induced rotation of particles. Opt. Express. 2005;13:7726-7731.

    Not in our library10.1364/opex.13.007726

  220. 220.

    Gong L, et al. Optical forces of focused femtosecond laser pulses on nonlinear optical Rayleigh particles. Photonics Res. 2018;6:138-143.

    Not in our library10.1364/prj.6.000138

  221. 221.

    Zhang YQ, et al. Nonlinearity-induced multiplexed optical trapping and manipulation with femtosecond vector beams. Nano Lett. 2018;18:5538-5543.

    Not in our library10.1021/acs.nanolett.8b01929

  222. 222.

    Shen Z, et al. Visualizing orbital angular momentum of plasmonic vortices. Opt. Lett. 2012;37:4627-4629.

    Not in our library10.1364/ol.37.004627

  223. 223.

    Zhang YQ, et al. A plasmonic spanner for metal particle manipulation. Sci. Rep. 2015;5:15446.

    Not in our library10.1038/srep15446

  224. 224.

    Richardson DJ, Fini JM, Nelson LE. Space-division multiplexing in optical fibres. Nat. Photonics. 2013;7:354-362.

    Not in our library10.1038/nphoton.2013.94

  225. 225.

    Wang J. Advances in communications using optical vortices. Photonics Res. 2016;4:B14-B28.

    Not in our library10.1364/prj.4.000b14

  226. 226.

    Willner AE, et al. Optical communications using orbital angular momentum beams. Adv. Opt. Photonics. 2015;7:66-106.

    Not in our library10.1364/aop.7.000066

  227. 227.

    Lavery MPJ, et al. Free-space propagation of high-dimensional structured optical fields in an urban environment. Sci. Adv. 2017;3:e1700552.

    Not in our library10.1126/sciadv.1700552

  228. 228.

    Li L, et al. High-capacity free-space optical communications between a ground transmitter and a ground receiver via a UAV using multiplexing of multiple orbital-angular-momentum beams. Sci. Rep. 2017;7:17427.

    Not in our library10.1038/s41598-017-17580-y

  229. 229.

    Yan Y, et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nat. Commun. 2014;5:4876.

    Not in our library10.1038/ncomms5876

  230. 230.

    Jia P, et al. Sidelobe-modulated optical vortices for free-space communication. Opt. Lett. 2013;38:588-590.

    Not in our library10.1364/ol.38.000588

  231. 231.

    Anguita, J. A., Herreros, J. & Cisternas, J. E. Generation and detection of multiple coaxial vortex beams for free-space optical communications. In Proc. Quantum Electronics and Laser Science Conference. (Optical Society of America, San Jose, California, United States, 2012).

    Not in our library

  232. 232.

    Heng XB, et al. All-fiber stable orbital angular momentum beam generation and propagation. Opt. Express. 2018;26:17429-17436.

    Not in our library10.1364/oe.26.017429

  233. 233.

    Xie ZW, et al. Integrated (de)multiplexer for orbital angular momentum fiber communication. Photonics Res. 2018;6:743-749.

    Not in our library10.1364/prj.6.000743

  234. 234.

    Lei T, et al. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light Sci. Appl. 2015;4:e257.

    Not in our library10.1038/lsa.2015.30

  235. 235.

    Ren YX, et al. Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications. Sci. Rep. 2016;6:33306.

    Not in our library10.1038/srep33306

  236. 236.

    D’Ambrosio V, et al. Complete experimental toolbox for alignment-free quantum communication. Nat. Commun. 2012;3:961.

    Not in our library10.1038/ncomms1951

  237. 237.

    Zhu L, et al. Orbital angular momentum mode groups multiplexing transmission over 2.6-km conventional multi-mode fiber. Opt. Express. 2017;25:25637-25645.

    Not in our library10.1364/oe.25.025637

  238. 238.

    Mafu M, et al. Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys. Rev. A. 2013;88:032305.

    Not in our library10.1103/physreva.88.032305

  239. 239.

    Sit A, et al. High-dimensional intracity quantum cryptography with structured photons. Optica. 2017;4:1006-1010.

    Not in our library10.1364/optica.4.001006

  240. 240.

    Nicolas A, et al. A quantum memory for orbital angular momentum photonic qubits. Nat. Photonics. 2014;8:234-238.

    Not in our library10.1038/nphoton.2013.355

  241. 241.

    Ding DS, et al. Quantum storage of orbital angular momentum entanglement in an atomic ensemble. Phys. Rev. Lett. 2015;114:050502.

    Not in our library10.1103/physrevlett.114.050502

  242. 242.

    Zhou ZQ, et al. Quantum storage of three-dimensional orbital-angular-momentum entanglement in a crystal. Phys. Rev. Lett. 2015;115:070502.

    Not in our library10.1103/physrevlett.115.070502

  243. 243.

    Chen LX, Lei JJ, Romero J. Quantum digital spiral imaging. Light Sci. Appl. 2014;3:e153.

    Not in our library10.1038/lsa.2014.34

  244. 244.

    Nagali E, et al. Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence. Nat. Photonics. 2009;3:720-723.

    Not in our library10.1038/nphoton.2009.214

  245. 245.

    Ndagano B, et al. Creation and detection of vector vortex modes for classical and quantum communication. J. Lightwave Technol. 2018;36:292-301.

    Not in our library10.1109/jlt.2017.2766760

  246. 246.

    Wang XL, et al. Quantum teleportation of multiple degrees of freedom of a single photon. Nature. 2015;518:516-519.

    Not in our library10.1038/nature14246

  247. 247.

    Wang XL, et al. 18-qubit entanglement with six photons’ three degrees of freedom. Phys. Rev. Lett. 2018;120:260502.

    Not in our library10.1103/physrevlett.120.260502

  248. 248.

    Toninelli E, et al. Concepts in quantum state tomography and classical implementation with intense light: a tutorial. Adv. Opt. Photonics. 2019;11:67-134.

    Not in our library10.1364/aop.11.000067

  249. 249.

    Sephton B, et al. A versatile quantum walk resonator with bright classical light. PLoS ONE. 2019;14:e0214891.

    Not in our library10.1371/journal.pone.0214891

  250. 250.

    Ndagano B, et al. Characterizing quantum channels with non-separable states of classical light. Nat. Phys. 2017;13:397-402.

    Not in our library10.1038/nphys4003

  251. 251.

    Vieira J, et al. Amplification and generation of ultra-intense twisted laser pulses via stimulated Raman scattering. Nat. Commun. 2016;7:10371.

    Not in our library10.1038/ncomms10371

  252. 252.

    Lenzini F, et al. Optical vortex interaction and generation via nonlinear wave mixing. Phys. Rev. A. 2011;84:061801.

    Not in our library10.1103/physreva.84.061801

  253. 253.

    Jiang W, et al. Computation of topological charges of optical vortices via nondegenerate four-wave mixing. Phys. Rev. A. 2006;74:043811.

    Not in our library10.1103/physreva.74.043811

  254. 254.

    Li GX, et al. Continuous control of the nonlinearity phase for harmonic generations. Nat. Mater. 2015;14:607-612.

    Not in our library10.1038/nmat4267

  255. 255.

    Tymchenko M, et al. Gradient nonlinear Pancharatnam-Berry metasurfaces. Phys. Rev. Lett. 2015;115:207403.

    Not in our library10.1103/physrevlett.115.207403

  256. 256.

    Keren-Zur S, et al. Nonlinear beam shaping with plasmonic metasurfaces. ACS Photonics. 2015;3:117-123.

    Not in our library10.1021/acsphotonics.5b00528

  257. 257.

    Li GX, Zentgraf T, Zhang S. Rotational Doppler effect in nonlinear optics. Nat. Phys. 2016;12:736-740.

    Not in our library10.1038/nphys3699

  258. 258.

    Musarra G, et al. Rotation-dependent nonlinear absorption of orbital angular momentum beams in ruby. Opt. Lett. 2018;43:3073-3075.

    Not in our library10.1364/ol.43.003073

  259. 259.

    Qiu CW, Yang YJ. Vortex generation reaches a new plateau. Science. 2017;357:645.

    Not in our library10.1126/science.aan6359

  260. 260.

    Toda Y, et al. Single orbital angular mode emission from externally feed-backed vertical cavity surface emitting laser. Appl. Phys. Lett. 2017;111:101102.

    Not in our library10.1063/1.4989479

  261. 261.

    Miao P, et al. Orbital angular momentum microlaser. Science. 2016;353:464-467.

    Not in our library10.1126/science.aaf8533

  262. 262.

    Wang J. Metasurfaces enabling structured light manipulation: advances and perspectives [Invited]. Chin. Opt. Lett. 2018;16:050006.

    Not in our library10.3788/col201816.050006

  263. 263.

    Huang LL, et al. Dispersionless phase discontinuities for controlling light propagation. Nano Lett. 2012;12:5750-5755.

    Not in our library10.1021/nl303031j

  264. 264.

    Sun YZ, et al. Vector beam generation via micrometer-scale photonic integrated circuits and plasmonic Nano-antennae. J. Opt. Soc. Am. B. 2016;33:360-366.

    Not in our library10.1364/josab.33.000360

  265. 265.

    Chen P, et al. Digitalizing self-assembled chiral superstructures for optical vortex processing. Adv. Mater. 2018;30:1705865.

    Not in our library10.1002/adma.201705865

  266. 266.

    Chen Y, et al. Mapping twisted light into and out of a photonic chip. Phys. Rev. Lett. 2018;121:233602.

    Not in our library10.1103/physrevlett.121.233602

  267. 267.

    Jin Y, et al. Dynamic modulation of spatially structured polarization fields for real-time control of ultrafast laser-material interactions. Opt. Express. 2013;21:25333-25343.

    Not in our library10.1364/oe.21.025333

  268. 268.

    Allegre OJ, et al. Complete wavefront and polarization control for ultrashort-pulse laser microprocessing. Opt. Express. 2013;21:21198-21207.

    Not in our library10.1364/oe.21.021198

  269. 269.

    Toyoda K, et al. Transfer of light helicity to nanostructures. Phys. Rev. Lett. 2013;110:143603.

    Not in our library10.1103/physrevlett.110.143603

  270. 270.

    Syubaev S, et al. Direct laser printing of chiral plasmonic nanojets by vortex beams. Opt. Express. 2017;25:10214-10223.

    Not in our library10.1364/oe.25.010214

  271. 271.

    Masuda K, et al. Azo-polymer film twisted to form a helical surface relief by illumination with a circularly polarized Gaussian beam. Opt. Express. 2017;25:12499-12507.

    Not in our library10.1364/oe.25.012499

  272. 272.

    Takahashi F, et al. Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle. Sci. Rep. 2016;6:21738.

    Not in our library10.1038/srep21738

  273. 273.

    Torner L, Torres JP, Carrasco S. Digital spiral imaging. Opt. Express. 2005;13:873-881.

    Not in our library10.1364/opex.13.000873

  274. 274.

    Tan PS, et al. High-resolution wide-field standing-wave surface plasmon resonance fluorescence microscopy with optical vortices. Appl. Phys. Lett. 2010;97:241109.

    Not in our library10.1063/1.3525173

  275. 275.

    Zhang CL, et al. Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging. Appl. Phys. Lett. 2016;108:201601.

    Not in our library10.1063/1.4948249

  276. 276.

    Xie XS, et al. Harnessing the point-spread function for high-resolution far-field optical microscopy. Phys. Rev. Lett. 2014;113:263901.

    Not in our library10.1103/physrevlett.113.263901

  277. 277.

    Wei SB, et al. Sub-100nm resolution PSIM by utilizing modified optical vortices with fractional topological charges for precise phase shifting. Opt. Express. 2015;23:30143-30148.

    Not in our library10.1364/oe.23.030143

  278. 278.

    Kozawa Y, Matsunaga D, Sato S. Superresolution imaging via superoscillation focusing of a radially polarized beam. Optica. 2018;5:86-92.

    Not in our library10.1364/optica.5.000086

  279. 279.

    Willig KI, et al. STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis. Nature. 2006;440:935-939.

    Not in our library10.1038/nature04592

  280. 280.

    Wang SB, Chan CT. Lateral optical force on chiral particles near a surface. Nat. Commun. 2014;5:3307.

    Not in our library10.1038/ncomms4307

  281. 281.

    Brullot W, et al. Resolving enantiomers using the optical angular momentum of twisted light. Sci. Adv. 2016;2:e1501349.

    Not in our library10.1126/sciadv.1501349

  282. 282.
  283. 283.

    Jeffries GDM, et al. Using polarization-shaped optical vortex traps for single-cell nanosurgery. Nano Lett. 2007;7:415-420.

    Not in our library10.1021/nl0626784

  284. 284.

    Stellinga D, et al. An organic vortex laser. ACS Nano. 2018;12:2389-2394.

    Not in our library10.1021/acsnano.7b07703

  285. 285.

    Lavery MPJ, et al. Detection of a spinning object using light’s orbital angular momentum. Science. 2013;341:537-540.

    Not in our library10.1126/science.1239936

  286. 286.

    Cvijetic N, et al. Detecting lateral motion using light’s orbital angular momentum. Sci. Rep. 2015;5:15422.

    Not in our library10.1038/srep15422

  287. 287.

    Kravets VG, et al. Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection. Nat. Mater. 2013;12:304-309.

    Not in our library10.1038/nmat3537

  288. 288.

    Xie GD, et al. Using a complex optical orbital-angular-momentum spectrum to measure object parameters. Opt. Lett. 2017;42:4482-4485.

    Not in our library10.1364/ol.42.004482

  289. 289.

    Fu SY, Gao CQ. Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams. Photonics Res. 2016;4:B1-B4.

    Not in our library10.1364/prj.4.0000b1

  290. 290.

    Li Y, Yu L, Zhang YX. Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean. Opt. Express. 2017;25:12203-12215.

    Not in our library10.1364/oe.25.012203

  291. 291.

    Min CJ, et al. Plasmonic nano-slits assisted polarization selective detour phase meta-hologram. Laser Photonics Rev. 2016;10:978-985.

    Not in our library10.1002/lpor.201600101

  292. 292.

    Xie ZW, et al. On-chip spin-controlled orbital angular momentum directional coupling. J. Phys. D Appl. Phys. 2017;51:014002.

    Not in our library10.1088/1361-6463/aa9947

  293. 293.

    Zhang C, Ma L. Detecting the orbital angular momentum of electro-magnetic waves using virtual rotational antenna. Sci. Rep. 2017;7:4585.

    Not in our library10.1038/s41598-017-04313-4

  294. 294.

    Mei ST, et al. On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits. Nanoscale. 2016;8:2227-2233.

    Not in our library10.1039/c5nr07374j

  295. 295.

    Foo G, Palacios DM, Swartzlander GA. Optical vortex coronagraph. Opt. Lett. 2005;30:3308-3310.

    Not in our library10.1364/ol.30.003308

  296. 296.

    Lee JH, et al. Experimental verification of an optical vortex coronagraph. Phys. Rev. Lett. 2006;97:053901.

    Not in our library10.1103/physrevlett.97.053901

  297. 297.

    Swartzlander GA, et al. Astronomical demonstration of an optical vortex coronagraph. Opt. Express. 2008;16:10200-10207.

    Not in our library10.1364/oe.16.010200

  298. 298.

    Mawet D, et al. Annular groove phase mask coronagraph. Astrophys. J. 2005;633:1191-1200.

    Not in our library10.1086/462409

  299. 299.

    Absil, O. et al. Three years of harvest with the vector vortex coronagraph in the thermal infrared. In Proc. SPIE 9908, Ground-based and Airborne Instrumentation for Astronomy VI. 99080Q (SPIE, Edinburgh, United Kingdom, 2016).

    Not in our library

  300. 300.

    Aleksanyan A, Kravets N, Brasselet E. Multiple-star system adaptive vortex coronagraphy using a liquid crystal light valve. Phys. Rev. Lett. 2017;118:203902.

    Not in our library10.1103/physrevlett.118.203902

  301. 301.

    Aleksanyan A, Brasselet E. High-charge and multiple-star vortex coronagraphy from stacked vector vortex phase masks. Opt. Lett. 2018;43:383-386.

    Not in our library10.1364/ol.43.000383

  302. 302.

    Tamburini F, et al. Twisting of light around rotating black holes. Nat. Phys. 2011;7:195-197.

    Not in our library10.1038/nphys1907

  303. 303.

    Battersby S. Twisting the light away. New Sci. 2004;182:36-40.

    Not in our library

  304. 304.

    Yin JY, et al. Microwave vortex-beam emitter based on spoof surface plasmon polaritons. Laser Photonics Rev. 2018;12:1600316.

    Not in our library10.1002/lpor.201600316

  305. 305.

    Marzo A, Caleap M, Drinkwater BW. Acoustic virtual vortices with tunable orbital angular momentum for trapping of Mie particles. Phys. Rev. Lett. 2018;120:044301.

    Not in our library10.1103/physrevlett.120.044301

  306. 306.

    Bialynicki-Birula I, Charzyński S. Trapping and guiding bodies by gravitational waves endowed with angular momentum. Phys. Rev. Lett. 2018;121:171101.

    Not in our library10.1103/physrevlett.121.171101

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