[1] [1] Wang J. Metasurfaces enabling structured light manipulation: advances and perspectives[J]. Chinese Optics Letters, 2018, 16(5): 050006.

[2] [2] Yi A L, Yan L S, Pan Y, et al. Transmission of multi-dimensional signals for next generation optical communication systems[J]. Optics Communications, 2018, 408: 42-52.

[3] [3] Winzer P J. Modulation and multiplexing in optical communications[C]//Conference on Lasers & Electro-Optics, Baltimore, Maryland United States, 2009.

[4] [4] Zhou X, Yu J J. Multi-level, multi-dimensional coding for high-speed and high-spectral-efficiency optical transmission[J]. Journal of Lightwave Technology, 2009, 27(16): 3641-3653.

[5] [5] Richter T, Palushani E, Schmidt-Langhorst C, et al. Transmission of single-channel 16-QAM data signals at terabaud symbol rates[J]. Journal of Lightwave Technology, 2012, 30(4): 504-511.

[6] [6] Gnauck A H, Winzer P J, Chandrasekhar S, et al. Spectrally efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM[J]. Journal of Lightwave Technology, 2011, 29(4): 373-377.

[7] [7] Zhou X, Yu J J, Huang M F, et al. 64-Tb/s, 8 b/s/Hz, PDM-36QAM transmission over 320 km using both pre- and post-transmission digital signal processing[J]. Journal of Lightwave Technology, 2011, 29(4): 571-577.

[8] [8] Winzer P J. Making spatial multiplexing a reality[J]. Nature Photonics, 2014, 8(5): 345-348.

[9] [9] Willner A E, Huang H, Yan Y, et al. Optical communications using orbital angular momentum beams[J]. Advances in Optics and Photonics, 2015, 7(1): 66-106.

[10] [10] Guo Z Y, Qu S L, Liu S T. Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses[J]. Optics Communications, 2007, 273(1): 286-289.

[11] [11] Guo Z Y, Qu S L, Sun Z H, et al. Superposition of orbital angular momentum of photons by a combined computer-generated hologram fabricated in silica glass with femtosecond laser pulses[J]. Chinese Physics B, 2008, 17(11): 4199-4203.

[12] [12] Ran L L, Qu S L, Guo Z Y. Surface mico-structures on amorphous alloys induced by vortex femtosecond laser pulses[J]. Chinese physics B, 2010, 19(3): 034204.

[13] [13] Li Y, Guo Z Y, Qu S L. Living cell manipulation in a microfluidic device by femtosecond optical tweezers[J]. Optics and Lasers in Engineering, 2014, 55: 150-154.

[14] [14] Zhu L, Guo Z Y, Xu Q, et al. Calculating the torque of the optical vortex tweezer to the ellipsoidal microparticles[J]. Optics Communications, 2015, 354: 34-39.

[15] [15] Liu C X, Guo Z Y, Li Y, et al. Manipulating ellipsoidal micro-particles by femtosecond vortex tweezers[J]. Journal of Optics, 2015, 17(3): 035402.

[16] [16] Nye J F, Berry M V. Dislocations in wave trains[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1974, 336(1605): 165-190.

[17] [17] Berry M V, Nye J F, Wright F J. The elliptic umbilic diffraction catastrophe[J]. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1979, 291(1382): 453-484.

[18] [18] 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.

[19] [19] Yuan X C, Jia P, Lei T, et al. Optical vortices and optical communication with orbital angular momentum[J]. Journal of Shenzhen University (Science & Engineering), 2014, 31(4): 331-346.

[20] [20] Gibson G, Courtial J, Padgett M J, et al. Free-space information transfer using light beams carrying orbital angular momentum[J]. Optics Express, 2004, 12(22): 5448-5456.

[21] [21] Liu Y D, Gao C Q, Gao M W, et al. Superposition and detection of two helical beams for optical orbital angular momentum communication[J]. Optics Communications, 2008, 281(14): 3636-3639.

[22] [22] Krenn M, Fickler R, Fink M, et al. Communication with spatially modulated light through turbulent air across Vienna[J]. New Journal of Physics, 2014, 16(11): 113028.

[23] [23] Krenn M, Handsteiner J, Fink M, et al. Twisted light transmission over 143 km[J]. Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(48): 13648-13653.

[24] [24] Willner A J, Ren Y X, Xie G D, et al. Experimental demonstration of 20 Gbit/s data encoding and 2 ns channel hopping using orbital angular momentum modes[J]. Optics Letters, 2015, 40(24): 5810-5813.

[25] [25] Li S H, Wang J. Experimental demonstration of optical interconnects exploiting orbital angular momentum array[J]. Optics Express, 2017, 25(18): 21537-21547.

[26] [26] Fu S Y, Zhai Y W, Yin C, et al. Mixed orbital angular momentum amplitude shift keying through a single hologram[J]. OSA Continuum, 2018, 1(2): 295-308.

[27] [27] Kai C H, Huang P, Shen F, et al. Orbital angular momentum shift keying based optical communication system[J]. IEEE Photonics Journal, 2017, 9(2): 7902510.

[28] [28] Du J, Wang J. High-dimensional structured light coding/decoding for free-space optical communications free of obstructions[J]. Optics Letters, 2015, 40(21): 4827-4830.

[29] [29] Li X K, Li Y, Zeng X N, et al. Perfect optical vortex array for optical communication based on orbital angular momentum shift keying[J]. Journal of Optics, 2018, 20(12): 125604.

[30] [30] Awaji Y, Wada N, Toda Y. Demonstration of spatial mode division multiplexing using Laguerre-Gaussian mode beam in telecom-wavelength[C]//2010 23rd Annual Meeting of the IEEE Photonics Society, Denver, CO, USA, 2010: 551-552.

[31] [31] Wang J, Yang J Y, Fazal I M, et al. Demonstration of 12.8-bit/s/Hz spectral efficiency using 16-QAM signals over multiple orbital-angular-momentum modes[C]//2011 37th European Conference and Exhibition on Optical Communication, Geneva, Switzerland, 2011: 1-3.

[32] [32] Wang J, Yang J Y, Fazal I M, et al. 25.6-bit/s/Hz spectral efficiency using 16-QAM signals over pol-muxed multiple orbital-angular-momentum modes[C]//IEEE Photonic Society 24th Annual Meeting, Arlington, VA, USA, 2011: 587-588.

[33] [33] Fazal I M, Wang J, Yang J Y, et al. Demonstration of 2-Tbit/s data link using orthogonal orbital-angular-momentum modes and WDM[C]//Frontiers in Optics 2011, San Jose, California United States, 2011.

[34] [34] Wang J, Yang J Y, Fazal I M, et al. Terabit free-space data transmission employing orbital angular momentum multiplexing[J]. Nature Photonics, 2012, 6(7): 488-496.

[35] [35] Huang H, Xie G D, Yan Y, et al. 100 Tbit/s free-space data link using orbital angular momentum mode division multiplexing combined with wavelength division multiplexing[C]//2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, USA, 2013: 1-3.

[36] [36] Huang H, Xie G D, Yan Y, et al. 100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength[J]. Optics Letters, 2014, 39(2): 197-200.

[37] [37] Wang J, Li S H, Li C, et al. Ultra-high 230-bit/s/Hz spectral efficiency using OFDM/OQAM 64-QAM signals over pol-muxed 22 orbital angular momentum (OAM) modes[C]//Optical Fiber Communications Conference & Exhibition, San Francisco, CA, USA, 2014: 1-3.

[38] [38] Wang J, Li S H, Luo M, et al. N-dimentional multiplexing link with 1.036-Pbit/s transmission capacity and 112.6-bit/s/Hz spectral efficiency using OFDM-8QAM signals over 368 WDM pol-muxed 26 OAM modes[C]//2014 the European Conference on Optical Communication, Cannes, France, 2014: 1-3.

[39] [39] Wang J, Liu J, Lv X, et al. Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals[C]//2015 European Conference on Optical Communication (ECOC), Valencia, Spain, 2015: 1-3.

[40] [40] Lei T, Zhang M, Li Y R, et al. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings[J]. Light: Science & Applications, 2015, 4(3): e257.

[41] [41] Zhu Y X, Zou K H, Zheng Z N, et al. 1 λ× 1.44 Tb/s free-space IM-DD transmission employing OAM multiplexing and PDM[J]. Optics Express, 2016, 24(4): 3967-3980.

[42] [42] Li S H, Wang J. Multi-orbital-angular-momentum multi-ring fiber for high-density space-division multiplexing[J]. IEEE Photonics Journal, 2013, 5(5): 7101007.

[43] [43] Yue Y, Yan Y, Ahmed N, et al. Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber[J]. IEEE Photonics Journal, 2012, 4(2): 535-543.

[44] [44] Li S H, Wang J. A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 rings × 22 modes)[J]. Scientific Reports, 2014, 4: 3853.

[45] [45] Baghdady J, Miller K, Morgan K, et al. Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing[J]. Optics Express, 2016, 24(9): 9794-9805.

[46] [46] Ren Y X, Li L, Wang Z, et al. Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications[J]. Scientific Reports, 2016, 6: 33306.

[47] [47] Wang W, Wang P, Cao T, et al. Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence[J]. IEEE Photonics Journal, 2017, 9(5): 7905315.

[48] [48] Zhao Y F, Wang A D, Zhu L, et al. Performance evaluation of underwater optical communications using spatial modes subjected to bubbles and obstructions[J]. Optics Letters, 2017, 42(22): 4699-4702.

[49] [49] Zhao Y F, Xu J, Wang A D, et al. Demonstration of data-carrying orbital angular momentum-based underwater wireless optical multicasting link[J]. Optics Express, 2017, 25(23): 28743-28751.

[50] [50] Wang A D, Zhu L, Zhao Y F, et al. Adaptive water-air-water data information transfer using orbital angular momentum[J]. Optics Express, 2018, 26(7): 8669-8678.

[51] [51] Gori F, Guattari G, Padovani C. Bessel-gauss beams[J]. Optics Communications, 1987, 64(6): 491-495.

[52] [52] Zhu L, Wang J. Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode[J]. Optics Letters, 2015, 40(23): 5463-5466.

[53] [53] Ahmed N, Lavery M P, Huang H, et al. Experimental demonstration of obstruction-tolerant free-space transmission of two 50-Gbaud QPSK data channels using Bessel beams carrying orbital angular momentum[C]//2014 The European Conference on Optical Communication (ECOC), Cannes, France, 2014: 1-3.

[54] [54] Li S H, Wang J. Adaptive free-space optical communications through turbulence using self-healing Bessel beams[J]. Scientific Reports, 2017, 7: 43233.

[55] [55] Mphuthi N, Gailele L, Litvin I, et al. Free-space optical communication link with shape-invariant orbital angular momentum Bessel beams[J]. Applied Optics, 2019, 58(16): 4258-4264.

[56] [56] Ostrovsky A S, Rickenstorff-Parrao C, Arrizón V. Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator[J]. Optics Letters, 2013, 38(4): 534-536.

[57] [57] Wang Y J, Li X Z, Li H H, et al. Research progress of perfect vortex field[J]. Laser & Optoelectronics Progress, 2017, 54(9): 090007.

[58] [58] Vaity P, Rusch L. Perfect vortex beam: Fourier transformation of a Bessel beam[J]. Optics Letters, 2015, 40(4): 597-600.

[59] [59] Zhu F Q, Huang S J, Shao W, et al. Free-space optical communication link using perfect vortex beams carrying orbital angular momentum (OAM)[J]. Optics Communications, 2017, 396:50-57.

[60] [60] Wang L, Jiang X C, Zou L, et al. Two-dimensional multiplexing scheme both with ring radius and topological charge of perfect optical vortex beam[J]. Journal of Modern Optics, 2019, 66(1): 87-92.

[61] [61] Zhan Q W. Cylindrical vector beams: from mathematical concepts to applications[J]. Advances in Optics and Photonics, 2009, 1(1): 1-57.

[62] [62] Fu S Y, Gao C Q. Selective generation of arbitrary vectorial vortex beams (Invited Paper)[J]. Acta Optica Sinica, 2019, 39(1): 0126014.

[63] [63] Ndagano B, Nape I, Cox M A, et al. Creation and detection of vector vortex modes for classical and quantum communication[J]. Journal of Lightwave Technology, 2018, 36(2): 292-301.

[64] [64] Lavery M P J, Milione G, Nguyen T A, et al. Space division multiplexing in a basis of vector modes[C]//2014 The European Conference on Optical Communication (ECOC), Cannes, France, 2014: 1-3.

[65] [65] Zhao Y F, Wang J. High-base vector beam encoding/decoding for visible-light communications[J]. Optics Letters, 2015, 40(21): 4843-4846.

[66] [66] Zhang J B, Li F, Li J P, et al. 120 Gbit/s 2× 2 vector-modes-division-multiplexing DD-OFDM-32QAM free-space transmission[J]. IEEE Photonics Journal, 2016, 8(6): 7907008.

[67] [67] Li P, Zhang Y, Liu S, et al. Generation of perfect vectorial vortex beams[J]. Optics Letters, 2016, 41(10): 2205-2208.

[68] [68] Fu S Y, Wang T L, Zhang Z Y, et al. Selective acquisition of multiple states on hybrid Poincare sphere[J]. Applied Physics Letters, 2017, 110(19): 191102.

[69] [69] Okida M, Omatsu T, Itoh M, et al. Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO 4 1.3-μm bounce laser[J]. Optics Express, 2007, 15(12): 7616-7622.

[70] [70] Lee A J, Omatsu T, Pask H M. Direct generation of a first-Stokesvortex laser beam from a self-Raman laser[J]. Optics Express,2013, 21(10): 12401-12409.

[71] [71] Lee A J, Zhang C Y, Omatsu T, et al. An intracavity, frequency-doubled self-Raman vortex laser[J]. Optics Express, 2014,22(5): 5400-5409.

[72] [72] Miao P, Zhang Z F, Sun J B, et al. Orbital angular momentummicrolaser[J]. Science, 2016, 353(6298): 464-467.

[73] [73] Wang S, Zhang S L, Qiao H C, et al. Direct generation of vortexbeams from a double-end polarized pumped Yb:KYW laser[J].Optics Express, 2018, 26(21): 26925-26932.

[74] [74] Beijersbergen M W, Coerwinkel R P C, Kristensen M, et al.Helical-wavefront laser beams produced with a spiral phaseplate[J]. Optics Communications, 1994, 112(5-6): 321-327.

[75] [75] Turnbull G A, Robertson D A, Smith G M, et al. The generationof free-space Laguerre-Gaussian modes at millimetre-wavefrequencies by use of a spiral phaseplate[J]. Optics Communications,1996, 127(4-6): 183-188.

[76] [76] Oemrawsingh S S R, Van Houwelingen J A W, Eliel E R, et al.Production and characterization of spiral phase plates for opticalwavelengths[J]. Applied Optics, 2004, 43(3): 688-694.

[77] [77] Sueda K, Miyaji G, Miyanaga N, et al. Laguerre-Gaussian beamgenerated with a multilevel spiral phase plate for high intensitylaser pulses[J]. Optics Express, 2004, 12(15): 3548-3553.

[78] [78] Massari M, Ruffato G, Gintoli M, et al. Fabrication and characterizationof high-quality spiral phase plates for optical applications[J]. Applied Optics, 2015, 54(13): 4077-4083.

[79] [79] Rafighdoost J, Sabatyan A. Spirally phase-shifted zone plate forgenerating and manipulating multiple spiral beams[J]. Journal ofthe Optical Society of America B, 2017, 34(3): 608-612.

[80] [80] Lin J, Yuan X C, Tao S H, et al. Synthesis of multiple collinearhelical modes generated by a phase-only element[J]. Journal ofthe Optical Society of America A, 2006, 23(5): 1214-1218.

[81] [81] Wei S B, Wang D P, Lin J, et al. Demonstration of orbital angularmomentum channel healing using a Fabry-Pérot cavity[J]. Opto-Electronic Advances, 2018, 1(5): 180006.

[82] [82] Ke X Z, Xue P. Generation of Orbital Angular Momentum superpositionsand its test[J]. Infrared and Laser Engineering,2018, 47(4): 417007.

[83] [83] Mirhosseini M, Magana-Loaiza O S, Chen C C, et al. Rapidgeneration of light beams carrying orbital angular momentum[J].Optics Express, 2013, 21(25): 30196-30203.

[84] [84] Heckenberg N R, McDuff R, Smith C P, et al. Generation ofoptical phase singularities by computer-generated holograms[J].Optics Letters, 1992, 17(3): 221-223.

[85] [85] Beijersbergen M W, Allen L, Van der Veen H E L O, et al. Astigmaticlaser mode converters and transfer of orbital angularmomentum[J]. Optics Communications, 1993, 96(1-3):123-132.

[86] [86] Marrucci L, Manzo C, Paparo D. Optical spin-to-orbital angularmomentum conversion in inhomogeneous anisotropic media[J].Physical Review Letters, 2006, 96(16): 163905.

[87] [87] Karimi E, Piccirillo B, Nagali E, et al. Efficient generation andsorting of orbital angular momentum eigenmodes of light bythermally tuned q-plates[J]. Applied Physics Letters, 2009,94(23): 231124.

[88] [88] Cardano F, Karimi E, Slussarenko S, et al. Polarization patternof vector vortex beams generated by q-plates with different topologicalcharges[J]. Applied Optics, 2012, 51(10): C1-C6.

[89] [89] Marrucci L, Karimi E, Slussarenko S, et al. Spin-to-orbital conversionof the angular momentum of light and its classical andquantum applications[J]. Journal of Optics, 2011, 13(6): 064001.

[90] [90] Devlin R C, Ambrosio A, Rubin N A, et al. Arbitraryspin-to-orbital angular momentum conversion of light[J].Science, 2017, 358(6365): 896-901.

[91] [91] Guo Z Y, Wang Y Z, Zheng Q, et al. Advances of research onantenna technology of vortex electromagnetic waves[J]. Journalof Radars, 2019, 8(5): 631-655.

[92] [92] Karimi E, Schulz S A, De Leon I, et al. Generating optical orbitalangular momentum at visible wavelengths using a plasmonicmetasurface[J]. Light: Science & Applications, 2014, 3(5): e167.

[93] [93] Du J, Wang J. Design of on-chip N-fold orbital angular momentummulticasting using V-shaped antenna array[J]. ScientificReports, 2015, 5: 9662.

[94] [94] Du J, Wang J. Dielectric metasurfaces enabling twisted lightgeneration/detection/(de) multiplexing for data informationtransfer[J]. Optics Express, 2018, 26(10): 13183-13194.

[95] [95] Zhao Z, Wang J, Li S H, et al. Metamaterials-based broadbandgeneration of orbital angular momentum carrying vectorbeams[J]. Optics Letters, 2013, 38(6): 932-934.

[96] [96] Wang W, Li Y, Guo Z Y, et al. Ultra-thin optical vortex phaseplate based on the metasurface and the angular momentumtransformation[J]. Journal of Optics, 2015, 17(4): 045102.

[97] [97] Zhao Y F, Du J, Zhang J R, et al. Generating structured lightwith phase helix and intensity helix using reflection-enhanced plasmonic metasurface at 2 μm[J]. Applied Physics Letters,2018, 112(17): 171103.

[98] [98] Ma Z J, Li Y, Li Y, et al. All-dielectric planar chiral metasurfacewith gradient geometric phase[J]. Optics Express, 2018, 26(5):6067-6078.

[99] [99] Inavalli V V G K, Viswanathan N K. Switchable vector vortexbeam generation using an optical fiber[J]. Optics Communications,2010, 283(6): 861-864.

[100] [100] Yan Y, Wang J, Zhang L, et al. Fiber coupler for generatingorbital angular momentum modes[J]. Optics Letters, 2011,36(21): 4269-4271.

[101] [101] Yan Y, Zhang L, Wang J, et al. Fiber structure to convert aGaussian beam to higher-order optical orbital angular momentummodes[J]. Optics Letters, 2012, 37(16): 3294-3296.

[102] [102] Yan Y, Yue Y, Huang H, et al. Efficient generation and multiplexingof optical orbital angular momentum modes in a ring fiberby using multiple coherent inputs[J]. Optics Letters, 2012,37(17): 3645-3647.

[103] [103] Fang L, Wang J. Flexible generation/conversion/exchange of fiber-guided orbital angular momentum modes using helical gratings[J]. Optics Letters, 2015, 40(17): 4010-4013.

[104] [104] Li S H, Mo Q, Hu X, et al. Controllable all-fiber orbital angular momentum mode converter[J]. Optics Letters, 2015, 40(18): 4376-4379.