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

[2] Molina-Terriza G, Torres J P, Torner L. Twisted photons[J]. Nature Physics, 3, 305-310(2007).

[3] Xu W H, Shou Y C, Luo H L. Spin-orbit interaction of light[J]. Chinese Journal of Quantum Electronics, 39, 159-181(2022).

[4] Andersen M, Ryu C, Cladé P et al. Quantized rotation of atoms from photons with orbital angular momentum[J]. Physical Review Letters, 97, 170406(2006).

[5] Shen Y J, Wang X J, Xie Z W et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities[J]. Light: Science & Applications, 8, 1-29(2019).

[6] Ke X Z, Xie Y C, Zhang Y. Orbital angular momentum measurement of vortex beam and its performance improvement[J]. Acta Optica Sinica, 39, 0126017(2019).

[7] Huang X M, Wang F, Lu B L et al. Modulation for giant kerr nonlinear effect via orbital angular momentum exchange[J]. Acta Optica Sinica, 42, 2219002(2022).

[8] Chang N, Jin L W, Gao W. Frequency doubling and propagation characteristics of orbital angular momentum beams based on spiral phase modulation[J]. Acta Optica Sinica, 39, 0319001(2019).

[9] Ruffato G, Massari M, Romanato F. Generation of high-order Laguerre–Gaussian modes by means of spiral phase plates[J]. Optics Letters, 39, 5094-5097(2014).

[10] Chen P, Ge S J, Ma L L et al. Generation of equal-energy orbital angular momentum beams via photopatterned liquid crystals[J]. Physical Review Applied, 5, 044009(2016).

[11] Zhao Y G, Wang Z P, Yu H H et al. Direct generation of optical vortex pulses[J]. Applied Physics Letters, 101, 031113(2012).

[12] Yu H H, Xu M M, Zhao Y G et al. Dual-wavelength laser with topological charge[J]. AIP Advances, 3, 092129(2013).

[13] Yan Q Y, Miao Y, Song Q Y et al. Characteristic analysis and research progress of vortex beam produced by optical microcavity[J]. Laser & Optoelectronics Progress, 59, 0100002(2022).

[14] Ohtake Y, Ando T, Fukuchi N et al. Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator[J]. Optics Letters, 32, 1411-1413(2007).

[15] Padgett M, Bowman R. Tweezers with a twist[J]. Nature Photonics, 5, 343-348(2011).

[16] Lafong A, Hossack W J, Arlt J et al. Time-Multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications[J]. Optics Express, 14, 3065-3072(2006).

[17] Rego L, Dorney K M, Brooks N J et al. Generation of extreme-ultraviolet beams with time-varying orbital angular momentum[J]. Science, 364, eaaw9486(2019).

[18] Dorney K M, Rego L, Brooks N J et al. Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation[J]. Nature Photonics, 13, 123-130(2019).

[19] Huang C, Zhang C, Xiao S M et al. Ultrafast control of vortex microlasers[J]. Science, 367, 1018-1021(2020).

[20] McGloin D, Simpson N B, Padgett M J. Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam[J]. Applied Optics, 37, 469-472(1998).

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

[22] Arlt J, Dholakia K, Allen L et al. The production of multiringed Laguerre–Gaussian modes by computer-generated holograms[J]. Journal of Modern Optics, 45, 1231-1237(1998).

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

[24] Yuan S Z, Tian J L, Yang G. Hermitian-Gaussian and Laguerre-Gaussian and the conversion between them[J]. Guangxi Physics, 32, 19-24(2011).

[25] Fang X Y, Kuang Z Y, Chen P et al. Examining second-harmonic generation of high-order Laguerre–Gaussian modes through a single cylindrical lens[J]. Optics Letters, 42, 4387-4390(2017).

[26] Pan J, Shen Y J, Wan Z S et al. Index-tunable structured-light beams from a laser with an intracavity astigmatic mode converter[J]. Physical Review Applied, 14, 044048(2020).

[27] Dholakia K, Simpson N B, Padgett M J et al. Second-harmonic generation and the orbital angular momentum of light[J]. Physical Review A, 54, R3742-R3745(1996).

[28] Fang X Y, Wei D Z, Liu D M et al. Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTaO3 crystal[J]. Applied Physics Letters, 107, 161102(2015).

[29] Wang Y M, Wei D Z, Zhu Y Z et al. Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation[J]. Applied Physics Letters, 109, 081105(2016).

[30] Li Y, Zhou Z Y, Ding D S et al. Sum frequency generation with two orbital angular momentum carrying laser beams[J]. Journal of the Optical Society of America B, 32, 407-411(2015).

[31] Wei D, Guo J L, Fang X Y et al. Multiple generations of high-order orbital angular momentum modes through cascaded third-harmonic generation in a 2D nonlinear photonic crystal[J]. Optics Express, 25, 11556-11563(2017).

[32] Fang X Y, Yang G, Wei D Z et al. Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystal[J]. Optics Letters, 41, 1169-1172(2016).

[33] Ellenbogen T, Voloch-Bloch N, Ganany-Padowicz A et al. Nonlinear generation and manipulation of Airy beams[J]. Nature Photonics, 3, 395-398(2009).

[34] Shapira A, Juwiler I, Arie A. Nonlinear computer-generated holograms[J]. Optics Letters, 36, 3015-3017(2011).

[35] Shapira A, Shiloh R, Juwiler I et al. Two-dimensional nonlinear beam shaping[J]. Optics Letters, 37, 2136-2138(2012).

[36] Hong X H, Yang B, Zhang C et al. Nonlinear volume holography for wave-front engineering[J]. Physical Review Letters, 113, 163902(2014).

[37] Kurz J R, Schober A M, Hum D S et al. Nonlinear physical optics with transversely patterned quasi-phase-matching gratings[J]. IEEE Journal of Selected Topics in Quantum Electronics, 8, 660-664(2002).

[38] Imeshev G, Proctor M, Fejer M M. Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings[J]. Optics Letters, 23, 673-675(1998).

[39] Qin Y Q, Zhang C, Zhu Y Y et al. Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures[J]. Physical Review Letters, 100, 063902(2008).

[40] Yang B, Hong X H, Yue Y Y et al. Nonlinear optical Fourier transform in an optical superlattice with “x+2” structure[J]. Optics Express, 23, 18310-18315(2015).

[41] Kogelnik H, Li T. Laser beams and resonators[J]. Applied Optics, 5, 1550-1567(1966).

[42] Forbes A, Dudley A, McLaren M. Creation and detection of optical modes with spatial light modulators[J]. Advances in Optics and Photonics, 8, 200-227(2016).

[43] Abramochkin E, Volostnikov V. Beam transformations and nontransformed beams[J]. Optics Communications, 83, 123-135(1991).

[44] Armstrong J A, Bloembergen N, Ducuing J et al. Interactions between light waves in a nonlinear dielectric[J]. Physical Review, 127, 1918-1939(1962).

[45] Zhou M S, Ma J C, Zhang C et al. Numerical simulation of nonlinear field distributions in two-dimensional optical superlattices[J]. Optics Express, 20, 1261-1267(2012).

[46] Zhao R Z, Xu Y G, Lu R E et al. Second-harmonic generation of single-mode Laguerre-Gaussian beams with an improved quasi-phase-matching method[J]. Optics Express, 28, 39241-39249(2020).