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

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

[3] R Fickler, G Campbell, B Buchler, et al. Quantum entanglement of angular momentum states with quantum numbers up to 10, 010. Proceedings of the National Academy of Sciences of the United States of America, 113, 13642-13647(2016).

[4] R Fickler, R Lapkiewicz, W N Plick, et al. Quantum entanglement of high angular momenta. Science, 338, 640-643(2012).

[5] O Emile, J Emile. Naked eye picometer resolution in a Michelson interferometer using conjugated twisted beams. Optics Letters, 42, 354-357(2017).

[6] T Omatsu, K Miyamoto, K Toyoda, et al. A new twist for materials science: the formation of chiral structures using the angular momentum of light. Advanced Optical Materials, 7, 1801672(2019).

[7] T Omatsu, K Miyamoto, K I Yuyama, et al. Laser-induced forward-transfer with light possessing orbital angular momentum. Journal of Photochemistry and Photobiology C: Photochemistry Reviews, 52, 100535(2022).

[8] J Leach, B Jack, J Romero, et al. Quantum correlations in optical angle–orbital angular momentum variables. Science, 329, 662-665(2010).

[9] B Wang, J Shi, T Zhang, et al. Improved lateral resolution with an annular vortex depletion beam in STED microscopy. Optics Letters, 42, 4885-4888(2017).

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

[11] V V Kotlyar, S N Khonina, A A Almazov, et al. Elliptic Laguerre-Gaussian beams. Journal of the Optical Society of America, A. Optics, Image Science, and Vision, 23, 43-56(2006).

[12] D Mcgloin, K Dholakia. Bessel beams: Diffraction in a new light. Contemporary Physics, 46, 15-28(2005).

[13] P W Smith. Mode selection in lasers. Proceedings of the IEEE, 60, 422-440(1972).

[14] Y Zhang, H Yu, H Zhang, et al. Self-mode-locked Laguerre-Gaussian beam with staged topological charge by thermal-optical field coupling. Optics Express, 24, 5514-5522(2016).

[15] M T Chang, H C Liang, K W Su, 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. Optics Express, 24, 8754-8762(2016).

[16] Y Yang, W Wang, P Moitra, et al. Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation. Nano Letters, 14, 1394-1399(2014).

[17] A A Malyutin, V A Ilyukhin. Generation of high-order Hermite-Gaussian modes in a flashlamp-pumped neodymium phosphate glass laser and their conversion to Laguerre-Gaussian modes. Quantum Electronics, 37, 181(2007).

[18] Y Chen, Z X Fang, Y X Ren, et al. Generation and characterization of a perfect vortex beam with a large topological charge through a digital micromirror device. Applied Optics, 54, 8030-8035(2015).

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

[20] Miaojun Gu, Jun Zeng, Jinhong Li. Generation and Interference of vortex beam based on spiral phase plate. Laser & Optoelectronics Progress, 53, 092602(2016).

[21] J Xin, K Dai, L Zhong, et al. Generation of optical vortices by using spiral phase plates made of polarization dependent devices. Optics Letters, 39, 1984-1987(2014).

[22] Y Yan, L Zhang, J Wang, et al. Fiber structure to convert a Gaussian beam to higher-order optical orbital angular momentum modes. Optics Letters, 37, 3294-3296(2012).

[23] E Karimi, S A Schulz, Leon I De, et al. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light: Science & Applications, 3, e167(2014).

[24] Z Qiao, G Xie, Y Wu, et al. Generating high‐charge optical vortices directly from laser up to 288 th order. Laser & Photonics Reviews, 12, 1800019(2018).

[25] D Naidoo, F S Roux, A Dudley, et al. Controlled generation of higher-order Poincaré sphere beams from a laser. Nature Photonics, 10, 327-332(2016).

[26] J W Kim, W A Clarkson. Selective generation of Laguerre-Gaussian (LG_0n) mode output in a diode-laser pumped Nd:YAG laser. Optics Communications, 296, 109-112(2013).

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

[28] X Huang, B Xu, S Cui, et al. Direct generation of vortex laser by rotating induced off-axis pumping. IEEE Journal of Selected Topics in Quantum Electronics, 24, 1-6(2018).

[29] Y Yuan, L Tong, F Cai, et al. Direct generation of optical vortex arrays by rotating in an all-solid-state Yb: CALGO laser. Optical Materials Express, 11, 1594-1602(2021).

[30] D J Kim, J W Kim. Direct generation of an optical vortex beam in a single-frequency Nd:YVO₄ laser. Optics Letters, 40, 399-402(2015).

[31] Y F Chen, Y P Lan, S C Wang. Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers. Applied Physics B, 72, 167-170(2001).

[32] M Wang, Y Ma, Q Sheng, et al. Laguerre-Gaussian beam generation via enhanced intracavity spherical aberration. Optics Express, 29, 27783-27790(2021).

[33] Q Sheng, A Wang, Y Ma, et al. Intracavity spherical aberration for selective generation of single-transverse-mode Laguerre-Gaussian output with order up to 95. PhotoniX, 3, 4(2022).

[34] Z Qiao, Z Wan, G Xie, et al. Multi-vortex laser enabling spatial and temporal encoding. PhotoniX, 1, 1-14(2020).

[35] Lunbin Zhou, Kai Feng, Dong Wang, et al. Research on direct generation of high-power and high-order vortex lasers using defect-mirror technology (Invited). Infrared and Laser Engineering, 50, 20210408(2021).

[36] A Ito, Y Kozawa, S Sato. Generation of hollow scalar and vector beams using a spot-defect mirror. Journal of the Optical Society of America, A. Optics, Image Science, and Vision, 27, 2072-2077(2010).

[37] S P Chard, P C Shardlow, M J Damzen. High-power non-astigmatic TEM₀₀ and vortex mode generation ina compact bounce laser design. Applied Physics B, 97, 275-280(2009).

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

[39] A J Lee, H M Pask, T Omatsu. A continuous-wave vortex Raman laser with sum frequency generation. Applied Physics B, 122, 1-7(2016).

[40] J C Tung, Y Y Ma, K Miyamoto, et al. Bottle beam generation from a frequency-doubled Nd:YVO₄ laser. Scientific Reports, 8, 1-6(2018).

[41] N Matsumoto, T Ando, T Inoue, et al. Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators. Journal of the Optical Society of America A, 25, 1642-1651(2008).

[42] K Sueda, G Miyaji, N Miyanaga, et al. Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses. Optics Express, 12, 3548-3553(2004).

[43] N A Chaitanya, A Aadhi, M V Jabir, et al. Frequency-doubling characteristics of high-power, ultrafast vortex beams. Optics Letters, 40.11, 2614-2617(2015).

[44] X Hui, S Zheng, Y Hu, et al. Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam. IEEE Antennas & Wireless Propagation Letters, 14, 966-969(2015).

[45] N Chaitanya, A Aadhi, M V Jabir, et al. Frequency-doubling characteristics of high-power, ultrafast vortex beams. Optics Letters, 40, 2614-2617(2015).

[46] [46] Sasaki Y, Yusufu T, Miyamoto K, et al. Highly efficient frequency doubling of optical vtex[C]Conference on Lasers & Electrooptics Pacific Rim, 2015: 15717830.

[47] T Yusufu, Y Sasaki, S Araki, et al. Beam propagation of efficient frequency-doubled optical vortices. Applied Optics, 55, 5263-5266(2016).

[48] N A Chaitanya, S C Kumar, K Devi, et al. Ultrafast optical vortex beam generation in the ultraviolet. Optics Letters, 41, 2715-2718(2016).

[49] [49] Yoshihiro Nishigata, ChengYeh Lee, Yuji Miyamoto, et al. Optical vtex pumped solidstate Raman laser[C]Solid State Lasers XXVI: Technology Devices, SPIE, 2017, 10082: 1316.

[50] R K Saripalli, A Ghosh, N A Chaitanya, et al. Frequency-conversion of vector vortex beams with space-variant polarization in single-pass geometry. Applied Physics Letters, 115, 051101(2019).

[51] P Schemmel, G Pisano, B Maffei. Modular spiral phase plate design for orbital angular momentum generation at millimetre wavelengths. Optics Express, 22, 14712-14726(2014).

[52] Mingwei Gao, Chunqing Gao, Zhifeng Lin. Generation of twisted stigmatic beam and transfer of orbital angular momentum during the beam transformation. Acta Physica Sinica, 56, 2184-2190(2007).

[53] Y Shen, Y Meng, X Fu, et al. Wavelength-tunable Hermite-Gaussian modes and an orbital-angular-momentum-tunable vortex beam in a dual-off-axis pumped Yb:CALGO laser. Optics Letters, 43, 291-294(2018).

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

[55] J C Tung, K W Liu, S C Chen. Generating multiple optical vortices in orange beams induced by selectively pumped frequency-doubled solid-state Raman lasers with mode conversion. Optics Letters, 47, 945-948(2022).

[56] J Pan, Y Shen, Z Wan, et al. Index-tunable structured-light beams from a laser with an intracavity astigmatic mode converter. Physical Review Applied, 14, 44048(2020).

[57] C Kränkel, D T Marzahl, F Moglia, et al. Out of the blue: semiconductor laser pumped visible rare‐earth doped lasers. Laser & Photonics Reviews, 10, 548-568(2016).

[58] [58] Ma Y, Tung J C, Chen Y F, et al. Hedness control of visible optical vtex output from a diodepumped Pr3+:YLF Laser[C]European Quantum Electronics Conference. Institute of Electrical Electronics Engineers Inc, 2019: 19148864.

[59] [59] Ma Y, Tung J C, Miyamoto K, et al. Direct generation of vtex beams from a diodepumped Pr3+:YLF laser [C]CLEO: Applications Technology, 2019: 18846954.

[60] Y Ma, A Vallés, J C Tung, et al. Direct generation of red and orange optical vortex beams from an off-axis diode-pumped Pr³⁺: YLF laser. Optics Express, 27, 18190-18200(2019).

[61] A S Rao, K Miamoto, T Omatsu. Ultraviolet intracavity frequency-doubled Pr³⁺: LiYF₄ orbital Poincaré laser. Optics Express, 28, 37397-37405(2020).

[62] A S Rao, T Miike, K Miamoto, et al. Direct generation of 523 nm orbital Poincaré mode from a diode-pumped Pr³⁺: LiYF₄ laser with an off-axis optical needle pumping geometry. Optics Express, 29, 30409-30418(2021).

[63] [63] Rao A S, Miyamoto K, Omatsu T. Direct generation of vtex lattice modes from an intracavity frequency doubled Pr:YLF laser[C]2021 Conference on Lasers ElectroOptics (CLEO), 2021: 21411084.

[64] X Lin, M Chen, Q Feng, et al. LD-pumped high-power CW Pr³⁺:YLF Laguerre-Gaussian lasers at 639 nm. Optics & Laser Technology, 142, 107273(2021).

[65] X Lin, Q Feng, Y Zhu, et al. Diode-pumped wavelength-switchable visible Pr³⁺:YLF laser and vortex laser around 670 nm. Opto-Electronic Advances, 4, 210006(2021).

[66] Q Y Tian, B Xu, N Li, . et al. Direct generation of orthogonally polarized dual-wavelength continuous-wave and passively Q-switched vortex beam in diode-pumped Pr:YLF lasers. Optics Letters, 44, 5586-5589(2019).

[67] N Li, J J Huang, B Xu, et al. Direct generation of an ultrafast vortex beam in a CVD-graphene-based passively mode-locked Pr:LiYF₄ visible laser. Photonics Research, 7, 1209-1213(2019).

[68] N Li, B Xu, S W Cui, et al. High-order vortex generation from CW and passively Q-switched Pr:YLF visible lasers. IEEE Photonics Technology Letters, 31, 1457-1460(2019).

[69] S Luo, Z Cai, C Sheng, et al. 604-nm high-order vortex beams directly generated from a Pr:YLF laser with a cavity-loss-induced gain switching mechanism. Optics & Laser Technology, 127, 106185(2020).

[70] X J Lin, S W Cui, S H Ji, et al. LD-pumped high-power high-efficiency orange vortex Pr³⁺:YLF lasers. Optics & Laser Technology, 133, 106571(2021).

[71] S Cui, N Li, B Xu, et al. Direct generation of visible vortex Hermite-Gaussian modes in a diode-pumped Pr:YLF laser. Optics & Laser Technology, 131, 106389(2020).

[72] Y Zhao, Q Liu, W Zhou, et al. ~1 mJ pulsed vortex laser at 1645 nm with well-defined helicity. Optics Express, 24, 15596(2016).

[73] D Lin, J M O Daniel, W A Clarkson. Controlling the handedness of directly excited Laguerre-Gaussian modes in a solid-state laser. Optics Letters, 39, 3903-3906(2014).

[74] J Li, Y Yao, J Yu, et al. Efficient vortex laser with annular pumping formed by circle Dammann grating. IEEE Photonics Technology Letters, 28, 473-476(2015).

[75] H S He, Z Chen, J Dong. Direct generation of vector vortex beams with switchable radial and azimuthal polarizations in a monolithic Nd:YAG microchip laser. Applied Physics Express, 10, 052701(2017).

[76] M D Wei, Y S Lai, K C Chang. Generation of a radially polarized laser beam in a single microchip Nd:YVO₄ laser. Optics Letters, 38, 2443-2445(2013).

[77] Z Fang, Y Yao, K Xia, et al. Actively Q-switched and vortex Nd:YAG laser. Optics Communications, 347, 59-63(2015).

[78] Q Yang, Z X Yang, D Y Cai, et al. Direct generation of continuous-wave and passively Q-switched visible vortex beams from a doughnut-shaped diode-pumped Pr:YLF laser. Optics Express, 30, 23909-23917(2022).

[79] Y Senatsky, J F Bisson, A Shelobolin, et al. Circular modes selection in Yb:YAG laser using an intracavity lens with spherical aberration. Laser Physics, 19, 911-918(2009).

[80] [80] Rao A S, Mohashi T, Miike T, et al. Generation of circular geometric modes from Pr3+: YLF laser with spherical aberration [C]Conference on Lasers ElectroOpticsPacific Rim. US: Optica Publishing Group, 2022: CThP1H_02.

[81] A S Rao, T Morohashi, W R Kerridge-Johns, et al. Generation of higher-order Laguerre–Gaussian modes from a diode-pumped Pr³⁺:LiYF₄ laser with an intra-cavity spherical aberration. Journal of the Optical Society of America B-Optical Physics, 40, 406-411(2023).

[82] J Zou, Z Kang, R Wang, et al. Green/red pulsed vortex-beam oscillations in all-fiber lasers with visible-resonance gold nanorods. Nanoscale, 11, 15991-16000(2019).

[83] Z Dong, H Sun, Y Zhang, et al. Visible-wavelength-tunable, vortex-beam fiber laser based on a long-period fiber grating. IEEE Photonics Technology Letters, 33, 1173-1176(2021).

[84] H Xu, L Yang. Conversion of orbital angular momentum of light in chiral fiber gratings. Optics Letters, 38, 1978-1980(2013).

[85] H Yao, F Shi, Z Wu, et al. A mode generator and multiplexer at visible wavelength based on all-fiber mode selective coupler. Nanophotonics, 9, 973-981(2020).

[86] Jinhai Zou, Hongjian Wang, Weiwei Li, et al. Visible-wavelength all-fiber vortex laser. IEEE Photonics Technology Letters, 31, 1487-1490(2019).

[87] Honggang Sun, Jinhai Zou, Qiujun Ruan, et al. Visible-wave-length all-fiber mode-locked vortex laser. Journal of Lightwave Technology, 40, 191-195(2022).

[88] W R Kerridge-Johns, A S Rao, Y Fujimoto, . et al. Red, orange, and dual wavelength vortex emission from Pr:WPFGF fiber laser using a microscope slide output coupler. Optics Express, 31, 16607-16614(2023).