[1] [1] Mao Ning, Wei Hongyan, Cai Dongmei, et al. Simulation for measuring the topological charges of composite vortex beams[J]. Chinese Journal of Lasers, 2019, 46(1): 0104008.

[2] [2] 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.

[3] [3] Yang Yuanjie, Ren Yuxuan, Chen Mingzhou, et al. Optical trapping with structured light: a review[J]. Advanced Photonics, 2021, 3(3): 0340011-40.

[4] [4] Liu Zhanwei, Huang Yiwen, Liu Haigang, et al. Non-line-of-sight optical communication based on orbital angular momentum[J]. Optics Letters, 2021, 46(20): 5112-5115.

[5] [5] Tao Hujun, Tai Yuping, Zhu Liuhao, et al. Optical vortex with multi-fractional orders[J]. Applied Physics Letters, 2020, 116(20): 2011071-5.

[6] [6] Bai Yihua, Lv Haoran, Fu Xin, et al. Vortex beam: generation and detection of orbital angular momentum[J]. Chinese Optics Letters, 2022, 20(1): 0126011-15.

[7] [7] Yu Fangren, Qian Junyu, Peng Yujie, et al. Femtosecond infrared optical vortex lasers based on optical parametric amplification[J]. High Power Laser Science and Engineering, 2022, 10(e29): 1-6.

[8] [8] Kuan Chenzhen, Zheng Shuiqin, Lu Xiaoming, et al. Forty-five terawatt vortex ultrashort laser pulses from a chirpedpulse amplification system[J]. High Power Laser Science and Engineering, 2022, 10(e32): 1-7.

[9] [9] Pan Wangjun, Liang Xiaoyan, Yu Lianghong, et al. Generation of terawatt-scale vortex pulses based on optical parametric chirped-pulse amplification[J]. IEEE Photonics Journal, 2020, 12(3): 1-7.

[10] [10] Lin Y C, Midorikawa K, Nabekawa Y. Wavefront control of subcycle vortex pulses via carrier-envelope-phase tailoring[J]. Light: Science & Applications, 2023, 12(1): 2791-12.

[11] [11] Lyu Baida, Luo Shirong. High-power laser modeling: flattened Gaussian beams[J]. Infrared and Laser Engineering, 2001, 30(6): 457-461.

[12] [12] Tan Yi, Li Xinyang. Influence of filling factor on far-field intensity distribution in coherent beam combination[J]. Acta Physica Sinica, 2014, 63(9): 0942021-11.

[13] [13] Zhang Lingyu, Zhang Hao, Huang Hongtao, et al. Generation of ultra-intense vortex laser from a binary phase square spiral zone plate[J]. Optics Express, 2024, 32(4): 5161-5173.

[14] [14] Shen Y R. The principles of nonlinear optics[M]. New York: John Wiley and Sons, Inc. 1984.

[15] [15] Konoplev O A, Meyerhofter D D. Cancellation of B-integral accumulation for CPA lasers[J]. IEEE Journal of Selected Topics in Quantum Electronics. 1998, 4(2): 459-469.

[16] [16] Erickson M A, Cohen S J, Di Nicola J M, et al. Spatially resolved B-integral measurements on the NIF laser[C]//Proc. SPIE 11259, Solid State Lasers XXIX: Technology and Devices, 1125917 (21 February 2020).