[1] SHEPPARD C J. Bessel pulse beams and focus wave modes[J]. Journal of the Optical Society of America A, 18, 2594-2600(2001).

[2] ZHU Long, WANG Jian. Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode[J]. Optics Letters, 40, 5463-5466(2015).

[3] GARCÉS-CHÁVEZ V, MCGLOIN D, MELVILLE H et al. Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam[J]. Nature, 419, 145-147(2002).

[4] WEI Zhangfan, SUN Chuan, GUO Kai et al. Study on Bessel lens for picosecond laser cutting[J]. Acta Photonica Sinica, 49, 1022001(2020).

[5] GORI F, GUATTARI G, PADOVANI C. Bessel-Gauss beams[J]. Optics Communications, 64, 491-495(1987).

[6] YANG Guiyang, MA Guolu, ZENG Guoying. Influence of the surface deviation axicon on the propagation characteristics of non-diffracting beam[J]. Acta Photonica Sinica, 48, 0126002(2019).

[7] VETTER C, STEINKOPF R, BERGNER K. Realization of free‐space long‐distance self‐healing Bessel beams[J]. Laser & Photonics Reviews, 13, 1900103(2019).

[8] ZHI Zihao, NA Quanxin, XIE Qijie et al. On-chip generation of Bessel–Gaussian beam via concentrically distributed grating arrays for long-range sensing[J]. Light: Science & Applications, 12, 92(2023).

[9] LIU Huilong, HU Zonghua, XIA Jing et al. Generation of non-diffractive beams and their applications[J]. Acta Physica Sinica, 67, 10-28(2018).

[10] GIBSON G, COURTIAL J, PADGETT M J. Free-space information transfer using light beams carrying orbital angular momentum[J]. Optics Express, 12, 5448-5456(2004).

[11] WILLNER A E. Optical communications using orbital angular momentum beams[J]. Advances in Optics and Photonics, 7, 66-106(2015).

[12] YUE Xifu, GE Xiaolu, Yudong LYU. Mean intensity of lowest order Bessel-Gaussian beams with phase singularities in turbulent atmosphere[J]. Optik, 219, 165215(2020).

[13] EYYUBOĞLU H T, SERMUTLU E, BAYKAL Y. Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere[J]. Applied Physics B, 93, 605-611(2008).

[14] JunOU, JIANG Yuesong, ZHANG Jiahua. Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence[J]. Optics Communications, 318, 95-99(2014).

[15] WANG Wanjun, WU Zhensen, SHANG Qingchao et al. Propagation of Bessel Gaussian beams through non-Kolmogorov turbulence based on Rytov theory[J]. Optics Express, 26, 21712-21724(2018).

[16] ZHENG Shuiqin, CAI Yi, LI Jingzhen et al. Rotating wave packet caused by the superposition of two Bessel-Gauss beams[J]. Journal of Optics, 17, 125602(2015).

[17] LI Siyao, DING Zhoulin, HOU Chunyu et al. Spiral phase spectrum of perfect vortex beams propagating through atmospheric turbulence[J]. Acta Optica Sinica, 44, 0601002(2024).

[18] YAN Yan, XIE Guodong, LAVERY MARTIN P J et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing[J]. Nature Communications, 5, 4876(2014).

[19] FU Shiyao, GAO Chunqing. Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams[J]. Photonics Research, 4, B1(2016).

[20] SPRANGLE P, HAFIZI B, TING A et al. High-power lasers for directed-energy applications[J]. Applied Optics, 54, F201-F209(2015).

[21] BISWAS A, KOVALIK J M, SRINIVASAN M et al. Deep space laser communications[C], 209-223(2016).

[22] BALI Reza S, BULDT F et al. Structured light signal transmission through clouds[J]. Journal of Applied Physics, 133, 043102(2023).

[23] GEBHARDT F G. High power laser propagation[J]. Applied Optics, 15, 1479-1493(1976).

[24] LU Lu, WANG Zhiqiang, ZHANG Pengfei et al. Thermal blooming induced phase change and its compensation of a Gaussian beam propagation in an absorbing medium[J]. Optics Letters, 46, 4304-4307(2021).

[25] DING Zhoulin, LI Xiaoqing, CAO Jianyong et al. Influence of thermal blooming on the beam quality of an array of Hermite-Gaussian beams propagating in the atmosphere[J]. Applied Optics, 59, 10944-10952(2020).

[26] GEBHARDT F G, SMITH D C. Self-induced thermal distortion in the near field for a laser beam in a moving medium[J]. IEEE Journal of Quantum Electron, 7, 63-73(1971).

[27] FLECK J A, MORRIS J R. Time-dependent propagation of high energy laser beams through the atmosphere[J]. Applied Physics, 10, 129-160(1976).

[28] MOLCHAN M A, DOKTOROV E V, VLASOV R A. Propagation of vector fractional charge Laguerre-Gaussian light beams in the thermally nonlinear moving atmosphere[J]. Optics Letters, 35, 670-672(2010).

[29] QIU Die, TIAN Boyu, TING He et al. Mitigation of thermal blooming by rotating laser beams in the atmosphere[J]. Applied Optics, 60, 8458-8465(2021).

[30] INDEBETOUW G. Optical vortices and their propagation[J]. Optica Acta International Journal of Optics, 40, 73-87(1993).

[31] WANG Jian, YANG Jengyuan, FAZAL IRFAN M et al. Terabit free-space data transmission employing orbital angular momentum multiplexing[J]. Nature Photonics, 6, 488-496(2012).

[33] ZHAO Lu, WANG Jing, GUO Miaojun et al. Steady-state thermal blooming effect of vortex beam propagation through the atmosphere[J]. Optics and Laser Technology, 139, 106982(2021).

[34] LI Xiaoqing, JI Xiaoling. Theoretical research progress on the influence of atmospheric turbulence and thermal blooming on characteristics and beam quality of laser array beams propagating in the atmosphere[J]. High Power Laser and Particle Beams, 35, 041007(2023).

[35] ZHU Yun, ZHANG Licheng, HU Zhengda et al. Effects of non-Kolmogorov turbulence on the spiral spectrum of Hypergeometric-Gaussian laser beams[J]. Optics Express, 23, 9137-9146(2015).