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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[34] Xiaoqing LI, Xiaoling JI. 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. High Power Laser and Particle Beams, 35, 041007(2023).

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