[1] Gbur G, Wolf E. Spreading of partially coherent beams in random media[J]. Journal of the Optical Society of America A, 19, 1592-1598(2002).

[2] Zheng G. Coherent property evolution of partially coherent elliptical vortex beam propagation through turbulence[J]. Laser & Optoelectronics Progress, 58, 0901001(2021).

[3] Chen K, Li S Z, Pan Y Q et al. Tight focusing properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beam[J]. Acta Optica Sinica, 42, 2226002(2022).

[4] Zhang R, Liu X G, Xu H F. Radial polarization twisted rectangular multi-Gaussian-Schell mode beams and their propagation characteristics[J]. Laser & Optoelectronics Progress, 59, 1103001(2022).

[5] He R. Study on deep focusing and OAM characteristics of partially coherent vector vortex beams[D](2022).

[6] Ding C L, Qi X X, Pan L Z. Coherent switch in spatio-temporal coherent vortex[J]. Acta Optica Sinica, 42, 2026004(2022).

[7] Perez-Garcia B, Yepiz A, Hernandez-Aranda R I et al. Digital generation of partially coherent vortex beams[J]. Optics Letters, 41, 3471-3474(2016).

[8] Guo L N, Chen Y H, Liu X L et al. Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam[J]. Optics Express, 24, 13714-13728(2016).

[9] Mei Z R, Korotkova O. Cosine-gaussian Schell-model sources[J]. Optics Letters, 38, 2578-2580(2013).

[10] Wang D D. Study on propagation properties of partially coherent Laguerre Gaussian beams in turbulent atmosphere[D], 27-31(2012).

[11] Wang T J, Chen N, Guo H et al. Principle and research progress of atmospheric remote sensing by intense femtosecond lasers[J]. Laser & Optoelectronics Progress, 59, 0700001(2022).

[12] Zheng H Y, Yin F K, Wang T J et al. Diffraction analysis method of femtosecond laser filamentation[J]. Chinese Journal of Lasers, 49, 2408001(2022).

[13] Hao J J, Liu H Y, Chen H S et al. Research progress of Kerr lens mode-locked disk laser oscillator[J]. Chinese Journal of Lasers, 49, 1201002(2022).

[14] Fan H L, Guo Z J, Li M Q et al. Simulation study on self-focusing and filamentation of vortex beam in plasma[J]. Acta Physica Sinica, 72, 014206(2023).

[15] Miao R C, Shen C Y, Ye Q et al. Self-focusing effect of circle spot laser beam in Kerr-medium[J]. Acta Photonica Sinica, 32, 204-208(2003).

[16] Ma C L, Jia M Z, Lin W B. Nonlinear Propagation of annular Gaussian beams with different energy in air[J]. High Power Laser and Particle Beams, 28, 10-14(2016).

[17] Dicaire I, Jukna V, Praz C et al. Spaceborne laser filamentation for atmospheric remote sensing[J]. Laser & Photonics Reviews, 10, 481-493(2016).

[18] Wolf E. New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources[J]. Journal of the Optical Society of America, 72, 343-351(1982).

[19] Wolf E[M]. Introduction to the theory of coherence and polarization of light(2007).

[20] Gori F, Santarsiero M. Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams[J]. Optics Letters, 40, 1587-1590(2015).

[21] Fan X L. Kerr effect on propagation characteristics of Hermite-gaussian beams[D](2020).