[1] [1] FANG G J,TIAN B,PU J X. Focusing properties of the double-vortex beams through a high numerical-aperture objective［J］. Optics and Laser Technology,2012,44(2):441-445.

[2] [2] ZHAO J H,WANG Q, ZHU B W,et al. Compact focusing properties of radial vector beam with vortex phase encoding［J］. Laser Technology,2017,41(2):187-190(in Chinese).

[3] [3] HUANG S, WANG X L, ZHU Z Q, et al. Focusing field of the radial vector beams with multi-vortex phases［J］.Optics Communications,2016,366:142-147.

[4] [4] PING C C, LIANG C H, WANG F, et al. Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties［J］.Optics Express, 2017,25(26):32475-32490.

[5] [5] XU J G, GENG T, GAO X M, et al. Generation of a dark spot beyond the diffraction limit with a radially polarized vortex beam［J］. Journal of the Optical Society of America, 2017, A34(12): 2165-2169.

[6] [6] WANG X L, ZHU B W, DONG Y X, et al.Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays［J］.Optics Express,2017, 25(22): 26844-26852.

[7] [7] FAN C J, LIU Y G, WANG X Y, et al. Trapping two types of particles by using a tightly focused radially polarized power-exponent-phase vortex beam［J］.Journal of the Optical Society of America, 2018, A35(6): 903-907.

[8] [8] ZHANG Z M, PU J X, WANG X Q. Focusing of partially coherent Bessel-Gaussian beams through a high-numerical-aperture objective［J］. Optics Letters,2008,33(1): 49-51.

[9] [9] CHEN B S, ZHANG Z M, PU J X. Tight focusing of partially cohe-rent and circularly polarized vortex beams［J］. Journal of the Optical Society of America,2009, A26(4): 862-869.

[10] [10] FISCHER D G, VISSER T D. Spatial correlation properties of focused partially coherent light ［J］. Journal of the Optical Society of America, 2004, A21(11):2097-2102.

[11] [11] GUO L N, TANG Z L, LIANG C Q, et al. Characterization of tightly focused partially coherent radially polarized vortex beams［J］. Chinese Optics Letters,2010,8(5):520-523 .

[12] [12] GUO L N, TANG Z L, LIANG C Q, et al. Intensity and spatial co-rrelation properties of tightly focused partially coherent radially pola-rized vortex beams［J］.Optics & Laser Technology,2011,43(4): 895-898.

[13] [13] DONG Y M, CAI Y J, ZHAO C L. Degree of polarization of a tightly focused partially coherent dark hollow beam［J］. Applied Phy-sics, 2011,B105(2):405-414.

[14] [14] LIU P S, YANG H J, RONG J, et al. Focusing of stochastic electromagnetic Gaussian Schell-model beams through a high numerical a-perture objective［J］.Optics Communications,2011, 284(4):909-914.

[15] [15] LI J, GAO X M, CHEN Y R. Tight focusing of J0-correlated Gaussian Schell-model beam through high numerical aperture［J］.Optics Communications,2012,285(16):3403-3411.

[16] [16] RAO L Z , LIN H C,XU G Z. Tight focusing of J0-correlated azimuthally polarized vortex beams［J］. High Power Laser and Particle Beams,2013,25(8):1945-1950(in Chinese).

[17] [17] RAO L Z, LIN H C, SUN Q Q. Spatial correlation properties of tightly focused J0-correlated azimuthally polarized vortex beams［J］.Chinese Physics Letters, 2013, 30(5):054211.

[18] [18] XU H F, ZHOU Y,WU H W, et al. Focus shaping of the radially polarized Laguerre-Gaussian-correlated Schell-model vortex beams［J］.Optics Express, 2018, 26(16):20076-20088.

[19] [19] MARIYAL C, SURESH P, RAJESH K B, et al. Effect of annular obstruction on tight focusing of partially coherent radially polarized Vortex beam［J］. Optik, 2014, 125(12):2934-2937.

[20] [20] XU H F, ZHANG R, SHENG Z Q, et al. Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge ［J］. Optics Express, 2019, 27(17):23959-23969.

[21] [21] GU M. Advanced optical imaging theory［M］. Berlin,Germany:Springer-Verlag, 1999:17-21.

[22] [22] MANDEL L, WOLF E. Optical coherence and quantum optics［M］. Cambridge,UK: Cambridge University, 1995:37-39.

[23] [23] PALMA C, BORGHI R, CINCOTTI G. Beams originated by J0-co-rrelated Schell-model planar sources［J］. Optics Communications ,1996,125(1):113-121.