Fig. 1. Spiral wavefront structures[93]. (a)-(c) Right-handed spirals; (d)-(f) left-handed spirals

Fig. 2. Intensity and phase of vortex beam at source plane (z=0)[94]. (a) |l|=1; (b) l=1; (c) l=-1; (d) |l|=3; (e) l=3; (f) l=-3

Fig. 3. Far-field intensity distributions of partially coherent vortex beams with different coherent lengths[59]. (a) High coherence; (b) moderate coherence; (c) low coherence

Fig. 4. Far-field modulus and phase distributions of spectral degree of coherence of partially coherent vortex beam with topological charge of 1[58]. (a)(b) Modulus; (c)(d) phase

Fig. 5. Intensity distribution and corresponding cross line (ρy=0) of focused Laguerre-Gaussian correlated Schell-model vortex beam at focal plane for different values of initial coherence width δ0.(a1)-(d1) Intensity distribution; (a2)-(d2) corresponding cross line (ρy=0) of intensity distribution in Figs. 5(a1)-(d1); (a3)-(d3) intensity distribution; (a4)-(d4) corresponding cross line (ρy=0) of intensity distribution in Figs. 5(a3)-(d3)

Fig. 6. Evolution of state of polarization for partially coherent radially polarized vortex beam with different topological charges at several propagation distances in free space[101]

Fig. 7. Evolution of spectral degree of coherence of partially coherent LG11 beam[79]. (a1)-(d1) Without occlusion; (a2)-(d2) with occlusion

Fig. 8. Generation of partially coherent vortex beam by rotating ground-glass disk and spatial light modulator[113]. (a) Experimental setup; (b) experimental results

Fig. 9. Generation of Laguerre-Gaussian correlated Schell-model vortex beam by modulating correlation function[87]

Fig. 10. Generation of partially coherent vortex beam by incoherent superposition of fully coherent modes[123]. (a) Experimental setup; (b) comparison between experimental and theoretical results

Fig. 11. Schematic of generation of partially coherent vortex beam by pure digital holography[125]

Fig. 12. Generation of partially coherent vortex beams with different coherent lengths by pure digital holography[125].(a) High coherence; (b) moderate coherence;(c)low coherence

Fig. 13. Experimental setup for measuring degree of coherence by four-order correlation function[128]

Fig. 14. Experimental setup for measuring complex degree of coherence by coherent superposition[135]

Fig. 15. Experimental results of partially coherent vortex beam with topological charge of l=3 but for four different spatial coherences[118]. (a1)-(a4) Focused intensities; (b1)-(b4) corresponding Fourier transform patterns corresponding to Figs. 15(a1)-(a4)

Fig. 16. Distributions of mutual correlation function of partially coherent LG0l beam at focal plane for different spatial coherences[118]

Fig. 17. Distributions of normalized average intensity and modulus of different correlation functions of partially coherent LG11 beam at focal plane[79]. (a1)-(d1) Theoretical results; (a2)-(d2) experimental results

Fig. 18. Experimental setup for measuring topological charge of partially coherent LG0l beam by a couple of cylindrical lenses[112]

Fig. 19. Evolution of intensity and mutual correlation function of partially coherent LG0l beam passing through a couple of cylindrical lenses[112]. (a1)-(a8) Intensity; (b1)-(b8) mutual correlation function

Fig. 20. Experimental setup for ghost imaging by partially coherent vortex beam propagating in turbulence

Fig. 21. Experimental results of ghost imaging by partially coherent vortex beam propagating in turbulence

Fig. 22. Application of partially coherent vortex beam in information transmission and encryption. (a)(b) Intensity; (c)(d) degree of coherence