Fig. 1. Schematic of regular hexagonal multi-hole array and its effect on LG beams with different topological charge numbers. (a) Diagram; (b) l=1; (c) l=2; (d) l=3; (e) l=4; (f) l=5; (g) l=6

Fig. 2. Diffraction fields of high order vortex beams with different topological charge numbers l . (a) l=7; (b) l=8; (c) l=9

Fig. 3. Gray histograms of diffraction fields with different topological charge numbers l and Bhattacharyya distances. (a) l=1;(b) l=7;(c) curves of Bhattacharyya distance

Fig. 4. Transverse intensity distributions of diffraction fields and L0 and L1 under different topological charge numbers.(a) Light intensity, l=1,k=0; (b) light intensity, l=13,k=2; (c) light intensity, l=25,k=4; (d) light intensity, l=5,k=0; (e) light intensity, l=17,k=2; (f) L0 and L1, l=6k+1; (g) L0 and L1, l=6k+5

Fig. 5. Transverse intensity distributions of diffraction fields under different r0 and relationship between w1/2 and r0.(a)r0=50 μm; (b)r0=100 μm; (c)r0=150 μm; (d) relationship between w1/2 and r0

Fig. 6. Transverse intensity distributions of diffraction fields under different r and relationship of fringe width and density with side length of regular hexagon. (a) r=0.4 mm; (b)r=0.6 mm; (c)r=0.8 mm; (d) relationship curves

Fig. 7. Diffraction experiment of vortex beam. (a) Diagram; (b) physical map

Fig. 8. Fork grating. (a) Schematic; diffraction diagrams when (b) l=1 and (c) l=2

Fig. 9. Diffraction field under l=1