Fig. 1. Experimental device. λ/2, half-wave plate; λ/4, 1/4-wave plate; lens with focal length of 100 mm; SLM, space light modulator; CCD, charge coupled device.

Fig. 2. Simulation and experimental comparison. (a)–(d) are simulation plots, and (e)–(h) are experimental plots. (a), (e) m=3, n=3; (b), (f) m=4, n=6; (c), (g) m=5, n=5; (d), (h) m=5, n=8.

Fig. 3. When the vortex parameter l=5, the HG beam pattern is vortex modulated by different orders. (a) m=1, n=1; (b) m=2, n=2; (c) m=3, n=4; (d) m=4, n=5; (e) m=5, n=5; (f) m=6, n=4; (g) m=7, n=2; (h) m=8, n=3.

Fig. 4. Diagram of HG beams with m=5, n=8, and different topological charge l. (a) l=2, (b) l=3, (c) l=4, (d) l=5, (e) l=6, (f) l=7, (g) l=8, and (h) l=10.

Fig. 5. Sinusoidal vortex modulated HG beam diagram with different-order vortex parameters, l=5. (a) m=1, n=1; (b) m=2, n=2; (c) m=3, n=4; (d) m=4, n=5; (e) m=5, n=5; (f) m=6, n=4; (g) m=7, n=2; (h) m=8, n=3.

Fig. 6. Sinusoidal vortex modulated HG beam with m=5, n=8, and different topological charge l. (a) l=2, (b) l=3, (c) l=4, (d) l=5, (e) l=6, (f) l=7, (g) l=8, and (h) l=10.

Fig. 7. Data analysis diagram of sinusoidal vortex modulation with parameters m=5, n=8, and l=8. (a) Light intensity distribution collected by CCD. (b) A cross section perpendicular to the x axis. (c) A cross section perpendicular to the y axis. (d) Three-dimensional intensity distribution.