Fig. 1. Generation process of VIG mode based on IG even and odd mode superposition. (a) IG6e mode distribution; (b) IG12o mode distribution; (c) VIG6 mode distribution

Fig. 2. Schematic of experimental light path

Fig. 3. Schematic of phase mask generation. (a) Phase pattern of VIG mode; (b) blazed grating; (c) amplitude distribution A(x,y) of VIG mode; (d) phase mask pattern in SLM

Fig. 4. Intensity and phase distributions of VIGp mode at different orders p. (a1)-(e1) Experimental intensity distributions of VIG mode; (a2)-(e2) simulated intensity distributions of VIG mode; (a3)-(e3) simulated phase distributions of VIG mode, the green solid line indicates the location of intensity

Fig. 5. Limiting condition of VIG mode generation

Fig. 6. Intensity and phase distributions of VIGpe,φ mode. (a)-(l) Intensity distributions of VIG mode after initial phase is added to even mode; (a1)-(l1) phase distributions of VIG mode after initial phase is added to even mode, the green solid line indicates the location of intensity

Fig. 7. Gradient force of VIG mode with parameter p=4. (a) Simulated intensity distribution of VIG mode; (f) gradient force distribution of VIG mode; (b-e) and (g-j) corresponding to the gradient force distribution of the eight “V” shape light petals

Fig. 8. Gradient force distributions of VIG mode obtained by (a) simulation and (b) experiment

Fig. 9. (a1)-(e1) Intensity distributions of three branches VIG mode obtained by experiment; (a2)-(e2) intensity distributions of three branches VIG mode obtained by simulation