Fig. 1. Schematic diagram of the vortex beam generated by continuous mirror deformation mirror

Fig. 2. Schematic diagram of using DM to generate vortex beams.L₁, L₂, L₃: convex lens; T: aperture; DM: deformation mirror; f: focal length

Fig. 3. Fitting of the integer order spiral wavefront. (a)~(e) Target wavefront with the integer order l =1~5; (f)~(j) Fitting wavefront of the integer order l=1~5

Fig. 4. Fitting of integer order vortex beams with topological charge is 2. (a) Unfiltered intensity at u₂; (b) Filtered intensity at u₄; (c) Unfiltered phase at u₂; (d) Filtered phase at u₄

Fig. 5. The light field and phase of the integer order vortex beam after focusing and filtering. (a)~(d) Intensity with topological charges l=1, 3, 4, and 5; (e)~(h) Phase with topological charges l=1, 3, 4, and 5

Fig. 6. Fitting of the fractional order spiral wavefront. (a)~(e) Target wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5; (f)~(j) Fitting wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5

Fig. 7. Filtering results of the fractional order vortex beam. (a)~(e) Intensity of target wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u₄; (f)~(j) Intensity of fitting wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u₄

Fig. 8. Filtering results of the fractional order vortex beam. (a)~(e) Phase of target wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u₄; (f)~(j) Phase of fitting wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u₄

Fig. 9. Fitting of multi-fractional spiral wavefront. (a), (b) Target wavefront; (c), (d) Fitting wavefront

Fig. 10. The light field and phase of the multi-fractional order target wavefront and the fitting wavefront after filtering. (a), (b) Intensity of multi-fractional order target wavefront at u₄; (c), (d) Intensity of multi-fractional order fitting wavefront at u₄; (e), (f) Phase of multi-fractional order target wavefront at u₄; (g), (h) Phase of multi-fractional order fitting wavefront at u₄

Fig. 11. Superposition target wavefront and fitting wavefront. (a)~(d) Target wavefront with topological charges l=±1, ±2, ±3, and ±4; (e)~(h) Fitting wavefront with topological charges l=±1, ±2, ±3, and ±4

Fig. 12. The light field and phase of the superposition fitting wavefront after filtering. (a)~(d) Intensity of fitting wavefront at with topological chrages l=±1，±2，±3, and ±4 at u₄; (e)~(h) Phase of fitting wavefront at with topological chrages l=±1，±2，±3, and ±4 at u₄

Fig. 13. The mode purity of the superposition fitting wavefront after filtering. (a) l=±1; (b) l=±2; (c) l=±3; (d) l=±4

Fig. 14. Dynamic manipulation of integer order vortex beams. (a1)~(a6) Intensity with topological charge l=2; (b1)~(b6) Spiral phase with topological charge l= 2; (c1)~(c6) Intensity with topological charge l=3; (d1)~(d6) Spiral phase with topological charge l= 3