Fig. 1. Schematic of the theoretical frame based on the DSI technique (see the text for details).

Fig. 2. Experimental setup for studying the diffraction of a twisted beam from a triangular aperture. Inset (a) is the triangular aperture, (b) is the holographic grating to produce the LG30 mode, and (c) is the hologram displayed on the SLM.

Fig. 3. Spiral spectra of the triangular aperture based on DSI. (a) Intensity spectrum |Aℓ,p|2, (b) phase spectrum arg(Aℓ,p) (c) ℓ spectrum Cℓ=∑p|Aℓ,p|2 as a sum over all the p indices, (d) simulation results of the total initial field at the z=0 plane.

Fig. 4. Numerical (upper row) and experimental (lower row) results of diffraction of the OAM beam with ℓ=3, which illustrate the gradual birth of the triangular optical lattices.