Extended Data Fig. 3: Experimental results showing the comparison between topologically protected and unprotected transport of a high-order (l = 3) vortex.

a1 Input intensity pattern of the \(l=3\) vortex beam. a2-a3 Output intensity patterns after free propagation (in the crystal without lattice structure) taken at (a2) 10-mm and (a3) 20-mm propagation distances, exhibiting diffraction. a4 Interferogram of the pattern in (a3) with a spherical wave, displaying the high-order vorticity. b1 A laser-written nontrivial \({C}_{5}\) disclination structure featuring twofold topological protection. b2-b4 Topologically protected output results obtained from the nontrivial disclination, presenting guided output with preserved vorticity. c1-c4 Corresponding results from a deformed \({C}_{5}\) disclination structure (c1), where the lattice parameters (for the dimer chains along two marked directions) are tuned intentionally so as the two-fold topological protection is disrupted. The lattice parameter tuning leads to the VRS breaking since the rotational symmetry is no longer satisfied. As the propagation distance increases, the vortex beam breaks up and disintegrates into multiple low-order vortices (marked by small dashed circles in c4).