Figure 1. Schematic of a diffraction-resisting singular beam curving in free space.

(a) Propagation of the beam along a curved trajectory, where rays emitted from expanding circles on the input plane are skewed but converged along a specified focal curve. (b) Corresponding helical phase structure of the beam along the curve. Due to the self-acceleration, the center of the singular beam shifts laterally during propagation, but its donut shape and vorticity remain intact (see Media 1).