Fig. 4: Intensity and phase information of an experimentally generated photonic toroidal vortex.

a,b, Three-dimensional iso-intensity profile of the photonic toroidal vortex in different views. The maximum intensity is set to 1 and the isovalue is 0.02, meaning that the isosurface profile includes all points with an intensity larger than 0.02. The spatiotemporal spiral phase (\({\varPhi }_{{{r}_ \bot ,}\,{{t}}}\)) is marked with curved colourful arrows and the local OAM density (jOAM) is marked with light green arrows. c, Circulating spiral phase in the radial–temporal plane. The topological charge of the spiral phase is 1.