Figure 3: Experimental images of the cut vortex beams and their m-dependent rotations with the propagation distance.
(a) Experimental images of the row of the cut vortex beams with different m at different positions of the knife edge, zk (Fig. 2). The scale bar is 50 nm. The opposite inclination of the opposite-m states is because of the residual Gouy-phase diffraction effect46,47. At the same time, one can see a slow rotation of the m>0 modes with zk, while the m<0 states remain motionless. A quantitative analysis of these m-dependent rotations is depicted in b. The azimuthal orientations of the cut modes ϕ (with respect to the extrapolated reference azimuth 
) are plotted versus zk and the corresponding timescale tk=zk/v (on the top). Three lines correspond to the zero, Larmor and cyclotron rotations predicted for the Landau states in equation (4). Error bars include the uncertainty in reading, knife-edge roughness and stage positioning.
