Vortex strength and beam propagation factor of fractional vortex beams

Fractional vortex beams (FVBs) with non-integer topological charges attract much attention due to unique features of propagations, but different viewpoints still exist on the change of their total vortex strength. Here we have experimentally demonstrated the distribution and number of vortices contained in FVBs at the Fraunhofer diffraction region. We have verified that the jumps of total vortex strength for FVBs happen only when non-integer topological charge is before and after (but very close to) any even integer number that originates from two different mechanisms for generation and movement of vortices on focal plane. Meanwhile, we have also measured the beam propagation factor (BPF) of such FVBs and have found that their BPF values almost increase linearly in the x component (along the initial edge dislocation) and oscillate increasingly in the y component (vertical to the initial edge dislocation). Our experimental results are in good agreement with numerical results.