Dynamics of Fractional Vortex Beams at Fraunhofer Diffraction Zone

Fractional vortex beams (FVBs) possess unique topological properties that are manifested in the vortex distribution. However, there are still discrepancies in the value of the vortex strength of FVBs at the far field. In this work we present a complete picture of the behavior of the phase singularities of non-integer (commonly known as fractional) beams in the Fraunhofer diffraction region and demonstrate a very good correspondence between experiments and simulations. As shown in the text, the original beam waist (Formula presented.) was found to be a key factor relating to the beam profile topology. This variable was measured in the process of calibrating the experiment. Finally, an experimental method to obtain the non-integer topological charge is proposed. This method only requires an analysis of the intensity, knowledge of the transition behaviors, and the beam waist.