Is it possible to create a perfect fractional vortex beam?

Laguerre-Gaussian beams of integer azimuthal index satisfy the fundamental principle of quantization of orbital angular momentum. Here, we consider light-induced orbiting of a trapped microparticle as a probe of the local orbital angular momentum density in both integer- and fractional-index perfect vortex beams.
Simulations suggest that the distribution and the corresponding light-induced motion of the particle, may be uniform in beams with integer azimuthal index but fundamentally this cannot be achieved in beams with fractional index. We experimentally verify these predictions by light-induced trapping and rotation of individual microparticles in fractional index beams where we distribute the phase dislocations around the annular profile.