Propagation of integral and fractional perfect vortex beams in a gradient-index medium

The analytical expressions for the complex amplitude of integral and fractional perfect vortex (PV) beams propagating in a gradient-index (GRIN) medium are derived. The intensity and phase distributions, propagation trajectories, Poynting vectors, and the effects of topological charge and refractive index at the medium axis on the intensity of both beams in the medium are numerically investigated. It is shown that both beams propagate periodically in the GRIN medium with alternating spot focusing and reconstruction. Unlike the integral PV beam, the fractional PV beam has a dark line in intensity profiles and a line edge dislocation in phase distributions along the positive x-axis. These properties persist during the beam propagation in the GRIN medium. Moreover, the topological charge and the refractive index at the medium axis have little effect on the intensity of the PV beam propagating in the GRIN medium. The results presented in this paper may be useful for the application of integral and fractional PV beams in optical guiding and optical communications.