Propagation of a Pearcey–Gaussian–vortex beam in free space and Kerr media

The propagation of a Pearcey–Gaussian–vortex beam (PGVB) has been investigated numerically in free space and Kerr media. In addition, we have done a numerical experiment for the beam in free space. A PGVB maintains the characteristics of auto-focusing, self-healing and form-invariance which are possessed by a Pearcey beam and a Pearcey–Gaussian beam. Due to the influence of the optical vortex, a bright speck occurs in front of the main lobe. Compared with a Pearcey beam and a Pearcey–Gaussian beam, a PGVB has the most remarkable intensity singularity and the phase singularity. It is worth noting that the impact of the vortex at the coordinate origins means that a PGVB in the vicinity carries no angular momentum or transverse energy flow. We have investigated and numerically simulated the transverse intensity of a PGVB in Kerr media. We find that the auto-focusing of a PGVB in a Kerr medium becomes stronger with increasing power.