Paraxial modal analysis technique for optical vortex trajectories

A method for computing the trajectories of optical vortices in complicated situations is described. The Gaussian beam in which the vortices are embedded is expressed in terms of paraxial modes. The positions of the vortices as a function of the propagation distance can then be computed analytically. It is shown that the method reproduces the familiar propagation for a single decentered vortex and an isopolar vortex pair. The case of a vortex dipole is analyzed and shown to undergo annihilation and revival of the pair under certain conditions. Expressions are provided for the trajectories of a decentered symmetrical vortex dipole. The analytical predictions are compared with numerical simulations.