Critical point trajectory bundles in singular wave fields

The close relationships that exist between vortex trajectories and their associated stationary point trajectories are studied for the phase and the intensity of optical beams. It is found that trajectories of these two different types of critical points join together at a junction to form what we call colloquially a bundle. This bundle has a definite topology and a small number of possible geometries. These geometries are illustrated using simple analytical models, and are shown to be present in realistic Gaussian laser beams using numerical simulations. The effects of different foliations of the beam are considered, and it is shown that there generally exists a broad range of foliations within which changes in foliation preserve the geometry of a bundle and simply slide its junction along the parent vortex trajectory. (C) 2001 Elsevier Science B.V. All rights reserved.