Abstract
Stochastic vortex fields are found in laser speckle, in scintillated beams propagating through a turbulent atmosphere,
in images of holograms produced by Iterative Fourier Transform methods and in the beams produced
by certain diffractive optical elements, to name but a few. Apart from the vortex fields found in laser speckle,
the properties and dynamics of stochastic vortex fields are largely unexplored. Stochastic vortex fields with
non-equilibrium initial conditions exhibit a surprisingly rich phenomenology in their subsequent evolution during
free-space propagation. Currently there does not exist a general theory that can predict this behavior and
only limited progress has thus far been made in its understanding. Curves of the evolution of optical vortex
distributions during free-space propagation that are obtained from numerical simulations, will be presented. A
variety of different stochastic vortex fields are used as input to these simulations, including vortex fields that
are homogeneous in their vortex distributions, as well as inhomogeneous vortex fields where, for example, the
topological charge densities vary sinusoidally along one or two dimensions. Some aspects of the dynamics of
stochastic vortex fields have been uncovered with the aid of these numerical simulations. For example, the
numerical results demonstrate that stochastic vortex fields contain both diffusion and drift motions that are
driven by local and global variations in amplitude and phase. The mechanisms for these will be explained. The
results also provide evidence that global variations in amplitude and phase are caused by variations in the vortex
distributions, giving rise to feedback mechanisms and nonlinear behavior.
