Evolution of optical vortex distributions in stochastic vortex fields

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.