Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen

The spatial evolution of the energy distribution and local wave-propagation vector of a fluctuating laser vortex beam is studied. The beam’s fluctuations are induced by its propagation through a thin (in comparison with the total propagation path) layer of a turbulent medium (phase screen). It is shown that the vortex energy flow typical for a coherent beam is also manifested in the mean parameters of a partially coherent beam. In particular, the mean wave tilt is representable as a sum of the vortex and potential components. The rotor of the vector field of mean wave tilts plays the determining part in the circular energy motion. The vortex component for a screen with a quadratic structure function of phase fluctuations corresponds to one of the models of rotational fluid motion called the Scully vortex. The potential component of the mean energy direction field can result in beam focusing with an increase in the distance from the screen. The direction of the mean energy flow lines (mean diffraction rays) allows for an analogy between the evolution of an optical vortex carried by a Laguerre-Gaussian beam and the breakdown of the rotational fluid flow.