Modeling of laser beam propagation through turbulence

Abstract

Our approach for modeling laser beam propagation through turbulence involves parabolic equation method and results of experimental investigation in laboratory. The analytic solution to the problem of the Gaussian beam propagation through non-uniform gas has been derived. The solution depends on the refracted index, i.e. on the gas density. The density distribution can be found from the Navier-Stokes system. The appropriate solution may be constructed by two ways : (i) as a series in powers of vorticity which is supposed to be small; (ii) with the aid of the parametrix method which includes an iterative procedure. It follows from the solution that acoustic radiation of vortex rings arises. Statistical properties of the propagating beam were found from the solution to the parabolic equation as average over time. In experiments the propagation path was equal to 7 m. The laser beam propagation was accompanied by convection and lateral wind. The frequency of turbulent fluctuations was equal to 2-10 Hz. Phase trajectories were found as well as statistical properties of the beam intensity in turbulent gas flow. The conclusion is as follows. Statistical characteristics traditionally used for the estimation of the laser beam special distortions in the open space transmission channels are to be complemented by the dynamic parameters such as the space of embeddings dimension, characteristic frequencies for the phase trajectories and so on.