Fluctuations of the orbital angular momentum of a laser beam, carrying an optical vortex, in the turbulent atmosphere

The evolution of the orbital angular momentum (OAM) of a Laguerre-Gaussian beam interacting with turbulent inhomogeneities of the atmosphere is studied theoretically. The integral representations are obtained for the OAM in terms of the distributions of the random intensity and random field of the permittivity of the medium, and also for OAM statistical characteristics in terms of corresponding correlation functions. It is found that the average OAM value is preserved during the propagation of the laser beam in a random medium. The dependence of the dispersion of OAM fluctuations on the atmospheric turbulence and beam parameters is calculated. It is shown that the dependence of the OAM dispersion on the initial angular momentum of the laser beam disappears in the case of very strong turbulence.