Statistical properties of electromagnetic anomalous vortex beam with orbital angular momentum in atmospheric turbulence

Statistical properties of an electromagnetic anomalous vortex (EAV) beam with orbital angular momentum (OAM) through a turbulent atmosphere are studied. Analytical formulae for the average intensity (AI) and degree of polarization (DOP) of EAV beam in a strong turbulence are derived. Accurate analytical formulae (without any approximations) for M-2-factor of EAV beam under all turbulence conditions are also derived based on the second-order moments of the Wigner distribution function. Numerical results show that the transverse distributions for Al of EAV beam depend mainly on topological charge, beam order and structure constant of turbulence. An anomalous result is found that the on-axis intensity is larger for an EAV beam in a stronger turbulence (i.e., larger structure constant and smaller inner scale). Inner scale effects of DOP of the EAV beam in strong turbulence are also investigated. Off-axis DOPs of an EAV beam will appear oscillation near the propagation axis. It can be also found that M-2-factor of an EAV beam propagating through the strong and weak turbulence are smaller for smaller transverse coherent length and structure constant of turbulence, larger beam order, topological charge and inner scale of turbulence.