Dynamic evolution of coherent vortex dipole in atmospheric turbulence

The analytical expression for the cross-spectral density function of Gaussian Schell-model (GSM) beams with coherent vortex dipole (CVD) propagating through atmospheric turbulence is derived, which enables us to study the evolution process of CVD propagating through atmospheric turbulence, where the influences of the beams parameters and atmospheric turbulence parameters on the ratio of critical off-axis distance to the waist width are stressed. It shows that the evolution process of the CVD depends on the off-axis distance. The larger the off-axis distance is, the more the number of CVD is. When the off-axis distance is zero, the position of coherent vortices with positive and negative topological charge of CVD propagating through atmospheric turbulence is always symmetry. When the off-axis distance is big enough, compared with the situation at source plane, the orientation of the positive coherent vortex of inherent CVD and negative coherent vortex of that rotates 180° in the far field. The larger the structure constant and the waist width are, as well as the smaller the spatial correlation length and the inner scale are, the smaller the ratio ac/w0 is. Besides, the ratio ac/w0 will no longer change when the spatial correlation length or the inner scale increases to a certain value, whereas the outer scale has no effect on the ratio.