Dynamic evolution of circular edge dislocations in free space and atmospheric turbulence

Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of circular edge dislocation beams propagating through atmospheric turbulence and free space have been derived, and used to study the dynamic evolution of circular edge dislocations. It is shown that the number of circular edge dislocations on propagation equals that at the source plane when propagating through free space. The radius of circular edge dislocations increases with increasing propagation distance z. n-circular edge dislocations vanish and transform to n pairs of optical vortices with the opposite topological charge when propagating through atmospheric turbulence, and the position of each pair of optical vortices are symmetric about the slanted axis y = x. All the optical vortices will annihilate as soon as the propagation distance becomes large enough. The smaller radius of circular edge dislocation corresponds with the sooner annihilation of optical vortices. The structure constant affects the annihilation distance of the pairs of optical vortices, and the annihilation distance of the pairs of optical vortices will increase with the decrement of the structure constant.