Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c_1 and c_2 of two edge dislocations are non-zero, and the condition k^2w_0^8+32c_1c_2(w_0^2-2c_1c_2)z^2>0 is fulfilled (k-wave number, w_0-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.