Optical Vortices and Their Propagation

Free space propagation of an array of optical vortices nested in a smooth (Gaussian) beam is studied in the paraxial regime. It is found that when the vortices have all the same charge, their relative positions, as well as their positions within the host beam are invariant upon propagation. The array simply expands or contracts with the host beam and rotates rigidly. Vortices of opposite charges, in contrast, attract each other. Pairs can collide and annihilate. As an illustration, numerical simulation is used to compare the propagation of a pair of vortices of equal charges with that of a pair of opposite charges.