Propagation dynamics of off-axis noncanonical vortices in a collimated Gaussian beam

It is widely accepted that an off-axis noncanonical vortex moves across the free-space diffracting Gaussian beam without rotation. But our analysis shows that the vortex swirls a while before it approaches infinite. By neglecting the divergence of the host beam, we focus on this rotation characteristics of the vortices in linear homogeneous media. For the symmetrical host beam, it is found that the vortex moves along an elliptical trajectory, while the topological charge and the angular momentum of the vortex core relative to the beam axis are conserved. For the asymmetrical host beam, the vortex trajectory is rather complicated, since the noncanonical parameter varies as the light propagates, resulting in topological charge inversion. But we find that the vortices are always confined in a rectangular area, and the rotation direction is determined by the topological charge.