Evolution of composite off-axis vortexes embedded in the propagation-invariant beams

Study of singularities embedded in the propagation-invariant beams has opened up a niche area of research. We report the study of a single and composite off-axis vortexes embedded in the propagation-invariant beams. The influence of radial wavevector of the propagation-invariant beam (host beam) on the evolution of an off-axis vortex to the centre of the beam (recovery distance) is reported in the paper. The recovery distance of an off-axis vortex also depends on the topological charge of the vortex and the offset distance of the vortex from the centre of the beam. Furthermore, the composite off-axis vortexes stably add their topological charges at the centre of the beam during the free-space propagation.