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As is well known, the vortex beams have significant potential applications in both quantum and classical communication systems. In this paper, we study the existence and robustness to propagation of families of multi-vortex waveforms, namely multi-vortex optical beams in nonlinear self-focusing cubic (Kerr) media with harmonic potential wells. The intensity patterns, phase structures, transverse energy flow, and gradient forces (upon micro-particles) of those multi-vortex beams are presented and we found that they are all different from those of the ordinary vortex beams. The evolution during propagation of the intensities and widths of the multi-vortex beams is investigated in detail. The obtained results show that the one-vortex beams have asymmetric patterns and spiral propagation trajectories, depending on the off-axis parameter of the vortices. The two-vortex beams and the higher than two-vortex waveforms have symmetric patterns, which rotate during propagation, and the rotation direction can be controlled by the sign of the topological charge. [ABSTRACT FROM AUTHOR]

We introduce a kind of Hermite-Gaussian (HG) solitons, with off-axis and chirp parameters, propagating in nonlinear media with harmonic potential wells. The general formula for the trajectory of solitons is derived, and the propagation properties also be analyzed. The results shown that the off-axis HG solitons can present three different propagation states (including serpentine, elliptically and circularly spiral trajectory) depending on the value of the chirp parameter. Accordingly, we propose the concept of cluster composing of several HG solitons. The cluster shape depending on the off-axis parameters of each constituent soliton, and the chirp parameters also play important roles in the evolution of the clusters. Some typical examples are numerically demonstrated for graphically illustrating the propagation properties. Obviously, the controllable trajectory and shape of clusters may be applied in optical communication and particle controlling. • The propagating of HG solitons with off-axis and chirp parameters in harmonic potential wells was investigated. • The off-axis HG solitons can present different propagation states depending on the value of the chirp parameter. • The cluster shape depending on the off-axis parameters of each constituent soliton. • The chirp parameters play important roles in the evolution of the clusters. [ABSTRACT FROM AUTHOR]