Abstract
We analyze the dynamics of vortex solitons and the formation of soliton clusters with controllable attributes in a nonlinear metamaterial waveguide. We consider the nonlinear Schrödinger equation with cubic and quintic nonlinearities as the propagation model and identify stable as well as filamentation regions with different combinations of nonlinearities on performing a linear stability analysis. By adopting a numerical analysis, we also confirm our analytical results. When the vortex beam propagates in the cubic nonlinear metamaterial waveguide, we numerically observe the formation of the annular soliton clusters as a result of instability. On the other hand, the competing cubic and quintic nonlinear metamaterial will not support any splitting of vortex beam, instead it stabilizes the unstable dynamics. The number of annular solitons increases with the increase of azimuthal index of the vortex. It is well known that metamaterials allow engineering of the material parameters at will. Utilizing this engineering freedom to tune the nonlinear parameters of metamaterial, we also examine the possibility to generate tailored filaments as well as ways to observe the stable dynamics of the vortex beams.
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