Globally-linked vortex clusters

Abstract

We show the existence of a rich variety of fully stationary vortex structures made of an increasing number of vortices nested in paraxial wave fields confined by symmetric and asymmetric harmonic trapping potentials in both static and rotating reference frames. In the static reference frame the clusters are built by means of Hermite-Gauss functions, being termed H-clusters, whereas in the rotating frame they are generated by using the Laguerre-Gauss functions, being thus termed L-clusters. These complex vortex-structures consist of globally linked vortices, rather than independent vortices and, in symmetric traps, they feature monopolar global wave front. Nonstationary or flipping circular vortex-clusters can be built in symmetric traps and they feature multipolar phase front. In asymmetric traps, the existing stationary vortex clusters can feature multipolar wave fronts, depending on the ratio of the trap frequencies. In the nonlinear case, corresponding to nonrotating Bose-Einstein condensates, the stationary vortex clusters also exist and some of these highly excited collective states display dynamical stability.