Spatiotemporal vortices in optical fiber bundles

We analyze complex spatiotemporal semidiscrete solitons in a model of a set of nonlinear optical fibers which form a square lattice in the cross section. The medium was recently realized as a set of parallel waveguides written in fused silica. The model also applies to a self-attracting Bose-Einstein condensate trapped in a very strong quasi-two-dimensional optical lattice. By means of the variational approximation (VA) and using numerical methods, we construct several species of the semidiscrete solitons, including vortices of rhombus (alias cross) and square types, with vorticity S = 1 and 2, and quadrupoles. The VA is developed for narrow cross vortices with S = 1 and quadrupoles, which turn out to be the most stable species. Two finite stability intervals are also found for the square-shaped vortices with S = 1, while all the vortices with S = 2 are unstable. For the unstable solitons, several scenarios of the instability development are identified, such as fusion of the entire complex into a single fundamental soliton, or splitting into coherent soliton pairs.