Spatiotemporal vortex solitons in hexagonal arrays of waveguides

By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly-coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semi-discrete complexes (which are continuous in the longitudinal direction), with embedded vorticity S: triangular modes with S=1, hexagonal ones with S=2, both centered around an empty central core, and compact triangles with S=1, which do not not include the empty site. Collisions between stable triangular vortices are studied too. These waveguiding lattices can be realized in optics and BEC.