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

Spatiotemporal vortex solitons in hexagonal arrays of waveguides