Vortex twins and anti-twins supported by multi-ring gain landscapes

We address the properties of multi-vortex soliton complexes supported by multi-ring gain landscapes in focusing Kerr nonlinear media with strong two-photon absorption. Stable complexes incorporating two, three, or four vortices featuring opposite or identical topological charges are shown to exist. In the simplest geometries with two amplifying rings vortex twins with equal topological charges exhibit asymmetric intensity distributions, while vortex anti-twins may be symmetric or asymmetric, depending on the gain level and separation between rings. Different arrangements of amplifying rings allow generation of stable multi-vortex soliton complexes with various topologies, with twins and anti-twins as building blocks.