Dissipative spin-orbit coupled vortex rings in vector exciton-polariton condensates

Exciton-polariton condensates are explored using coupled driven-dissipative Gross-Pitaevskii equations under the Keeling-Berloff approximation in the presence of photonic spin-orbit coupling (SOC). An extended dissipative variational approximation method uses analytical expressions for coupled vortex ring solitons as minimizing functions of a generalized Lagrangian framework. The results reveal that the amplitudes of the vortices are linked to losses and gain, while the topological charges of the vortices are tied to the width of the vortex rings. Numerically, using the proposed solution as initial conditions, the emergence of even-numbered multilobed rings takes place as the topological charges of the seeded vortices are increased. The analytical results are then confronted by a detailed numerical analysis that further elucidates the rich vortex dynamics inferred by SOC and other combinations of various system parameters.