Stable patterns in the Lugiato-Lefever equation with a confined vortex pump

We introduce a model of a passive optical cavity based on a novel variety of the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5, stable confined vortex-ring states (vortex pixels) are produced by means of a variational approximation and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump and loss parameters. When the vortex-rings are unstable, they are destroyed by azimuthal perturbations which break the axial symmetry. The results suggest new possibilities for mode manipulations in passive nonlinear photonic media by means of appropriately designed pump beams.