Skyrmions in Scalar Fields of Non-Hermitian Optical Microcavities: Spontaneous Formation, Nonlinear Control, and Optical Forces.

Topological textures of light offer powerful routes to structure optical fields, control wave transport, and manipulate matter. Skyrmions, long studied as topological solitons in vector fields, have recently been extended to scalar wave systems, including acoustics, hydrodynamics, and plasmonics. However, their realization in two-dimensional scalar wave propagation with nonlinearities and in quantum fluids remains uncharted. Here, we establish such a Skyrmion framework for scalar fields in optical microcavities. With a focus on exciton-polaritons, we show that nonresonant excitation without imposed phase can spontaneously generate isolated Skyrmions and self-organized Skyrmion lattices in a polariton condensate. We trace this mechanism to gain- and loss-induced phase curvature together with outward polariton flow. We further demonstrate that polariton nonlinearities provide all-optical control of these topological textures, enabling switching of the Skyrmion number and reconfiguration of Skyrmion moiré lattices through resonant and nonresonant excitation schemes. These results establish nonlinear non-Hermitian resonators as a versatile platform for the spontaneous generation and active control of scalar topological light fields.