Non-Hermitian Dirac Vortex: Minimal Theory for Topological-Cavity Surface-Emitting Laser

We construct a non-Hermitian Dirac-vortex model that combines a complex-mass winding with an infinite-imaginary-potential boundary, extending the Jackiw-Rossi and neutrino-billiard models to the dissipative regime. Moreover, this model serves as a minimal theory for the recently proposed topological-cavity surfaceemitting laser (TCSEL): the imaginary mass encodes vertical radiation loss and the absorbing boundary defines the active region. We derive closed-form expressions for the modal frequencies, thresholds, and tunable vectorbeam polarizations, which are validated experimentally. Our work provides a rare example in which an analytical non-Hermitian topological theory captures the essential physics for engineering practical optoelectronic devices.