  Cavity design is crucial for single-mode semiconductor lasers such as the
distributed feedback (DFB) and vertical-cavity surface-emitting lasers (VCSEL).
By recognizing that both optical resonators feature a single mid-gap mode
localized at the topological defect in a one-dimensional (1D) lattice, we
generalize the topological cavity design into 2D using a honeycomb photonic
crystal with a vortex Dirac mass -- the analog of Jackiw-Rossi zero modes. We
theoretically predict and experimentally demonstrate that such a Dirac-vortex
cavity can have a tunable mode area across a few orders of magnitudes,
arbitrary mode degeneracy, robustly large free-spectral-range, vector-beam
output of low divergence, and compatibility with high-index substrates. This
topological cavity could enable photonic crystal surface-emitting lasers
(PCSEL) with stabler single-mode operation.
