Far fields of two-dimensional TM modes in Dirac-vortex topological cavity.

Dirac-vortex cavities have single-mode emitting, scalable mode areas, arbitrary mode degeneracies, and vector-beam vertical emission, which attract more and more researchers' attention. Here, we demonstrate the single-mode of two-dimensional transverse magnetic (TM) Dirac-vortex topological cavity modes that are not only generally available for high power topological surface-emitting lasers (TCSEL) but also are one of the excellent candidates for refractive index sensors. The principle for winding number is studied, and the scaling laws are shown with cavity mode diameters. The methods can be directly guidance for far-field detection of the Dirac-vortex cavity TM mode in experiment. It is promising for an extremely wide range of applications for Dirac-vortex cavities.