Fig. 2. Numerical simulations of the topological cavity.

a Band diagram of a hexagonal supercell with a Kekulé modulation (left panel) and the unmodulated photonic crystal (right panel). The bandgap has ≥12% relative width. Inset: schematic of the hexagonal supercell and its Brillouin zone. b The phase of the Kekulé pattern, which has winding number of +1. The colorbar defines the smooth phase varying from 0 to 2π. c Modulation of the photonic structure’s air-hole radii, using a vortex core radius of two periods ($\xi =2a$). The colorbar defines the smooth radii varying from $R_0-△R$ to $R_0+△R$, here $R_0=0.35a$ and $△R=0.15a$, respectively. d Calculated electric field (E_z) for the photonic MZM, which is tightly confinement to the vortex core. e Calculated far-field intensity pattern of the photonic MZM, which exhibits a doughnut-like profile characteristic of cylindrical vector (CV) beams.