Chiral wave propagation manifold of the photonic quantum-ring laser

A torus knot model is presented to analyze the chiral wave propagation of photonic quantum-ring lasers in a three-dimensional Rayleigh–Fabry–Perot toroidal cavity. The Rayleigh–Fabry–Perot cavity gives rise to peculiar multichromatic spectra with nonequal intermode spacings. In particular, the knot model analysis suggests a strange three-dimensional effective index ellipsoid for the cavity with a large birefringence of neff3D(z)−neff2D(x,y)≈0.4–0.5.