Spin-orbit interaction of photons and fine splitting of levels in ring dielectric resonator

We consider eigenmodes of a ring resonator made of a circular dielectric waveguide. Taking into account the polarization corrections, which are responsible for the interaction of polarization and orbital properties of electromagnetic waves (spin-orbit interaction of photons), results in fine splitting of the levels of scalar approximation. The basic features of this fine structure of the levels are similar to that of electron levels in an atom. Namely: (1) sublevels of the fine structure are defined by an additional quantum number: product of helicity of the wave and its orbital moment; (2) for a waveguide with a parabolic profile of the refractive index each level of the scalar approximation splits into N sublevels (N is the principal quantum number), while for any other profile it splits into 2 sublevels; (3) each level of the fine structure remains twice degenerated due to local axial symmetry of the waveguide. Numerical estimations show that the described fine splitting of levels may be observed in optic-fiber ring resonators.