  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.
