Splitting of levels in a cylindrical dielectric waveguide

A splitting of modes in a cylindrical graded-index optical fiber is demonstrated by solving the full Maxwell equations using the perturbation analysis. It is shown that the degeneracy of vortex Laguerre-Gauss modes with distinct orbital angular momentum and polarization (spin) but the same total angular momentum is lifted due to the spin-orbit (vector) and tensor forces. Numerical estimations of group delays of modes in optical fiber and frequency splitting in Fabry-Perot and ring resonators are presented.