The nature of the topological phase of optical eddies in a small-mode fiber
is studied. It is shown that the topological phase results from precession
of the Poynting vector of the normal wave and characterizes the polarizati
on correction delta beta to the propagation constant. The operator of spin-
orbit interaction of normal eddies is constructed. The average physical val
ue of this operator is equal to the polarization correction delta beta. The
operator of spin-orbit interaction consists of two parts. One part determi
ned polarization corrections to CV-eddies and the second one, polarization
corrections to TE- and TM-modes. Such a separation of the operator into two
parts, which describe different optical processes, implies that two types
of birefringence take place in the locally isotropic inhomogeneous medium.