  We show that under the presence of a static magnetic field the photon
eigen-frequencies of a circular gyromagnetic cylinder experience a splitting
that is proportional to the angular momentum density of light at the cylinder
surface. Such a splitting of the photonic states is similar to the Zeeman
splitting of electronic states in atoms. This leads to some unusual decoupling
properties of these non-degenerate photonic angular momentum states, which are
demonstrated through numerical simulations.
