Zeeman Splitting of Photonic Angular Momentum States in Gyromagnetic Cylinder

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.