Discrete-symmetry vortices as angular Bloch modes.

The most general form for symmetric modes of nonlinear discrete-symmetry systems with nonlinearity depending on the modulus of the field is presented. Vortex solutions are demonstrated to behave as Bloch modes characterized by an angular Bloch momentum associated to a periodic variable, periodicity being fixed by the order of discrete point-symmetry of the system. The concept of angular Bloch momentum is thus introduced to generalize the usual definition of angular momentum to cases where O2 symmetry no longer holds. The conservation of angular Bloch momentum during propagation is demonstrated.