  Rabi oscillation, an inter-band oscillation, depicts the periodic flopping
between two states that belong to different energy levels in the presence of an
oscillatory driving field. In photonics, Rabi oscillation can be mimicked by
applying a weak longitudinal periodic modulation to the refractive index change
of the system. However, the Rabi oscillation of nonlinear states has yet to be
discussed. We report Rabi oscillations of azimuthons---spatially modulated
vortex solitons---in weakly nonlinear waveguides with different symmetries,
both numerically and theoretically. The period of Rabi oscillation can be
determined by applying the coupled mode theory, which largely depends on the
modulation strength. Whether the Rabi oscillation between two states can be
obtained or not is determined by the spatial symmetry of the azimuthons and the
modulating potential. In this paper we succeeded in obtaining the Rabi
oscillation of azimuthons in the weakly nonlinear waveguides with different
symmetries. Our results not only enrich the Rabi oscillation phenomena, but
also provide a new avenue in the study of pattern formation and spatial field
manipulation in nonlinear optical systems.
