Rabi oscillations of azimuthons in weakly nonlinear waveguides

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.