Steering between Bloch oscillation and dipole oscillation in parabolic optical waveguide arrays

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We study the optical oscillations of supermodes in planar optical waveguide arrays with parabolically graded propagation constant in individual waveguide interacting through nearest neighbor couplings. In these arrays, we have identified a transition between a symmetric dipole oscillation (DO) and a symmetry-breaking Bloch oscillation (BO) under appropriate conditions. There exist obvious correspondences between gradon localization and various optical oscillations. By virtue of an analogue between the oscillation of optical system and that of a plane pendulum, we propose a shift of the graded profile to cause a transition from BO to DO. We confirm the optical transition by means of Hamiltonian optics, as well as by the field evolution of the supermodes. The results offer great potential applications in optical switching, which can be applied to design suitable optical devices.