Harmonic oscillations and their switching in elliptical optical waveguide arrays

We have studied harmonic oscillations in an elliptical optical waveguide array in which the coupling between neighboring waveguides is varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, long-living Bloch oscillation (BO) and dipole oscillation (DO) are obtained when a linear gradient in the propagation constant is applied. Moreover, we achieve a switching from DO to BO or vice versa by ramping up the gradient profile. The various optical oscillations as well as their switching are investigated by field evolution analysis and confirmed by Hamiltonian optics. The equally spaced eigenvalues in the propagation constant allow viable applications in transmitting images, switching and routing of optical signals.