  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.
