Nonadiabatic Landau-Zener Tunneling in Waveguide Arrays with a Step in the Refractive Index

Landau-Zener tunneling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave ``acceleration'' and thus induces strongly nonadiabatic Landau-Zener tunneling. Theoretically, the analysis is performed by considering a Schr\"odinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.