  Landau-Zener tunnelling 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 is achieved using two waveguide arrays with different
refractive indices, which amounts to consider a Schr\"odinger equation in a
periodic potential with a step. The step causes wave "acceleration" and thus
induces Landau-Zener tunnelling. 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.
