Bloch oscillation and Landau–Zener tunnelling in a modulated optical lattice in a photovoltaic photorefractive crystal

We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau–Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau–Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau–Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.