Electrons in crystalline solids or semiconductor superlattices, cold atoms in optical lattices, light beams in photonic crystals or waveguide arrays have the energies confined to Bloch bands separated by band gaps. The system response to a weak linear potential (i.e., a weak constant tilt) manifests itself in the form of Bloch oscillations as well as interband transitions known as Landau-Zener tunnelling. While the majority of previous studies considered only one dimensional systems, in a recent experiment the interband transitions have been observed for the first time in a two-dimensional periodic structure of square symmetry [1]. Multi-dimensional optical lattices are also routinely used for trapping of ultracold atoms and condensates of degenerate quantum gases, where more sophisticated trapping geometries have been shown experimentally. Simple theories are especially important for understanding the wave dynamics in the periodic structures and the theory of Zener tunnelling in hexagonal photonic lattices has recently been developed [2, 3].
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