Discrete beam acceleration in uniform waveguide arrays

Within the framework of the tight-binding model we demonstrate that Wannier-Stark states can freely accelerate in uniform optical lattices. As opposed to accelerating Airy wave packets in free space, our analysis reveals that in this case the beam main intensity features self-bend along two opposite hyperbolic trajectories. Two-dimensional geometries are also considered and an asymptotic connection between these Wannier-Stark ladders and Airy profiles is presented.