Optical Bloch oscillations in general waveguide lattices

We study the dynamics of excitations in general two-dimensional (2D) lattices with an external spatial linear potential. Analytical expressions for the energy eigenspectrum (Wannier-Stark ladder) and the eigenstates (Wannier-Stark states) of the lattice Schrödinger equation are given, and the resulting periodic motion of localized excitations (Bloch oscillations) is investigated for arbitrary excitation, including single site and broad beam excitation.