Solitonic Bloch oscillations in two-dimensional optical lattices

A theoretical description for nonlinear beam propagation in a two-dimensional optical lattice in the presence of a refractive-index gradient has been developed. This problem is associated with nonlinear Bloch oscillations; it has been reduced to a nonlinear Schroedinger equation with a varying dispersion coefficient. It is shown that, if the periodicity of longitudinal modulation coincides with the transverse gradient of the refractive index, a stationary oscillatory picture emerges in the nonlinear regime.