Long-range interaction in waveguide lattices

We introduce an analytical expression for the dynamics of light propagation in a two-dimensional waveguide lattice including general long range coupling. Additionally, the diffraction properties in such general systems are investigated in detail. Using these very general results, particular geometries are discussed, including the possibility of diffraction-free propagation in the center of the Brillouin zone. Furthermore, the transition from the discrete to the continuum limit is analyzed.