Surface solitons in two-dimensional chirped photonic lattices

We study surface modes in semi-infinite chirped two-dimensional photonic lattices in the frame- work of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode localization near the surface, and we find numerically the families of surface modes, in linear lattices, and discrete surface solitons, in nonlinear lattices. We demonstrate that, in a sharp contrast to one-dimensional discrete surface solitons, in two-dimensional lattices the mode threshold power is lowered by the action of both the surface and lattice chirp. By manipulating with the lattice chirp, we can control the mode position and its localization.