M.I. Molina, Kartashov YV , Kivshar Y.S. and Torner L
PHYSICAL REVIEW A 77, 5 (2008)
We numerically study both linear and nonlinear surface modes in semi-infinite chirped two-dimensional photonic lattices in the framework of an effective discrete nonlinear model. We demonstrate that the lattice chirp can dramatically change the conditions for the mode localization near the surface even in the linear limit, and we find surface modes, in linear lattices, and the families of discrete surface solitons, in nonlinear lattices. In a sharp contrast to one-dimensional discrete surface, solitons, we demonstrate that the mode threshold power in two-dimensional lattices is lowered by the action of both the surface and lattice chirp. By manipulating the lattice chirp, we can control the mode position and its localization.