Surface solitons at interfaces of arrays with spatially-modulated   nonlinearity
  We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear refractive index attains its maxima, we found that nonlinear surface waves exist and can be made stable only within a limited band of input energy flows, and for lattice depths exceeding a lower threshold. 
Y. V. Kartashov, V. A. Vysloukh, A. Szameit, F. Dreisow, M. Heinrich,   S. Nolte, A. Tunnermann, T. Pertsch, L. Torner