  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.
