Surface defect solitons at the interface between simple lattices and superlattices with spatially modulated nonlinearities

We present the properties of surface defect solitons at the interface between simple lattices and superlattices with spatially modulated nonlinearities. Numerical results reveal that for positive defects, surface defect solitons can only stably exist in low-power region of semi-infinite gap and are nonexistent in the first gap. While for the negative defects, surface defect solitons can stably exist in the moderate-power region of semi-infinite gap, but in the first gap, surface defect solitons are stable in the most of the whole existence region. The stability region of surface defect soliton narrows as the depth of modulation of nonlinearity increases regardless of defects.