Switching of Discrete Solitons in Engineered Waveguide Arrays
  We demonstrate a simple method for controlling nonlinear switching of discrete solitons in arrays of weakly coupled optical waveguides, for both cubic and uadratic nonlinearities. Based on the effective discrete nonlinear equations describing the waveguide arrays in the tight-binding approximation, we develop the concept of the array engineering by means of a step-like variation of the waveguide coupling. We demonstrate the digitized switching of a narrow input beam for up to eleven neighboring waveguides, in the case of the cubic nonlinearity, and up to ten waveguides, in the case of quadratic nonlinearity. We discuss our predictions in terms of the physics of the engineered Peierls-Nabarro (PN) potential experienced by strongly localized nonlinear modes moving in a lattice and calculate, for the first time, the PN potential for the quadratic nonlinear array. We also confirm our concept and major findings for a full-scaled continuous model and realistic parameters, by means of the beam propagation method. 
R. A. Vicencio, M. I. Molina and Y.S. Kivshar