Discrete gap solitons in binary positive-negative index nonlinear waveguide arrays with strong second-order couplings

We report on the existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. The zigzag quasi-one-dimensional configuration of the waveguide array introduces strong next-to-nearest neighbor interaction in addition to nearest neighbor coupling. Effective diffraction can be controlled both in size and in sign by the value of the next-to-nearest neighbor coupling coefficient and can even be canceled completely. In the regime where instabilities occur, we found different families of discrete solitons bifurcating from the gap edges of the linear spectrum. We show that both staggered and unstaggered discrete solitons can become highly localized states near the zero diffraction points even for low powers. Stability analysis has shown that the soliton solutions are stable over a wide range of parameters and can exist in focusing, defocusing, and even in an alternating focusing-defocusing array.