Modulation instability in two-dimensional waveguide arrays with alternating signs of refractive index

We consider the propagation of coupled forward and backward waves in two-dimensional arrays of alternating waveguides with positive and negative refractive indices. The array has a cross section in the form of a face-centered square lattice. The unit cell consists of three different waveguides with different optical properties. We obtain the condensate solutions for electromagnetic pulse propagation in such an array of waveguides. The base equations describing this model have solutions that correspond to the static and homogeneous intensity distribution on the waveguides. The stability of these solutions in both normal and anomalous dispersion regimes is also investigated using modulation instability analysis.