Modulation instability in a zigzag array of nonlinear waveguides with alternating positive and negative refractive indices

The modulation instability is analytically investigated in a zigzag array of tunnel-coupled optical waveguides with alternating refractive indices and Kerr nonlinearity. Particular solutions to a system of coupled nonlinear equations are found. They describe the propagation of electromagnetic waves that are uniform along the waveguide and their instability is studied. It is shown that the coupling coefficient between the waveguides, which are non-nearest neighbours, has a significant effect on the instability of the waves in question. When the coupling coefficient exceeds a certain threshold, the modulation instability disappears regardless of the radiation power. The influence of the ratio of the wave amplitudes in adjacent waveguides to the instability of the particular solutions is studied. Different variants of the nonlinear response in waveguides are considered. The studies performed present a new unusual type of the modulation instability in nonlinear periodic systems.