Modulation instability in nonidentical metamaterial waveguide arrays by graph Laplacian approach

Abstract

We theoretically investigate modulation instability (MI) in a nonidentical waveguide array, which is made up of positive and negative index metamaterial waveguides. The unit cell of the optical waveguide array consists of three waveguides arranged in a triangular manner. Waveguides 1 and 3 are made up of positive index material (PIM) channels and waveguide 2 is by negative index material (NIM) channels, as a result, they show different light propagation characteristics. We model this array of waveguides using a generalized nonlinear Schro¨dinger equation, replacing the Laplacian operator with the graph Laplacian. Following linear stability analysis, we will discuss MI for different values of transverse wave number, as it determines the order of the Brillouin zone. We also discuss the effect of input power on periodic MI in normal and anomalous dispersion regimes. Thus we report a comprehensive study on the MI and hence the better ways to generate and manipulate the solitons or ultra-short pulses in NIM PIM waveguide arrays.