Modulational instability in photonic Lieb lattice: a graph Laplacian approach

This paper presents a theoretical investigation on modulational instability in a face-centered square lattice waveguide array. Each unit cell comprises three metamaterial waveguides with tunable optical properties. We model electromagnetic wave propagation in the array using the coupled nonlinear Schrödinger equation (NLSE), substituting the Laplacian operator with the graph Laplacian. Our analysis reveals a flat band in the dispersion curve, enabling the array to support diffractionless modes. We then employ linear stability analysis to examine the modulation instability of these diffractionless modes.