Tunable Bands in Photonic Lieb Lattice by Graph Laplacian Approach

Abstract

We theoretically investigate the dispersion relation of a waveguide array made of metamaterials. The unit cell contains three waveguides with adjustable optical properties. We model the propagation of high-intensity electromagnetic waves in the array by a generalized nonlinear Schrodinger equation replacing the Laplacian operator with the graph Laplacian. We found that when the nonlinear coefficient matrix is a null matrix, the dispersion curve supports three branches, each corresponding to three energy bands and one perfectly flat. On the other hand when it is a matrix of ones the degeneracy of the dispersion curve is decreased and the flat band is located on the top of the dispersive bands. Hence, this study revealed the impact of high-intensity optical light to manipulate the band structure of a photonic Lieb lattice made of metamaterial.