Modulational instability in a non-Kerr photonic Lieb lattice with metamaterials

Abstract

We present an analysis of modulational instability of diffractionless waves in a face-centered-square lattice of waveguides featuring non-Kerr nonlinearity, which are composed of a combination of positive and negative refractive indices. The unit cell of the lattice consists of three different waveguides with different optical properties. The dispersion curve of the lattice supports flatbands and thereby the base equations describing the model have particular solutions that correspond to the diffractionless waves propagating along the waveguides. We also observe a unique ramification of nonlinearities in controlling the flatbands optically. The diffractionless wave solutions are derived and the stability of these distributions is investigated concisely by adopting the standard linear stability approach.