Modulational instability in non-Kerr photonic Lieb lattice with metamaterials

TL;DR

This paper investigates the modulational instability of diffractionless waves in a non-Kerr nonlinear photonic Lieb lattice with positive and negative refractive index waveguides, highlighting the control of flat bands through nonlinear effects.

Contribution

It introduces a model of a face-centered square waveguide lattice with non-Kerr nonlinearity and analyzes the stability of diffractionless waves, emphasizing the nonlinear control of flat bands.

Findings

Existence of diffractionless wave solutions in the lattice

Nonlinearities can control flat band properties

Stability analysis of diffractionless waves

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 constituted by 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 flat bands 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 flat bands optically. The diffractionless wave solutions are derived and the stability of these distributions are investigated in a nutshell by adopting the standard linear stability approach.