Strong Optical Nonlinearity of Graphene Nanoribbons*

Many nonlinear nanophotonics applications require strong nonlinear light-matter interaction; hence, there is ongoing research on finding materials with a strong nonlinear optical response. Here, we calculate the third-order Kerr susceptibility and the third-harmonic-generation susceptibility of graphene nanoribbons (GNRs) and show that, in the long-wavelength regime, GNRs have a remarkably strong nonlinear optical response, particularly the Kerr optical response, in a broad frequency range: from terahertz to near-infrared. The strong optical nonlinearity of GNRs in the long-wavelength region enables stacking them on top of one another and embedding them in the on-chip semiconductor waveguides, and therefore makes GNRs a promising material for integrated nonlinear nanophotonics applications. Our analysis is based on perturbatively solving a Lindblad-type quantum-master equation. We show that electron scattering plays a nontrivial role in the nonlinear optical response of GNRs and semiclassical approaches, such as the relaxation-time approximation, are not accurate for calculating the GNRs optical nonlinearity.