Analytical description of the nonlinear plasmonic response in nanographene

Abstract

Graphene exhibits a remarkably high intrinsic nonlinearity that can be pushed even further when the optical frequency is tuned to the plasmon resonances of the material. Atomistic simulations provide an accurate description of these phenomena, although their computational cost is prohibitive for large graphene nanostructures. An alternative formalism consists in relying on classical electromagnetism, using the local nonlinear conductivities extracted from extended graphene. We show that both of these approaches are in excellent agreement for sufficiently large structures (10s nm lateral size) when describing second- and third-harmonic generation, as well as Kerr nonlinearities. Additionally, we exploit an eigenmode decomposition of the optical field in the classical formalism to obtain analytical expressions for the plasmon-driven resonant response of graphene ribbons and finite islands, in excellent agreement with full numerical calculations. This analytical description constitutes a valuable asset to explore nonlinear phenomena in the context of graphene plasmonics and is equally useful to model nonlinearities in other planar plasmonic materials, such as thin metal layers and exfoliated chalcogenides.