Analytical description of nonlinear plasmonic phenomena in nanostructured graphene

Abstract

The remarkably-high intrinsic optical nonlinearity of graphene can be pushed even further when the optical frequency is tuned to plasmon resonances hosted by the material when it is doped [1-4]. Atomistic simulations provide an accurate description of these phenomena, although their computational cost is prohibitive for large graphene nanostructures [3, 4]. An alternative formalism consists in relying on classical electromagnetism, using the local nonlinear conductivities extracted from models of extended graphene. Here we present an analytical, classical electromagnetic description of the nonlinear optical response associated with tunable plasmons in graphene nanostructures, in excellent agreement with atomistic simulations of sufficiently large structures (10s of nm in lateral size) when describing second- and third-harmonic generation, as well as the Kerr nonlinearity. We base our analytical approach on an eigenmode decomposition of the optical field associated with the plasmon-driven resonant response of graphene ribbons and finite islands. The analytical description constitutes a valuable asset to explore nonlinear optical phenomena in the context of graphene plasmonics, and can also be applied to model nonlinearities in other planar plasmonic materials, such as thin metal layers and black phosphorous.