Quantum Effects in the Nonlinear Response of Graphene Plasmons

Abstract

The ability of graphene to support long-lived, electrically tunable plasmons that interact strongly with light, combined with its highly nonlinear optical response, has generated great expectations for application of the atomically-thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Here we show that finite-size effects produce large contributions that increase the nonlinear response of nanostructured graphene to significantly higher levels than those predicted by classical theories. We base our analysis on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation. While classical and quantum descriptions agree well for the linear response when either the plasmon energy is below the Fermi energy or the size of the structure exceeds a few tens of nanometers, this is not always the case for the nonlinear response, and in particular, third-order Kerr-type nonlinearities are generally underestimated by the classical theory. Our results reveal the complex quantum nature of the optical response in nanostructured graphene, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.

Polarization control using passive and active crossed graphene gratings

“…Thus, in this paper we only consider the third-harmonic generation, namely m = 3 and the conductivity tensor is described by a single scalar function. This function can be written as [10][11][12]:…”

Nonlinear graphene plasmonics

“…There are a number of theoretical papers discussing the effect of plamonics on graphene's nonlinearity [122,126,[132][133][134]. Pertaining to waveguide structures, as early as 2010, Skryabin et al [131] derived a set of expressions from the nonlinear Schrödinger equations (NLSEs) to describe the surface effects of various subwavelength plasmonic waveguide structures and coined the term SINE.…”

“…It was found that, due to its highly resonant structure, the TPA process could be switched on or off depending on the Fermi level of the graphene dot. In later works, Cox and co-workers also studied triangularshaped graphene nanoislands [133,143] and found that the nonlinear response varies with the size, Fermi level as well as the edge structures (armchair or zigzag) of graphene, as shown in figure 16. You et al [144] studied the nonlinear enhancement of graphene ribbons and discs on the third-harmonic generation efficiency.…”

Nonlinear plasmonic sensing with nanographene

“…Additionally, the anharmonic electron motion associated with the Dirac cones of this material [42,43] gives rise to an extraordinary nonlinear response in extended samples [44][45][46]. LSPs in graphene nanoislands have been predicted to produce unprecedentedly high harmonic generation and wave mixing [47,48], indicating their strong capability for nonlinear optical sensing.In this Letter, we show through atomistic quantummechanical simulations that both the linear and nonlinear optical response of graphene nanoislands can be dramatically altered by the presence of a single neighboring molecule that carries either an elementary charge or a permanent dipole of only a few Debye. As a proofof-principle demonstration, we focus on small graphene nanohexagons (GNHs), similar to those produced with high quality through chemical synthesis [49,50].…”

“…Additionally, the anharmonic electron motion associated with the Dirac cones of this material [42,43] gives rise to an extraordinary nonlinear response in extended samples [44][45][46]. LSPs in graphene nanoislands have been predicted to produce unprecedentedly high harmonic generation and wave mixing [47,48], indicating their strong capability for nonlinear optical sensing.…”