Origins of All-Optical Generation of Plasmons in Graphene

This is the final version. Available on open access from Nature Research via the DOI in this recordGraphene, despite its centrosymmetric structure, is predicted to have a substantial second order nonlinearity, arising from non-local effects. However, there is disagreement between several published theories and experimental data. Here we derive an expression for the second order conductivity of graphene in the non-local regime using perturbation theory, concentrating on the difference frequency mixing process, and compare our results with those already published. We find a second-order conductivity (σ (2)≈ 10−17AmV−2 ) that is approximately three orders of magnitude less than that estimated from recent experimental results. This indicates that nonlinear optical coupling to plasmons in graphene cannot be described perturbatively through the electronic nonlinearity, as previously thought. We also show that this discrepancy cannot be attributed to the bulk optical nonlinearity of the substrate. As a possible alternative, we present a simple theoretical model of how a non-linearity can arise from phFundacio Privada Cellex, Spanish MINECO Severo Ochoa ProgrammeCERCA Programme/Generalitat de CatalunyaEngineering and Physical Sciences Research Council (EPSRC)Royal SocietyTATAEuropean Commissio