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. In the weak-field, cw regime, an alternative formalism consists in relying on classical electromagnetism, using the local nonlinear conductivities extracted from perturbative models of extended graphene. We show that both of these approaches are in excellent agreement for sufficiently-large structures (10s of nm in lateral size) when describing second- and third-harmonic generation, as well as the Kerr nonlinearity. Additionally, we exploit an eigenmode decomposition of the optical field in the classical formalism to obtain analytical expressions for the plasmon-driven response of graphene ribbons and finite islands, in excellent agreement with atomistic calculations.
In contrast to the instantaneous nonlinear response, where input and output fields maintain relative coherences, a delayed nonlinearity also takes place as a consequence of the strong dependence of the graphene response on the temperature of its conduction electrons. Here we show that transient plasmons arising from the elevated electronic temperature in graphene upon ultrafast optical pumping can produce strong modulations of the optical absorption. Our nonperturbative time-domain simulations indicate that the strong incoherent nonlinearity associated with plasmons in doped graphene nanostructures can be used for all-optical switching in nonlinear optical devices.
Joel D. Cox and Javier García de Abajo, "Instantaneous and transient nonlinearities of graphene plasmons (Conference Presentation)," Proc. SPIE 10345, Active Photonic Platforms IX, 1034516 (Presented at SPIE Nanoscience + Engineering: August 08, 2017; Published: 29 September 2017); https://doi.org/10.1117/12.2273932.5593117176001.
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