Nonlocal and cascaded effects in nonlinear graphene nanoplasmonics

The ability of plasmons to focus light on nanometer length scales opens a wide range of enticing applications in optics and photonics, among which the enhancement of nonlinear light-matter interactions for all-optical modulation and spectral diversification emerges as a prominent theme. However, the subwavelength plasmonic near-field enhancement in good plasmonic materials such as noble metals is hindered by large ohmic losses, while conventional phase-matching of fields in bulk nonlinear crystals is not suitable for realizing nonlinear optical phenomena on the nanoscale. In contrast, anharmonic electron motion of free charge carriers in highly-doped graphene, which supports long-lived, highly-confined, and actively-tunable plasmons, renders the carbon monolayer an excellent platform for both plasmonics and nonlinear optics. Here we theoretically explore the enhancement in nonlinear response that can be achieved by interfacing multiple graphene nanostructures in close proximity to trigger nonlocal effects associated with large gradients in the electromagnetic near field. Focusing on second- and third-harmonic generation, we introduce a semianalytical formalism to describe interacting graphene nanoribbons with independent width, location, and electrical doping, so as to realize configurations in which plasmonic resonances may simultaneously enhance both the fundamental optical excitation frequency and harmonic intermediary and/or output frequencies. Our findings reveal the importance of both passive and active tuning in the design of atomically-thin nanostructures for nonlinear optical applications, and in particular emphasize the role played by nonlocal effects in generating an even-ordered nonlinear response that may contribute to other nonlinear optical processes through a cascaded interaction. We anticipate that our findings can aid in the design of actively-tunable nonlinear plasmonic resonators and metasurfaces.