Quasi-phase matching for efficient long-range plasmonic third-harmonic generation via graphene.

We propose and numerically investigate an efficient method for long-range third-harmonic generation (THG) of propagating surface plasmon polaritons (SPP) waves on graphene sheets for nonlinear plasmonic purposes in the terahertz (THZ) gap region of the electromagnetic spectrum via a developed nonlinear finite-difference time-domain technique. We reveal that although extended and unmodulated graphene sheets with low Fermi levels can offer high-conversion efficiency (CE) for SPP THG at short distances, suitable for miniaturized plasmonic circuits, they suffer from inherent absorption loss induced by graphene that noticeably reduces the CE of the THG at long ranges. We suggest a structure benefiting from low Fermi-level graphene regions of strong nonlinear response as oscillators and high Fermi-level ones of low loss as a propagating medium in a periodic manner, which satisfies the quasi-phase matching condition and shows considerable efficiency improvement at long propagation distances. We predict that such a configuration can find valuable potential applications in the realm of nonlinear THz plasmonics for generating new frequencies and also in spectroscopy, signal processing, and so on.