Graphene plasmons (GPs) are broadband and electrically tunable mid-infrared (MIR)/terahertz (THz) excitations, exhibiting high confinement factors exceeding two orders of magnitude. Such highly confined modes are extremely attractive for nonlinear frequency conversion owing to the large inherent field enhancement. However, this high confinement is also accompanied by losses, and together with the centrosymmetric nature of graphene practical usage of its properties in second-order nonlinear processes remains hindered. In this paper, we introduce an approach for realizing quasi-phase-matching (QPM) of propagating GPs, by placing the graphene on an orientationally patterned GaAs substrate—a transparent material in the MIR/THz range with a large second-order nonlinear coefficient. We analyze the complete frequency/Fermi-level space for QPMed second-harmonic generation of GPs in the MIR and THz and demonstrate GP amplification and loss compensation. We find that our approach provides extended GP propagation lengths that are more than twice larger than the state-of-the-art cryogenic temperature propagation lengths. The approach is general to all second-order nonlinear processes, such as sum and difference frequency generation, thus opening a path for efficient and electrically tunable QPM nonlinear processes at the atomic scale.

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