The enhanced artificial sum frequency generation (SFG) is realized by graphene-gold metamolecules at the mid-infrared without any natural nonlinear material. The unit cell of the proposed metamolecules combines an inner graphene cut-wire meta-atom and an outer gold split-ring resonator meta-atom. In order to achieve high efficiency of the artificial SFG, not only the novel material of graphene with high mobility is used as the constituent material, but also the double resonances at two fundamental frequencies are excited to form an intensive magnetic Lorentz force. Both time domain response and frequency domain response are analyzed numerically. Results show that the SFG efficiency is at least two orders of magnitude larger than that of second-harmonic generation, which involves only a single resonance. The tunability of graphene on the SFG is studied as well. This work will facilitate the engineering of nonlinear metamaterials, whose nonlinear properties can be customized by artificial structuring, in their practical applications.
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