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A graphene-embedded plasmonic rib waveguide (GEPRW) is designed for the mid-infrared electro-optic modulator. The mode characteristics and electro-optic (EO) modulation performances are simulated and optimized by using the finite element method. The results show that propagation length of 103mm and figure of merit of 106 are obtained by adjusting the bias voltage applied to the GEPRW. The EO wavelength tunings are -66.69 and -78.87nm/V for peak L and peak R in the loss spectra when w=3µm and h1=2µm. For a 100 µm long GEPRW, the modulati