We study analytically the plasmonic modes in the graphene-coated dielectric nanowire, based on the explicit form of nonlinear surface conductivity of graphene. The propagation constants of different plasmonic modes can be tuned by the input power at the order of a few tenths of mW. The lower and upper mode bifurcation branches are connected at the limitation value of the input power. Moreover, due to the nonlinearity of graphene, the dispersion curves of plasmonic modes at different input powers form an energy band, which is in sharp contrast with the single dispersion curve in the limit of zero input power.
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