Graphene induced bifurcation of energy levels at low input power

We study analytically the energy states in the waveguide system of graphene coated dielectric nanowire based on the explicit form of nonlinear surface conductivity of graphene. The energy levels of different plasmonic modes can be tuned by the input power at the order of a few tenths of mW. The self-focusing behavior and self-defocusing behavior are exhibited in the lower and upper bifurcation branches, respectively, which are separated by a saturation of input power. Moreover, due to the nonlinearity of graphene, the dispersion relations for different input powers evolve to an energy band which is in sharp contrast with the discrete energy level in the limit of zero power input.