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.
We study light-beam propagation in a nonlinear coupler with an asymmetric double-channel waveguide and derive various analytical forms of optical modes. The results show that the symmetry-preserving modes in a symmetric double-channel waveguide are d
eformed due to the asymmetry of the two-channel waveguide, yet such a coupler supports the symmetry-breaking modes. The dispersion relations reveal that the system with self-focusing nonlinear response supports the degenerate modes, while for self-defocusingmedium the degenerate modes do not exist. Furthermore, nonlinear manipulation is investigated by launching optical modes supported in double-channel waveguide into a nonlinear uniform medium.
