Exact dispersion relation for nonlinear plasmonic waveguides

We derive an exact dispersion relation for the surface plasmon polaritons of a nonlinear plasmonic waveguide using exact field decomposition of TM waves. Our approach generalizes the known linear dispersion relations to the case of a medium nonlinearity of the form epsilon(NL) = epsilon(L) + alpha vertical bar E vertical bar(2n). We apply the unique dispersion relation to a plasmonic waveguide with a Kerr-type nonlinearity (n = 1) and show that it enables backward-propagating modes. It also introduces critical points in the energy spectrum of surface plasmon polaritons that result in enhanced interaction of nonlinear modes with each other and external electromagnetic fields.