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 εNL=εL+α|E|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.
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Rukhlenko et al. (2011) studied this question.
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