Guided modes of surface plasmon polaritons in linear dielectric-metal-nonlinear dielectric waveguide

We investigate the guided modes of the surface plasmon polaritons in metal waveguide with a nonlinear dielectric substrate and a linear dielectric cladding. It is shown that the nonlinear fundamental guided mode is always absent for any waveguide parameters. The exact dispersion relations of the surface plasmon polaritons are obtained in the form of the propagation constant versus the frequency and the waveguide thickness. We also investigate the slow-wave guided modes in the metal waveguide and show that only lowest-order mode can exist.