Nonlinear dispersion relation for surface plasmon at a metal-Kerr medium interface

The dispersion relation for the plasmon at the interface of a metal and a nonlinear Kerr medium is studied by applying a semi-analytic theory established in the literature. Explicit analytical results are obtained and are compared to those from a certain approximate treatment appeared in the literature. It is found that for large electric field strengths, both the dispersion relation and the surface plasmon frequency from the approximate treatment deviate significantly from those obtained in the exact approach, especially for the case with a negative Kerr susceptibility.