Surface plasmon dispersion relation of a metallic wire in a nonlinear dielectric medium

The surface plasmon dispersion relation of a cylindrical metallic rod embedded in a Kerr nonlinear dielectric medium is studied using an integral approach. A formalism for the dispersion relation of the azimuthal symmetric mode is presented, in which an integral has to be treated numerically. We invoke an approximation based on weak nonlinearity. The results are in good agreement with numerical results obtained by requiring the fields to decay properly away from the rod. The formalism recovers the previous results of a metallic rod in a linear dielectric medium and a planar metallic/nonlinear interface as special cases.