Abstrakt:
Linear Maxwell equations for transverse magnetic (TM) polarized fields support single frequency surface plasmon polaritons (SPPs) localized at the interface of a metal and a dielectric. Metals are typically dispersive, i.e. the dielectric function depends on the frequency. We prove the bifurcation of localized SPPs in dispersive media in the presence of a cubic nonlinearity and provide an asymptotic expansion of the solution and the frequency. We also show that the real frequency exists in the nonlinear setting in the case of $\PT$-symmetric materials.
This talk is based on joint works with Tomas Dohnal (Halle).