Exact surface plasmon dispersion relation with ponderomotive nonlinearity in a metal/dielectric structure

The nonlinear effects in a metal due to the ponderomotive potential, which is induced by a steep spatial gradient in the electric field intensity, on the surface plasmon dispersion relation at a planar metal/dielectric interface are studied exactly. Previous studies invoked an approximation that amounts to keeping only the lowest order Kerr-like term in the metal dielectric constant. Comparing the exact result with the Kerr approximation reveals that the Kerr approximation often overestimates a cutoff frequency for the existence of surface waves and gives erroneous results in the range of frequencies below the overestimated cutoff and the real cutoff. Our result thus sheds light on the applicability of the Kerr approximation. Properly expanding the exact results recovers the standard linear results and the results starting with a Kerr-like approximation.