Dynamical response of a dipole near the surface of a nonlocal metal

Expressions are derived for the potential of an oscillating point charge near the surface of a metal described by a nonlocal dielectric constant. The induced field at the site of a dipole outside the surface is found, and this result is used to calculate the renormalized polarizability of a dipole oscillator. Calculations are carried out using a hydrodynamic nonlocal dielectric constant, and the effects of nonlocal surface-plasmon dispersion and coupling to bulk plasmons are apparent. Expressions for the potential are also found if the added charge is placed within the nonlocal medium