Non-Local Optical Effects at Metal Surfaces

The non-local response of an irradiated metal surface is discussed in terms of the induced density in response to an external field. The field and the induced charge near the surface can be determined by solving Maxwell equations in the surface region and match the solution to the incoming and reflected wave in vacuum and to the asymptotic solution in the bulk of the solid. For incoming fields of wave lengths long in comparison with the extension of the surface region a key quantity is the center of gravity of the screening charge. This complex function of the frequency is important for a number of properties such as the reflectivity, the surface plasmon dispersion, image fields, van der Waals interactions between a molecule and a metal surface, etc. Considerations similar to the ones for a planar surface are also applied to the surface properties of a small metallic sphere.