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A calculation is performed of the second-harmonic radiation generated by the reflection of incident radiation from a metal surface in a model that considers only plasma effects and neglects periodic lattice structure in the metallic bulk and any form of surface roughness. The radiation is due to three kinds of currents: one localized to within a few angstroms of the surface and parallel to it, another also localized at the surface but normal to it, and a bulk current in the skin-depth region of the incident light, a region several hundred angstroms thick. Previous expressions for the normal surface current are found to be incorrect, and a new expression is derived. The second-harmonic radiation due to the surface currents is sensitive to surface conditions, while the contribution of the bulk current is only weakly sensitive to them. Theoretical estimates suggest that changes in the radiation intensity with variation in surface condition are caused primarily by changes in the parallel surface currents due to variations in surface scattering. In the course of this investigation general relationships and explicit forms for the second-order response of an isotropic electron gas are given.
Rudnick et al. (Wed,) studied this question.