Hydrodynamic-model calculation of second-harmonic generation at a metal surface

Abstract

Using a hydrodynamic model of collective electronic motion we calculate the efficiency of second-harmonic generation in a simple reflection geometry. The model applies to a smooth, jellium metal surface, which is treated as having a sequence of steps in the equilibrium electron-density profile. We derive both the equations of motion and additional boundary conditions necessary for our approach. The final formulas are numerically evaluated for various values of the system’s parameters. The results show considerable variation with frequency, especially when multipole modes are present in the linear response. We demonstrate that the general results can be usefully paramet- rized in terms of bulk optical properties and a pair of complex, frequency-dependent parameters that summarize the response at the surface.