Second-harmonic generation at simple metal surfaces

The time-dependent density-functional approach is used to determine the frequency dependence of second-harmonic generation (SHG) at various simple metal surfaces. In particular, the function a () which characterizes the perpendicular surface contribution to the nonlinear polarization is calculated for realistic ground-state density profiles and by taking into account the nonlocal nature of the self-consistent electronic screening response to the applied fields. At the laser frequency of 1. 17 eV, the real part of a () is much larger than the imaginary part and is typically 25--100 % larger than in the static limit. Ima () exhibits a feature for 2 near the threshold for electron emission and a second one for 2 near 0. 8₏, where ₏ is the bulk-plasma frequency.