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({ω}) 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({ω}) is much larger than the imaginary part and is typically 25--100 % larger than in the static limit. Ima({ω}) exhibits a feature for 2{ω} near the threshold for electron emission and a second one for 2{ω} near 0.8ωₚ, where ωₚ is the bulk-plasma frequency.