Theory for the nonlinear optical response at noble-metal surfaces with nonequilibrium electrons

We present a theory for the electron-temperature dependence T-el of optical second harmonic generation (SHG). Such an analysis is required to study the dynamics of metallic systems with many hot electrons not at equilibrium with the lattice. Using a tight-binding theory for the nonlinear susceptibility chi((2))(omega,T-el) and the Fresnel coefficients we present results for the SHG intensity I-(2)(omega,T-el) and its dependence on T-el for Cu. Note, chi((2))(omega,T-el) rather than the Fresnel coefficients determines essentially this temperature dependence. Most interestingly we find frequency ranges where I-(2)(omega,T-el) increases for small Light intensities, while it decreases for large light intensities. Our theory yields also that SHG probes effects due to hot electrons more sensitively than linear optics. The results of our calculations are compared with recent experiments on Cu and Au.