Theory for the Dependence of Optical Second Harmonic Generation Intensity on Non-equilibrium Electron Temperatures at Metal Surfaces

摘要

We present a theory for the electron-temperature dependence $T_{el}$ ofoptical second harmonic generation (SHG). Such an analysis is required to studythe dynamics of metallic systems with many hot electrons not at equilibriumwith the lattice. Using a tight-binding theory for the nonlinear susceptibility\cwtel and the Fresnel coefficients we present results for the SHG intensity\iwtel for a Cu monolayer. In the case of linear optical response we find thatthe intensity will decrease monotonously for increasing $T_{el}$. In agreementwith experiment we find a frequency range where \iwtel may be enhanced orreduced depending on electron temperature. Note, \cwtel rather than the Fresnelcoefficients determines essentially the temperature dependence. Our theoryyields also that SHG probes effects due to hot electrons more sensitively thanlinear optics. We also discuss the $T_{el}$-dependence of SHG for Au and Ag.