Second harmonic generation at conductor surfaces with continuous profiles

Summary form only given. We have extended the hydrodynamic model to calculate the linear and non-linear response and the nonlinear efficiency of semiinfinite metals taking account the electronic density profile at their surface. The surface nonlinear susceptibility and its efficiency display a series of very large peaks, several orders of magnitude larger than those obtained for abrupt profiles, corresponding to the excitation of multipolar surface modes at w and 2w. Our results suggest that the multipolar modes, which are difficult to observe in electron scattering experiments, might be observed through SHG spectroscopy. We hope this calculation encourages more experiments to measure the frequency dependence of the SHG signal