Nonlinear optical response of a gold surface in the visible range: A study by two-color sum-frequency generation spectroscopy. II. Model for metal nonlinear susceptibility.

We present a modeling of the nonlinear optical response of a metal surface in order to account for recent experimental results from two-color Sum-Frequency Generation (SFG) experiments on gold. The model allows calculating the surface and bulk contributions and explicitly separates free and bound electron terms. Contrary to the other contributions, the perpendicular surface component is strongly model-dependent through the surface electron density profiles. We consider three electron density schemes at the surface, with free and bound electrons overlapping or spilling out of the bulk, for its calculation. The calculated SFG signals from the metal rely only on bulk quantities and do not need an explicit definition of the density profiles. In the particular case of gold, when the free electrons overlap with the bound ones or spill out of the bulk, the free electron response completely dominates through the perpendicular surface terms. When the bound electrons spill out, the situation is more balanced, still in favor of the free electrons, with lower amplitudes and different dispersion line shapes. As for silver, the free electron contributions dominate and the calculated slow amplitude growth from blue to red follows the experimental trends.