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.

中文翻译：

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可见光范围内金表面的非线性光学响应：双色和频发生光谱研究。二、金属非线性磁化率模型

我们提出了金属表面非线性光学响应的​​模型，以解释最近对金的双色和频生成 (SFG) 实验的实验结果。该模型允许计算表面和体积贡献，并明确区分自由和束缚电子项。与其他贡献相反，垂直表面分量通过表面电子密度分布强烈依赖于模型。我们考虑了表面的三种电子密度方案，自由和束缚电子重叠或溢出，用于计算。计算出的来自金属的 SFG 信号仅依赖于体积量，不需要明确定义密度分布。在金的特殊情况下，当自由电子与束缚电子重叠或溢出时，自由电子响应完全通过垂直表面项占主导地位。当束缚电子溢出时，情况更加平衡，仍然有利于自由电子，具有较低的幅度和不同的色散线形状。至于银，自由电子贡献占主导地位，计算出的从蓝色到红色的缓慢幅度增长遵循实验趋势。