Second-order nonlinear optical processes do not manifest in the bulk of centrosymmetric materials, but may occur in the angstroms-thick layer at surfaces. At such length scales, quantum mechanical effects come into play which could be crucial for an accurate description of plasmonic systems. In this article, we develop a theoretical model based on the quantum hydrodynamic description to study free-electron nonlinear dynamics in plasmonic systems. Our model predicts strong resonances induced by the spill-out of electron density at the metal surface. We show that these resonances can boost second-harmonic generation efficiency up to four orders of magnitude and can be arbitrarily tuned by controlling the electron spill-out at the metal surface with the aid of thin dielectric layers. These results offer a possibility to artificially increase nonlinear susceptibilities by engineering optical properties at the quantum level.

二阶非线性光学过程并未出现在大部分的中心对称材料中，而是可能出现在表面的埃厚层中。在这样的长度尺度上，量子力学效应开始起作用，这对于精确描述等离激元系统可能至关重要。在本文中，我们建立了一个基于量子流体动力学描述的理论模型，以研究等离子体系统中的自由电子非线性动力学。我们的模型预测了由金属表面电子密度的溢出引起的强烈共振。我们表明，这些共振可以将二次谐波的产生效率提高到四个数量级，并且可以借助薄的介电层通过控制金属表面的电子溢出来任意调节。