Free electrons act as a source of highly confined, spectrally broad optical fields that are widely used to map photonic modes with nanometer/millielectronvolt space/energy resolution through currently available electron energy-loss and cathodoluminescence spectroscopies. These techniques are understood as probes of the linear optical response, while nonlinear dynamics has escaped observation with similar degree of spatial detail, despite the strong enhancement of the electron evanescent field with decreasing electron energy. Here, we show that the field accompanying low-energy electrons can trigger anharmonic response in strongly nonlinear materials. Specifically, through realistic quantum-mechanical simulations, we find that the interaction between ≲100 eV electrons and plasmons in graphene nanostructures gives rise to substantial optical nonlinearities that are discernible as saturation and spectral shifts in the plasmonic features revealed in the cathodoluminescence emission and electron energy-loss spectra. Our results support the use of low-energy electron-beam spectroscopies for the exploration of nonlinear optical processes in nanostructures.

中文翻译：

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自由电子和纳米石墨烯之间的非线性相互作用。

自由电子充当高度受限的，光谱宽的光学场的来源，该场被广泛用于通过当前可用的电子能量损失和阴极发光光谱学来绘制具有纳米/毫伏空间/能量分辨率的光子模式。这些技术被理解为线性光学响应的​​探针，尽管电子瞬逝场随着电子能量的降低而大大增强，但非线性动力学却逃脱了相似程度的空间细节的观察。在这里，我们表明伴随低能量电子的场可以触发强非线性材料中的非谐响应。具体来说，通过现实的量子力学模拟，我们发现graph100 eV电子与石墨烯纳米结构中的等离激元之间的相互作用引起了显着的光学非线性，这可以通过在阴极发光发射和电子能量损失谱中揭示的等离激元特征的饱和度和光谱位移来辨别。我们的研究结果支持使用低能电子束光谱学探索纳米结构中的非线性光学过程。