Confining light to sharp metal tips has become a versatile technique to study optical and electronic properties far below the diffraction limit. Particularly near-field microscopy in the mid-infrared spectral range has found a variety of applications in probing nanostructures and their dynamics. Yet, the ongoing quest for ultimately high spatial resolution down to the single-nanometer regime and quantitative three-dimensional nano-tomography depends vitally on a precise knowledge of the spatial distribution of the near fields emerging from the probe. Here, we perform finite element simulations of a tip with realistic geometry oscillating above a dielectric sample. By introducing a novel Fourier demodulation analysis of the electric field at each point in space, we reliably quantify the distribution of the near fields above and within the sample. Besides inferring the lateral field extension, which can be smaller than the tip radius of curvature, we also quantify the probing volume within the sample. Finally, we visualize the scattering process into the far field at a given demodulation order, for the first time, and shed light onto the nanoscale distribution of the near fields, and its evolution as the tip-sample distance is varied. Our work represents a crucial step in understanding and tailoring the spatial distribution of evanescent fields in optical nanoscopy.

中文翻译：

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通过傅里叶解调分析量化近场显微镜中的纳米级电磁场

将光限制在尖锐的金属尖端上已成为研究远低于衍射极限的光学和电子特性的通用技术。特别是在中红外光谱范围内的近场显微镜，在探测纳米结构及其动力学方面具有多种应用。然而，对最终的高空间分辨率直至单纳米状态和定量三维纳米断层扫描的不断追求，在很大程度上取决于对从探头中出来的近场空间分布的精确了解。在这里，我们对尖端进行有限元模拟，该尖端具有在电介质样本上方振荡的真实几何形状。通过对空间中每个点的电场进行新颖的傅立叶解调分析，我们可以可靠地量化样品上方和内部的近场分布。除了推断可能小于尖端曲率半径的横向场扩展之外，我们还量化了样本内的探测体积。最后，我们首次以给定的解调顺序可视化了到远场的散射过程，并将光照射到近场的纳米级分布上，并且随着尖端样本距离的变化其演化。我们的工作是理解和定制光学纳米显微镜中e逝场空间分布的关键一步。并将光照射到近场的纳米级分布上，并且随着尖端样本距离的变化而变化。我们的工作是理解和定制光学纳米显微镜中e逝场空间分布的关键一步。并将光照射到近场的纳米级分布上，并且随着尖端样本距离的变化而变化。我们的工作是理解和定制光学纳米显微镜中e逝场空间分布的关键一步。