傅里叶红外光谱（FTIR）是材料表征的一种重要手段, 然而受限于光的衍射极限, 传统傅里叶红外光谱仪的极限空间分辨率在微米量级, 无法应用于纳米材料的表征。 纳米傅里叶红外光谱（Nano-FTIR）是一种新兴的超分辨光谱表面分析技术, 其以纳米级空间分辨率、 宽光谱范围和高化学灵敏性的特点在纳米材料表征研究中展现了巨大的潜力。 定性及定量的研究Nano-FTIR信号高空间分辨的来源和系统中光谱信号的提取过程, 可以为Nano-FTIR仪器的设计研发和样品光谱表征结果的解释提供重要依据。 该研究从典型的仪器结构和基本的工作原理出发, 在多物理场有限元分析软件COMSOL中建立了等效研究模型, 并对模型的重要细节和数值计算过程分别进行了说明。 在仿真研究中, 首先基于麦克斯韦电磁波理论计算了模型空间的电磁场增强情况, 再模拟了探针在介电常数差异巨大的两种材料交界处的“线扫”过程, 探讨了针尖近场增强信号的空间分辨率。 随后, 以探针与样品的散射功率为数值模型的研究对象, 仿真了探针“轻拍”对信号的调制和解调提取的过程, 并讨论了不同入射倾角和解调频率对光谱信号提取的影响。 最后, 为了验证模型的合理性, 仿真了20, 100和300 nm三种厚度SiO2薄膜样品在900～1 250 cm-1波数范围的光谱响应, 并将仿真得到的光谱与实测结果进行了对比。 结果表明随着样品厚度的增厚, 光谱信号得到相应的增强, 模型预测的谱图与实测谱图波形与波峰位置较为一致, 且与以往一些文献中采用针尖-样品间电场强度表示针尖处散射信号强弱的方法相比, 获得的谱图在峰形上更为接近。 提出的数值模型可用于Nano-FTIR光谱的预测, 此外, 模型也具有一定的通用性, 可以为其他基于散射型近场光学显微（s-SNOM）技术的太赫兹光谱技术和针尖增强拉曼光谱研究提供一定的借鉴。

Fourier infrared spectroscopy (FTIR) technology is an important method for material characterization. However, it is limited by the diffraction limit. The spatial resolution limit of traditional Fourier infrared spectrometer is on the order of micrometers and cannot be applied to the characterization of nanomaterials. Nano Fourier transforms infrared spectroscopy (Nano-FTIR) is an emerging super-resolution spectroscopic surface analysis technology, which exhibits tremendous performance in nanomaterial characterization research with the characteristics of nano-scale spatial resolution, wide spectral range and high chemical sensitivity. Qualitative and quantitative research on the source of the high spatial resolution of Nano-FTIR signals and the extraction process of spectral signals in the system can provide the important basis for the design and development of Nano-FTIR instruments and the interpretation of sample spectral characterization results. Based on the typical instrument structure and basic working principles, an equivalent research model is established in the multi-physics finite element analysis software COMSOL, and the important details of the model and the numerical calculation process are explained separately. In the simulation study, the model first calculated the electromagnetic field enhancement in the model space based on Maxwell’s electromagnetic wave theory, and then simulated the “line sweep” process of the probe at the interface between two materials with large differences in dielectric constants, discussed the near-field enhancement of the tip-sample and the spatial resolution of the signal. Subsequently, a numerical model was proposed with the scattered power of the probe and sample as the research object, and the process of the modulation and demodulation extraction of the signal by the probe tapping, different incident angle of light and demodulation frequencies were also discussed. Finally, in order to verify the rationality of the model, the spectral responses of SiO2 thin film samples of three thicknesses of 20, 100 and 300 nm in the wavenumber range of 900～1 250 cm-1 were simulated, and the simulated spectra were compared with the measured results. The results show that as the thickness of the sample increases, the spectral signal is correspondingly enhanced and predicted spectra in agreement with the experimental spectra. Spectra predicted by our model are more consistent in peak shape compare with spectra simulated by the tip-sample electric field strength used to some previous studies. The proposed numerical model can be used for the prediction of Nano-FTIR spectra, in addition, the model also has certain generality, and can be used for Tip-enhanced Raman spectra and Terahertz spectra based on scattering near-field optical microscopy (s-SNOM) technology.