The unique physical and chemical properties of interfaces are governed by a finite depth that describes the transition from the topmost atomic layer to the properties of the bulk material. Thus, understanding the physical nature of interfaces requires detailed insight into the different structures, chemical compositions, and physical processes that form this interfacial region. Such insight has traditionally been difficult to obtain from experiments, as it requires a combination of structural and chemical sensitivity with spatial depth resolution on the nanometer scale. In this contribution, we present a vibrational spectroscopic approach that can overcome these limitations. By combining phase-sensitive sum and difference frequency-generation (SFG and DFG, respectively) spectroscopy and by selectively determining different nonlinear interaction pathways, we can extract precise depth information and correlate these to specific vibrationally resonant modes of interfacial species. We detail the mathematical framework behind this approach and demonstrate the performance of this technique in two sets of experiments on selected model samples. An analysis of the results shows an almost perfect match between experiment and theory, confirming the practicability of the proposed concept under realistic experimental conditions. Furthermore, in measurements with self-assembled monolayers of different chain lengths, we analyze the spatial accuracy of the technique and find that the precision can even reach the sub-nanometer regime. We also discuss the implications and the information content of such depth-sensitive measurements and show that the concept is very general and goes beyond the analysis of the depth profiles. The presented SFG/DFG technique offers new perspectives for spectroscopic investigations of interfaces in various material systems by providing access to fundamental observables that have so far been inaccessible by experiments. Here, we set the theoretical and experimental basis for such future investigations.

中文翻译：

---

相位敏感的振动和差频率产生光谱在界面处实现纳米深度分析

界面的独特物理和化学性质由描述从最顶层原子层到块状材料性质的过渡的有限深度控制。因此，了解界面的物理性质需要详细了解形成该界面区域的不同结构、化学成分和物理过程。传统上，这种洞察力很难从实验中获得，因为它需要将结构和化学敏感性与纳米尺度的空间深度分辨率相结合。在这篇文章中，我们提出了一种可以克服这些限制的振动光谱方法。通过结合相位敏感的和频和差频生成（SFG 和 DFG，分别）光谱和通过选择性地确定不同的非线性相互作用路径，我们可以提取精确的深度信息并将这些信息与界面物质的特定振动共振模式相关联。我们详细介绍了这种方法背后的数学框架，并在选定模型样本的两组实验中展示了这种技术的性能。对结果的分析表明，实验和理论几乎完美匹配，证实了所提出的概念在现实实验条件下的实用性。此外，在不同链长的自组装单分子层的测量中，我们分析了该技术的空间精度，发现精度甚至可以达到亚纳米级。我们还讨论了这种深度敏感测量的含义和信息内容，并表明该概念非常笼统，超出了对深度剖面的分析。所提出的 SFG/DFG 技术通过提供对迄今为止实验无法访问的基本可观察物的访问，为各种材料系统中界面的光谱研究提供了新的视角。在这里，我们为未来的研究奠定了理论和实验基础。