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.

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