Nonlinear optical interactions in focused beams and nanosized structures

Thin-film materials from [Formula: see text]m thickness down to single-atomic-layered 2D materials play a central role in many novel electronic and optical applications. Coherent, nonlinear optical (NLO) [Formula: see text]-spectroscopy offers insight into the local thickness, stacking order, symmetry, or electronic and vibrational properties. Thin films and 2D materials are usually supported on multi-layered substrates leading to (multi-)reflections, interference, or phase jumps at interfaces during [Formula: see text]-spectroscopy, which all can make the interpretation of experiments particularly challenging. The disentanglement of the influence parameters can be achieved via rigorous theoretical analysis. In this work, we compare two self-developed modeling approaches, a semi-analytical and a fully vectorial model, to experiments carried out in thin-film geometry for two archetypal NLO processes, second-harmonic and third-harmonic generation. In particular, we demonstrate that thin-film interference and phase matching do heavily influence the signal strength. Furthermore, we work out key differences between three and four photon processes, such as the role of the Gouy-phase shift and the focal position. Last, we can show that a relatively simple semi-analytical model, despite its limitations, is able to accurately describe experiments at a significantly lower computational cost as compared to a full vectorial modeling. This study lays the groundwork for performing quantitative NLO [Formula: see text]-spectroscopy on thin films and 2D materials, as it identifies and quantifies the impact of the corresponding sample and setup parameters on the NLO signal, in order to distinguish them from genuine material properties.