Obtaining extended insight into molecular systems by probing multiple pathways in second-order nonlinear spectroscopy

Second-order nonlinear spectroscopy is becoming an increasingly important technique in the study of interfacial systems owing to its marked ability to study molecular structures and interactions. The properties of such a system under investigation are contained within their intrinsic second-order susceptibilities which are mapped onto the measured nonlinear signals (e.g. sum-frequency generation) through the applied experimental settings. Despite this yielding a plethora of information, many crucial aspects of molecular systems typically remain elusive, for example the depth distributions, molecular orientation and local dielectric properties of its constituent chromophores. Here, it is shown that this information is contained within the phase of the measured signal and, critically, can be extracted through measurement of multiple nonlinear pathways (both the sum-frequency and difference-frequency output signals). Furthermore, it is shown that this novel information can directly be correlated to the characteristic vibrational spectra, enabling a new type of advanced sample characterization and a profound analysis of interfacial molecular structures. The theory underlying the different contributions to the measured phase of distinct nonlinear pathways is derived, after which the presented phase disentanglement methodology is experimentally demonstrated for model systems of self-assembled monolayers on several metallic substrates. The obtained phases of the local fields are compared to the corresponding phases of the nonlinear Fresnel factors calculated through the commonly used theoretical model, the three-layer model. It is found that, despite its rather crude assumptions, the model yields remarkable similarity to the experimentally obtained values, thus providing validation of the model for many sample classes.