Complex phase of the nonresonant background in sum frequency generation spectroscopy

Abstract

Sum frequency generation (SFG) spectroscopy is an interface-selective spectroscopic technique that enables us to selectively observe the vibrational or electronic resonances of molecules within a very thin interface layer. The interfacial properties probed by SFG are contained in a complex quantity called the second-order nonlinear susceptibility (χ2). It is usually believed that the imaginary part of χ2 (Im χ2) exhibits the resonant responses of the system, whereas the nonresonant responses appear solely in the real part of χ2 (Re χ2). However, it was recently theoretically pointed out that a portion of the nonresonant responses actually contributes to the observed Im χ2 spectra when the finite thickness of the interface layer is taken into account. In this study, by considering a simple air/liquid interface without any solutes as a model system, we theoretically evaluate the nonresonant contribution to experimentally accessible Im χ2 as well as to Re χ2, from which the complex phase of the nonresonant background is estimated. It is shown that the deviation of the complex phase from 0° or 180° is less than 1° even if the thickness of the interface layer is taken into account. This means that the nonresonant contribution to Im χ2 is practically negligible, and it is a very good approximation to think that the nonresonant background appears solely in Re χ2 in the case of air/liquid interfaces. This result implies that Im χ2 practically contains only the resonant responses of the system, and molecular resonances at the interface can be conveniently studied using Im χ2 spectra at such interfaces.