Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces

Vibrational sum frequency generation (VSFG) spectroscopy is a powerful tool for selective probing of interfaces based on second-order nonlinear optics. The line shapes of observed VSFG spectra are governed by second-order nonlinear susceptibility as well as Fresnel factors for constituent light fields. Hence, determination of the second-order nonlinear susceptibility requires exact knowledge about the Fresnel factors for the light fields. However, the latter has been less examined than the former for interpretation of VSFG spectra to date and is sometimes hard to calculate due to a lack of optical constants, especially in the infrared regions. The present work employs ATR-IR measurements and model fitting to determine the complex refractive indices of organic solvents and clarifies the effect of the Fresnel factor on the line shape analysis of VSFG spectra. As an example, we determine the complex refractive indices of organic carbonates, which are typical solvents for lithium-ion battery, in the C=O and C-H stretch vibration regions, and then examined the effect of frequency-dependent Fresnel factor on the VSFG spectra of electrode/carbonate as well as air/carbonate interfaces by model calculations. The Fresnel factor in the C=O stretch region has considerable dispersion due to the large extinction coefficient, which strongly influences the line shape of VSFG spectra at LiCoO2/carbonate interfaces, especially for the SPS polarization combination. On the contrary, the frequency-dependent Fresnel factor in the C-H stretch region has little effect on the line shape of the band. The present systematic study of Fresnel factor revealed that the effect of Fresnel factor on the VSFG line shape becomes significant when (i) the frequency dependence of complex refractive index is large in the range of the band and (ii) nonresonant amplitude of nonlinear susceptibility is considerable relative to the resonant amplitude.