Retrieval of complex χ((2)) parts for quantitative analysis of sum-frequency generation intensity spectra

Vibrational sum-frequency generation (SFG) spectroscopy has become an established technique for in situ surface analysis. While spectral recording procedures and hardware have been optimized, unique data analysis routines have yet to be established. The SFG intensity is related to probing geometries and properties of the system under investigation such as the absolute square of the second-order susceptibility χ((2)) (2). A conventional SFG intensity measurement does not grant access to the complex parts of χ((2)) unless further assumptions have been made. It is therefore difficult, sometimes impossible, to establish a unique fitting solution for SFG intensity spectra. Recently, interferometric phase-sensitive SFG or heterodyne detection methods have been introduced to measure real and imaginary parts of χ((2)) experimentally. Here, we demonstrate that iterative phase-matching between complex spectra retrieved from maximum entropy method analysis and fitting of intensity SFG spectra (iMEMfit) leads to a unique solution for the complex parts of χ((2)) and enables quantitative analysis of SFG intensity spectra. A comparison between complex parts retrieved by iMEMfit applied to intensity spectra and phase sensitive experimental data shows excellent agreement between the two methods.