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

Abstract

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.

Role of Ions on the Surface-Bound Water Structure at the Silica/Water Interface: Identifying the Spectral Signature of Stability

“…the complex total (2) spectrum rather than the | total (2) | 2 intensity spectrum) is required. To this end, SFG spectral analysis was performed with the maximum entropy method (MEM) [60][61][62][63][64][65][66][67][68][69] to predict the relative phase of the SF response at all frequencies by maximizing the spectral entropy and forbidding the growth of resonances over time. 70 However, because the MEM models an autoregressive process, there is an associated error spectrum of unknown phase.…”

Vibrational Stark shift spectroscopy of catalysts under the influence of electric fields at electrode–solution interfaces

“… 58 However, despite these obvious advantages, there is currently no in situ electrochemical HD-VSFG result reported in the literature to the best of our knowledge. Recent efforts by Hofmann and Koelsch 59 introduced a new fitting scheme (iMEMfit) based on iterative phase-matching between complex spectra retrieved from maximum entropy method (MEM) analysis 60,61 and fitting of SFG intensity spectrum. This leads to a unique solution of the complex part of χ (2) that shows excellent agreement with that of experimental PS-VSFG spectrum, 57,62 enabling quantitative spectral analysis.…”

The Role of Ions on the Surface-Bound Water Structure at the Silica/Water Interface: Identifying the Spectral Signature of Stability

“…the complex total (2) spectrum rather than the | total (2) | 2 intensity spectrum) is required. To this end, SFG spectral analysis was performed with the maximum entropy method (MEM) [60][61][62][63][64][65][66][67][68][69] to predict the relative phase of the SF response at all frequencies by maximizing the spectral entropy and forbidding the growth of resonances over time. 70 However, because the MEM models an autoregressive process, there is an associated error spectrum of unknown phase.…”