Phase measurement in nondegenerate three-wave mixing spectroscopy

Phase of the second-order susceptibility in vibrational sum frequency generation spectroscopy: Origins, utility, and measurement techniques

Vibrational sum frequency generation can provide valuable structural information at surfaces and buried interfaces. Relating the measured spectra to the complex-valued second-order susceptibility χ(2) is at the heart of the technique and a requisite step in nearly all subsequent analyses. The magnitude and phase of χ(2) as a function of frequency reveal important information about molecules and materials in regions where centrosymmetry is broken. In this tutorial-style perspective, the origins of the χ(2) phase are first described, followed by the utility of phase determination. Finally, some practical methods of phase extraction are discussed.

Wedge-Based Design for Phase Stable and Phase Accurate Heterodyne-Detected Sum-Frequency Generation Spectroscopy

Phase sensitive and heterodyne-detected (HD) sum-frequency generation (SFG) spectroscopy offers the ability to separate the nonlinear susceptibility into its real and imaginary components. This provides information about the absolute orientation of molecules at interfaces while also producing an absorptive spectrum that is linear in spectral composition and can easily be decomposed into different spectral components. However, simultaneously obtaining phase accuracy and phase stability remains a challenge in SFG. Here we present a new experimental design for HD-SFG spectroscopy that incorporates a wedge pair to accurately control the timing between the local oscillator and the sample signal. This experimental approach provides high phase accuracy and long-time phase stability in a compact and flexible configuration.

Assessing the Molecular Specificity and Orientation Sensitivity of Infrared, Raman, and Vibrational Sum-Frequency Spectra

Linear programming was used to assess the ability of polarized infrared absorption, Raman scattering, and visible–infrared sum-frequency generation to correctly identify the composition of a mixture of molecules adsorbed onto a surface in four scenarios. The first two scenarios consisted of a distribution of species where the polarity of the orientation distribution is known, both with and without consideration of an arbitrary scaling factor between candidate spectra and the observed spectra of the mixture. The final two scenarios have repeated the tests, but assuming that the polarity of the orientation is unknown, so the symmetry-breaking attributes of the second-order nonlinear technique are required. The results indicate that polarized Raman spectra are more sensitive to orientation and molecular identity than the other techniques. However, further analysis reveals that this sensitivity is not due to the high-order angle dependence of Raman, but is instead attributed to the number of unique projections that can be measured in a polarized Raman experiment.

Structure of water and polymer at the buried polymer/water interface unveiled using heterodyne-detected vibrational sum frequency generation

Heterodyne-detected vibrational sum frequency generation reveals the molecular-level structure of the polymer/water interface that is different from what has been argued.

Validation of Spectra and Phase in Sub-1 cm(-1) Resolution Sum-Frequency Generation Vibrational Spectroscopy through Internal Heterodyne Phase-Resolved Measurement

Reliable determination of the spectral features and their phases in sum-frequency generation vibrational spectroscopy (SFG-VS) for surfaces with closely overlapping peaks has been a standing issue. Here we present two approaches toward resolving such issue. The first utilizes the high-resolution and accurate line shape from the recently developed subwavenumber high-resolution broadband SFG-VS (HR-BB-SFG-VS), from which the detail spectral parameters, including relative spectral phases, of overlapping peaks can be determined through reliable spectral fitting. These results are further validated by using the second method that utilizes the azimuthal angle phase dependence of the z-cut α-quartz crystal, a common phase standard, through the spectral interference between the SFG fields of the quartz surface, as the internal phase reference, and the adsorbed molecular layer. Even though this approach is limited to molecular layers that can be transferred or deposited onto the quartz surface, it is simple and straightforward, as it requires only an internal phase standard with a single measurement that is free of phase drifts. More importantly, it provides unambiguous SFG spectral phase information on such surfaces. Using this method, the absolute phase of the molecular susceptibility tensors of the CH3, CH2, and chiral C-H groups in different Langmuir-Blodgett (LB) molecular monolayers and drop-cast peptide films are determined. These two approaches are fully consistent with and complement to each other, making both easily applicable tools in SFG-VS studies. More importantly, because the HR-BB-SFG-VS technique can be easily applied to various surfaces and interfaces, such validation of the spectral and phase information from HR-BB-SFG-VS measurement demonstrates it as one of the most promising tools for interrogating the detailed structure and interactions of complex molecular interfaces.