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 chi((2)) is at the heart of the technique and a requisite step in nearly all subsequent analyses. The magnitude and phase of chi((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 chi((2)) phase are first described, followed by the utility of phase determination. Finally, some practical methods of phase extraction are discussed.