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Time-resolved and two-dimensional sum frequency generation (TR-SFG and 2D-SFG) spectroscopies are promising tools in the experimental study of molecular dynamics, specifically at interfaces. Most implementations of TR/2D-SFG spectroscopy rely on a pump-probe scheme, where an excitation pulse excites a fraction of interfacial molecules into the first excited state of a specific vibrational mode, and a subsequent SFG probe pair detects the time-dependent changes of the surface vibrational response. In steady state SFG spectroscopy, phase-resolved detection (also known as heterodyne-detection), as opposed to SFG intensity measurements, has been shown to be useful in unraveling the steady-state response of interfacial vibrations. Here, we explore the merits of phase-resolved TR/2D-SFG spectroscopy. This purely theoretical and numerical study reveals that, for a typical response from aqueous interfaces, the intensity 2D-SFG measurements contain the same information content as phase-resolved 2D-SFG measurements. We specifically analyze the frequency-dependence of the bleach lifetime (reflecting vibrational relaxation), and the time-dependent slope of the on-diagonal features observed in a 2D spectra. We show that for different systems, the intensity-based and phase-resolved 2D-SFG measurements provide the same information and are quantitatively very similar. We investigate the effect of different lineshapes, anharmonicity, and nonresonant signal contributions, and show that none of these effects substantially change the conclusion that intensity-based and phase-resolved 2D-SFG measurements provide equivalent information.

Time-Resolved Sum Frequency Generation Spectroscopy: A Quantitative Comparison Between Intensity and Phase-Resolved Spectroscopy