Sum frequency dual null angle approach and its use in surface hyperpolarizability ratio measurements

Null angle measurements are a recognized method for accurately determining the ratio of optical constants in linear and nonlinear optical spectroscopy. Here, we extend the established null angle scheme in vibrational sum-frequency generation where the sum-frequency beam is linearly polarized at ±45° to include a second scheme where the IR beam is polarized at ±45°. We illustrate that measurement of the null angles obtained in both schemes may be used together to calibrate the SFG response between three polarization combinations. We then demonstrate that these two null angles provide the required phase information to determine the surface hyperpolarizability ratio, even at buried interfaces where calibration is typically more difficult, and without requiring a heterodyne scheme. This makes extracting the electronic structure information directly from the SFG spectra more accurate and truly independent of the molecular orientation distribution.