Interference, VSFS vibrational modes

FIGURE 2.2. Energy diagram showing interference between vibrational modes. Interference arises because VSFS is a coherent process. The multiple paths are analogous to those in the double slit experiment. 

The interference between different vibrations (including those of different molecules) resulting from the coherent nature of the experiment makes the analysis of VSFS spectra considerably more complicated than that of spectra recorded with linear spectroscopic techniques. However, this complexity can be exploited to provide orientational information if a complete analysis of the VSF spectrum is employed taking into account the phase relationships of the contributing vibrational modes to the sum-frequency response [15,16]. In the analysis it is possible to constrain the average orientation of the molecules at the surface by relating the macroscopic second-order susceptibility, Xs g of the system to the molecular hyperpolaiizabilities, of the individual... 

Since VSFS is a coherent technique, and as Equation (25) implies, the oscillating electric field from each vibrational state involved in the generation of sum-frequency light can interfere with that from every other state and with that from the non-resonant response. This is quite different from IR spectroscopy where spectra are simple superpositions of intensity from individual vibrational modes. As such, VSFS leads to interesting line shapes that can be interpreted incorrectly if spectral intensities are compared visually without fitting the spectrum. 

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