Interference and phase mismatch effects in coherent triple sum frequency spectroscopy

Triply resonant sum frequency is a fully coherent method for multidimensional vibrational/electronic spectroscopy that creates cross-peaks between fundamental, overtone, and combination band vibrational states and electronic/vibronic states if they are coupled. It is also a methodology that cannot be phase matched. This paper explores the consequences of coherent interference and phase matching on the multidimensional spectra obtained in experiments performed in sample cells. Fringes appear in the multidimensional spectra and simulations show the character of the fringes depend on the refractive index dispersion, the thickness of different parts of the sample cell, the volume of the excitation region, and the relative third order susceptibility of the sample and the windows. It is suggested that the fringes provide a mechanism for determining the third order susceptibility and its multidimensional dispersion.