Doubly resonant SFG and DFG spectroscopies: An analytic model for data analysis including distorted and rotated...

The influence of vibration mode distortion and mode mixing in the vibronic structure of molecules on the doubly resonant sum (SFG) and difference frequency generation spectroscopies is systematically studied in several examples. These phenomena modify the spectral overlap function at the heart of the modeling of the doubly resonant processes. When the visible beam is tuned, under the Franck-Condon approximation, each vibration mode generates two main peaks corresponding to the resonance of the molecular electronic transition with the visible and SFG energies, together with higher order ones driven by the amplitudes of the vibronic displacements. For a single mode system, mode distortion modifies the positions of the main peaks and the excitations of the higher order ones. For a two-mode system, mode mixing induces in addition a deep change in the balance between the intensities of the mixed modes. It also changes the phases of the vibrations, which makes curve fitting difficult. For multimode systems, mode mixing may greatly enhance intensity of a poorly active mode. For all these reasons, it seems mandatory to take mode distortion and mode mixing into account for an accurate analysis of second-order nonlinear spectroscopic experimental data.