Methyl groups at dielectric and metal surfaces studied by sum-frequency generation in co- and counter-propagating configurations

The optimum experimental geometry for visible-infrared sum-frequency generation experiments depends rather sensitively on the molecules adsorbed at the surface, their orientation, and the nature of the adjacent bulk media. We consider the commonly encountered case of methyl groups situated at air-water, air-gold, and polymer-water interfaces. We provide expressions that may be used to determine the optimal visible and IR beam incident angles, considering the symmetric and antisymmetric modes separately and then together. The analysis is carried out for co-propagating (collinear and non-collinear geometries) and counter-propagating configurations. We first consider that one or more vibrational modes are of interest, and the goal is to study them quantitatively under a single polarization scheme; our results enable the user to set the beam angles for such an experiment. In the second case, molecular orientation information is desired, and so the calibrated response is required in all accessible polarization schemes for full characterization of the nonlinear susceptibility tensor.