Sum frequency generation scattering from the interface of an isotropic particle: Geometrical and chiral effects

We describe second-order vibrational sum frequency scattering from a spherical isotropic particle covered with a dielectric film. We use the concept of an effective particle susceptibility, which we decompose in trigonometric terms. With this method, we find that only 13 elements out of 27 of the effective particle susceptibility tensor are nonvanishing. We calculate the scattering pattern in three dimensions and develop a simple method to obtain the orientation of surface molecules. Also, we consider the consequences of chirality and scattering geometry on the scattering pattern and compare the results to vibrational sum frequency generation on flat interfaces.