Can second order nonlinear spectroscopies selectively probe optically "dark" surface states in small semiconductor nanocrystals?

Second order nonlinear responses such as sum frequency and second harmonic generation arise from the response of a material system to the second power of an incident electromagnetic field through the material's first hyperpolarizability or second-order optical susceptibility. These quantities are nonzero only for noncentrosymmetric systems, but different length scales of the noncentrosymmetry give rise to second harmonic or sum frequency radiation with different spatial and coherence characteristics. This perspective discusses the possible contributions to the second-order signal from films of small semiconductor quantum dots and addresses whether such experiments are expected to selectively enhance transitions to surface defects or trap states in such systems. It points out how "surface" and "bulk" contributions to the sum frequency or the second harmonic signal should be distinguishable through their angular dependence in a scattering geometry. It also explores possible mechanisms whereby second order spectroscopies might provide access to surface states that are very weak or absent in other forms of optical spectroscopy.