Determination of Hyperpolarizability Tensor Ratios in the Absence of Kleinman Symmetry by Depolarized Hyper-Rayleigh Scattering

A complete theoretical description of depolarized hyper-Rayleigh scattering under an electric field is obtained, providing a way to determine the quadratic hyperpolarizability tensor ratio in the absence of Kleinman symmetry. From a simulation for a cylindrically shaped molecule possessing C_∞v symmetry, it is shown that the depolarization ratio depends strongly on the quadratic hyperpolarizability tensor ratios in the hyper-Rayleigh scattering measurement. It is suggested that the quadratic hyperpolarizability tensor ratios can be uniquely determined by the depolarization measurement in the presence of an external electric field.