Depolarization and reversal ratios from diagonally dominated (hyper)polarizabilities

This work provides the mathematical proofs of two simple rules that concern the exact theoretical values of the depolarization (DR) and reversal (RR) ratios for any incoherent elastic scattering process at any harmonic performed on isotropic samples. In particular, within the electric-dipole approximation, when the corresponding (hyper)polarizability tensor of rank n is dominated by a single diagonal component, then DR = 2n - 1 and RR = 1. These relations are valid for any scattering angle between the input and scattered beams. Taken together, these relations can be of great importance in the experimental characterization of the molecular response at any (n - 1)th harmonic.