Quantum limits of the hyper-Rayleigh scattering susceptibility

Sum rules have been used to show that there is an upper limit to molecular susceptibilities. Such calculations have been applied to the diagonal part of the second-order susceptibility tensor as measured with electric-field-induced second-harmonic generation, and to a variety of third-order measurements. The results show that the off-resonant susceptibilities of all molecules measured fall within the calculated limits. In this contribution, we show that the most susceptibilities measured with hyper Rayleigh scattering (HRS) fall below the two-dimensional theoretical limit, and discuss the issue of why some molecules appear to break this limit.