Mechanisms for forbidden hyper-Rayleigh scattering

Hyper-Rayleigh scattering (HRS) is an incoherent variant of second harmonic generation. The theory involves terms of increasing order of optical nonlinearity: for molecules or unit cells that are centrosymmetric, and which accordingly lack even-order susceptibilities, HRS is often regarded as formally forbidden. However, for the three-photon interaction, theory based on the standard electric dipole approximation, represented as E13, does not include the detail required to describe what is observed experimentally, in the absence of a static field. New results emerge upon extending the theory to include
E12E2 and E12M1, incorporating one electric quadrupolar or magnetic dipolar interaction respectively. Both additional interactions require the deployment of higher orders in the multipole expansion to govern these processes, with the E12E2 interaction analogous in rank and parity to a four-wave susceptibility. A key feature of the present work is its foundation upon a formal tensor derivation which does not oversimplify the molecular components, yet leads to results whose interpretation can be correlated with experimental observations. Results are summarized for the perpendicular detection of both parallel and perpendicular polarizations. Using such methods to investigate molecular systems that might have useful nonlinear characteristics, HRS therefore provides a route to data with direct physical interpretation, to enable more
sophisticated design of molecules with sought optical properties.