Theory of second harmonic generation in randomly oriented species

It is well known that second harmonic generation (SHG) is a process forbidden within atomic and molecular fluids. Nonetheless recent experimental observations of second harmonic evolution in suspensions of randomly oriented Halobacterium halobium purple membranes have raised new questions about the precise criteria which determine prohibition of the second harmonic. To address the problem a theoretical framework for SHG is developed that specifically deals with molecular systems, and is therefore cast in terms of molecular properties with more regard to the influence of the local structure. This contrasts with the classical approach based on bulk susceptibilities, which has not proved adequate to explain the conflicting experimental results. By properly formulating the detailed procedure for dealing with the necessary orientational averages, the present theory discloses a relationship between the coherent process of second harmonic generation and a directed component of its incoherent counterpart, hyper-Rayleigh scattering. Inter alia, the theory explains the SHG detected in purple membrane suspensions. The polarisation features of the harmonic evolution are also considered more generally, and in particular it is shown that the SHG signal will persist under conditions of circularly polarised pumping. This specific polarisation feature will allow experimental validation of the theory.