Theory of second harmonic generation in randomly oriented species

Abstract

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 circulady polarised pumping. This specific polarisation feature will allow experimental validation of the theory.

Local coherence and the temporal development of second harmonic emission

“…The paradox was resolved when it was shown that the unusually strong signal detected from isotropic suspensions, notably of purple membrane material, is attributable to optical coherence within the separate particles of the suspension [14]. As such, the harmonic emission displays an amalgam of the characteristics associated with full coherence (second harmonic generation) and incoherence (hyper-Rayleigh scattering).…”

“…a significant intrinsic rigidity. Following the work of Andrews et al [14,15] the intensity of harmonic generation in the absence of prior optical excitation is given by the following expression:…”

Second harmonic generation in partially ordered media and at interfaces: analysis of dynamical and orientational factors

“…In situations where such isotropy can be removed or is naturally lacking, SHG is allowed and can hence provide a very sensitive tool for detecting preferential molecular orientation. For example SHG has been used to gauge molecular orientation: at fluid interfaces [2,3]; within cell membranes [4,5]; of dipolar chromophores in poled polymers [6,7] and of molecules within molecular sieves [8]. In circumstances where preferential orientation arises, theory requires the application of suitably weighted three-dimensional rotational ensemble averages in order to arrive at the nett media response.…”

Dephasing-Induced Vibronic Resonances in Difference Frequency Generation Spectroscopy

“…shows that the excited-state contribution bd (2) does not contain a vibrational resonance. This implies that as the visible pulse frequency ω 1 -ω eg is detuned away from the electronic resonance the signal must vanish along ω 1 -ω 2 )1070 cm -1 (Figure 3, parts A and C).The ground-state resonances do not show this cancellation (Figure 3, parts A and B).…”