Polarisation analysis of bimolecular excitations mediated by energy transfer: A common theoretical framework for fluorescence migration and sequential Raman scattering

Abstract

When polarised light interacts sequentially with two independently mobile molecules or chromophores, radiation of a longer wavelength and a changed polarisation state is commonly detected. One well-known example is the case where energy migrates from a molecule initially excited by input radiation to another which fluoresces. Another such process is sequential Raman scattering by two separate molecules. In this paper a theoretical framework is developed that formally establishes the link between these two processes. The theory encompasses the most general case; the intermolecular energy transfer can be either radiative or non-radiative, and the transition dipole moments, for the upward and downward processes within each chromophore, can be either parallel or non-parallel. For the Raman processes, resonance features are also accommodated. Results for the fluorescence anisotropy and Raman depolarisation ratio are explicitly presented as well as more general rate equations applicable to arbitrary polarisation conditions.

Two-photon fluorescence: Resonance energy transfer

“…7,8 Firstly the same factor of 7 appears as the difference between the radiative and Förster-type energy transfer results; secondly a similar relationship is observed with the corresponding single center results, enabling the anisotropy of two-photon energy transfer to be expressed in terms of its single centre result…”

“…7,8 In general, the limiting FRET residual anisotropy ratios for n-photon excitation processes can be calculated from the corresponding single-center n-photon fluorescence anisotropy r 0 , using Eq. ͑28͒ and r 0 (n)ϭ(n/2nϩ3)(3 cos 2 Ϫ1), always subject to stringent conditions on the relative directions of the transition dipoles involved.…”

“…8,36 This involves the expansion of Eq. ͑16͒ and contraction of indices as determined by the Kronecker deltas.…”

“…The detailed results for the residual anisotropy, first derived by Galanin, 2 have now been extended to fluorescence resonance energy transfer ͑FRET͒ beyond the Förster limit, including long-range ͑wave-zone͒ transfer. 7,8 Here we consider the two-photon analogue of this now rather well understood process. Interest in such a process stems from a number of considerations, not least the fact that the states excited by twophoton absorption, often high in energy, will generally display an even greater tendency to shed their energy to suitable acceptors before luminescent emission occurs.…”

On the interactions between molecules in an off-resonant laser beam: Evaluating the response to energy migration and optically induced pair forces

“…28,29 Another case is the formal link between fluorescence resonance energy transfer ͑FRET͒ and sequential Raman scattering. 30 While some of the above examples are of primarily theoretical interest, the broader purpose of the present analysis is to address a system in which various physical effects are not only mathematically but also physically interlinked. Calculations accommodating both mechanical forces and electronic processes, accurate to fourth order in perturbation theory, have not to our knowledge been attempted before.…”