Two-photon excited fluorescence depolarisation and electronic energy migration within donor-donor pairs

A unified theoretical description is presented for one- and two-photon excited fluorescence depolarisation and electronic energy migration within pairs of chromophores. Two weakly coupled donor groups are linked via a rigid macromolecule with the ability to undergo restricted reorienting motions. Describing these reorienting motions as well as their influence on the coupling is rather complex, but can be accounted for by using the extended Forster theory. Here explicit expressions have been derived for chromophores belonging to the point groups D-2h, D-2 and C-2v when residing in uniaxial potentials (i.e. C-infinity v symmetry). From the given basic equations, it is possible however, to derive the relevant equations for molecules of arbitrary symmetry in any uniaxial orienting potential. The expected time-resolved fluorescence anisotropy for different two-photon absorption tensors are compared for reorienting fluorophores in liquids, as well as in anisotropic systems. Simulated fluorescence depolarisation data are also displayed that mimic energy migration within pairs of two-photon excited donor molecules, which simultaneously undergo reorienting motions within effectively isotropic and uniaxially anisotropic environments. The obtained results demonstrate that the time-resolved fluorescence anisotropy strongly depends on the properties of the two-photon absorption tensor, as well as on using a linear or a circular polarisation of the excitation field.