Dipole-dipole electronic energy transfer. Fluorescence decay functions for arbitrary distributions of donors and acceptors: systems with planar geometry

We derive an expression for direct non-radiative electronic energy transfer which accommodates the possibility of a distribution of donor environments. At present we deal with situations in which the sample has a plane of symmetry for the concentration profiles. The relation enables one to evaluate donor fluorescence decay functions ID(t) from a knowledge of donor/acceptor concentration profiles, CD(z) and CA(z), along the sample axis z. It reduces to known expression in the case of DET in infinite media, and allows simplified asymptotic solutions or facile numerical analysis in systems with more complicated concentration profiles.