One-phonon assisted energy transfer in periodic arrays of optically active ions

Energy transfer in periodic arrays of optically active ions is investigated. It is assumed that the transfer of excitation between ions takes place incoherently via a one-phonon process where the wavelength of the phonon is large in comparison with the inter-ion spacing. It is pointed out that the energy transfer can only occur where there is a mismatch in energy between the excited states of the two ions. The energy diffusion constant is calculated in an effective medium approximation assuming a Gaussian lineshape with no correlation between the excited state energies of neighboring ions. The temperature dependence of the diffusion constant is established for cubic lattices with nearest-neighbor transfer. Energy transfer in one-dimensional arrays with nearest-neighbor transfer is studied using an extension of the coherent exchange approximation developed for random ferromagnets. The coherent exchange approximation reproduces the asymptotic non-diffusive behavior found in numerical studies of fluorescence line narrowing in one-dimensional systems.