Generalisation of the rate equations for modelling of pair donor-acceptor energy transfer in rare-earth-doped media

Abstract A generalisation of rate equations simulating donor-acceptor energy transfer and describing the time evolution of donors' and acceptors' luminescence power is proposed. The rate equations were supplemented by a time-dependent probability of the direct static disordered donor-acceptor energy transfer. The equations are completely consistent with the well-known earlier results for modelling the donors’ luminescence decay. They allow one to give a clear physical interpretation of the terms in the equations describing the various stages of the D-A energy transfer. The fitting procedure, based on the obtained rate equations, was applied to luminescence decay curves, 3H4→3F4, for thulium-doped crystals Tm:KYW and Tm:KLuW. The calculated parameters allowed to model the time evolution of luminescence power at the transition 3F4→3H6 of Tm3+ ions after a short light pulse excitation of the 3H4 level, and they are in good agreement with the results obtained by analytical methods. This model can be applied to other rare-earth ions to describe direct static disordered and migration-accelerated D-A energy transfer and model luminescence power for donors and acceptors for a pulse and stationary mode of excitation.