Exact solution to the general non-radiative energy transfer master equations in crystalline materials

The microscopic general non-radiative energy transfer master equations are solved for the case of co-doped crystalline materials. With the calculated exact solution, the macroscopic dopant emissions are obtained. In particular, it is shown that our solution unifies the predictions for the donor emission reported by other models for the cases of direct energy transfer and migration among donors. In particular, we refer to the Forster–Dexter, D.L. Huber, Yokota–Tanimoto, and A.I. Burshtein models. Further, our modeling includes the back-transfer and migration among acceptor processes.