“…1,14,15 An appropriate way to describe the interaction between the Er 3+ ions is through the Inokuti-Hirayama theory that allows identification of the dominant interaction potential between the ions. 16 Accordingly, the temporal behavior of the PL signal can be described by I͑t͒ = I 0 exp͓−t / R − P͑t͔͒, where P͑t͒ = ␥t 3/s is a function that depends on the interaction potential between donors and acceptors and s = 6, 8, and 10 corresponds to dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interaction, respectively.…”