Origin of the deviation between the fluorescence intensity ratio of a thermally coupled level and the Boltzmann distribution law

The temperature dependence of the fluorescence intensities of the thermally coupled pairs of some typical rare-earth ions was studied. The fluorescence intensity ratios (FIRs) of the thermally coupled pairs increased exponentially with increasing temperature. However, except for Er³⁺ and Nd³⁺, the FIRs of other rare-earth ions exhibited significant deviation from the Boltzmann distribution law. We suppose the deviation originates from the non-thermal population in the upper level of the coupled pairs. The temperature dependence of the deviation is discussed. Eliminating the deviation is beneficial for the development of FIR thermometry; only by clearly understanding the deviation can we eliminate it.