Abstract

By separating the thermal and nonradiative relaxation population, the fluorescence intensity ratio (FIR) of a pair of thermally coupled energy levels of rare-earth ion is reformulated. For a pair of thermally coupled levels, if the ratio of the thermal population in the upper level to the total population of the lower level abides by the Boltzmann distribution law, the general FIR would be modulated by the proportion of the total population to the thermal population in the upper level. By defining the reciprocal of the proportion as the thermal population degree ($\eta$), the product $\eta \mathrm{FIR}$ will follow the pure Boltzmann distribution law. Considering the fluorescent transient process, the $\eta$ values may be obtained from the weights of the fluorescent dynamic components of the upper level. A method to calculate this $\eta$ factor is presented.

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