A route for determining absorption and emission cross-sections of rare-earth luminescence centers based on McCumber theory and Einstein coefficients

McCumber theory describes the relationship between the absorption and emission cross-sections of ionic luminescence centers and is frequently used for determining absorption and emission cross-sections. However, the present application method of this theory seems complicated and exposes some faultiness. In this work, we proposed a simple and reliable procedure for determining the absorption and emission cross-sections based on McCumber theory with the assistance of Einstein's A/B coefficient relationship. The route we proposed was applied to confirm the absorption cross-sections of the transitions from ⁴I_15/2 to ²H_11/2⁴S_3/2⁴F_9/2⁴I_11/2, and ⁴I_13/2 of Er³⁺ in the NaY(WO₄)₂ compound. The absorption cross-sections determined from our proposed route were compared with those derived from a traditional approach, and it was found that the results derived from our route are reliable. Moreover, the corresponding parameters in the McCumber theoretical expression are referenced for other Er³⁺-doped luminescent materials.