Dependence of Judd-Ofelt parameters on integrated absorption coefficient or cross-section of an individual transition of Er3+

Abstract

Dependences of two factors on Judd-Ofelt (JO) intensity parameters Ω t (t = 2,4,6) have been studied theoretically by exemplifying the widely studied Er 3+ ion, which is doped into Gd 3 Ga 5 O 12 , LiNbO 3 and SrGdGa 3 O 7 bulk single-crystals and β-NaYF 4 powder. The two factors include 1) selection of induced electric-dipole transitions for JO calculation and 2) integrated absorption coefficient (IAC) or integrated absorption cross-section (IACS) of individual electric-dipole transition of Er 3+ . Absolute and relative root-mean-square methods were considered in the JO fits and consistent results were obtained. Ω t depends mainly on strong and medium-intensity transitions. These transitions must be all included in the fit. The exclusion of an individual transition from the fit leads to deviation of Ω t . From the matrix elements [ U (t) ] 2 values, it is possible to rate how the inclusion or not of a transition affects the Ω t . The study also shows that the Ω t changes almost linearly with the IAC or IACS of an individual transition, and the relevant linear slope may have a positive or negative sign, depending on the [ U (t) ] 2 value. Moreover, the larger the [ U (t) ] 2 value is, the larger the corresponding Ω t value is. In addition, the Ω 2 , Ω 4 and Ω 6 are dependent of each other because it is the summation ∑ t Ω t [ U ( t ) ] 2 instead of its component term Ω t [ U ( t ) ] 2 that has a linear relationship to the IAC or IACS.