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

Dependences of two factors on Judd-Ofelt (JO) intensity parameters Omega(t) (t = 2,4,6) have been studied theoretically by exemplifying the widely studied Er3+ ion, which is doped into Gd3Ga5O12, LiNbO3 and SrGdGa3O7 bulk single-crystals and beta-NaYF4 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 Er3+. Absolute and relative root-mean-square methods were considered in the JO fits and consistent results were obtained. Omega(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 Omega(t). From the matrix elements [U-(t)](2) values, it is possible to rate how the inclusion or not of a transition affects the Omega(t). The study also shows that the Omega(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 Omega(t) value is. In addition, the Omega(2), Omega(4) and Omega(6) are dependent of each other because it is the summation n-ary sumation Omega(t)[U-(t)](2) instead of its component term t Omega(t)[U-(t)](2) that has a linear relationship to the IAC or IACS.

Automated summary

The study shows that Omega(t) mainly depends on strong and medium-intensity transitions, which must all be included in the fit to obtain accurate results. Additionally, Omega(t) changes almost linearly with the IAC or IACS of an individual transition, with the linear slope depending on the size of the [U-(t)](2) value. Furthermore, Omega(2), Omega(4) and Omega(6) are interdependent due to their relationship with the n-ary summation Omega(t)[U-(t)](2).