Self-referenced approach to calculating Judd-Ofelt coefficients in analyzing optical absorption spectra of rare earth elements: A case study of LiNbO3 activated by Er3+

Judd–Ofelt (JO) analysis is widely used for extracting the electric-dipole intensity parameters Ω 2 , Ω 4 and Ω 6 , for rare-earth ions. Conventional absorption coefficient-based work depends on an accurate knowledge of the dopant concentration ( N ) and sample thickness ( d ). Prior work has suggested that magnetic-dipole (MD) transitions can be used as a host-insensitive internal standard, and such use has indeed been demonstrated recently for Eu 3+ , primarily for emission spectra. In this paper we report a self-referenced absorption method that (i) generalizes MD-normalization beyond Eu 3+ to yield absolute Ω 2 , Ω 4 , Ω 6 (not just ratios), and (ii) exploits the fitted absolute oscillator strength ( f calc ) of the MD-rich reference line to extract N from the same dataset. The approach herein references integrated areas of selected electric dipole (ED) bands to a ground-state MD-dominated transition so that N and d cancel during fitting, and then restores the absolute scale via f calc . The proposed method is demonstrated for LiNbO 3 :Er 3+ using the 4 I 15/2 → 4 I 13/2 band as reference. The deduced Ω parameters reproduce measured radiative properties, notably the 4 I 13/2 → 4 I 15/2 lifetime, and, importantly, the deduced N agrees with the experimental composition of the sample. We believe that this absorption-based approach that does not need the ion concentration enables reliable and absolute JO characterization and a simultaneous concentration determination from a single optical transmission experiment on rare-earth doped bulk crystals. The extracted JO value are Ω 2 = 8.46×10 -20 cm 2 , Ω 4 = 1.26×10 -20 cm 2 , Ω 6 = 1.16×10 -20 cm 2 and the 4 I 13/2 → 4 I 15/2 lifetime is 2.36 ms. • A self-referencing methodology is developed that allows Judd-Ofelt parameters to be extracted from absorption spectra, without the knowledge of the rare-earth ion concentration N • Relative oscillator strengths are obtained by normalizing the transition oscillator strength to the that of a reference with a substantial magnetic dipole component with significant intensity ( 4 I 15/2 → 4 I 13/2 ) • Methodology is confirmed by analyzing the absorption spectrum of Er 3+ ions in a single crystal of LiNbO 3 and extracting the Judd-Ofelt parameters Ω 2 , Ω 4 , Ω 6 , the 4 I 13/2 → 4 I 15/2 lifetime τ and the Er 3+ -ion concentration, N. • Extracted τ and N is in excellent agreement with the reported measured value and there is a near perfect agreement of N from the analysis with the value of the Er 3+ -concentration determined independently. • Methodology automatically excludes all RE ions that are not optically active