Inverse Judd–Ofelt Formalism Based on Radiative Lifetime for Comparative Spectroscopy of RE3+ Ions in Glass

This work shows that inverse Judd–Ofelt (JO) analysis of relative absorption spectra, anchored by a single lifetime, provides JO parameters and radiative rates without absolute calibration. The method is applied to Er3+, Dy3+, and Sm3+ in a compositionally identical oxyfluoride glass. Three well-resolved ground-state 4f–4f absorption bands were selected. After baseline removal and wavenumber-domain integration, their normalized strengths Srel,k (k = 1, 2, 3; k∈S) define a 3 × 3 system solved by non-negative least squares to obtain the anchor-independent ordering (Ω2:Ω4:Ω6). Absolute scaling uses a single lifetime anchor. We report lifetime-scaled Ωt and Arad, and the normalized fractions pk within the selected triplets; as imposed by the method, the anchor-independent ordering (Ω2:Ω4:Ω6) is analyzed, while absolute Arad and Ωt scale with τref. The extracted parameters fall within the expected ranges for oxyfluoride hosts and reveal clear ion-specific trends: Ω2 follows Dy3+ > Er3+ > Sm3+ (site asymmetry/hypersensitive response), while the ordering Ω4 > Ω6 holds across all ions (oxide-rich networks). Er3+ exhibits the largest Ω4 and the smallest Ω6, indicative of pronounced medium-range “rigidity” with suppressed long-range polarizability; Sm3+ shows the lowest Ω2 (more symmetric/less covalent coordination); and Dy3+ the highest Ω2 (strong hypersensitive behavior). Uncertainty was quantified by Monte Carlo resampling of the preprocessing steps, yielding compact 95% confidence intervals; the resulting JO-parameter trends (Ω2, Ω4, Ω6) and normalized fk fractions reproduce the characteristic spectroscopic behavior known for each ion. This method enables quantitative JO outputs from uncalibrated spectra, allowing direct spectroscopic comparisons and quick screening when only relative absorption data are available.