Exploring Inverse Judd–Ofelt Formalism for Comparative Spectroscopy of RE³⁺ Ions in Glass | #Sciencefather #Researcherawards


Introduction

The inverse Judd–Ofelt (JO) formalism represents a major advancement in the analysis of rare-earth-doped materials, providing a pathway to extract meaningful spectroscopic parameters without the need for absolute absorption calibration. By anchoring only a single radiative lifetime, this approach yields the complete set of JO intensity parameters (Ω₂, Ω₄, Ω₆) and radiative transition rates directly from relative absorption spectra. Applied to rare-earth ions such as Er³⁺, Dy³⁺, and Sm³⁺ in oxyfluoride glass matrices, this model demonstrates remarkable consistency with traditional JO analysis results. The method simplifies data processing, reduces experimental complexity, and enables fast comparative studies of luminescent materials, particularly in systems where absolute absorption measurements are challenging.

Methodological Approach in Inverse Judd–Ofelt Analysis

The inverse JO technique relies on the analysis of normalized absorption band strengths obtained after baseline correction and spectral integration in the wavenumber domain. Using three well-defined 4f–4f transitions, a system of equations is solved via non-negative least squares to extract the relative ordering of Ω₂, Ω₄, and Ω₆ parameters. The method circumvents the need for precise intensity calibration and instead utilizes a single reference lifetime (τref) for absolute scaling. This mathematical foundation ensures reproducibility and objectivity in determining spectroscopic parameters across different lanthanide ions.

Application to Oxyfluoride Glass Systems

Oxyfluoride glasses serve as excellent hosts for rare-earth ions due to their mixed ionic-covalent bonding characteristics and optical transparency. In this study, the inverse JO formalism was applied to Er³⁺, Dy³⁺, and Sm³⁺ ions embedded in a compositionally identical oxyfluoride matrix. The derived JO parameters align with known optical behaviors in such systems, validating the reliability of this technique. The glass composition provides an ideal testbed to observe variations in site asymmetry and local bonding characteristics among different rare-earth ions.

Comparative Spectroscopic Behavior of RE³⁺ Ions

Distinct spectral trends were observed across the studied ions. Dy³⁺ showed the highest Ω₂ value, indicating strong hypersensitive behavior associated with asymmetric environments. Er³⁺ exhibited the largest Ω₄ and smallest Ω₆, reflecting a rigid medium-range network and low long-range polarizability. Conversely, Sm³⁺ revealed the smallest Ω₂, corresponding to a more symmetric coordination with reduced covalency. These comparative results highlight the method’s ability to capture ion-specific spectroscopic nuances even from uncalibrated data.

Uncertainty Quantification and Validation

Monte Carlo resampling of the preprocessing steps provided robust 95% confidence intervals for the extracted JO parameters, ensuring statistical reliability. The narrow error ranges confirm the stability and precision of the inverse JO formalism. The resulting trends in Ωt values and normalized transition fractions (pk) consistently reproduce established spectroscopic behavior, confirming both internal consistency and external validity when compared with literature data for oxyfluoride systems.

Significance and Future Research Perspectives

The inverse JO approach opens new pathways for rapid spectroscopic characterization of rare-earth-doped materials, particularly in high-throughput screening and comparative optical studies. Its independence from absolute absorption calibration makes it ideal for materials with weak or overlapping absorption bands. Future research could extend this model to complex glass-ceramics, nanophosphors, and mixed host systems, providing a universal analytical framework for optical materials science and photonics research.

 Global Particle Physics Excellence Awards


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