{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:36:23Z","timestamp":1768012583147,"version":"3.49.0"},"reference-count":52,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:00:00Z","timestamp":1760313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Photonics"],"abstract":"<jats:p>This work shows that inverse Judd\u2013Ofelt (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\u20134f absorption bands were selected. After baseline removal and wavenumber-domain integration, their normalized strengths Srel,k (k = 1, 2, 3; k\u2208S) define a 3 \u00d7 3 system solved by non-negative least squares to obtain the anchor-independent ordering (\u03a92:\u03a94:\u03a96). Absolute scaling uses a single lifetime anchor. We report lifetime-scaled \u03a9t and Arad, and the normalized fractions pk within the selected triplets; as imposed by the method, the anchor-independent ordering (\u03a92:\u03a94:\u03a96) is analyzed, while absolute Arad and \u03a9t scale with \u03c4ref. The extracted parameters fall within the expected ranges for oxyfluoride hosts and reveal clear ion-specific trends: \u03a92 follows Dy3+ &gt; Er3+ &gt; Sm3+ (site asymmetry\/hypersensitive response), while the ordering \u03a94 &gt; \u03a96 holds across all ions (oxide-rich networks). Er3+ exhibits the largest \u03a94 and the smallest \u03a96, indicative of pronounced medium-range \u201crigidity\u201d with suppressed long-range polarizability; Sm3+ shows the lowest \u03a92 (more symmetric\/less covalent coordination); and Dy3+ the highest \u03a92 (strong hypersensitive behavior). Uncertainty was quantified by Monte Carlo resampling of the preprocessing steps, yielding compact 95% confidence intervals; the resulting JO-parameter trends (\u03a92, \u03a94, \u03a96) 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.<\/jats:p>","DOI":"10.3390\/photonics12101011","type":"journal-article","created":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T05:48:21Z","timestamp":1760420901000},"page":"1011","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Inverse Judd\u2013Ofelt Formalism Based on Radiative Lifetime for Comparative Spectroscopy of RE3+ Ions in Glass"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5935-870X","authenticated-orcid":false,"given":"Helena Cristina","family":"Vasconcelos","sequence":"first","affiliation":[{"name":"Faculty of Science and Technology, University of the Azores, S. Miguel, Azores, 9500-321 Ponta Delgada, Portugal"},{"name":"Laboratory of Instrumentation, Biomedical Engineering and Radiation Physics (LIBPhys, UNL), Department of Physics, NOVA School of Science and Technology, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9356-3045","authenticated-orcid":false,"given":"Maria Gabriela","family":"Meirelles","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, University of the Azores, S. Miguel, Azores, 9500-321 Ponta Delgada, Portugal"},{"name":"Research Institute of Marine Sciences of the University of the Azores (OKEANOS), Faial, Azores, 9901-862 Horta, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5893-0660","authenticated-orcid":false,"given":"Re\u015fit","family":"\u00d6zmente\u015f","sequence":"additional","affiliation":[{"name":"Vocational School of Health Services, Bitlis Eren University, 13100 Bitlis, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1021\/cr020357g","article-title":"Upconversion and anti-Stokes processes with f and d ions in solids","volume":"104","author":"Auzel","year":"2004","journal-title":"Chem. 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