Judd-Ofelt analysis of thulium-doped alumino-silicate optical glass prepared by MCVD combined with nanoparticle doping

Full Length Article Judd-Ofelt analysis of thulium-doped alumino-silicate optical glass prepared by MCVD combined with nanoparticle doping Petr Vaˇ r´ ak a,b,* , Michal Kamr´ adek a , Pavla Nekvindov´ a b , Jan Hrabovský c , Pavel Peterka a a Institute of Photonics and Electronics of the Czech Academy of Sciences, Chabersk´ a 1014/57, 182 00, Prague, Czech Republic b Department of Inorganic Chemistry, University of Chemistry and Technology, Technick´ a 5, 166 28, Prague, Czech Republic c Charles University, Faculty of Mathematics and Physics, Ke Karlovu 5, Prague 2, Prague, 121 16, Czech Republic ABSTRACT In this work, we present a comprehensive theoretical evaluation of Judd-Ofelt (JO) analysis for thulium-doped alumino-silicate glass in a wide range of compositions. The optical fiber preforms containing 5–10 mol. % Al 2 O 3 and 0.1–1.3 mol. % Tm 2 O 3 were prepared via the MCVD method combined with nanoparticle doping. The absorption spectra were measured, the absorption cross sections were evaluated and Judd-Ofelt (JO) analysis was carried out. The JO intensity parameters were found in the ranges Ω 2 =(6.1–6.6)•10 −20 cm −2 , Ω 4 =(2.3–2.9)•10 −20 cm −2 and Ω 6 =(1.0–1.5)•10 −20 cm −2 . These JO parameters, along with the calculated transition probabilities, branching ratios and radiative lifetimes showed relatively small variations across all measured samples. The calculated spectroscopic parameters may thus be used in theoretical calculations and simulations for materials in a wide range of compositions. Furthermore, the calculated radiative lifetime of the first excited level, 3 F 4 , was around 4 ms for the nanoparticle-doped preforms. The fluorescence lifetime was then measured and found to decrease from 0.9 ms to 0.7 ms with increasing concentration, providing values of quantum efficiency in the 17–22 % range. These values are significantly higher than 10 % determined for a reference solution-doped optical fiber preform and from literature, demonstrating the beneficial contribution of the nanoparticle doping method on the resulting quantum efficiency. 1. Introduction The trivalent ions of rare earth (RE) elements from the 6th row of the periodic table are well known for their sharp and intense absorption and emission bands in the UV, visible and infrared region, which are relatively independent on the host matrix, owing to the 4f-4f transitions of the well-shielded, inner electrons [1]. The RE-doped optical fibers find application in various fields of human activity, such as lasers and amplifiers [2], or detectors of high-energy radiation, so-called scintillators [3]. Amongst others, the thulium-doped fiber lasers and amplifiers (TDFL and TDFA) represent a perspective option for emission around 2.0 μ m, also called „eye-safe“ region thanks to high absorption of radiation in the eye’s vitreous parts, minimizing the damage to retina tissue [4,5]. Thanks to various advantages, such as high-quality beam, highly efficient operation, alignment-free configuration, and practicality of use, the TDFLs and TDFAs have rapidly found applications in many areas of human activity, including materials processing, research, sensors, telecommunications, defense and medicine [4,6]. The most commonly used material in the fiber-optic technology for laser applications remains silica glass, owing to high mechanical durability, as well as resistance to thermal damage and chemical corrosion [7]. For laser applications, the active core containing Tm 3+ ions is typically doped with Al 2 O 3 , which increases the refractive index, improves the homogenous distribution of Tm 3+ ions, thus preventing concentration quenching, and reduces the multiphonon relaxation, i.e. the unwanted dissipation of energy as heat into the matrix. The traditional method for the fabrication of RE-doped alumino-silicate fibers is the Modified Chemical Vapor Deposition (MCVD) combined with solution doping, where a porous silica layer is deposited on the inner side of a pure silica tube using gaseous SiCl 4 , and subsequently soaked with a solution containing AlCl 3 and RECl 3 [8,9]. However, this method is limited in the achievable Al 2 O 3 concentration around 5 mol. %, which also limits the maximum RE content before the onset of concentration quenching [10]. This deficiency can be overcome, e.g., by employing the nanoparticle doping method. This technique can be seen as a special modification of the traditional solution doping, where a dispersion of Al 2 O 3 or other nanoparticles, either directly doped with RE ions or mixed with RECl 3 , is used instead of the AlCl 3 solution [11–13]. The nanoparticles are dissolved at temperatures around 2000 ◦C, required for the preform collapse and fiber drawing [14]. In materials with up to 5 mol. % Al 2 O 3 , this process leads to a homogenous, amorphous alumino-silicate matrix, where the RE ion environment is * Corresponding author. Institute of Photonics and Electronics of the Czech Academy of Sciences, Chabersk´ a 1014/57, 182 00, Prague, Czech Republic. E-mail address: [email protected] (P. Vaˇ r´ ak). Contents lists available at ScienceDirect Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin https://doi.org/10.1016/j.jlumin.2025.121601 Received 8 August 2025; Received in revised form 23 September 2025; Accepted 4 October 2025 Journal of Luminescence 288 (2025) 121601 Available online 6 October 2025 0022-2313/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). indistinguishable from the traditional solution-doped fibers [13]. However, the advantage of the method lies in the possibility of incorporating higher Al 2 O 3 concentrations in the fiber-optic material, up to 10 mol. %, which permits to also increase the RE doping content without the negative effects of concentration quenching [15,16]. Moreover, we have previously demonstrated that for highly-doped preforms and fibers above 5 mol. % Al 2 O 3 , the matrix undergoes phase separation into Al-enriched alumino-silicate amorphous nanoparticles, which represent a highly beneficial environment for RE ions, while having no negative effect on the optical losses [16,17]. The nanoparticle doping combined with MCVD thus represents a highly prospective method for the fabrication of high-quality, highly-doped fibers for use in advanced lasers and amplifiers. In general, the rapidly advancing development and research of thulium-doped devices towards high efficiencies and high output powers requires reliable theoretical data, which serve as input in various theoretical tasks, e.g. calculation of emission cross sections and energy transfer coefficients [18,19], or the simulation of laser performance [20, 21], including the effects of temperature [22,23]. Amongst the most important theoretical parameters are transition probabilities, branching ratios and radiative lifetimes. The most straightforward method to obtain these parameters is the Judd-Ofelt (JO) analysis [24]. The Judd-Ofelt theory was published independently by B. R. Judd and G. S. Ofelt in 1962 [25,26]. Measured absorption cross sections are used in JO analysis to obtain quantities called „line strengths“ of each 4f-4f electronic transition, and calculate three phenomenological JO parameters, Ω 2 , Ω 4 and Ω 6 . These make it possible to calculate the transition probabilities, branching ratios and radiative lifetimes. The detailed description of the theory and analysis can be found in reviews by Hrabovsky et al. [27], Walsh [24] and Hehlen et al. [28], and dissertation thesis by Caspary [29]. Despite the ubiquity and rapid research of thulium-doped devices based on alumino-silicate glass, a comprehensive and reliable theoretical analysis is missing in literature. The JO analysis of an aluminosilicate optical fiber was conducted by Walsh & Barnes [30]. However, this study was limited to one fiber, prepared by the conventional solution doping method and with unclear composition. Moreover, no details about the absorption measurement and JO analysis were provided. Wang et al. reported a study of alumino-silicate glass prepared by sol-gel method, but the results of JO analysis were reported only for one composition containing 12 mol. % Al 2 O 3 and 0.8 mol. % Tm 2 O 3 [31]. Various studies report on the JO analysis of optical glass and fibers based on other systems, such as chalcogenide [32], tellurite [33], fluoro-indate [34], oxy-fluoroborate [35], alkali-silicate [36,37], germano-silicate [38] and many others, but the theoretical parameters obtained on other materials are not applicable to alumino-silicate glass. A comprehensive investigation is essential to advance both the experimental and theoretical understanding of advanced, highly-doped silica fibers fabricated via nanoparticle doping, a field with significant potential for novel optical performance and device applications. In this work, we conduct a systematic theoretical study of a large set of alumino-silicate optical fiber preforms prepared by MCVD combined with nanoparticle doping. The absorption cross section spectra were measured and calculated, and JO analysis was conducted. The JO parameters were obtained and were used to calculate transition probabilities, branching ratios and radiative lifetimes. The results were compared with reference sample prepared by standard solution doping as well as literature and discussed. 2. Experimental 2.1. Sample preparation Optical fiber preforms doped with Tm 3+ ions and co-doped with Al 2 O 3 were prepared using the MCVD method combined with nanoparticle doping technique. The method was described in detail in Ref. [13]. A porous silica layer was deposited onto the inner wall of a pure silica tube (F300, Heraeus), soaked with an ethanolic dispersion of Al 2 O 3 nanoparticles (particle size <50 nm, Sigma Aldrich, 99.9 %) mixed with TmCl 3 ⋅6H 2 O, hence the term “nanoparticle doping”, and dried. The doped tubes were sintered under chlorine atmosphere at temperatures 1200–1800 ◦C and collapsed into preforms above 2000 ◦C. In total, 7 samples were prepared designated as “A”-“G”. As a reference, one sample was prepared by the MCVD method combined with conventional solution doping, designated as “SD”. After a measurement of the refractive index profiles (RIPs) of the preforms, samples with approx. 2 mm thickness and 9 mm diameter were cut for further analysis. The samples were polished to optical quality using diamond polishing disks and CEROX suspension. 2.2. Sample characterization The composition of the preforms was measured by a Jeol JXA-8230 electron probe microanalyzer (EPMA) in mol. %, the measurement error is approx. 2 rel. % for all values. For the samples A-G, the volume concentration was calculated using the assumed density of 2.30 g cm −3 , which is a reasonable assumption for alumino-silicate glass containing 5–10 mol. % Al 2 O 3 [39]. In the case of the reference “SD” sample, the density was taken as 2.25 g cm −3 . The refractive index profiles of the preforms were measured using a Photon Kinetics A2600 refractive index profiler. The dispersion of the preforms was approximated using the established dispersion of pure silica glass expressed by Sellmeier equation [40] and adding the measured value of the refractive index for the preform. The approximated curve was re-fitted by Sellmeier function of the first order, equation (1). n2(λ) = AS+BSλ2 λ2−CS (1) The parameters A S , B S , and C S were obtained. The fluorescence decay curves of the 2 μ m emission were measured using identical setup and procedure as described in Ref. [41] and the experimental fluorescence lifetime was retrieved by single exponential regression. The absorption spectra were measured using PerkinElmer Lambda 1050+UV/Vis/NIR spectrophotometer in the 220–2050 nm range with 0.2 nm step, using PMT detector in 220–900 nm range, with 0.4 s integration time and 1 nm slit, and InGaAs detector in 900–2050 nm range, with 1.0 s integration time and 2 nm slit. A mask was applied on the samples to ensure transmission only through the core. The absorption coefficient, α , and absorption cross section, σ ABS , were calculated from the measured transmittance, T, using equations (2) and (3). α (λ) = 1 L⋅log 1 T(λ)cm−1(2) σ ABS(λ) = ln 10 N⋅ α (λ)cm2(3) Where L is sample thickness (in cm) and N is the Tm 3+ ion volume concentration (in cm −3 ). The spectra were processed in OriginPro 2018b; a baseline was created by manual input of datapoints and using the spline function. Following a baseline subtraction, the integrated values of absorption cross sections and mean central wavelength for each of the ground state absorption band were obtained. The JO analysis was calculated using the newly developed on-line software LOMS.cz, the entire procedure, including all necessary equations, is described in Refs. [27,42]. The standard deviations of the JO parameters were calculated according to procedure described in Refs. [27,43]. The calculation was performed using ASCII input files containing all necessary values, i.e., Sellmeier parameters, reduced squared matrix elements, integrated absorption cross sections, and mean central wavelengths; the input files of all samples can be found in Ref. [44]. P. Vaˇ r´ ak et al. Journal of Luminescence 288 (2025) 121601 2 3. Results 3.1. General characterization of the prepared preforms The composition of the preforms was measured by EPMA. The typical concentration profile of a representative preform “G” is shown in Fig. 1, the others exhibited identical shapes. The concentrations of Al 2 O 3 and Tm 2 O 3 ions exhibited a typical cylindrical shape with a flat maximum in the center. The refractive index profile possessed a corresponding shape. The compositions of the investigated preforms are summarized in Table 1. In the case of the nanoparticle-doped preforms from “A” to “G”, the Al 2 O 3 concentration was kept in the range 5–10 mol. % Al 2 O 3 . The Tm 2 O 3 concentration varied between 0.1 and 1.3 mol. %. The reference “SD” sample prepared by the conventional solution doping contained comparatively lower concentration of Al 2 O 3 . As apparent from Table 1, the nanoparticle method permits to achieve significantly higher Al/Tm ratio even for highly-doped samples in excess of 1 mol. % of Tm 2 O 3 . 3.2. Absorption spectra The absorption coefficient spectra of the preforms are summarized in Fig. 2a and exhibit generally similar features across all samples. Observed low background losses were likely caused by the light scatter at air-glass interfaces. The slight discontinuity and increased noise around 900 nm are due to detector and monochromator grating changeover. Note that none of the above-mentioned effects affected the proper calculation of the JO parameters in the following section. Several ground state absorption bands, corresponding to 4f-4f transitions from the Tm 3+ : 3 H 6 ground state to excited energy levels are well distinguished in the spectra, namely 3 F 4 (≈1660 nm), 3 H 5 (≈1210 nm), 3 H 4 (≈790 nm), 3 F 2+3 (≈683 nm), 1 G 4 (≈468 nm), 1 D 2 (≈355 nm), and a cluster of overlapping transitions 1 I 6 (≈291 nm), 3 P 0 (≈285 nm), 3 P 1 (≈276 nm), 3 P 2 (≈262 nm). The mean wavelengths of the transitions are nearly identical for all samples. The intensities of the absorption bands increase in good agreement with the thulium concentrations in the preforms. The baseline subtraction is depicted in Fig. 2b on the example of sample “G”. The processed and calculated spectra of absorption cross section are pictured in Fig. 3. The absorption cross sections are very similar for all samples prepared by the nanoparticle doping. Slight differences can be observed for the reference “SD” sample, mainly in the 1 D 2 and 3 F 2+3 bands. The values of the absorption cross sections for the bands 3 H 4 and 3 F 4 are around 9•10 −21 cm 2 and 4.5•10 −21 cm 2 , resp., which is in excellent agreement with literature [45,46]. 3.3. Low wavelength region (240–300 nm) The low wavelength (LW) region below 300 nm represents a significant challenge to analyze properly. The four bands in this region are relatively weak, exhibit a significant overlap, and are also located well into the UV absorption edge. Great care must be taken to obtain reliable values of absorption cross sections, and the results may be strained by a significant error. For this reason, it is typically advised to exclude such transitions from the JO analysis [42,47]. In this work, we attempted to approximate these absorption bands by gaussian deconvolution. The absorption cross section spectra, along with the fit of the UV absorption edge and gaussian deconvolution of the bands, performed similarly as in Ref. [48], are shown in Fig. 4 on the example of the highest-doped sample “G”. 3.4. Judd-Ofelt analysis The Judd-Ofelt analysis was performed for all samples primarily without the low wavelength region bands, which means using the six intense and well-distinguished transitions from ground state 3 H 6 to excited states 3 F 4 , 3 H 5 , 3 H 4 , 3 F 2+3 , 1 G 4 and 1 D 2 . The summary of the experimental and calculated line strengths, as well as the root-meansquare deviations is listed in Table 2. The obtained JO parameters along with a summary of some results from literature for other glass systems are given in Table 3. The values of standard deviations are on the higher side, but remain in line with commonly achieved values in literature [43]. A graphical representation of the dependency of JO parameters on the thulium concentration is depicted in Fig. 5. Table 3 also lists the radiative lifetime, τ rad , of the lowest excited 3 F 4 level. The full results of transition analysis, i.e., the transition probabilities, branching ratios and radiative lifetimes of all available transitions can be found in Supplementary material S1. All nanoparticle-doped preforms exhibited values of the three JO parameters in the ranges Ω 2 =(6.1–6.6)•10 −20 cm −2 , Ω 4 =(2.3–2.9)• 10 −20 cm −2 and Ω 6 =(1.0–1.5)•10 −20 cm −2 , and radiative lifetime of the 3 F 4 level around ~4 ms. The reference preform “SD”, prepared by solution doping, exhibited similar values albeit with slightly higher Ω 2 and lower Ω 4 , Ω 6 parameters, and higher τ rad . These values are in reasonable agreement with results previously obtained by Walsh & Barnes on an optical fiber prepared by solution doping [30], as well as bulk glass prepared via sol-gel method by Wang et al. [31]. To check the reliability of using the low-wavelength transitions, which are buried in the UV absorption edge and experience a significant overlap, the JO analysis was also performed with their inclusion. The results and comparison with the previous calculation are demonstrated in Table 4 for the sample “G”. The remaining samples exhibited similar trends and behavior, and the results can be found in Supplementary material S2. As obvious from Table 4, the inclusion of the LW transitions leads to a generally poorer match between the experimental and calculated line strengths, the match is especially poor for the transitions Fig. 1. – Measured concentration and refractive index profiles (RIP) of the preform “G” Table 1 List of the investigated thulium-doped alumino-silicate optical fiber preforms with the measured Tm 2 O 3 and Al 2 O 3 concentrations and calculated Tm 3+ ion density. Preform Al 2 O 3 (mol. %) Tm 2 O 3 (mol. %) Tm 3+ (cm −3 ) Al/Tm ratio A 7.7 0.08 0.38•10 20 96 B 9.8 0.17 0.72•10 20 58 C 5.6 0.18 0.81•10 20 31 D 9.4 0.34 1.44•10 20 28 E 9.8 0.63 2.63•10 20 16 F 9.0 1.02 4.19•10 20 9 G 9.7 1.33 5.38•10 20 7 SD 2.2 0.50 2.16•10 20 4 P. Vaˇ r´ ak et al. Journal of Luminescence 288 (2025) 121601 3 1 I 6 , 3 P 0 and 3 P 1 . The value of the root-mean-square deviation is larger, compared to the calculation excluding the LW transitions, and the standard deviations of the JO parameters are slightly larger as well. The JO parameters show notable differences, the Ω 2 is smaller, the Ω 4 is higher, while the Ω 6 remains nearly identical. However, the radiative properties remain generally similar, as shown on the example of 3 F 4 radiative lifetime. 3.5. Experimental fluorescence lifetime and quantum efficiency The fluorescence decay curves of the 3 F 4 emission (~2 μ m) are depicted in Fig. 6. The decay curves were independent on the pump power. All samples exhibited single-exponential behavior and the fluorescence lifetime was retrieved by exponential regression; example of the fit is shown in the inset of Fig. 6 for the “G” sample and the results are summarized in Table 5. The measured fluorescence lifetime followed the well-known relationships; it decreased with increasing thulium content due to concentration quenching, while increasing Al 2 O 3 content showed a positive effect due to the reduction of multiphonon relaxation. In general, the spectroscopic properties are improved with increasing Al/ Tm ratio [16]. The quantum efficiency, η , of the 3 F 4 → 3 H 6 transition was determined Fig. 2. a) measured absorption coefficients of the thulium-doped alumino-silicate optical fiber preforms, b) baseline subtraction example on sample “G”. Fig. 3. Measured absorption cross sections of the thulium-doped alumino-silicate optical fiber preforms. P. Vaˇ r´ ak et al. Journal of Luminescence 288 (2025) 121601 4 as the ratio between the measured and calculated radiative lifetime. In general, the samples prepared by nanoparticle doping containing high Al 2 O 3 content exhibited high quantum efficiency around 20 %. A decrease from 22 % to 18 % can be observed with increasing concentration and decreasing Al/Tm ratio, along the same trend as the measured lifetime. The lowest value of 17 % was observed in the “C” sample, which was deficient in Al 2 O 3 compared to other samples. A generally comparable, but slightly lower quantum efficiency around 16 % was reported by Wang et al. for the sol-gel bulk sample containing 12 mol. % Al 2 O 3 . A significantly lower quantum efficiency is observed for the reference “SD” sample as well as the solution-doped fiber reported by Walsh & Barnes, around 10 %, due to the significantly lower Al 2 O 3 content and thus higher rate of multiphonon relaxation. 4. Discussion Several aspects of the work will now be discussed in more detail. The absorption spectra measured in this work exhibited a large number of bands corresponding to the 4f-4f transitions of Tm 3+ ion spanning from the UV region to the infrared. It was previously shown that the selection of absorption bands may significantly influence the results of the JO analysis as well as its error [42]. In this work, the inclusion of the UV bands located up to 300 nm introduced a higher error to the least-squares calculation and the JO analysis compared to the calculation without these bands, which may be ascribed to several factors, e.g., the strong overlap with the UV absorption edge as well as the mutual overlap of the bands themselves and the necessity for deconvolution, all of which may introduce additional error. This finding is in good agreement with literature, where the use of absorption bands strongly overlapping with the UV absorption edge is often discouraged [42,47]. In Fig. 4. analysis of the low wavelength region for the sample G. Table 2 Summary of the experimental and calculated values of line strengths. All quantities are given in (10 −20 cm 2 ). The analysis was performed without the low wavelength transitions. A B C D E F G SD 3 H 6 →S exp S calc S exp S calc S exp S calc S exp S calc S exp S calc S exp S calc S exp S calc S exp S calc 3 F 4 5.46 5.57 5.13 5.32 5.43 5.57 5.56 5.67 5.44 5.56 5.67 5.79 5.52 5.66 5.20 5.29 3 H 5 1.88 1.93 2.17 2.17 2.09 2.01 2.11 2.08 2.16 2.11 2.10 2.10 2.18 2.12 1.71 1.66 3 H 4 2.58 2.33 3.03 2.61 2.75 2.48 2.70 2.48 2.77 2.53 2.84 2.59 2.86 2.60 2.43 2.28 3 F 3+2 1.86 1.96 2.2 2.43 1.90 2.09 2.09 2.23 2.13 2.28 2.05 2.18 2.06 2.24 1.33 1.44 1 G 4 0.70 0.51 0.63 0.49 0.53 0.52 0.61 0.53 0.55 0.51 0.61 0.53 0.60 0.52 0.66 0.49 1 D 2 1.27 0.99 1.38 0.88 1.29 0.92 1.29 1.02 1.27 0.97 1.26 0.95 1.26 0.93 0.88 0.69 σ RMS,S 0.26 0.42 0.29 0.23 0.25 0.25 0.28 0.19 Table 3 Summary of the obtained JO parameters and radiative lifetimes of the lowest excited level, 3 F 4 , along with overview of results from literature. Ω 2 (10 −20 cm 2 ) Ω 4 (10 −20 cm 2 ) Ω 6 (10 −20 cm 2 ) τ rad , 3 F 4 (ms) Ref. A6.1 ±0.8 2.8 ±0.6 1.0 ±0.2 4.08 – B6.1 ±1.3 2.3 ±1.0 1.5 ±0.4 4.25 – C6.4 ±0.9 2.6 ±0.7 1.2 ±0.3 4.11 – D6.1 ±0.7 2.9 ±0.5 1.2 ±0.2 3.95 – E6.1 ±0.8 2.7 ±0.6 1.3 ±0.2 4.11 – F6.6 ±0.8 2.7 ±0.6 1.2 ±0.2 3.85 – G6.5 ±0.9 2.6 ±0.7 1.3 ±0.2 3.89 – SD 6.8 ±0.6 2.0 ±0.5 0.8 ±0.2 4.38 – Al 2 O 3 -SiO 2 (MCVD) 6.23 1.91 1.26 4.56 [30] Al 2 O 3 -SiO 2 (solgel) 6.94 1.80 1.33 5.01 [31] Na 2 O-SiO 2 2.16 0.16 0.5 –[36] CaO-SiO 2 3.59 0.99 0.86 –[36] Na 2 O-K 2 O-CaOSiO 2 3.08 0.99 0.40 7.91 [37] Germanosilicate 3.24 3.28 0.58 –[38] Germanate 6.14 1.54 0.87 4.05 [49] Chalcogenide 7.60 1.88 2.78 0.86 [32] Tellurite 4.40 1.97 1.22 2.10 [33] Fluoro-indate 1.77 2.30 1.69 7.84 [34] Oxyfluoroborate 8.37 3.20 4.34 2.08 [35] ZBLAN 1.96 1.63 1.16 11.1 [30] Fig. 5. The dependency of JO parameters on Tm 2 O 3 content in the thuliumdoped alumino-silicate optical fiber preforms. The reference „SD“ sample is represented by the faded colors. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) P. Vaˇ r´ ak et al. Journal of Luminescence 288 (2025) 121601 5 case of the Tm 3+ -doped alumino-silicate glass, the JO analysis is thus recommended to calculate using only the well-defined absorption bands in the 300–2000 nm range. The JO parameters and the spectroscopic properties are inherently tied to the matrix structure, the bonding and the local environment of the RE ions. Over the years, a strong correlation was shown between the three JO parameters and various material properties [50]. The Ω 2 parameter is tied to the symmetry of the RE ion environment and the covalency of the bonding. The relatively high values around 6•10 −20 cm 2 compared to most other glass systems, especially alkali-silicate, suggest a low symmetric environment around the Tm 3+ ions, consistent with the depolymerized and amorphous alumino-silicate matrix, as well as high covalency of the Tm-O bond. This finding is in good agreement with basic chemical relationships [51]. The Aluminium atom exhibits a rather high electronegativity compared to, e.g., alkali or alkaline-earth elements, which results in a smaller partial negative charge on oxygen atoms, and thus high covalency of the Tm-O bond. On the other hand, the Ω 4 and Ω 6 parameters are related to the rigidity of the host matrix, which scales inversely with the vibrational amplitude of the RE-ligand bond, although the correlations are not as clear as in the case of Ω 2 [28]. Generally, higher values of Ω 4 and Ω 6 correlate with lower rigidity of the matrix. The Al 2 O 3 -SiO 2 preforms show higher values compared to alkali-, alkaline earthor germano-silicate and germanate glasses, comparable to fluoro-indate or tellurate and lower than oxy-fluoroborate. Most importantly, the JO parameters and the radiative properties are almost identical in all the nanoparticle-doped preforms investigated, which suggests that the surrounding Tm 3+ ion environment is nearly independent of the thulium concentration, as well as Al 2 O 3 content in the range of 5–10 mol. %. The proximity of other ions has no significant impact on the symmetry, covalency or the local phonon energy of the Tm 3+ ion sites. These results show a great versatility of the obtained parameters, which can be interchangeably used in theoretical calculations for a wide range of glass and fiber compositions. A notable decrease with increasing thulium concentration, however, can be observed for the measured fluorescence lifetime of the 3 F 4 level and consequently the quantum efficiency, which shows the expected influence of concentration quenching, i.e., the presence of various inter-ionic energy transfer processes like energy transfer upconversion (ETU), cross relaxation (CR) or pair-induced quenching, which lead to non-radiative depopulation of the excited levels. The results obtained on the optical fiber preforms prepared by MCVD combined with nanoparticle doping can be compared with other alumino-silicate glass prepared by different fabrication methods. A sample prepared by conventional solution doping was prepared in this work, as well as sourced from literature by Walsh & Barnes [30], while Wang et al. reported alumino-silicate glass prepared by sol-gel method [31]. The results are in a reasonable agreement. Slight discrepancies with literature are difficult to ascertain since Walsh & Barnes do not report on the exact composition of the fiber, nor the details of the absorption measurement and the JO analysis. It must also be remembered that slight differences of spectroscopic properties and RE ion environment can be observed between the preforms and finished optical fibers due to fabrication conditions [17,41,52]. Furthermore, Wang et al. used a different fabrication method and processed the samples only up to 1750 ◦C, as opposed to over 2000 ◦C in this work. Such differences were previously reported to result in notable deviations in matrix structure and spectroscopic properties [14]. The quantum efficiency of the lowest excited level, 3 F 4 , calculated as a ratio of the measured and the theoretical radiative lifetime, represents a general measure of the spectroscopic „quality“. Higher quantum efficiency indicates less energy dissipated in non-radiative transitions, such as multiphonon relaxation and energy transfers, and higher proportion of pump power, which can be theoretically converted into radiative emission. The values obtained in silica-based glass are typically much lower than 100 %, since a significant portion of ions decay nonradiatively by multiphonon relaxation and the measured lifetime of the 3 F 4 level is much lower than the radiative one. Quantum efficiency close to 100 % may be typically observed in low-phonon materials such Table 4 summary of the line strengths, JO parameters and 3 F 4 radiative lifetime for calculation without and with the LW transitions for the sample “G” S exp (10 −20 cm 2 ) S calc (10 −20 cm 2 ) S exp , LW (10 −20 cm 2 ) S calc , LW (10 −20 cm 2 ) 3 F 4 5.52 5.66 5.52 5.75 3 H 5 2.18 2.12 2.18 2.13 3 H 4 2.86 2.60 2.86 2.38 3 F 3 2.06 2.24 2.06 2.36 1 G 4 0.60 0.52 0.60 0.54 1 D 2 1.26 0.93 1.26 1.19 1 I 6 – – 0.43 0.21 3 P 0 – – 0.26 0.09 3 P 1 – – 0.33 0.14 3 P 2 – – 1.53 0.93 σ RMS,S 0.28 0.35 Ω 2 (10 ¡20 cm 2 ) 6.5 ±0.9 5.6 ±1.0 Ω 4 (10 ¡20 cm 2 ) 2.6 ±0.7 3.4 ±0.7 Ω 6 (10 ¡20 cm 2 ) 1.3 ±0.2 1.2 ±0.3 τ rad , 3 F 4 (ms) 3.89 3.82 Fig. 6. measured decay curves of the thulium-doped alumino-silicate optical fiber preforms for the 3 F 4 emission (~2 μ m). Inset shows example of singleexponential fit for the G sample. Pumping power was 10 mW. Table 5 measured and calculated radiative lifetimes of the samples, and calculated values of quantum efficiency for the 3 F 4 emission (~2 μ m). τ rad , 3 F 4 (ms) τ meas , 3 F 4 (ms) η (%) A4.08 0.89 22 B4.21 0.85 20 C4.11 0.70 17 D3.95 0.83 21 E4.11 0.79 19 F3.85 0.73 19 G3.89 0.70 18 SD 4.38 0.45 10 Walsh [30] 4.56 0.42 9 Wang [31] 5.01 0.83 16 ZBLAN [30] 11.1 11.2 ~100 Germanate [49] 4.05 4.29 ~100 P. Vaˇ r´ ak et al. Journal of Luminescence 288 (2025) 121601 6 as ZBLAN or germanate glass, see Table 5. In our work, the nanoparticledoped preforms achieved a quantum efficiency in the range 17–22 %, which represents a significant improvement over solution-doped preforms and fibers, as prepared here, or sourced from Walsh & Barnes [30], where the quantum efficiency in both cases is significantly lower, around 10 %, which is owed especially to the significantly lower measured lifetime, around 0.45 and 0.42 ms, resp. This observation is in good agreement with literature. It was previously shown that the higher contents of Al 2 O 3 and thus higher Al/Tm ratio achieved by nanoparticle doping are beneficial to the environment of RE ions and the fluorescence lifetime when compared to the conventional solution doping [15,16]. The high Al/Tm ratio leads to the suppression of concentration quenching and multiphonon relaxation. Moreover, these phenomena may be amplified by matrix structure modifications. In a silica glass system containing more than 5 mol. % of Al 2 O 3 , such as achieved by nanoparticle doping, the matrix undergoes phase separation, and the Tm 3+ ions become located in the highly beneficial environment of Al 2 O 3 -enriched nanoparticles [16,17,53], which may further improve the quantum efficiency. Furthermore, Wang et al. prepared alumino-silicate glass by the sol-gel method, containing 12 mol. %, but the quantum efficiency, 16 %, still falls slightly short of the glass prepared by nanoparticle doping [31]. In summary, the nanoparticle doping thus represents a prospective and highly efficient method to prepare a highly-doped alumino-silicate optical glass, in excess of 1 mol. % Tm 2 O 3 , for use in advanced devices, e.g., high-power, highly efficient amplifiers [54] or high-power lasers with enhanced heat load management [55]. 5. Conclusion The absorption spectra of the thulium-doped alumino-silicate optical fiber preforms prepared via the MCVD method combined with nanoparticle doping were measured. The preforms contained 5–10 mol. % Al 2 O 3 and 0.1–1.3 mol. % Tm 2 O 3 . Absorption cross sections were evaluated and Judd-Ofelt (JO) analysis was carried out. The JO intensity parameters were found in the ranges Ω 2 =(6.1–6.6)•10 −20 cm −2 , Ω 4 = (2.3–2.9)•10 −20 cm −2 and Ω 6 =(1.0–1.5)•10 −20 cm −2 . These JO parameters, along with the calculated transition probabilities, branching ratios and radiative lifetimes showed relatively small variations across all measured samples. These results show a great versatility of the obtained parameters, which can be interchangeably used in theoretical calculations and laser simulations for a wide range of glass and fiber compositions. The calculated radiative lifetime of the first excited level, 3 F 4 , was around 4 ms for the nanoparticle-doped preforms. The experimental fluorescence lifetime was then measured and found to decrease from 0.9 ms to 0.7 ms with increasing concentration, providing values of quantum efficiency in the 17–22 % range. These values are significantly higher than 10 % determined for a reference solution-doped optical fiber preform and from literature, demonstrating the benefits of the nanoparticle doping method. CRediT authorship contribution statement Petr Vaˇ r´ ak: Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Michal Kamr´ adek: Writing – review & editing, Investigation. Pavla Nekvindov´ a: Writing – review & editing, Supervision, Resources, Funding acquisition. Jan Hrabovský: Writing – review & editing, Software. Pavel Peterka: Writing – review & editing, Supervision, Funding acquisition, Conceptualization. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the Czech Science Foundation, grant No. GA23-05507S. This work was co-funded by the European Union and state budget of the Czech Republic under the project LasApp CZ.02.01.01/00/22_008/0004573. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.jlumin.2025.121601. Data availability The data supporting the results of this study can be found in Ref. [44]. References [1] G.H. Dieke, H.M. 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