Combined theoretical and experimental study of
luminescence in Gd3+ -doped silica glass under ionizing
radiation

Ismail Zghari, Adriana Morana, Hicham El Hamzaoui, Bruno Capoen, Andy Cassez, Youcef Ouerdane, Sylvain Girard, Aziz Boukenter, Franck Mady, Mourad Benabdesselam, et al.

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To cite this version:

Ismail Zghari, Adriana Morana, Hicham El Hamzaoui, Bruno Capoen, Andy Cassez, et al. Com-bined theoretical and experimental study of luminescence in Gd3+ -doped silica glass under ionizing radiation. Optics Express, 2025, 33 (8), pp.16987. 10.1364/OE.549317 . hal-05028301

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Submitted on 10 Apr 2025

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# Combined theoretical and experimental study of luminescence in Gd<fnref n="3" />⁺-doped silica glass under ionizing radiation

ISMAIL ZGHARI,<fnref n="1" />,* ADRIANA MORANA,<fnref n="2" /> HICHAM EL HAMZAQUI,<fnref n="1" />
BRUNO CAPOEN,<fnref n="1" /> ANDY CASSEZ,<fnref n="1" /> YOUCEF OUERDANE,<fnref n="2" />
SYLVAIN GIRARD,<fnref n="2" />,<fnref n="3" /> AZIZ BOUKENTER,<fnref n="2" /> FRANCK MADY,<fnref n="4" />
MOURAD BENABDESSELAM,<fnref n="4" /> AND MOHAMED BOUAZAOUI<fnref n="1" />

**Abstract:** In the ionizing radiation dosimetry domain, there is still an important demand for a compact, reliable, and accurate sensor. Currently, among the dosimeters based on optical techniques, the fibered systems are the most promising solutions. Optical dosimeters usually exploit one of the physical processes, which is radioluminescence (RL), thermoluminescence (TL) or radiation-induced attenuation (RIA). In this paper, we present, to our knowledge, a new approach to measuring the dose of ionizing radiations that combines radioluminescence, phosphorescence, and thermoluminescence processes. To our knowledge, the integrated signals originating from these three processes have been collected at different temperatures through an optical fiber spliced to a Gd<fnref n="3" />⁺-doped silica glass rod for the first time. Using this fibered setup, the experimental study shows that the integrated response, originating from the three processes, is linear versus dose at least up to 300 Gy and temperature-independent between 153 K and 353 K. These experimental results have been explained and reproduced by a theoretical model, which is also able to predict the dosimeter response under various conditions. Moreover, as another novelty, to our knowledge, simultaneous optically stimulated luminescence (OSL) and RL measurements allowed the achievement of a real-time and temperature-independent dosimeter.

Published by Optica Publishing Group under the terms of the [Creative Commons Attribution 4.0 License](https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

## 1. Introduction

Optical fiber detectors, based on their interaction with various ionizing radiations, are the subject of extensive studies [1–7]. The interesting intrinsic properties of silica-based optical fibers, such as their high chemical and thermal stability and their insensitivity to most of the electromagnetic perturbations make them very promising candidates for the design of relatively inexpensive point sensors or distributed solutions in all the nuclear domains: for both industrial and research-devoted environments as well as in medical physics (radiotherapy and imaging). For point sensor applications purpose, either a fiber piece or a thin rod small piece can be attached to a transport fiber, yielding a sub-millimeter-diameter dosimeter [2,5]. In addition, due to their high spatial resolution (small size) and to the possibility of remote measurement, optical fibers are well suited for applications where space is limited and where microelectronics can not be deployed [8–10]. Indeed, several previous studies revealed that the fiber-based technologies have

<footnote n="1">¹Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France</footnote>

<footnote n="2">²Université Jean Monnet Saint-Étienne, CNRS, Institut d'Optique Graduate School, Laboratoire Hubert Curien UMR 5516, 42023 Saint-Étienne, France</footnote>

<footnote n="3">³Institut Universitaire de France (IUF), F-75005 Paris, France</footnote>

<footnote n="4">⁴Université Côte d'Azur, CNRS, Institut de Physique de Nice – INPHYNI UMR 7010, F-06108 Nice Cedex 2, France</footnote>

<footnote>*ismail.zghari@univ-lille.fr</footnote>
a much higher level of radiation tolerance than those of traditional micro- or opto-electronic technologies [11].

Ionizing radiation induces three main macroscopic changes in bulk glasses and silica-based optical fibers. The first is Radiation Induced Attenuation (RIA), which degrades the signal transmission capacity of the sensitive fiber. The RIA is caused by the generation of optically active point defects in both core and cladding of the irradiated optical fiber [11]. This technique is used for dose measurement in severe environments such as in nuclear facilities [12]. The second mechanism is Radiation Induced Refractive Index Change (RIRIC), which is mainly observed under exposure to high particle fluences. This leads to changes in the refractive index, impacting the guidance properties of fibers [13]. The last phenomenon is radiation induced emission (RIE), including radioluminescence (RL) and Cerenkov emission (CE), which can be exploited for active dosimetry, where the dose measurement takes place in real time during irradiation. The RL technique is suited for in vivo dosimetry, which involves a direct measurement of radiation dose on the patient during a radiotherapy treatment [14–16]. However, due to the presence of defect levels in the scintillating material, the RL emission is often followed, after the irradiation stop, by a very slow decrease of the optical signal, called Phosphorescence (PP) or afterglow [17–20]. A fourth phenomenon usually occurs after irradiating a glass or a fiber. This one is associated to the trapping of charge carriers onto deep defect energy levels in the matrix. After irradiation, if a sufficient energy amount is then provided to the material, the trapped carriers can be released, allowing them to recombine at a specific center, as it is the case in the RL process. The stimulation energy can be brought to the system either by heating, giving rise to thermoluminescence (TL), or through light irradiation, leading to Optically Stimulated Luminescence (OSL) [21].

Silica-based fibers doped with rare-earth (RE) ions are widely studied for their interesting properties, such as sensitivity to low dose rates and resistance to high doses, linear response over a wide range of dose / dose rate, as well as high time resolution [1,2]. In this context, due to their optical activity in the UV range, the incorporation of gadolinium ions ($Gd^{3+}$) inside oxide glasses leads to efficient scintillators and phosphor materials. However, only a few studies have been devoted to gadolinium-doped silica glasses without any co-dopant [22–24]. Recently, we showed that silica glasses doped with $Gd^{3+}$ ions are promising detection materials for dosimetry applications. In [22], we have shown the potential of this material for real-time X-ray dosimetry using the RL technique with a linear response in the dose rate range from 125 µGy (SiO$_2$)/s up to at least 12.25 Gy/s. Moreover, $Gd^{3+}$ ions-activated silica showed a linear radioluminescence response as a function of electron bunch size, ranging from $10^{-5}$ Gy/bunch to $1.5 \times 10^{-2}$ Gy/bunch for 3 µs electrons bunches having 20 MeV energy [23]. Another study investigated the dose profile of proton beams in water (Bragg peak) at energies between 6 and 63 MeV with dose rates from 0.02 Gy/s to 0.30 Gy/s [24]. It showed that the $Gd^{3+}$-doped sample approached the performance of the Markus chamber reference with better capabilities in this regard compared to the samples with other activating ions, such as $Ce^{3+}$ or $Cu^{+}$.

The above-presented physical processes, RIA, RL and TL, are generally studied separately and in this case, the associated signals are temperature-dependent. In this paper, we present an original approach to study experimentally and theoretically the joint processes of RL, PP and TL in glassy materials under ionizing radiations (X-rays, gamma rays, protons...). This approach, based on a fibered system including a radio-sensitive probe (here, a $Gd^{3+}$-doped silica glass rod), was validated under X-rays. The TL of doped glasses, when detected through an optical fiber, is not common and is called here Fibered Thermo-Stimulated Luminescence (FTSL). Collecting RL, PP and FTSL signals of doped silica rods through an optical fiber presents three advantages: a remote measurement with the same setup, a controlled delay between TL measurement and the end of irradiation, a versatile way of measuring the optical properties of the samples at high and low temperatures. Furthermore, this methodology leads to the direct comparison of the
different mechanisms contributions (RL, PP and FTSL), thus enabling to validate theoretical models [25–28].

The optical fiber setup allowed RL measurements at different dose rates and temperatures, followed by the detection of PP and then FTSL. The kinetics of the obtained RL and FTSL signals, at different temperatures, were modeled for the first time to our knowledge using a standard model involving 50 trap levels and one recombination center (RC). Finally, based on this fundamental study, an approach using OSL combined to RL was investigated for the achievement of a real-time and temperature-independent dosimeter.

## 2. Materials and methods

### 2.1. Sample preparation

Cylindrical Gd³⁺-doped silica glasses were prepared using the sol-gel process at FiberTech Lille platform of the University of Lille, as described elsewhere [22]. These 8 mm-diameter doped rods, obtained with a dehydration step, were first drawn to about 1.5 mm diameter at 2000°C. Then, they were drawn a second time at the same temperature to a diameter of 220 µm, well adapted to the radhard transport fiber they were fusion-spliced to in the scope of RL/FTSL/OSL measurements. Samples of length 1 cm were cut in these thin rods.

### 2.2. Characterization

Standard thermally stimulated luminescence (TL) measurements were performed on Gd³⁺-doped silica samples from room temperature (RT) to 650 K, with a linear heating rate of 60 K/min. The laboratory-made TL system makes use of a photomultiplier tube (PMT), with emission integration of the 250-650 nm spectral range. The sample was irradiated at INPHYNI institute to a dose of about 722 Gy using an X-ray tube (XRG3D-INEL), with a copper anode operated at 30 kV. The irradiation was calibrated by ionization chamber (PTW 23342) and the delay between the irradiation and the TL reading was 105 s.

For RL and FTSL measurements, as well as for the RL/OSL measurements, the experimental setup, as shown in Supplement 1 Fig. S1, was composed of 1 cm-long piece of the Gd³⁺-doped rod spliced on both sides to a multi-mode radiation-hard optical fiber of length 5 m and diameter 220 µm supplied by Exail. The external X-ray beam was delivered by the LABHX facility of Laboratoire Hubert Curien, operated at 100 kV and generating photons of ~ 40 keV mean energy-fluence. The X-ray dose rate was driven by the electric current of the equipment. The 1 cm-long piece of the doped rod was placed in a calibrated position of the X-irradiator. Under X-rays, the emission signal was then guided through the transport fiber toward a photomultiplier (PMT) or a UV/VIS mini-spectrometer (Ocean Insight QE PRO). On the other side, the second optical fiber was used to guide the stimulation light to the sample in order to perform OSL measurements. To this purpose, we employed a supercontinuum white light fiber laser, which delivers up to 2 W power in the entire 400-2400 nm region (SC-400-2 FIANIUM supercontinuum from NKT Photonics). An optical power of about 280 mW of this laser source reached the Gd-doped sample. However, for RL and FTSL measurements, the laser was evidently turned off. The signal detected by the PMT was collected at different temperatures behind a bandpass filter around 314 nm having a full width at half maximum (FWHM) of 5 nm (Edmund optics 34977).

To perform RIA measurements, a fibered setup similar to the one shown in Fig. S1 was used. It consisted of a rod connected via transport fibers at one end to a deuterium light source (DH2000 from Ocean Optics) while the other end was connected to a UV-visible spectrometer (QE6500 from Ocean Optics). All the transport fibers were shielded with lead and tungsten plates, to irradiate only the rod Gd-doped sample. An irradiation was performed at a dose-rate of 0.5 Gy(SiO₂)/s, for 300 s (equal to the t<sub>RL</sub> reported in the paper). We first irradiated the rod at 153 K and we recorded the RIA in real time for 300 s. After stopping the irradiation, the sample
was heated at 5 K/min to 353 K and then left at this temperature for 20 minutes for stabilization, leading to a total recovery time of 60 minutes. The RIA was then recorded in real time at 353 K for 300 s.

For the purpose of tuning the sample temperature, this one was placed on a temperature-controlled plate and measurements were carried out over a temperature range 153-353 K. At each temperature (*T*<sub>irr</sub>), the sample was exposed to five different dose rates between 50 and 1000 mGy/s. Then, the FTSL was recorded from the irradiation temperature (*T*<sub>irr</sub>) up to 353 K with a heating rate of 5 K/min. It should be noted that, in the RL experiment, the obtained signals were neither affected by the Cerenkov effect, since the irradiation source used here delivered photons of too low energies, nor by other spurious signal related to the transport fiber, as it was shielded by a thick lead cover.

**3. Results and discussion**

In order to limit the number of adjustable parameters in the model, some of them have been determined from standard TL measurements, presented below. This short paragraph is followed by the description of RL, PP and FTSL measurements. Then, the model describing these three physical processes and its validation are discussed. It will be shown that this model is able to anticipate the overall behavior of the three processes in various experimental conditions. Finally, combined OSL/RL experiments are presented in order to validate the practical potential of our integrated approach to design a temperature-independent dosimeter.

**3.1. TL measurements**

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** TL measurements performed on a Gd<sup>3+</sup>-doped silica sample, in the range RT – 650 K. (a) wavelength-resolved TL glow curves and (b) distribution of the trap levels estimated by the partial-cleaning initial rise method</figcaption></figure>
The TL measurements performed on a Gd³⁺-doped silica sample, from room temperature (RT) to 650 K, are presented in Fig. 1(a). It can be noticed that the main emission signal occurs at 314 nm, which is attributed to the RC, namely Gd³⁺ ions [22,24]. The shape of the glow curve is characterized by one main peak around 330 K and a shoulder around 450 K. The peak at 330 K is always present in the TL glow curve of silica-based materials and probably associated to Si-ODC defects [29,30]. The shoulder around 450 K is induced by the RE doping [31]. Figure 1(b) shows a continuous distribution of the trap levels between 0.8 and 1.4 eV, as estimated by the initial rise method from RT to 500 K [29]. It should be noted that these energy levels will be used as fixed parameters in the following model. These parameters are shown in Supplement 1 Table S1.

## 3.2. RL and FTSL measurements

In Fig. 2(a), we have plotted the normalized RL spectra acquired at different temperatures ranging from 193 to 353 K under a dose rate of 250 mGy/s. The measurement temperature was limited to 353 K in order to preserve the acrylate fiber coating. RL spectra are characterized by a narrow emission band, peaking at 314 nm, indicating that the RC responsible for the RL signal during irradiation is the Gd³⁺ ion. Indeed, this emission is attributed to the radiative transition between the ⁶P₇/₂ and ⁸S₇/₂ levels [22]. Furthermore, this sample keeps the same emission band over the investigated temperature range, as demonstrated by the excellent superposition of the different normalized spectra.

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Normalized RL spectra of the Gd³⁺-doped silica rod obtained (a) at different temperatures ranging from 193 K to 353 K, under 250 mGy/s dose rate and (b) for different dose rates at RT.</figcaption></figure>

In Fig. 2(b), the independence of the spectral shape on the dose rate is also shown. The fact that the spectral shape remained unchanged for each dose rate and each temperature suggests that the local silica environment surrounding the Gd³⁺ ions did not undergo major changes and that, to a great extent, the RC remained Gd³⁺ ion.

Figure 3 illustrates the time-dependent dynamics of the light emission, which begins with the RL signal. This one was obtained by exposing a Gd³⁺-doped sample to X-rays under a dose rate of 500 mGy/s for 300 s (accumulated dose of 150 Gy) and at different irradiation temperatures (*T*<sub>irr</sub>) ranging from 153 K to 353 K. Each RL curve (in red) is then followed, when the irradiation was stopped, by a phosphorescence (PP) signal for 180 s (in blue) at the same temperature *T*<sub>irr</sub> and then, when increasing temperature linearly up to 353 K, by FTSL signal (in pink). Two behaviors can be observed in the RL signal dynamics, regardless of the dose rate and of temperature conditions. The first behavior occurs when the irradiation is turned on, and is characterized by an initial abrupt jump from the background level, followed by a
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Signal response of the Gd<sup>3+</sup>-doped silica for a X-ray dose rate of 500 mGy/s and at different irradiation temperatures (*T*<sub>irr</sub>) ranging from 153 K to 353 K. Each RL curve is followed by phosphorescence and then, by FTSL from the *T*<sub>irr</sub> to 353 K with a heating rate of 5 K/min, starting from (a) 153 K, (b) 193 K, (c) 233 K, (d) 273 K, (e) 313 K, (f) 353 K.</figcaption></figure>
slow rise of the RL signal, which tends to a pseudo-plateau [32,33]. The second behavior was observed when the irradiation had been turned off: after a rapid decrease of the optical signal, this one underwent a monotonic and slow decrease over several minutes, consisting in the PP phenomenon. A most original observation lay in the FTSL signal, which appeared upon heating the sample from the initial measurement temperature ($T_{irr}$) to 353 K. On one hand, the slow dynamics of the RL signal, together with the occurrence of PP, have already been identified as the signature of shallow and intermediate traps in the bandgap of the silica matrix [32]. On the other hand, the TL phenomenon is classically attributed to the charge carrier release from deeper traps. We have calculated that, at the lowest irradiation temperature of 153 K, the integral of this FTSL signal added to the PP one ($2.29 \times 10^6$ counts) is almost equal to that of the RL signal ($2.37 \times 10^6$ counts). This result indicates that the number of deeply trapped carriers (FTSL + PP) is comparable to the recombined ones (RL).

In Fig. 4, we have plotted the evolution of the integrated RL signal (over 300 s) alone (in red on Fig. 3) as a function of X-ray dose for different irradiation temperatures. The RL signal linearly increases against the dose for all these temperatures. However, the RL intensity increases at higher irradiation temperature by a factor almost equal to 2 in comparison with the lowest temperature. This factor may be explained the quasi-equality of the integrated RL signal (over 300 s) and the PP + FTSL one at $T_{irr}$= 153 K as mentioned above (Fig. 3). Indeed, when the RL was performed at $T_{irr}$= 353 K, the integrated signal involved the contribution of all carriers, including the ones trapped at lower $T_{irr}$. The linear behaviour of the RL signal as a function of the dose is highly desirable for dosimetry applications and is a common feature that has been reported in various materials, such as glasses or crystals [22,34–36]. Unfortunately, the temperature dependence of the sensitivity might complicate the use of the sensors through the need of calibration.

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Integrated RL response (over 300 s) of the Gd$^{3+}$-doped silica versus X-ray dose at different irradiation temperatures ranging from 153 K to 353 K.</figcaption></figure>

In Fig. 5(a), the entire integrated signal $I_{sum}$, comprising RL, PP and FTSL (red, blue and pink on Fig. 3), is represented as a function of irradiation temperature. This shows that, considering the measurement uncertainty, $I_{sum}$ does not depend on temperature, but only on the dose. The latter has been estimated to 7% for the dose measurement and to 6% for the integrated signals. To underline this temperature-independence, in Fig. 5(b), $I_{sum}$ is plotted as a function of the dose for different irradiation temperatures. It can be stressed that this integrated signal $I_{sum}$ remains linear with X-ray dose, but is completely temperature-independent.
<figure><img src="image_8.png" /><figcaption>Fig. 5. Sum of the integrated RL (over 300 s), PP and FTSL signals (a) as a function of irradiation temperature for different doses and (b) as a function of the dose for different temperatures.</figcaption></figure>

### 3.3. Model

To simulate our experimental data, we used a mathematical model describing the electron-hole pairs generation, the carrier charge trapping-detrapping and the electron-hole recombination [26,32,33]. These processes are schematically represented in Supplement 1 Fig. S2. In the case of this study, the charge carriers trapped in the bandgap can be released by thermal activation, which has been considered in the model.

In this model, the RIA was neglected. The RIA measurements were considered at 325 nm to avoid the contribution of RL signal at 314 nm during the irradiation. As the RIA increases with time during the 300 s of irradiation (Fig. 6), the RIA mean values at 325 nm over the 300 s irradiation at 153 K and 353 K were estimated to 0.935 dB and 0.364 dB, respectively leading to optical losses of 19% and 8% for a 1 cm-length sample. This latter value is in relative agreement with the data given at room temperature on Gd-doped silica optical fibers fabricated using surface plasma chemical deposition [37]. It should be stressed that the effect of this RIA on the RL signal should be corrected due to the different path lengths followed by the light emitted homogeneously inside the whole volume of the rod. Indeed, the light emitted from one end of the rod experiences the longest pathway, while the one coming from the other rod extremity undergoes no attenuation due to RIA. When evaluating these geometric effects, a factor 2 is to be applied to the RL losses. Hence, we have estimated that the maximal power losses caused during the 300 s irradiation was about 9.5% at 153 K and 4% at 353 K. These values are in the same order of magnitude as the RL measurement uncertainties, which justifies that the RIA is not considered in the model.

The set of coupled differential equations describing the processes presented in Fig. S2, is as follows:

$$ \frac{dn_c}{dt} = X - \sum_{i=1}^{k} n_c(N_i - n_i)A_{ei} + \sum_{i=1}^{k} n_i s_i \exp\left(\frac{-E_i}{k_B T}\right) - n_c A_r m \quad (1) $$

$$ \frac{dn_i}{dt} = n_c(N_i - n_i)A_{ei} - n_i s_i \exp\left(\frac{-E_i}{k_B T}\right) \quad (i = 1, \dots, k) \quad (2) $$

$$ \frac{dm_v}{dt} = X - m_v(M - m)A_h \quad (3) $$

$$ \frac{dm}{dt} = m_v(M - m)A_h - n_c A_r m \quad (4) $$

$$ I = n_c A_r m \quad (5) $$
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Real-time RIA at 325 nm during irradiation under a dose-rate of 0.5 Gy(SiO₂)/s at two different temperatures: 153 K and 353 K.</figcaption></figure>

It should be stressed that electron traps are usually chosen to describe the emission processes of rare-earth ions such as Ce³⁺ [38]. These equations express the time variation of: (1) the electron concentration in the conduction band (CB), (2) the electron concentration in the iᵗʰ trap, (3) the hole concentration in the valence band (VB), (4) the hole concentration in the RC and (5) the emission intensity.

The differential equations set (1)–(5) was numerically solved using the Matlab software package. It should be noted that the number of unknowns is higher than the number of equations. Hence, a least square method was implemented in order to optimize the transition coefficients (A<sub>ei</sub>, A<sub>r</sub> and A<sub>h</sub>) and the trap concentrations N<sub>i</sub>, in order to reduce the number of unknowns, so that it corresponds to the number of equations [32,33].

The simulation includes three steps: the first one takes place during irradiation time (t<sub>RL</sub>), where the temperature T is constant and the electron-hole production rate X is proportional to the dose rate. The second stage is phosphorescence (during t<sub>PP</sub>), which occurs once the irradiation is stopped. During this step, the temperature is kept constant but the carrier production rate X is equal to zero. The last step corresponds to the fibered thermo-stimulated luminescence (FTSL), during which X is still equal to zero but the temperature T is increased according to a linear function T = T<sub>irr</sub> + βt, where T<sub>irr</sub> is the initial irradiation temperature, t is time and β (in K/s) is the heating rate. All the parameter values employed and adjusted in Eq. (1) to (5) have been compiled in Table S1 provided in *Supplement 1*.

In this study, 50 trap levels were used to reproduce a good modeling. It should be noticed that this number of traps is the minimal one to correctly describe the experiment. The actual number of traps is probably much higher in the silica matrix, but some of them do not play any role in the luminescence processes and 50 seems to be the better compromise to keep a reasonable number of the calculation parameters involved in the model. The values of these parameters have been found by different methods. Some of them were experimentally obtained using thermoluminescence measurements and the initial rise method, such as the energy depths E<sub>i</sub> and the frequency factors s. The RC concentration M was estimated using electron probe microanalysis (EPMA) as the Gd³⁺ concentration. More details on the calculation of these parameters can be found in our previous work [32,33]. It should be noted that these values remain unchanged for all dose rates, all irradiation and treatment temperatures.
3.4. *Simulation results*

Figure 7 presents the simulation results of the time-dependent emission signal (RL followed by PP and FTSL) from the irradiation temperature up to 353 K. The curves have been normalized to the maximum value of the RL signal. The numerical simulations satisfactorily reproduce the experimental data both during irradiation (RL) and after the end of irradiation (PP + FTSL). This reproduction of the experimental results has been checked for all other temperatures and for all doses. Most importantly, this good agreement was obtained by using a unique set of parameters.

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Measured and simulated RL + PP + FTSL signals under X-rays for a dose rate of 500 mGy/s at temperatures of 153 K (a) and 193 K (b). The model uses 50 trap levels ranging from 0.34 to 1.3 eV below conduction band (CB) and one RC.</figcaption></figure>

Figure 8 represents, for a given temperature, the concentration of the trapped electrons $n_i$ as a function of the trap energy level. Each curve results from the simulations, giving $n_i$ at the end of irradiation (at 300 s), following Eq. (2), for a dose of 150 Gy. When the temperature increases, it is clearly observed that the concentration of the shallowest trapped electrons decreases. This decrease consequently leads to an increase in the number of electrons available for recombination during the irradiation step (RL) while less electrons are trapped before the heating phase (FTSL). Consequently, the RL signal increases while the FTSL signal decreases as a function of $T_{irr}$. These two phenomena compensate each other, leading to the constant value of $I_{sum}$ versus temperature for a given dose in Fig. 5(a). It is also important to note that, for trap depth energies higher than 1 eV, the electron concentration apparently increases with the irradiation temperature. This phenomenon is explained by the stability of the corresponding trap levels, which act as a charge carrier reservoir for the successive irradiation runs. Moreover, the retrapping effect was also considered in the model.

Figure 9(a) compares the theoretical and experimental integrated intensities of the RL for a dose of 150 Gy, at different temperatures ranging from 153 to 353 K. In the same conditions, Fig. 9(b) reports the theoretical and experimental comparison of the sum of integrated PP and FTSL signals. The intensities have been normalized to allow a direct comparison between simulation and experimental results, showing a good agreement. It should be stressed that such a comparison has been successfully performed for all tested doses. Figure 9(c) shows the entire simulated signal $I_{sum}$ compared to the experimental one for a dose rate of 500 mGy/s (accumulated dose of 150 Gy), again stressing the good agreement between modelling and experiment. Furthermore, the model, as well as experiment (Fig. 5(a)), proves that $I_{sum}$ is temperature-independent. Figure 9(d) depicts the simulated $I_{sum}$ as a function of the dose at all the temperatures, clearly showing the universal linear behavior, which has already been experimentally obtained (Fig. 5(b)).
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Trapped electron concentration as a function of trap energy level, resulting from the simulation at different $T_{irr}$ and at the end of irradiation (at 300 s) with a dose rate of 500 mGy/s (accumulated dose of 150 Gy).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Comparison of experimental and simulated integrated signal intensities (a) of the RL, (b) of the PP + FTSL, and (c) of the RL + PP + FTSL ($I_{sum}$) for a dose rate of 500 mGy/s (accumulated dose of 150 Gy) at different temperatures from 153 to 353 K. These intensities have been normalized to their maximum values. (d) Representation of the simulated $I_{sum}$ as a function of the dose at irradiation temperatures.</figcaption></figure>
The above-presented results were obtained according to a given protocol, including precise times of irradiation and phosphorescence, as well as a given heating rate. However, the concept of considering the three physical processes (RL + PP + FTSL) in the total emission intensity consistently leads to an athermic *I*<sub>sum</sub> parameter for a given dose, and thus to a temperature-independent dosimeter.

### 3.5. Simulation prediction

In order to check the validity of this model, two specific situations, described in Fig. 10, have been predicted by using the same set of parameters, as previously determined. Then, the corresponding measurements have been performed. Figure 10 presents the simulation results of the RL signal at five different dose rates (50, 100, 150, 200 and 250 mGy/s, corresponding to accumulated doses of 15, 30, 45, 60 and 75 Gy, respectively), followed by a heating step, after a phosphorescence period of 180 seconds. The heating rates are either 0.6 K/s for the measurement of FTSL ranging from 193 K to 233 K (Fig. 10(a)), or 0.06 K/s for the measurement of FTSL ranging from 233 K to 273 K (Fig. 10(b)).

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Comparison of simulation prediction with the measured RL signal at five different dose rates (50, 100, 150, 200 and 250 mGy/s, corresponding to accumulated doses of 15, 30, 45, 60 and 75 Gy, respectively), followed by heating (FTSL) from 193 K to 233 K with a rate of 0.6 K/s (a) and from 233 K to 273 K with a rate of 0.06 K/s (b). The irradiation and phosphorescence times were 300 and 180 s, respectively.</figcaption></figure>

The model makes use of a sufficient number of trap levels and considers re-trapping and charge accumulation between the different X-ray runs. Hence, the RL and FTSL signals predicted by the simulations and the ones obtained by the experiment are in excellent agreement. This agreement between the predictions and the experimental observations consolidates the relevance of the simulations accuracy, suggesting that the mechanisms and the parameters taken into account faithfully describe the Gd<sup>3+</sup>-doped silica system. Moreover, it demonstrates the usefulness of our simulation model as a reliable prediction tool.

### 3.6. Combined RL and OSL approach as a practical prospect

The Optically Stimulated Luminescence (OSL) mechanism plays the same role as the heating in the FTSL process, consisting in electron detrapping through the supply of optical or thermal energy, respectively. According to the above results, it is possible to predict that the simultaneous measurement of RL and OSL signals would lead to the real-time evaluation of the dose rate as well as of the accumulated dose, independently of the measurement temperature. However, to efficiently release all the trapped electrons, as it is the case with the heating method (FTSL),
it is necessary to use a broadband stimulation laser in OSL, for instance a supercontinuum source, which has been made, as shown in Supplement 1 Fig. S1. Figure 11 presents the resulting evolution of the combined signal, that simultaneously includes RL and OSL processes, as a function of the measurement temperature ranging from 153 K to 353 K for a dose rate of 500 mGy/s. As expected, the measured signal does not depend on temperature, within the experimental uncertainty, estimated to 6%.

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Combined RL and OSL averaged signal over 300 s as a function of the measurement temperature for a dose rate of 500 mGy/s.</figcaption></figure>

**4. Conclusion**

In summary, we have developed an experimental fibered device allowing the study of three fundamental optical processes (RL, PP and FTSL) within glassy silica materials doped with $Gd^{3+}$. This approach yields precise dose measurements, independently of both dose rate and temperature, for cumulated dose at least up to 300 Gy with the tested material and as far as the RIA plays no role on the light collection. This paves the way for robust dosimetry that is adaptable to various environmental conditions.

The model developed in this paper is able to explain the obtained experimental results. Furthermore, this model also predicts specific situations, which was experimentally validated by varying dose rate, irradiation temperature and heating rate. In addition, this modelling explains that the temperature independence of the integrated intensities of the three fundamental processes results from the thermal detrapping of charge carriers. In the case where the RIA impact is not negligible, which is out of the scope of this study, the model should be adapted to take it into consideration.

This concept, based on a confrontation between theoretical and experimental data, opens vast perspectives for the design of fiber optic dosimeters adapted to environments where irradiation conditions fluctuate (dose rate and temperature). Finally, we have also shown that, by replacing FTSL with OSL, such a temperature-independent dosimeter is able to evaluate the accumulated dose in real time and with an increased flexibility of use, constituting a significant advance in the field of optical dosimetry.

**Funding.** Agence Nationale de la Recherche (ANR-20-CE19-0024, ANR-11-LABX-0007); Ministère de l'Enseignement supérieur, de la Recherche et de l'Innovation (Contrat de Plan Etat-Region (CPER) WaveTech@HdF); Conseil Régional Hauts-de-France (Contrat de Plan Etat-Region (CPER) WaveTech@HdF); Lille European Metropolis (MEL) (Contrat de Plan Etat-Region (CPER) WaveTech@HdF); Institute of Physics of the French National Centre for Scientific
Research (CNRS) (Contrat de Plan Etat-Region (CPER) WaveTech@HdF); European Regional Development Fund (Contrat de Plan Etat-Region (CPER) WaveTech@HdF).

**Acknowledgments.** This work was also supported by the IRCICA Institute and the FiberTech Lille platform of the University of Lille.

**Disclosures.** The authors declare that there are no conflicts of interest related to this article.

**Data availability.** Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

**Supplemental document.** See Supplement 1 for supporting content.

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