# Overview of laser imprinted refractive index changes and related thermal stability in mid-infrared optical glasses

Julien Ari, Yao Heng, Maxime Cavillon, Martin Bernier, Marc Dussauze, Matthieu Lancry

► To cite this version:

Julien Ari, Yao Heng, Maxime Cavillon, Martin Bernier, Marc Dussauze, et al. Overview of laser imprinted refractive index changes and related thermal stability in mid-infrared optical glasses. Optical Materials, 2025, 163, pp.116985. 10.1016/j.optmat.2025.116985. hal-05381573

HAL Id: hal-05381573

https://hal.science/hal-05381573v1

Submitted on 25 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Overview of laser imprinted refractive index changes and related thermal stability in mid-infrared optical glasses

Julien Ari<fnref n="1" />, Yao Heng<fnref n="1" />,<fnref n="2" />, Maxime Cavillon<fnref n="1" />,*, Martin Bernier<fnref n="3" />, Marc Dussauze<fnref n="4" />, Matthieu Lancry<fnref n="1" />

## Abstract:

Various glass compositions adapted to mid-infrared (heavy metal oxide, fluoride and chalcogenide glasses) have been irradiated by femtosecond laser and their refractive index variations were characterized as a function of the laser pulse energy. Their thermal stability using isochronal annealing conditions were studied in order to determine their erasure temperatures. The measured variations are compared to the values obtained in the literature for a broad range of glass candidates. Additional chalcogenide glasses studied in this article (e.g. GeSbS and 75GeS₂-15In₂S₃-10CsCl) present very high refractive index variations (up to 5.5·10⁻<fnref n="2" />), almost 3 times the maximum value reported in heavy metal oxide glasses (2·10⁻<fnref n="2" />, Corning 9754) or SiO₂, bringing interest for mid-infrared optical devices. Nevertheless, they can be limited by their relatively low thermal stability, since the refractive index variations fully erase around their glass transition temperatures (typ. 200-300 °C for chalcogenides studied herein).

## I. Introduction

The SWaP problem (reduction of Size, Weight and Power) is an important challenge today in infrared imaging applications for civilians (domotics, smartphone, automobile) but also security and military applications (vehicles steering, survey, weapons guidance, unmasking, countermeasure identification) <fnref n="1" />, <fnref n="2" />. In embedded optics, reducing the size, mass and power of systems while maintaining their quality is crucial to integrate them into ever-smaller carriers (optronic gimbals, micro-drones, etc.). In order to simplify an optical system and to keep high image quality, optical designers have to find new degrees of freedom in their designs. Several ways are thus explored including freeform optics <fnref n="1" />, GRIN (gradient index) optics <fnref n="2" /> and metasurfaces <fnref n="3" />. From this view, fs laser direct writing (FLDW) is a powerful technique to induce local transformations to create compact, low weight and miniaturized freeform optical components in IR materials. FLDW has been employed to induce local controllable and sizeable transformations in various materials including chalcogenide glasses (ChG), oxide-based glasses and crystals such as sapphire <fnref n="4" />⁻⁷. More specifically, ChG are known to be excellent materials for mid-infrared (mid-IR) applications ⁸⁻¹¹. They exhibit large nonlinear effects, high refractive indices and wide ranges of transparencies (up to 28 µm) in the infrared compared to oxide-based glasses because of the low phonon energy induced by the heavy chalcogen elements ¹²⁻¹⁴. However, this is at the expense of drawbacks such as return loss of 2.2 - 2.5 dB per facet when introduced into a photonic circuit and quite high bulk index-induced loss. Alternative glasses like germanates and fluorides are currently one of the best available materials, introducing a return loss of only 1.3 and 0.9 dB, respectively, for wavelengths up to 6 µm ¹⁵.

<footnote n="1">¹ Institut de Chimie Moléculaire et des Matériaux d'Orsay (ICMMO), Université Paris-Saclay, CNRS, 91405 Orsay, France</footnote>

<footnote n="2">² Department of Physics, Shanghai University, Shanghai 200444, China</footnote>

<footnote n="3">³ Centre d'Optique, Photonique et Laser (COPL), Université Laval, 2375 rue de la Terrasse, Québec (Québec) G1V0A6, Canada</footnote>

<footnote n="4">⁴ Institut des Sciences Moléculaires, UMR 5255, Université de Bordeaux, 351 cours de la Libération, Talence Cedex 33405, France</footnote>

<footnote>*maxime.cavillon@universite-paris-saclay.fr</footnote>
One key aspect of laser induced modifications is the ability to increase the glass refractive index in 3D, to make waveguides-based structures. Several publications have proved the ability to imprint self-organized periodic structures, gratings and waveguides using a femtosecond (fs) laser in $ChG^{16-19}$, and demonstrated potential applications such as high density optical data storage, lab-on-chip, lasers or gradient index lenses$^{20-24}$. On the latter, sulfide based glasses are commonly used as they offer a good transparency window to avoid two photons absorption depending on the laser wavelength$^{25}$. In particular, Ge-based $ChG$ are known to show a strong nonlinear effect after irradiation, demonstrating their potential for integrated waveguides. Among published results, some high index changes around $5 \cdot 10^{-2}$ were reported in $GeS_2$ based chalcogenide$^{26, 27}$, which is above the value obtain in silica (up to $2.2 \cdot 10^{-2}$)$^{28-30}$. Recent work has also push forward the limits of Fluoride glasses by engineering specific glass composition allowing to induce refractive index changes exceeding $2 \cdot 10^{-2}$$^{31, 32}$.

Thermal stability of these fs laser assisted modifications is another key parameter to investigate since i) $ChG$ and Fluoride glasses exhibit relatively low glass transition temperatures and the refractive index changes can subsequently relax at few 100s of °C, and ii) it is a mandatory information for optics in harsh environment or temperature sensors written in these glasses, based for instance on Bragg gratings, Fabry-Pérot or scattering based technologies. For example, early results of fiber Bragg gratings aging in $As_2S_3$ have already been performed using isothermal annealing at 100 °C$^{33, 34}$. Moreover, the thermal stability of fs laser-induced transformations in $ChG$ has not been extensively reviewed in the literature. Indeed, these transformations tend to be erased in silica-based glasses generally between 700-1400 °C and within few hours$^{35-39}$, which is strongly related to the viscosity and relaxation of the glass.

The two main objectives of this paper are to investigate the refractive index variations and their thermal stability upon fs laser irradiation in glasses adapted for mid-IR (typ. 2-8µm) applications, i.e., heavy metal oxide (HMO) glasses, fluoride glasses and $ChG$ (commercial and laboratory made glasses). In this view, the kinetics of refractive index modification inscribed by fs laser under varying laser pulse energy in HMO, fluorides and $ChG$ is monitored, and their thermal stability evaluated using isochronal annealing experiments. These overall results are then discussed in the light of the current state of the art.

## II. Experimental method

The samples investigated in this work are from three glass families dedicated to mid-IR spectral range: HMO, fluorides and $ChG$. The samples and their compositions investigated herein, either for refractive index variation ($\Delta n$) as a function of laser properties, or for phase shift variation as a function of temperature, are provided and summarized in Table I.

The first one corresponds to the HMO family, with two commercial samples: Corning 9754 and Schott SF10. Other HMO glasses are reported, including BGG, GGK, BGGK, BGGLaY1, BGGLAY2, and BGGLAY3. All the compositions are provided in mol% throughout this work. Detailed information is provided in$^{40, 41}$. The second family is a commercial fluoride glass, i.e., ZBLAN glass (ZFG bulk sample from Le Verre Fluoré). The third family is the $ChG$ one, with the samples $GeSbSNa-ANa0.5$, $GeSbSNa-BNa2$, $GeSbSNa-DNa2$, $GeS_2-In_2S_3-CsCl$, and $As_2S_3$. Details related to their synthesis are given in references$^{42, 43, 44}$ and$^{45}$. These three glass families are compared to the commercial $SiO_2$ (Infrasil301, Heraeus) which serves as a reference material mostly dedicated to near-IR applications but transparent up to 3.3 µm for ultralow OH concentration ($<8$ ppm) glasses.

The samples are irradiated using a fs laser 3D direct writing optical setup using a xyz computer-controlled stage as detailed in references$^{46, 47}$. Succinctly, a polarized 1030 nm fs-laser beam (Satsuma, Amplitude, Pessac, France) is focused using an aspherical lens (4 mm focal length) resulting in a 0.6 effective numerical aperture inside the glass sample. Pulse duration, repetition rate, and writing speed are fixed at respectively 800 fs, 100 kHz and 1 mm/s. The laser pulse energy, $E_p$, is varied between 0.001 µJ
and 2 µJ with an interval chosen as a function of the glass family. A linear polarization along the x-axis (defined by the plan of the laser compressor) is used to write either rectangles or disks while the movement (spiral with a 1 µm pitch) is a combination of displacements along two axes ⁴⁸. As a side note, only the ZBLAN glass was irradiated using slightly different conditions using an array of lines.

<table><caption>Table I. Samples investigated in this work.</caption><thead><tr><th>Family</th><th>Name</th><th>Composition (mol%)</th><th>Writing geometry</th><th>Δn measurement</th><th>Annealing of ΔΦ</th></tr></thead><tbody><tr><td rowspan="2">Silica glass</td><td>SiO<sub>2</sub></td><td>Commercial 100% SiO<sub>2</sub> (Suprasil CG, Heraeus)</td><td>Rectangle<sup>b</sup></td><td>-</td><td>From Ref. ³⁵</td></tr><tr><td>9754</td><td>Commercial (Corning)</td><td>Disk<sup>a</sup> (from Ref. ⁴⁶)</td><td></td><td>This work, 0,5 μJ</td></tr><tr><td rowspan="8">HMO glasses</td><td>SF10</td><td>Commercial (Schott)</td><td>Disk<sup>a</sup> (from Ref. ⁴⁶)</td><td></td><td></td></tr><tr><td>BGG</td><td>65GeO<sub>2</sub>-15Ga<sub>2</sub>O<sub>3</sub>-20BaO</td><td>Rectangle<sup>b</sup></td><td></td><td></td></tr><tr><td>BGGK</td><td>30Ga<sub>2</sub>O<sub>3</sub>-35GeO<sub>2</sub>-24BaO-11K<sub>2</sub>O</td><td>Rectangle<sup>b</sup></td><td></td><td></td></tr><tr><td>GGK</td><td>25Ga<sub>2</sub>O<sub>3</sub>-50GeO<sub>2</sub>-25K<sub>2</sub>O</td><td>Rectangle<sup>b</sup></td><td>This work</td><td>-</td></tr><tr><td>BGGLaY1</td><td>21Ga<sub>2</sub>O<sub>3</sub>-43GeO<sub>2</sub>-24BaO-6La<sub>2</sub>O<sub>3</sub>-6Y<sub>2</sub>O<sub>3</sub></td><td>Rectangle<sup>b</sup></td><td></td><td>-</td></tr><tr><td>BGGLaY2</td><td>15Ga<sub>2</sub>O<sub>3</sub>-60GeO<sub>2</sub>-13BaO-6La<sub>2</sub>O<sub>3</sub>-6Y<sub>2</sub>O<sub>3</sub></td><td>Rectangle<sup>b</sup></td><td></td><td>-</td></tr><tr><td>BGGLaY3</td><td>28Ga<sub>2</sub>O<sub>3</sub>-37GeO<sub>2</sub>-23BaO-6La<sub>2</sub>O<sub>3</sub>-6Y<sub>2</sub>O<sub>3</sub></td><td>Rectangle<sup>b</sup></td><td></td><td>-</td></tr><tr><td>Fluoride glass</td><td>ZBLAN</td><td>(ZFG bulk sample, Le Verre Fluoré)</td><td>Fiber Bragg gratings</td><td>From Ref. ⁴⁹</td><td>This work</td></tr><tr><td rowspan="5">ChG</td><td>GeSbSNa-ANa0.5</td><td>99.5(Ge<sub>25</sub>Sb<sub>10</sub>S<sub>65</sub>)-0.5Na</td><td>Disk<sup>a</sup> (this work)</td><td>This work</td><td>-</td></tr><tr><td>GeSbSNa-BNa2</td><td>98(Ge<sub>22.5</sub>Sb<sub>10</sub>S<sub>67.5</sub>)-2Na</td><td>Disk<sup>a</sup> (this work)</td><td></td><td></td></tr><tr><td>GeSbSNa-DNa2</td><td>98(Ge<sub>17.5</sub>Sb<sub>10</sub>S<sub>72.5</sub>)-2Na</td><td>Disk<sup>a</sup> (this work)</td><td></td><td></td></tr><tr><td>GeS<sub>2</sub>-In<sub>2</sub>S<sub>3</sub>-CsCl</td><td>75GeS<sub>2</sub>-15In<sub>2</sub>S<sub>3</sub>-10CsCl</td><td>Disk<sup>a</sup> (from Ref. ⁴⁶)</td><td></td><td>This work, 0,2 μJ</td></tr><tr><td>As<sub>2</sub>S<sub>3</sub></td><td>As<sub>2</sub>S<sub>3</sub></td><td>Disk<sup>a</sup> (this work)</td><td></td><td></td></tr></tbody></table>

After fs-laser irradiation, 30 min isochronal step annealing is performed by increasing the temperature from room temperature (RT) up to approximately 1.2T<sub>g</sub> (T<sub>g</sub> being the glass transition temperature) for the samples indicated in Table I (last column). Optical microscopy (using an Olympus BX51) was employed to characterize the samples after each annealing step (natural light and transmission mode conditions).

Refractive index variations are retrieved from quantitative phase microscopy (QPM) measurements and the optical thickness of the modified areas along z axis, i.e., the laser propagation direction. QPM analysis is performed at a wavelength around 750 nm with a 20x microscope objective attached to a piezoelectric stage. Each phase shift expressed in radians is extracted by solving the intensity transport equation from 3 optical images made at the focal point and +/- 3 µm defocus (i.e. within depth of field of the chosen objective). In addition, the depth of field of the microscope objective used for QPM measurements should match as much as possible the thickness of the index changed structure, noted Z<sub>object</sub>. Consequently, we employed a 0.15 low NA objective combined to a well-chosen width a of the inscribed objects (at least 15 µm). Indeed, as modeled in Ref ⁵⁰, there is a saturation behavior for the phase shift when the measured object becomes excessively thick, typ. when Z<sub>object</sub> > a²/λ. When the diameter of the object is small, this saturation occurs faster in accordance with diffraction theory. For instance, in our conditions, the saturation of the measured phase shift for an object exhibiting a width of 15 µm occurs at around Z<sub>object</sub>~300 µm when performing the measurement at λ = 750 nm. In the worst situation (for longer objects) the effective optical phase will be underestimated thus leading to an underestimated value of the photo-induced refractive index changes.

In the following since thickness Z<sub>object</sub> of the index structures can change a lot as a function of the glass and the energy utilized, the thickness was then measured for each glass and for each energy. For example,

<footnote>a Disks of 100 µm diameter are inscribed at 300 µm depth in the glass using a spiral trajectory with a 1 µm step.</footnote>

<footnote>b Rectangles 100 x 15 µm² composed of a series of lines with a 1 µm step inscribed at 300 µm depth.</footnote>
ChG are highly nonlinear, and this could induces self-focusing effect and filamentation, which will give a longer index structure thickness e.g. the longest we measured in this work was about 200 µm in GeSbS. The length of the photowritten index change structure generally depends on the pulse energy. The higher energy the longer the index structure length (thickness), especially in highly nonlinear glasses such as ChG. Moreover, the phase shifts exploited in this work are all taken at or near the center of the written disks, where the phase shift is the highest. Then by combining optical thickness measurements of the laser written modifications to the phase shift, we could estimate the refractive index changes. Indeed, the phase shift $\Delta\phi$ (in radians) is related to the refractive index variation ($\Delta n$) through the following relationship: $\Delta n = \frac{\lambda\Delta\phi}{2\pi L}$ where $\lambda$ and $L$ are the probe wavelength and the length of the index modified region, respectively.

### III. **Results**

#### III.1. Refractive index variation and comparison with the literature

Refractive index variations as a function of the laser pulse energy for a selection of both HMO and ChG are presented in Figure 1. Apart from the pulses energy all others laser parameters were kept fixed (1030 nm, 350 fs, 100 kHz, 0.6 NA, 1 mm/s) to provide a meaningful comparison of these writing kinetics.

<figure><img src="image_2.png" /><figcaption>Figure 1. Refractive index variations for the HMO and ChG investigated in this study as a function of pulse energy $E_p$. The laser writing conditions are provided in the experimental section. Here we focus our attention on Type I modification regime for glasses showing positive index changes.</figcaption></figure>

Regarding the HMO glasses, the commercial Corning 9754 (a calcium alumino-germanate glass) shows a significantly higher refractive index variation compared to the other oxide glasses. Indeed, the refractive index variation of this glass increases relatively fast, from 0 to ~1.2 $10^{-2}$ between 0 and 0.2 µJ. Then it is relatively constant between 0.2 µJ and 1.9 µJ. The maximum at plateau reaches a refractive index
variation of ~1.35 10⁻². In contrast, SF10 glass shows a maximum of 4.5 10⁻³ at 0.6 µJ, then stagnates around 3 10⁻³ between 0.8µJ and 2 µJ. All the other HMO compositions, mostly some barium gallo-germanate glasses (i.e. GGK, BGGK, BGGLaY1, BGGLaY2 and BGGLaY3), show quite similar values with respect to the measurement's uncertainty. Refractive index changes are slowly increasing between 0 to 0.8 µJ, then stays relatively constant from 0.8 to 2 µJ. Typical refractive index variations can reach up to 3 10⁻³ as for BGGK glass.

For the ChG, Ge-Sb-S-Na system (ANa0.5, BNa2 and DNa2) presents the same trend with a fast increase of the refractive index variations from 0 to 0.06 µJ, reaching the maximums of 4.9 10⁻², 4.2 10⁻² and 3 10⁻² for respectively ANa0.5, BNa2 and DNa2 glass compositions. Then the refractive index variations are slowly decreasing when increasing the pulse energy between 0.07 µJ to 0.9 µJ, reaching values around 3.2 10⁻² ±2 10⁻³. 75GeS₂-15In₂S₃-10CsCl glass shows the same tendency as the refractive index variation is always increasing, up to 2.7 10⁻² for the maximum laser energy tested in this study. Overall, the highest refractive index variation measured in all ChG in Figure 1 is at 4.9 10⁻² for ANa0.5 irradiated at 0.06 µJ. This value is almost four times higher than the maximum refractive index variation observed in the HMO glass Corning 9754 (1.35 10⁻²).

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Summary of the refractive index change for a series of optical glasses as a function their refractive index. Color code: blue = silica ³⁰ and silicate glasses ⁵¹⁻⁵³; purple = HMO glasses ⁴¹, ⁴⁶, ⁵⁴⁻⁵⁷; green = fluoride glasses ³¹, ³², ⁴⁹, ⁵⁴, ⁵⁸, and red = ChG ²², ⁴⁶, ⁵⁴, ⁵⁹⁻⁶². Both refractive index values and fs-induced index variations extracted from the literature can be found in the corresponding reference. The star and square symbols correspond respectively to the data from this work and from the literature.</figcaption></figure>

For all the tested optical materials, the easiest way to generate diffractive optical elements, optical waveguides or graded index lenses is a positive refractive index core surrounded by unmodified bulk glass, but some chemical compositions are leading to negative index changes with respect to the unmodified bulk material. Many works on femtosecond laser interaction with these mid-IR transparent glasses have been
done in bulk materials for waveguides or Bragg gratings fabrication. An overview of the best results showing
high refractive index variations as a function of their respective refractive index is presented in Figure 2 for
the main glass families namely HMO (in purple), fluorides (in green) and ChG (in red). For sake of
comparison, some classical near-IR silicate glasses (in blue) such as SiO₂, ULE and Eagle 2000, and BK7
are also presented.

Low refractive index materials such as commercial fluoride glasses (e.g. ZBLAN, IZSBGC) may look like an ideal platform for the fabrication of low-loss optical waveguides and fiber Bragg gratings whereas they tend to exhibit a quite low positive or negative refractive index changes (typ. < ±10⁻³) ⁴⁹, ⁵⁴, ⁵⁸, ⁶³⁻⁶⁶ which results in weak mode confinement and large bending losses for such applications (especially for long wavelengths). However a recent work ³² has demonstrated that in contrast to pure ZBLAN, a strong positive index changes of close to 6-8.10⁻³ can be induced in tailored zirconium/hafnium (Z/HBLAN) glasses through femtosecond laser direct writing. The best result was obtained when the HfF₄:ZrF₄ ratio is close to 0.5. As a result, waveguides owing a high NA that support a well confined 3.1 µm wavelength mode have been successfully fabricated. Last results in an optimized ZBLAN based and optimized composition, leads to record index changes exceeding 2.10⁻² allowing waveguides owing low propagation losses around 0.21 dB/cm at 1,62 µm and single mode up to 3,5 µm ³¹.

In contrast, ChG own quite large refractive indices, typ. between 2,1 and 2,5 in Figure 2. They also exhibit a larger transparency window in the IR, while exhibiting much larger optical nonlinearities (as opposed to fluoride glasses) that are interesting for many optical applications. From the point of view of index change amplitudes, while Gallium Lanthanum Sulfide (named GLS) own a positive response under fs-laser irradiation, the glass systems providing the best results were obtained in 75GeS₂-15Ga₂S₃-10CsCl and Ge-Sb-S ones. For the latter one, adjusting the S/Ge ratio and by adding Na to the Ge–Sb–S glass system helps to tailor the surface electrical potential ⁶⁷ but also the refractive index of the fs-written modifications. In this study, for fixed laser conditions, we observe a higher positive index difference for lower S/Ge ratio (e.g. ANa0.5 with 2.6 ratio compared to DNa2 with 4.2 ratio). However, for slightly different conditions, similar compositions, namely Ge₂₅Sb₁₀S₆₅ or Ge₂₃Sb₇S₇₀, were shown to have either positive or negative index depending on the deposited energy ²². Indeed it should be mentioned that many ChG own negative index changes mostly attributed to photo-expansion or porosification such as As₂S₃ ⁶⁸⁻⁷⁰ or Ge-As-S glasses, which can be exploited to imprint depressed cladding waveguides as reviewed in ⁵⁴.

Finally, HMO glasses such as Schott IRG-2 and SF10, and Corning 9754 offer a large scalability while having an intermediate refractive index (typ. from 1.6 up to 1.89) and a significant nonlinearity coupled to improve mechanical robustness compared to fluorides or ChG. Apart from IRG-2 (a lead silicate glass) most HMO glasses exhibit positive index changes. Following that point of view, barium gallermanate (BGG) glass family exhibits very scalable multifunctional properties: superior mechanical strength, chemical stability, a high rare-earth ions solubility, a wide optical transparency extended up to ~6 µm in the mid-IR as well as a high positive index change (typ. up to 15.10⁻³). Recently, this glass family was largely investigated by introducing various dopants: Yb³⁺ for optical amplification, Ta⁵⁺ used to increase the bulk refractive index ⁷¹, Gd³⁺-containing glass for Faraday magneto-optic effects thanks to its high Verdet constant and ZnO for its excellent piezoelectric properties.

### III.2. *Thermal stability of refractive index variation*

Figure 3 presents the normalized phase shift (proportional to changes in refractive index) obtained from the QPM measurements as a function of the annealing temperature for a selection of glasses tested in this study. The normalization is performed with respect to the initial value at room temperature and enables a direct comparison between the samples. The annealing corresponds to 30 minutes isochronal steps performed in air under similar experimental conditions for all samples, with QPM measurements taken at
room temperature after each thermal treatment. As shown in Figure 3, all samples exhibit a monotonous decrease in phase shift with increasing annealing temperature. It is worth noting that various underlying contributions may arise from point defects, stress fields, densification/expansion, or any type of refractive index changes, each having its own thermal stability curve³⁵.

The black stars represent the stability curve of Type-I modifications written in SiO₂ glass ⁷² while different kinds of modifications like Type-II ⁷² or Type-III ⁷³, ⁷⁴ can lead to even higher thermal stability. This glass has been extensively studied in the literature and is included here for sake of comparison. Its thermal stability is related to point defects that are bleached at relatively low temperatures (below 600 °C), while the remaining part is attributed to permanent densification and its associated stress field that typically relaxes within the 0.5Tₐ-0.8Tₐ temperature interval (Tₐ = glass annealing temperature at which log(η, Pa.s) = 12, η(T) being the glass viscosity), depending on the thermal treatment conditions ⁷⁵. A similar behavior can be met usually in most oxide glasses including HMO such as BGG and Corning 9754. They require significantly high temperatures to reduce the phase shift, needing 650 °C and 700 °C respectively to fully erase the phase shift. On the other hand, the phase shift for the fluoride and ChG decreases rapidly when increasing temperature due to their relatively low glass transition temperatures compared to oxide glasses. Indeed, the phase shift drops to zero between 250 °C and 400 °C for most of these glasses tested in this study. This apparent single-component decay indicates that most of the measured index changes are related to permanent volume changes, whether due to densification or photo-expansion, depending on the chemical composition.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Normalized phase shift as a function of annealing temperature for the selected glasses (under isochronal annealing experiments). T<sub>g</sub> or T<sub>a</sub> are also provided for each glass, which were retrieved from commercial datasheets for SiO<sub>2</sub> Suprasil CG, 9754, SF10, and from the literature for BGG<sup>40</sup>, ZBLAN<sup>76</sup>, As<sub>2</sub>S<sub>3</sub><sup>77</sup>, 75GeS<sub>2</sub>-15In<sub>2</sub>S<sub>3</sub>-10CsCl<sup>78,79</sup>, GeSbSNa-BNa2 and GeSbSNa-DNa2<sup>80</sup>.</figcaption></figure>
By placing $T_g$ or $T_a$ on the upper x-axis in Figure 3, we note that the full erasure of the phase shift is correlated to these values (as a first order approximation). Generally, the various contributions of the fs-induced index changes will anneal at different temperatures. However, the upper limit must be associated to structural relaxation, which is related to the shear stress glass relaxation time $\tau$. Here $\tau = \eta(T)/G$, where $\eta(T)$ is the glass viscosity and G is the shear modulus. It is worth pointing out that in glass G does not change significantly until temperatures in the order of $1.5T_g$<sup>81, 82</sup>. Therefore, we can consider that the normalized phase shift $\Delta\varphi_{norm}$ erasure over time and temperature, takes the equation $\Delta\varphi_{norm} = \Delta\varphi_{t,T}/\Delta\varphi_{t=0,T=RT}$. Considering that $\Delta\varphi_{norm}$ takes a first order chemical reaction in the form $\frac{d\Phi}{dt} = -k\Phi$, with the rate constant as $k = 1/\tau$, one gets after integration $\Delta\varphi_{norm} = \exp(-\frac{G}{\eta}t)$. Using the experimental data, G values and viscosity laws (through Vogel-Fulcher-Tammann equation), we can reproduce the experimental thermal treatment and observe if the predicted erasure temperature (<10% of $\Delta\varphi_{norm}$ remaining) corresponds to the experimental one. This was performed for $As_2S_3$, 9754, and $SiO_2$ for which G values and VFT laws are available in technical datasheets and<sup>83</sup> for $As_2S_3$. This gives erasure temperatures of 175 °C, 700 °C, 1050 °C respectively (close to the 225 °C, 700 °C, and 975 °C experimental ones). This simple expression of $\Delta\varphi_{norm}$ as a function of time and temperature highlights the link between the glass viscosity and the refractive index changes erasure. However, outside the scope of this work, more advanced models consider the disordered nature of a glass and its distributed nature through a distribution function of activation energies. An interested reader is redirected to the references<sup>84, 85</sup>.

#### IV. Discussion

The plurality of the refractive index values obtained above arises from a wide range of parameters, including glass compositions and laser parameters / inscription geometry employed. Nevertheless, some principal trends related to the variation of the glass refractive index during laser irradiation as a function of glass compositions can be discussed and rationalized below.

In most samples, refractive index changes depend on the laser-induced specific volume changes but also on additional contributions such as point defects formation and elemental migration. Speaking about defects that impact the glass polarizability and whose refractive index contribution, $\Delta n_{KK}$(defects), can be described through the well-known Kramers-Kronig relation, and it usually remains quite limited to a few $10^{-4}$<sup>86</sup>. Instead, the relation between the volume changes (densification or expansion depending on glass composition) and refractive index changes can be often described by a linear relation from an experimental point of view<sup>87</sup>. This suggests that the main origin of the observed refractive index changes can be mostly attributed to specific volume variations which can arise from multiple sources namely fast quenching, high pressures, bond breaking accumulation or even a combination of these factors. This results in a glass restructuring and eventually coordination changes at the origin of the observed densification or expansion. Note that the occurrence of such permanent volume changes can be investigated by directly measuring the topography after stress relaxation<sup>88</sup> (e.g., by cleaving the bulk sample or also in thin films).

The correlation between refractive index changes and permanent volume changes $\frac{\Delta V}{V}$ is given by the derivation of the Lorentz-Lorenz expression, which is deduced from the Clausius-Mossotti relation. For low deformations: $\frac{\Delta V}{V} = Tr(\varepsilon^p)$ where $\varepsilon^p$ is the so-called permanent strain tensor. In addition, if specific volume changes occur locally, then a stress field $\sigma$ is necessarily developed due to the elastic response $\varepsilon^e$ of the material in and out of the irradiated zone. Note that this stress field is strongly dependent on the writing geometry (lines, spirals, multipass or multiple layers, etc.). The application of such elastic strain will result directly in a modification of the index ellipsoid that can be written using photo-elastic relations. Consequently, $\Delta n$ can be written as follows<sup>89</sup>:
$$ \Delta n_{aa} = -\frac{n^3}{2} \left[ p_{11} \varepsilon_{aa}^e + p_{12} \left( \varepsilon_{\beta\beta}^e + \varepsilon_{\gamma\gamma}^e \right) \right] - \frac{(n^2-1)(n^2+2)}{6n} \cdot (1-\Omega) \cdot \mathrm{Tr}(\varepsilon^p) \quad (\text{Eq.1}) $$

where $\Omega$ is the ratio between the relative change in molecular polarizability to the relative change in the specific volume, $p_{11}$ and $p_{12}$ are the photo-elastic coefficients. Note that other contributions due to point defects or chemical migration can also be added to the global contribution of the refractive index change. From a spectral perspective, all these effects are associated with optical changes. Changes in the population of point defects (e.g., trapped holes or electrons) lead to UV-Vis spectral changes due to phenomena such as photodarkening (e.g., in Ge-As-S glass system ⁹⁰) or photobleaching. Volume changes naturally affect bond angles, which influence the vibrational signature and the glass electronic structure. This results in a shift of both the IR multiphonon absorption edge and the apparent electronic bandgap, known as the Urbach tail.

For example, in SiO₂, densification leads to a low-frequency shift of the main vibrational bands, as for example Si-O-Si asymmetric stretching as review in ⁹¹, while the optical bandgap undergoes only minor changes, typically less than 5-10% in densified silica ⁹². This outcome can generally be applied to most HMO glasses such as 9754 and BGG, where Raman spectra reveal significant densification of the glass network.

In ChG such as Ge-As-S ⁹³, ⁹⁴ or Ge-As-Se ⁹⁵, the structural rigidity significantly influences the photo-structural processes, primarily related to photo-expansion. According to the literature, ChG with lower average coordination numbers (e.g., Ge₆.₆₆As₆.₆₆Se₈₆.₆₆) exhibit strong photosensitivity in the sense it creates a high negative refractive index modification under femtosecond laser irradiation ⁹⁶. This phenomenon is usually associated with a bandgap shift towards lower energy, attributed to an increase in structural intermediate-range disorder ⁹⁷⁻⁹⁹. However, when the glass network is ideally coordinated or even constrained (e.g., Ge₂₀As₂₀Se₆₀), structural rearrangements become more difficult despite the partial release of structural constraints due to laser irradiation, such as the formation of point defects. Consequently, the imprinted volume expansion (and thus index changes) is reduced or even null while it is still possible to photo-induced point defects centers resulting a positive index changes contribution. Finally, mostly positive index changes (typ. up to 2.10⁻²) were reported in Ge₃₃As₁₂Se₅₅ ⁶¹, ⁶².

Conversely, many glasses like GeS₂, GeS₃, and GeS₄-based glasses exhibit high positive index changes. For example, in 80GeS₂-20Ga₂S₃ glass ¹⁰⁰, positive index changes can be induced at low energy (so called Type I regime), whereas a higher energy can also create voids (thus negative index changes). In this case, femtosecond laser irradiation increases the population of Ga and/or Ge triclusters and decreases both the fraction of S₃Ga-GaS₃ ethane-like units and the edge- and corner-sharing GeS₄/₂ tetrahedra. Positive refractive index changes are closely related to an increase in these mixed triclusters due to their efficient packing and hence higher density.

In Ge-Sb-S glasses, such as Ge₂₃Sb₇S₇₀ ²², the laser-irradiated zone (within Type I regime) shows stronger rigidity i.e., more Ge-S-Ge and less S-S homopolar bonds, with fewer isolated GeS₄/₂ groups compared to the pristine material. This has been attributed to fast resolidification, which causes different network connectivity after femtosecond laser irradiation, and this is likely what happen in the GeSbSNa glasses studied in this work. At higher energy, negative index changes was also observed in Ge₂₃Sb₇S₇₀, which can be attributed to the formation of nanovoids or some kind of porosification ²².

As a summary, the final modification whether photo-expansion or densification, heavily depends on the initial rigidity of the glass network. This rigidity is related not only to stoichiometry, average coordination number, number of homopolar bonds but also to the glass thermal history. Indeed recent work indicates that initial glass fictive temperature coupled to the laser heating-cooling profile itself (e.g. single pulse regime or repetitive regime versus pulse-to-pulse heat accumulation or even the pulse duration ²²) may
impact both the amplitude and the sign of the imprinted index changes. So major efforts have still to be made to rationalize the fs-laser effects especially in chalcogenide glasses.

## V. Conclusion

In this work, we have compiled a series of refractive index variations in silicate, HMO, fluoride and ChG, in addition to the one investigated. Various mid-IR transparent glasses have been successfully irradiated by femtosecond laser, and their refractive index variations investigated as function of laser pulse energy and the annealing temperature. Usually, maximum achievable index changes scale up from Fluoride to HMO glasses and then to ChG. ChG studied in this article are found to have the highest refractive index variation, but it is quite dispersed depending on chemical composition. Indeed, high refractive index variations were measured up to 4.9 $10^{-2}$ for GeSbS-ANa0.5. This relatively stable value as a function of the laser pulse energy between 0.03 µJ and 0.9 µJ is almost four times higher than the maximum variation observed in HMO glasses (i.e. Corning 9754 measured at $1.35 \ 10^{-2}$). Compared to the literature, GeSbSNa glasses show refractive index variations in a similar order of magnitude of 75GeS₂-15In₂S₃-10CsCl glass, which is one of the highest refractive index variations reported in the literature i.e. $5.5 \ 10^{-2}$, to the best of our knowledge. Thermal stability of these refractive index variations is connected to the structural relaxation of the glass. The associated phase shift starts to decrease at relatively low temperatures (typically around 100 °C) for the GeSbSNa glasses and reaches zero around 300 °C, thus limiting the potential temperatures dependent applications. Glass annealing or transition temperatures are close to the experimental erasure temperatures, which confirms the influence of the glass viscosity regarding the thermal stability of fs imprinted index changes for the glasses studied in this article.

## VI. Author declarations

### Conflict of interest

The authors have no conflicts to disclose.

### Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

### Acknowledgement

Funding Agences: Agence Nationale de la Recherche (ANR), Project REFRACTEMP ANR-22-CE08-0001-01 Project FLAG-IR ANR-18-CE08-0004-01, and project OPTOPHAB ANR-24-CE51-4059-01.

## VII. References

1. J. P. Rolland, M. A. Davies, T. J. Suleski, C. Evans, A. Bauer, J. C. Lambropoulos and K. Falaggis, *Optica* **8** (2), 161-176 (2021).

2. D. H. Lippman, N. S. Kochan, T. Yang, G. R. Schmidt, J. L. Bentley and D. T. Moore, *Optics Express* **29** (22), 36997-37012 (2021).

3. J. Hu, S. Bandyopadhyay, Y.-h. Liu and L.-y. Shao, *Frontiers in Physics* **8**, 586087 (2021).

4. B. W. McMillen, (2012).
5. D. L. Coq, J. Carcreff and P. Masselin, presented at the Proc.SPIE, 2019 (unpublished).

6. J. Choi and C. Schwarz, International Journal of Applied Glass Science **11** (3), 480-490 (2020).

7. W. Yang, C. Corbari, P. G. Kazansky and K. Sakaguchi, presented at the 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, 2007 (unpublished).

8. V. Nazabal, E. Baudet, R. Chahal, F. Starecki, C. Boussard, F. Verger, P. Nìmec, H. Lhermite, J. Charrier, J. L. Adam, B. Bureau, F. Colas, E. Rinnert, M. L. D. I. Chapelle, T. Toury, K. Michel, C. Compère, S. Marre, Y. Garaboss, P. Kern, C. Damico, J. Troles, G. Martin and R. Stoian, presented at the 2014 IEEE Photonics Society Summer Topical Meeting Series, 2014 (unpublished).

9. B. J. Eggleton, B. Luther-Davies and K. Richardson, Nature Photonics **5** (3), 141-148 (2011).

10. B. Bruno, B. Catherine, C. Shuo, C. Radwan, A. Marie-Laure, N. Virginie, S. Olivier, L. Olivier, L. Pierre, M. Valerie, D. Jean-Louis, C. Patrice, T. Hugues, C. Frédéric, Q. Lionel, A. Jean-Luc and L. Jacques, Optical Engineering **53** (2), 027101 (2014).

11. S. Jasbinder Singh, L. B. Shaw, E. B. Lynda, B. T. David and D. A. Ishwar, presented at the Proc.SPIE, 1999 (unpublished).

12. X. Zhang, B. Bureau, P. Lucas, C. Boussard-Pledel and J. Lucas, Chemistry – A European Journal **14** (2), 432-442 (2008).

13. J.-L. Adam and X. Zhang, (Woodhead Publishing, Oxford, 2014).

14. S. Serna, H. Lin, C. Alonso-Ramos, A. Yadav, X. Le Roux, K. Richardson, E. Cassan, N. Dubreuil, J. Hu and L. Vivien, Photon. Res. **6** (5), B37-B42 (2018).

15. A. Arriola, S. Gross, M. Ams, T. Gretzinger, D. Le Coq, R. Wang, H. Ebendorff-Heidepriem, J. Sanghera, S. Bayya and L. Shaw, Optical Materials Express **7** (3), 698-711 (2017).

16. Q. Du, Y. Huang, J. Li, D. Kita, J. Michon, H. Lin, L. Li, S. Novak, K. Richardson, W. Zhang and J. Hu, Optics Letters **41** (13), 3090-3093 (2016).

17. W. Hu, M. Kilinc, W. Gebremichael, C. Dorrer and J. Qiao, Optical Materials Express **12** (1), 360-373 (2022).

18. P. Masselin, E. Bychkov and D. Le Coq, IEEE Photonics Technology Letters **30** (24), 2123-2126 (2018).

19. S. H. Messaddeq, R. Vallée, P. Soucy, M. Bernier, M. El-Amraoui and Y. Messaddeq, Optics Express **20** (28), 29882-29889 (2012).

20. O. Efimov, L. Glebov, K. Richardson, E. Van Stryland, T. Cardinal, S. Park, M. Couzi and J. Brunéel, Optical Materials **17** (3), 379-386 (2001).

21. P. Delullier, G. Druart, F. De La Barrière, L. Calvez and M. Lancry, in *Applied Sciences* (2022), Vol. 12.

22. G. Torun, A. Yadav, K. A. Richardson and Y. Bellouard, Frontiers in Physics **10** (2022).

23. S. Juodkazis, A. V. Rode, E. G. Gamaly, S. Matsuo and H. Misawa, Applied Physics B **77** (2), 361-368 (2003).

24. M. Bernier, V. Fortin, N. Caron, M. El-Amraoui, Y. Messaddeq and R. Vallée, Optics Letters **38** (2), 127-129 (2013).

25. K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu and A. Jha, Applied Physics Letters **79** (13), 1939-1941 (2001).

26. P. Delullier, L. Calvez, G. Druart, F. De La Barrière, C. Humbert, B. Poumellec and M. Lancry, Applied Sciences **12** (17), 8813 (2022).

27. L. Petit, N. Carlie, T. Anderson, J. Choi, M. Richardson and K. C. Richardson, IEEE Journal of Selected Topics in Quantum Electronics **14** (5), 1323-1334 (2008).

28. K. Davis, K. Miura, N. Sugimoto and K. Hirao, Opt. Lett **21** (21), 1729-1731 (1996).

29. M. Hughes, W. Yang and D. Hewak, Applied Physics Letters **90** (13) (2007).

30. S. M. Eaton, M. L. Ng, R. Osellame and P. R. Herman, Journal of Non-Crystalline Solids (2010).
31. T. T. Fernandez, Y. Hwang, H. Mahmodi, D. Otten, L. Plenecassagne, S. Cozic, S. Gross, I. Kabakova, M. Withford and M. Poulain, Optics Express **32** (24), 42938-42950 (2024).

32. T. T. Fernandez, B. Johnston, S. Gross, S. Cozic, M. Poulain, H. Mahmodi, I. Kabakova, M. Withford and A. Fuerbach, Scientific Reports **12** (1), 14674 (2022).

33. M. Bernier, M. El-Amraoui, J. F. Couillard, Y. Messaddeq and R. Vallée, Optics Letters **37** (18), 3900-3902 (2012).

34. M. Bernier, L. Talbot, T. Boilard, L.-P. Pleau, A. Fuerbach, G. Bharathan and M. Ams, in *Mid-Infrared Fiber Photonics*, edited by S. Jackson, M. Bernier and R. Vallée (Woodhead Publishing, 2022), pp. 179-231.

35. Y. Wang, M. Cavillon, N. Ollier, B. Poumellec and M. Lancry, physica status solidi (a) **218** (12), 2100023 (2021).

36. M. Cavillon, Y. Wang, B. Poumellec, F. Brisset and M. Lancry, Applied Physics A **126** (11), 876 (2020).

37. S.-E. Wei, Y. Wang, H. Yao, M. Cavillon, B. Poumellec, G.-D. Peng and M. Lancry, Sensors **20** (3), 762 (2020).

38. Y. Wang, S. Wei, M. R. Cicconi, Y. Tsuji, M. Shimizu, Y. Shimotsuma, K. Miura, G.-D. Peng, D. R. Neuville, B. Poumellec and M. Lancry, Journal of the American Ceramic Society **103** (8), 4286-4294 (2020).

39. M. Cavillon, M. Lancry, B. Poumellec, Y. Wang, J. Canning, K. Cook, T. Hawkins, P. Dragic and J. Ballato, Journal of Physics: Photonics **1** (4), 042001 (2019).

40. H. Yao, R. Zaiter, M. Cavillon, P. Delullier, B. Lu, T. Cardinal, Y. Dai, B. Poumellec and M. Lancry, Ceramics International **48** (21), 31363-31369 (2022).

41. H. Yao, R. Zaiter, M. Cavillon, B. Sapaly, F. Calzavara, P. Delullier, T. Cardinal, Y. Dai, B. Poumellec and M. Lancry, Ceramics International **47** (24), 34235-34241 (2021).

42. M. El-Amraoui, G. Gadret, J. C. Jules, J. Fatome, C. Fortier, F. Désévédavy, I. Skripatchev, Y. Messaddeq, J. Troles, L. Brilland, W. Gao, T. Suzuki, Y. Ohishi and F. Smektala, Optics Express **18** (25), 26655-26665 (2010).

43. S. Mao, H. Tao, X. Zhao and G. Dong, Journal of Non-Crystalline Solids **354** (12), 1298-1302 (2008).

44. Y. Ledemi, B. Bureau, L. Calvez, M. L. Floch, M. Rozé, C. Lin, X. H. Zhang, M. Allix, G. Matzen and Y. Messaddeq, The Journal of Physical Chemistry B **113** (44), 14574-14580 (2009).

45. L. Karam, R. Alvarado, F. Calzavara, R. Dahmani, M. Kang, C. Blanco, F. Adamietz, K. A. Richardson and M. Dussauze, Optical Materials Express **12** (5), 1920-1931 (2022).

46. P. Delullier, L. Calvez, G. Druart, F. De La Barrière, C. Humbert, B. Poumellec and M. Lancry, in *Applied Sciences* (2022), Vol. 12.

47. J. Cao, B. Poumellec, F. Brisset, A.-L. Helbert and M. Lancry, J. Opt. Soc. Am. B **33** (4), 741-747 (2016).

48. R. Desmarchelier, M. Lancry, M. Gecevicius, M. Beresna, P. Kazansky and B. Poumellec, Applied Physics Letters **107** (18) (2015).

49. J.-P. Bérubé, M. Bernier and R. Vallée, Optical Materials Express **3** (5), 598-611 (2013).

50. A. Abou Khalil, W. Gebremichael, Y. Petit and L. Canioni, Optics Communications **485**, 126731 (2021).

51. D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach and M. J. Withford, Journal of Raman Spectroscopy **42** (4), 715-718 (2011).

52. S. Eaton, H. Zhang, M. Ng, J. Li, W. Chen, S. Ho and P. Herman, Optics Express **16** (13), 9443-9458 (2008).

53. H. Tomohiro and T. Shuhei, presented at the Proc.SPIE, 2011 (unpublished).

54. A. Arriola, S. Gross, M. Ams, T. Gretzinger, D. Le Coq, R. P. Wang, H. Ebendorff-Heidepriem, J. Sanghera, S. Bayya, L. B. Shaw, M. Ireland, P. Tuthill and M. J. Withford, Optical Materials Express **7** (3), 698-711 (2017).
55. J. Bai, X. Long, X. Liu, G. Huo, W. Zhao, R. Stoian, R. Hui and G. Cheng, Appl. Opt. **52** (30), 7288-7294 (2013).

56. M. Khalid, G. Y. Chen, H. Ebendorff-Heidepreim and D. G. Lancaster, Scientific Reports **11** (1), 10742 (2021).

57. T. Guérineau, A. Dupont, J. Lapointe, R. Vallée and Y. Messaddeq, Optical Materials Express **13**, 2036 (2023).

58. S. Gross, D. G. Lancaster, H. Ebendorff-Heidepriem, T. M. Monro, A. Fuerbach and M. J. Withford, Optical Materials Express **3** (5), 574-583 (2013).

59. S. H. Messaddeq, J. P. Bérubé, M. Bernier, I. Skripachev, R. Vallée and Y. Messaddeq, Optics Express **20** (3), 2824-2831 (2012).

60. J. P. Bérubé, S. H. Messaddeq, M. Bernier, I. Skripachev, Y. Messaddeq and R. Vallée, Optics Express **22** (21), 26103-26116 (2014).

61. H. L. Butcher, D. G. MacLachlan, D. Lee, R. R. Thomson and D. Weidmann, Optics Express **26** (8), 10930-10943 (2018).

62. W. Hu, W. Gebremichael, J. Fernandes, M. Kilinc, C. Dorrer and J. Qiao, Optics Express **31** (12), 18949-18963 (2023).

63. M. Heck, S. Nolte, A. Tünnermann, R. Vallée and M. Bernier, Optics Letters **43** (9), 1994-1997 (2018).

64. K. Miura, J. Qiu, T. Mitsuyu and K. Hirao, Journal of Non-Crystalline Solids **256-257**, 212-219 (1999).

65. A. Dupont, J. Lapointe, S. Pouliot and R. Vallée, Optics Letters **46** (16), 3925-3928 (2021).

66. D. G. Lancaster, S. Gross, H. Ebendorff-Heidepriem, K. Kuan, T. M. Monro, M. Ams, A. Fuerbach and M. J. Withford, Optics Letters **36** (9), 1587-1589 (2011).

67. R. Alvarado, L. Karam, R. Dahmani, A. Lepicard, F. Calzavara, A. Piarristeguy, A. Pradel, T. Cardinal, F. Adamietz, E. Fargin, M. Chazot, K. Richardson, L. Vellutini and M. Dussauze, The Journal of Physical Chemistry C **124** (42), 23150-23157 (2020).

68. O. Caulier, D. L. Coq, E. Bychkov and P. Masselin, Optics Letters **38** (20), 4212-4215 (2013).

69. P. Masselin, D. Le Coq and E. Bychkov, Optical Materials **33** (6), 872-876 (2011).

70. D. Le Coq, P. Masselin, C. Przygodski and E. Bychkov, Journal of Non-Crystalline Solids **355** (37), 1832-1835 (2009).

71. G. Poirier, M. Dussauze, V. Rodriguez, F. Adamietz, L. Karam, T. Cardinal and E. Fargin, The Journal of Physical Chemistry C **123** (43), 26528-26535 (2019).

72. D. Grobnic, C. W. Smelser, S. J. Mihailov and R. B. Walker, Measurement Science and Technology **17** (5), 1009-1013 (2006).

73. A. Martinez, I. Y. Khrushchev and I. Bennion, Electronics Letters **41**, 176-178 (2005).

74. A. Lerner, T. Blanchet, R. Cotillard, M. Sosa, N. Roussel, G. Bouwmans and G. Laffont, presented at the European Workshop on Optical Fibre Sensors (EWOFS 2023), 2023 (unpublished).

75. Y. Wang, M. Cavillon, N. Ollier, B. Poumellec and M. Lancry, physica status solidi (a) **218** (12), 2100023 (2021).

76. F. Huang, X. Liu, L. Hu and D. Chen, Scientific Reports **4** (1), 5053 (2014).

77. P. Koštál, J. Shánělová and J. Málek, International Materials Reviews **65** (2), 63-101 (2020).

78. A. Brehault, L. Calvez, T. Pain, P. Adam, J. Rollin and X. H. Zhang, presented at the Proc.SPIE, 2014 (unpublished).

79. H. Tao, C. Lin, S. Chu, S. Mao, Y. Gong, X. Zhao, S. Wang and Q. Gong, Journal of Non-Crystalline Solids **354** (12), 1303-1307 (2008).

80. A. Lepicard, 2016.

81. J. A. Bucaro and H. D. Dardy, Journal of Applied Physics **45** (12), 5324-5329 (1974).

82. A. Polian, V.-T. Dung and P. Richet, Europhysics Letters **57** (3), 375 (2002).
83. P. Koštál, M. Včeláková and J. Málek, Journal of the American Ceramic Society **107** (2), 844-858 (2024).

84. Y. Wang, M. Lancry, M. Cavillon and B. Poumellec, Optics Letters **47** (5), 1242-1245 (2022).

85. B. Poumellec and M. Lancry, Fibers **3** (3), 206-252 (2015).

86. M. Lancry and B. Poumellec, Physics Reports-Review Section of Physics Letters **523** (4), 207-229 (2012).

87. C. W. Ponader, J. F. Schroeder and A. M. Streltsov, Journal of Applied Physics **103** (6), 063516 (2008).

88. N. F. Borrelli, C. Smith, D. C. Allan and T. P. Seward, J. Opt. Soc. Am. B **14** (7), 1606-1615 (1997).

89. M. Lancry, N. Groothoff, B. Poumellec and J. Canning, Applied Physics B: Lasers and Optics **94** (4), 589-597 (2009).

90. K. Tanaka, physica status solidi (b) **258** (8), 2100180 (2021).

91. M. Lancry, E. Régnier and B. Poumellec, Progress in Materials Science **57** (1), 63-94 (2012).

92. E. Güler, G. Uğur, Ş. Uğur and M. Güler, Chinese Journal of Physics **65**, 472-480 (2020).

93. M. Zhang, T. Li, Y. Yang, H. Tao, X. Zhang, X. Yuan and Z. Yang, Optical Materials Express **9** (2), 555-561 (2019).

94. C. D'Amico, C. Caillaud, P. K. Velpula, M. K. Bhuyan, M. Somayaji, J. P. Colombier, J. Troles, L. Calvez, V. Nazabal, A. Boukenter and R. Stoian, Optical Materials Express **6** (6), 1914-1928 (2016).

95. L. Zhu, D. Yang, L. Wang, J. Zeng, Q. Zhang, M. Xie, P. Zhang and S. Dai, Optical Materials **85**, 220-225 (2018).

96. L. Calvez, Z. Yang and P. Lucas, Journal of Physics D: Applied Physics **43** (44), 445401 (2010).

97. T. Shimizu, M. Kumeda, I. Watanabe and Y. Nakagaki, Solid State Communications **27** (3), 223-227 (1978).

98. G. Pfeiffer, M. A. Paesler and S. C. Agarwal, Journal of Non-Crystalline Solids **130** (2), 111-143 (1991).

99. R. A. Street, Solid State Communications **24** (5), 363-365 (1977).

100. P. Masselin, D. Le Coq, A. Cuisset and E. Bychkov, Optical Materials Express **2** (12), 1768-1775 (2012).