Pavel Loiko

Alain Braud

Lauren Guillemot

Jean-Louis Doualan

Abdelmjid Benayad

Patrice Camy

Cross-relaxation and ion clustering in Tm3+:CaF2 crystals

Keywords: calcium fluoride, thulium ions, cross-relaxation, ion clustering, luminescence

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INTRODUCTION

Cubic (fluorite-type) calcium fluoride (CaF2) crystals are well-known for fabrication of optical elements because of their good thermo-mechanical properties (thermal conductivity: κ ~9.7 W/(mK) for an undoped crystal), broad transparency range (0.13-10 μm) and low refractive index (n = 1.424 at ~2 μm). CaF2 crystals are also suitable for doping with trivalent rare-earth ions (RE 3+ ) for laser applications [START_REF] Druon | On Yb:CaF2 and Yb:SrF2: review of spectroscopic and thermal properties and their impact on femtosecond and high power laser performance[END_REF][START_REF] Camy | Tm 3+ :CaF2 for 1.9 μm laser operation[END_REF][START_REF] Labbe | The 2.8 μm laser properties of Er 3+ doped CaF2 crystals[END_REF]. They feature a strong RE 3+ ion clustering even at low doping concentrations about 0.1-1 at.% [START_REF] Petit | Spectroscopy of Yb 3+ :CaF2: from isolated centers to clusters[END_REF][START_REF] Renard | CaF2 doped with Tm 3+ : A cluster model[END_REF] resulting in broad and smooth spectral bands both in absorption and emission (the so-called glassy-like spectroscopic behavior). It is of interest for broadly tunable [START_REF] Lucca | Highpower tunable diode-pumped Yb 3+ :CaF2 laser[END_REF] and mode-locked [START_REF] Lucca | High-power diode-pumped Yb 3+ :CaF2 femtosecond laser[END_REF][START_REF] Friebel | Diode-pumped 99 fs Yb:CaF2 oscillator[END_REF] lasers. The good thermal properties of the host matrix allow for power scaling.

Thulium (Tm 3+ ) doped CaF2 crystals exhibit a broadband emission at ~1.9 μm due to the 3 F4 → 3 H6 electronic transition. Efficient Tm 3+ :CaF2 lasers were reported [START_REF] Camy | Tm 3+ :CaF2 for 1.9 μm laser operation[END_REF][START_REF] Liu | 1886-nm mode-locked and wavelength tunable Tm-doped CaF2 lasers[END_REF]. Camy et al. reported on a laser-pumped Tm:CaF2 laser delivering ~135 mW at 1887 nm with a slope efficiency of 41% and a laser threshold of only 68 mW [START_REF] Camy | Tm 3+ :CaF2 for 1.9 μm laser operation[END_REF]. Liu et al. reported on power scaling of a Tm:CaF2 laser under diode-pumping yielding 2.71 W with a higher slope efficiency of 70.1% [START_REF] Liu | 1886-nm mode-locked and wavelength tunable Tm-doped CaF2 lasers[END_REF]. The same group of authors demonstrated continuous wavelength tunability for this laser between 1.85 and 2.04 μm (189 nm broad) and mode-locked operation employing a SESAM. In the latter case, 15 ps-long pulses were obtained at a central wavelength of 1886.8 nm with a repetition rate of 96.35 MHz [START_REF] Liu | 1886-nm mode-locked and wavelength tunable Tm-doped CaF2 lasers[END_REF]. Thin films of Tm:CaF2 were grown [START_REF] Brasse | Liquid Phase Epitaxy growth of Tm 3+ -doped CaF2 thin-films based on LiF solvent[END_REF].

It was proven that the ion clustering determines the emission properties of Tm 3+ ions in CaF2 [START_REF] Renard | CaF2 doped with Tm 3+ : A cluster model[END_REF]. For low doping levels (0.01-0.1 at.%), the Tm 3+ ions are mostly isolated and they accommodate in sites with different symmetry depending on the charge compensation mechanism involving interstitial F -anions. For higher doping levels, ion clusters are formed. To prevent the clustering of active ions, the CaF2 crystals were codoped by Tm 3+ ions and optically passive "buffer" ions Ln 3+ such as Gd 3+ , Lu 3+ , La 3+ or Y 3+ [START_REF] Liu | Growth and lasing performance of a Tm,Y:CaF2 crystal[END_REF][START_REF] Zhang | High-efficiency 2 μm continuous-wave laser in laser diode-pumped Tm 3+ ,La 3+ :CaF2 single crystal[END_REF]. Laser operation with such codoped crystals was also demonstrated. Zhang et al. reported on a Tm,La:CaF2 laser delivering 4.27 W at 1921 nm with a slope efficiency of 67.8% [START_REF] Zhang | High-efficiency 2 μm continuous-wave laser in laser diode-pumped Tm 3+ ,La 3+ :CaF2 single crystal[END_REF].

A key spectroscopic process which determines the laser efficiency of ~1.9 μm Tm lasers is the cross-relaxation (CR) for adjacent Tm 3+ ions, 3 H4(Tm1) + 3 H6(Tm2) → 3 F4(Tm1) + 3 F4(Tm2), potentially leading to a pump quantum efficiency of 2 [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ∼80% slope efficiency[END_REF]. This means that after an excitation at ~0.8 μm (to the 3 H4 pump level), there can be up to 2 excited ions in the upper laser level ( 3 F4). CR in Tm 3+ -doped laser materials increases the laser slope efficiency and reduces the heat dissipation. Up to now, no detailed study of CR for Tm:CaF2 crystals was performed. *e-mail: pavel.loiko@ensicaen.fr

The aim of the present work is to study the cross-relaxation (and other energy-transfer processes, such as energy-transfer upconversion (ETU)) in Tm:CaF2 crystals accounting for the ion clustering. For this, we involve the spectroscopic model of distinct ion classes which was recently developed [START_REF] Loiko | Stochastic model of energy-transfer processes among rare-earth ions. Example of Al2O3:Tm 3+[END_REF].

EXPERIMENTAL RESULTS

For the spectroscopic studies, we grew a series of Tm 3+ :CaF2 crystals with the doping level ranging from 0.01 at.% to 7 at.%. The Tm:CaF2 crystals were grown using a conventional Bridgman technique with a homemade furnace. A mixture of high purity (4N) CaF2 and TmF3 powders was introduced in a graphite crucible. A good vacuum (<10 -5 mbar) was realized before introducing Ar and CF4 gases to avoid oxygen pollution. The furnace temperature was set to about 50 K higher than the melting point of CaF2. After soaking, the charge was thoroughly melted and the crystal growth was carried out with a rate of 2-4 mm/h. When the growth was finished, the crystal was cooled down to room temperature (RT, 293 K) within 48

Absorption and luminescence

The RT absorption spectra of Tm 3+ :CaF2 crystals containing predominantly isolated ions (0.05 at.% Tm) and ion clusters (1.5 at.% and 4.5 at.% Tm) are shown in Fig. 1. It is known that in Tm 3+ -doped CaF2 crystals with very low doping levels, the active ions are distributed over three types of sites with the symmetry C3v (trigonal), C4v (tetragonal) or Oh (cubic). The particular symmetry depends on the charge compensation mechanism (as trivalent Tm 3+ ions are replacing the divalent Ca 2+ ones). The latter is provided by an interstitial fluorine anion (Fi -). Here, we do not consider the possible charge compensation by oxygen (O 2-) or univalent alkali metal cations (Na + , K + ) leading to other types of sites. As a result, the absorption spectra of the 0.05 at.% Tm 3+ :CaF2 crystal represent a superposition of sharp absorption lines of Tm 3+ ions in all three sites. For high doping levels, the Tm 3+ ions are mostly arranged in clusters leading to smooth and broad spectral bands. There is no significant change in the absorption spectra of 1.5 at.% Tm and 4.5 at.% Tm-doped crystals, except of the 3 H6 → 3 H5 transition. The small changes may reflect the transition from simple clusters (dimers, trimers) to large agglomerates of active ions. For the 3 H6 → 3 H4 pump transition, the maximum absorption cross-section σabs is 0.46×10 -20 cm 2 at 766.2 nm and the full width at half maximum (FWHM) of the absorption band is 13.2 nm (for the 4.5 at.% Tm doping). For the 0.05 at.% Tm doping, the peak σabs value is much lower, 0.17×10 -20 cm 2 at ~768 nm.

The evolution of RT luminescence spectra for the 3 H4 → 3 H6 (at ~0.8 μm) and 3 F4 → 3 H6 (at ~1.9 μm) transitions in emission was studied for a broad range of Tm doping concentrations (0.01-7 at.%). This comparative study revealed a critical Tm concentration (0.5-0.7 at.%) for which a significant change in the shape of the emission bands is observed: the spectra become smooth and broad and they resemble to a great extent those for Tm 3+ -doped fluoride glasses. This is an indication of a change in the predominant ion coordination (a transition from isolated ions to clusters). Figure 2 shows such a comparison for the emission from the pump level ( 3 H4) at ~0.8 μm.

Figure 2. Normalized RT luminescence spectra of Tm 3+ :CaF2 crystals with different doping concentrations (the 3 H4 → 3 H6 transition), λexc = 769 nm (non-selective excitation).

Luminescence decay

We monitored the decay of Tm 3+ luminescence from the 3 H4 and 3 F4 multiplets for a broad range of Tm doping levels (0.01-7 at.%) in CaF2. Figure 3 shows the measured luminescence decay curves for the 3 H4 → 3 H6 transition in emission (at ~0.8 μm). For very low doping level (0.01 at.% Tm), the luminescence decay curve is close to a single-exponential one with a characteristic lifetime τlum of 3.55 ms. Despite the existence of several species contributing to this emission (namely, isolated Tm 3+ ions in various sites), the intrinsic lifetimes of the 3 H4 state for the C3v and C4v coordinated Tm 3+ ions in CaF2 are rather close: 3.03 ms and 3.59 ms, respectively (as determined in site-selective excitation experiments). With increasing Tm doping, the decay from the 3 H4 state becomes faster and the luminescence decay curves notably deviate from the single-exponential law. To explain this behavior, we used the model of spectroscopically distinct ion classes [START_REF] Loiko | Stochastic model of energy-transfer processes among rare-earth ions. Example of Al2O3:Tm 3+[END_REF]. A simplified scheme of Tm 3+ energy-levels was considered, Fig. 4. The populations of the Tm 3+ ground-state ( 3 H6) and two relevant excited-states ( 3 F4 and 3 H4) were monitored; the population of the intermediate 3 H5 excited-state was assumed to be almost zero as this state is depopulated by very efficient multi-phonon non-radiative (NR) relaxation. The states above 3 H4 were not taken into account. The following spectroscopic processes were considered: (i) radiative (R) decay from the 3 F4 and 3 H4 states, (ii) cross-relaxation (CR) 3 H4(Tm1) + 3 H6(Tm2) → 3 F4(Tm1) + 3 F4(Tm2), (iii) energy-transfer upconversion, 3 F4(Tm1) + 3 F4(Tm2) → 3 H6(Tm1) + 3 H4(Tm2) (ETU1) and 3 F4(Tm1) + 3 F4(Tm2) → 3 H6(Tm1) + 3 H5(Tm2) (ETU2), and (iv) energymigration (EM) to impurities leading to de-excitations from the 3 F4 and 3 H4 multiplets. We assumed the existence of two distinct ion classes: (a) isolated ions showing no energy-transfer processes (CR and ETU) and (b) ions with neighbors exhibiting both CR and ETU. The fraction of ions with neighbors f, the macroscopic rates of CR (WCR) and ETU (WETU1 and WETU2) and the 3 H4 level lifetime τ3 accounting for EM were used as free parameters of the fitting (for luminescence decay curves shown in Fig. 3). The model gives a satisfactory agreement with the experiment. Figure 4. The scheme of energy-levels of Tm 3+ ions (for a free-ion) showing relevant spectroscopic processes associated with the conventional pumping scheme (to the H4 state): Rradiative relaxation, NRmultiphonon non-radiative relaxation, CRcross-relaxation, ETUenergy-transfer upconversion, EMenergy-migration.

DISCUSSION

The results on the fraction of Tm 3+ ions with neighbors f are shown in Fig. 5. With increasing the Tm doping level, the fraction of isolated ions (1f) gradually decreases. The critical Tm doping level for which at least half of the active ions are clustered is only 0.7±0.1 at.%. This agrees well with our conclusion drawn from the measured luminescence spectra at ~0.8 μm. The dependence of f on the doping concentration was fitted using a statistical approach [START_REF] Loiko | Stochastic model of energy-transfer processes among rare-earth ions. Example of Al2O3:Tm 3+[END_REF][START_REF] Voron'ko | Effect of donor-donor and donor-acceptor interactions on the decay kinetics of the metastable state of Nd 3+ in crystals[END_REF]:

    , ! 1 . ! ! nm m mn n P p p m n m     (1)
Figure 5. Ion clustering in Tm 3+ :CaF2: fraction of ions with neighbors f, symbolsdata extracted from the modeling of the experimental luminescence decay curves using the rate-equation model of distinct ion classes, curvetheir fit using a statistical approach.

Here, Pm,n is the probability for occurrence of neighbor Tm 3+ ions in the first coordination sphere of the considered Tm 3+ ion, n is the coordination number (C.N.) by nearest-neighbor rare-earth sites, m is the actual number of Tm 3+ ions in the first coordination sphere (m = 0 corresponds to a single ion and m ≥ 1 -to an ion pair or cluster), and p = NTm/Nmax represents the relative doping concentration (Nmax is the maximum possible concentration). The expression for the fraction of ions with neighbors (m ≥ 1, not specifying the exact m number) is:

C.N. Tm max 1 [1 ( / )] . f N N    (2)
For calculation, we assume Nmax = 10 at.% and C.N. = 10 which gives a good agreement with the data obtained from the measured luminescence curves.

The model also yields the macroscopic rates WCR, WETU1 and WETU2 [in s -1 ], as shown in Fig. 6. The CR is Tm:CaF2 is much stronger than the ETU. WCR and WETU1( 2) show a quadratic dependence on the Tm doping concentration (NTm):

2 CR CR Tm , W C N  (3a) 2 ETU1(2) ETU1(2) Tm , W C N  (3b)
where CCR and CETU1( 2) are the concentration-independent microscopic energy-transfer parameters. CR in Tm 3+ :CaF2 is about one order of magnitude stronger than that in other well-known fluoride crystal, Tm 3+ :LiYF4 [START_REF] Loiko | Efficient Tm:LiYF4 lasers at 2.3 μm: Effect of energy-transfer upconversion[END_REF].

CONCLUSIONS

To conclude, we have quantified ion clustering (in terms of fraction of ions with neighbors) and CR and ETU energytransfer processes (in terms of macroscopic rates and microscopic concentration-independent parameters) in Tm 3+ -doped CaF2 crystals, for the first time, to the best of our knowledge. This information is of key importance for the design of Tm:CaF2 lasers operating on the 3 F4 → 3 H6 (~1.9 μm) and 3 H4 → 3 H5 (~2.3 μm [START_REF] Pinto | Tm 3+ :YLF laser continuously tunable between 2.20 and 2.46 μm[END_REF]) transitions. Indeed, for the ~1.9 μm lasers, quantification of CR is important to determine the possibility to reach high pump quantum efficiency of 2 for the upper laser level ( 3 F4) [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ∼80% slope efficiency[END_REF]. For the ~2.3 μm lasers which have not been demonstrated yet in Tm:CaF2, in contrast, CR is a detrimental effect as it quenches the lifetime of the upper laser level ( 3 H4). However, ETU1 in such lasers can play a key role in refilling the 3 H4 state leading to increased laser slope efficiency [START_REF] Loiko | Efficient Tm:LiYF4 lasers at 2.3 μm: Effect of energy-transfer upconversion[END_REF][START_REF] Guillemot | Close look on cubic Tm:KY3F10 crystal for highly efficient lasing on the 3 H4 → 3 H5 transition[END_REF]. The proposed spectroscopic model can be extended to describe the ion clustering in Tm 3+ ,Ln 3+ :CaF2 crystals codoped with "buffer" ions.

Figure 1 .

 1 Figure 1. RT absorption cross-section, σabs, spectra of Tm 3+ :CaF2 crystals with different Tm doping concentrations (0.05 at.%, 1.5 at.% and 4.5 at.%): transitions from the ground-state ( 3 H6) to the excited-states: (a) 3 F4, (b) 3 H5, (c) 3 H4 and 3 F2,3, and (d) 1 G4 and 1 D2.

Figure 3 .

 3 Figure 3. Luminescence decay curves from the 3 H4 Tm 3+ state in Tm 3+ :CaF2: blackexperimental data, redtheir fitting with the rate-equation model of distinct ion classes, λexc = 765 nm, λlum = 820 nm. Measured under ns pulse excitation.

Figure 6 .

 6 Figure 6. Energy-transfer processes in Tm 3+ :CaF2: macroscopic rates of cross-relaxation (CR) WCR and energy-transfer upconverison (ETU) WETU1(2), symbolsdata extracted from the modeling of the experimental luminescence decay curves using the rate-equation model of distinct ion classes, linestheir quadratic fits.

ACKNOWLEDGEMENTS

This work was supported by the Agence Nationale de la Recherche (ANR), SPLENDID2 Project; European Community funds FEDER; Normandie region, NOVAMAT Project.


Elena Gorohova

Ivan Venevtsev

Sergey Eron'ko

Liza Basyrova

Irina Alekseeva

Aleksander Khubetsov

Olga Dymshits

Aleksandr Zhilin

Pavel Loiko

Zinc Oxide Optical Ceramic Codoped with Er 3+ and Yb 3+ Ions

Zinc oxide (ZnO) is a well-known wide-bandgap semiconductor possessing a hexagonal wurtzite-type structure. In the past years, ZnO nanostructures of various shapes attracted a lot of attention for applications in UV emitters, scintillators, phosphors, etc. [1]. The absorption and emission properties of ZnO-based materials are related to defect states and can be further adjusted by doping with rare-earth ions RE 3+ due to efficient ZnO ↔ RE 3 + energy transfer. In the present work, we report on the fabrication, microstructure and spectroscopic properties of ZnO optical ceramics containing erbium (Er 3+ ) and ytterbium (Yb 3+ ) ions.

ZnO optical ceramic codoped with 0.6 wt% Er and 0.8 wt% Yb was prepared by uniaxial hot pressing of ZnO, Er 2 O 3 and Yb 2 O 3 commercial powders at 1180 °C in vacuum [START_REF] Peter | [END_REF]. The ceramic disk (Ф25 mm, thickness: 0.5 mm) had grey coloration, Fig. 1(a). The structure of ceramics (hexagonal, sp. gr. P6 3 mc, unit-cell parameters: a = 3.251 Å, c = 5.202 Å) was confirmed by XRD, Fig. 1(b). The XRD pattern also revealed the crystallization of Er 2 O 3 and Yb 2 O 3 phases with a cubuc bixbyite-type structure (sp. gr. Ia3¯, a = 10.545 Å and 10.441 Å, respectively), inset in Fig. 2(a). The average size of RE 2 O 3 crystals was about 75 nm. According to the EDX analysis, Fig. 2(c-e), apart from the stoichiometric RE 2 O 3 phases, the Er 3+ and Yb 3+ ions are also localized on the surfaces of ZnO grains. The maximum total transmittance of the ceramic disk is 50.9% at ~0.6 μm, Fig. 2(a). The absorption bands are due to Er 3+ and Yb 3+ ions in the corresponding RE 2 O 3 phases. The X-ray luminescence spectrum, Fig. 2(b), has two intense emission bands both being characteristic of ZnO. The band at ~388 nm is due to the near-band-edge (NBE) transitions. The second broad band centered at ~514 nm represents the defect emissions. The spectral "holes" coincide with the absorption of Er 3+ ions. The average X-ray luminescence decay time in the "fast" time domain of 0-50 ns is 6-8 ns, Fig. 2(c). Note that it is about 65 ns for undoped ZnO ceramic [START_REF] Peter | [END_REF], indicating the ZnO → RE 3 + energy transfer. Under optical excitation at 488 nm, the photoluminescence spectrum contains emission bands assigned to Er 3+ ions in RE 2 O 3 crystals, Fig. 2(d). The work on determining the most promising Er 3+ /Yb 3+ codoping ratio is in progress. The developed Er 3+ ,Yb 3+ -codoped ZnO optical ceramic demonstrates high radiation stability. It is promising for optoelectronic applications.

Fig. 1

 1 Fig. 1 Er,Yb:ZnO optical ceramic: (a) photograph of the polished ceramic disk; (b) XRD pattern, inset -a close look on the main diffraction peaks of Er 2 O 3 and Yb 2 O 3 ; (c) SEM image of the polished and etched surface of the ceramic; (d,e) EDX element mapping of (d) Er (Mα) and (e) Yb (Mα).

Fig. 2

 2 Fig. 2 Spectroscopy of Er,Yb:ZnO optical ceramic: (a) total transmission spectrum (thickness: 0.5 mm); (b) X-ray luminescence spectrum, vertical lines: deeps due to the Er 3+ absorption; (c) decay curve of X-ray luminescence; (d) photoluminescence spectrum, λ exc = 488 nm.


G Gorisse

C Dubosc

O Christmann

S Fleury

K Poinsot

S Richir

Effect of Avatar Anthropomorphism on Body Ownership, Attractiveness and Collaboration in Immersive Virtual Environments

Figure 1: Screenshot of the three avatars embodied by the participants in the immersive collaborative virtual environment of the experiment.

Introduction

Understanding the processes allowing people to collaborate in immersive virtual environments is a current challenge at the crossroad of computer science and psychology for virtual reality researchers. It is necessary to understand such mechanisms to develop applications allowing users to interact together through vir-search uses eye tracking technologies and/or full-body tracking. However, there is a technological gap between lab experiments and most available virtual reality applications. In this context, we decided to conduct an experiment based on lightweight setups avoiding relying on full-body tracking to control virtual legs and arms to be in line with a lot of use cases and mass market virtual reality devices. Therefore, we designed an experiment involving three robotic avatars allowing to use non-human body schema (no legs, and floating hands) presenting different anthropomorphic facial properties (Figure 1). First, we are interested to analyze if, whether or not, more realistic anthropomorphic facial properties favor attractiveness [ZAJ * 15, FMR * 17, GCHR18] as well as users' sense of body ownership [SMESV09]. Second, we aim at investigating if such facial properties allow for better performance in collaborative tasks thanks to a better adequacy between verbal and non-verbal communication. Finally, we explore the relationship between body ownership, attractiveness and users' performance in immersive virtual environments.

The next section presents a state of the art relative to both body ownership and attractiveness as well as an overview of several factors influencing communication and collaboration in immersive virtual environments. Section 3 presents the design of the experiment and its protocol. Results are analyzed in Section 4, discussed in Section 5 and limits are highlighted in Section 6. Section 7 presents the conclusion of the study and Section 8 introduces our future work.

Related Work

Body Ownership

The sense of body ownership is part of the embodiment process in virtual environments. The sense of embodiment refers to the feeling of being located inside, of owning and controlling another body. According to Kilteni et al. [KGS12], the sense of embodiment towards a virtual body could be defined as the sense that emerges when the virtual body's properties are processed as if they were the properties of one's own biological body. Three dimensions are identified as part of the sense of embodiment in immersive virtual environments:

• Self-location, corresponding to a determinate volume in space where users feel located. While self-location and agency are important to embody avatars in virtual environments, our study focuses especially on the sense of body ownership. Indeed, according to previous work, none of our variables are supposed to impact other dimensions of the sense of embodiment. The famous Rubber Hand Illusion (RHI) paradigm [BC98] demonstrated that it was possible to induce a proprioceptive drift through synchronous visuotactile stimulation between a real and a fake hand resulting in a sense of ownership over the fake limb. Based on such results, the same paradigm has been replicated in virtual environments [START_REF] Slater | Towards a digital body: the virtual arm illusion[END_REF] demonstrating that multisensory integration (e.g. visuomotor and visuotactile synchrony) [KS14] is a critical contributor to the emergence of a sense of ownership that allows the embodiment of avatars with different morphological and demographic characteristics [BGS13, KBS13, PSAS13, SSSVB10]. It is also demonstrated that morphological similarities can impact positively the sense of ownership [AHTL16, LRG * 17, WGR * 18, GCHR19]. That's why, thanks to visuomotor synchrony (head, torso and hand positions and rotations), we expect participants to be able to embody every robotic avatar proposed in our application, as it has already been observed in previous experiments [START_REF] Lugrin | Avatar anthropomorphism and illusion of body ownership in vr[END_REF], but that the different facial properties can impact the sense of ownership. In addition, it should be noted that sharing a virtual environment with other users, as in the proposed experiment, does not impact the sense of embodiment [FAHL18].

Attractiveness

It is acknowledged that attractiveness of avatars has a significant impact in both single and multi-user applications. On the one hand it can impact the way participants evaluate their avatar and to what extent they feel comfortable using this one [START_REF] Gorisse | From robot to virtual doppelganger: Impact of avatar visual fidelity and self-esteem on perceived attractiveness[END_REF]. On the other hand, it can affect the way people behave and interact when they are exposed to social situations in immersive virtual environments [START_REF] Bailenson | The Proteus effect: The effect of transformed self-representation on behavior[END_REF] or even their performance in massively multiplayer online games [YBD09]. Several characteristics can affect attractiveness evaluations of virtual characters. For instance, previous studies demonstrated that realism is not a good predictor of attractiveness [ZAJ * 15, FMR * 17]. The work of Zell et al. [ZAJ * 15] illustrates the importance of consistency between the level of stylization of the shapes and materials of the characters, with inconsistencies having a negative impact on their attractiveness. The work of Fleming et al. [FMR * 17] also reveals the significant influence of shapes and proportions. Their results showed that attractiveness evaluations are more favorable for avatars with an intermediate level of stylization compared to the original and highly realistic scanned 3D models. However, McDonnell et al. [MBB12] demonstrated that both highly realistic and highly abstract character could be rated as more appealing, which may be explained by the occurrence of an uncanny valley effect for intermediate conditions [MMK12, SN07]. Therefore, avatar visual fidelity has to be taken into account when designing virtual characters as it affects the way users behave when controlling and interacting with their avatar [START_REF] Gorisse | From robot to virtual doppelganger: Impact of avatar visual fidelity and self-esteem on perceived attractiveness[END_REF][START_REF] Gorisse | From Robot to Virtual Doppelganger: Impact of Visual Fidelity of Avatars Controlled in Third-Person Perspective on Embodiment and Behavior in Immersive Virtual Environments[END_REF]. According to Garau [START_REF] Garau | The Impact of Avatar Fidelity on Social Interaction in Virtual Environments[END_REF], visual fidelity of virtual characters can be categorized in three criteria:

• Anthropomorphism (non-humanoid <-> humanoid): Morphological characteristics of the virtual character. Therefore we designed this experiment using three avatars presenting different facial properties to investigate if anthropomorphism impact attractiveness evaluations and collaboration in immersive virtual environments.

Materials and Methods

In order to investigate the impact of anthropomorphism, each pair of participants embodies one of the three characters (same avatar for each pair of participants (Figure 2)) in a between subject design. They have to collaborate to solve two puzzle games (Figure 3). Each participant has the plan corresponding to his/her partner's puzzle. It creates an asymmetric collaborative situation where they have to explain alternately where to place the 3D parts on the game boards. At the end of the experiment, the participants evaluate the attractiveness of the avatar as well as their sense of body ownership. These data are then compared with their performance to achieve the collaborative task. The three avatar conditions are classified according to their facial properties:

• Robot 1 (R1) (Figure 2a): screen based face that displays a set of textures to animate both the eyes and the mouth using different Non-verbal communication can be either conscious, when it comes to intentional behaviors such as gestures, body postures, facial expressions, or unconscious such as micro-expressions. Used in combination with verbal communication, gestures add an emotional valence and help to communicate. Regarding virtual characters, it has been demonstrated that more accurate gestures allow for a better non-verbal communication [WWJ * 19]. In addition, unconscious and therefore uncontrolled expressions have been sets of textures. The robot's mouth is animated when the user is talking using a sequence of six textures.

• Robot 2 (R2) (Figure 2b): physical eyes and virtual mouth. The virtual mouth is an equalizer displaying bars matching the intensity of the user's vocal frequencies. • Robot 3 (R3) (Figure 2c): physical eyes and jaw. The physical jaw moves according to the user's voice intensity.

It should be noted that in this experiment, the different anthropomorphism levels require different gaze implementation due to the nature of the eyes (texture versus mesh) to achieve a convincing gaze behavior.

VR application

The virtual reality application used for the experiment was developed using the real-time 3D engine Unity. The environment consists in a room matching the avatars' appearance and textures to create a coherent and plausible environment. Both avatars appear in the center of the room on each side of the table where the game boards are located. Participants are able to communicate using both verbal and non-verbal communication, but they cannot see their partner's plan required to complete their own puzzle.

Apparatus

Two HTC Vive pro are used to display the virtual environment at a refresh rate of 90 Hz with a resolution of 2880 x 1600 pixels (1440 x 1600 pixels per eye) and a field of view of 110 degrees (Figure 4). Computers are composed of an Intel Xeon E5-1607 @ 3.10 GHz processor and a Nvidia GeForce GTX 1080 graphics card.

Participants

36 participants (10 females and 26 males), aged from 21 to 47 (M = 23.42, SD = 4.34), were recruited for the experiment. Each subject has a correct or corrected vision thanks to vision glasses allowing them to use the VR headset. All the participants had prior experience with immersive virtual reality and 29 of them play video games at least 2 hours a week. 22 out of 29 are used to playing multiplayer online games. We recruited experienced participants as we believe our results will be more relevant for future use cases considering the fact that in a near future most people will have such an experience with virtual reality. Indeed, participants experiencing VR for the first time may be distracted by the novelty and might be less focused on the task and their partner, which could have an impact on the results in terms of both performance and subjective measures.

Procedure and Measures

Prior to the experiment, each participant read and signed a consent form. Participants were informed that they were free to withdraw from the experiment at any time without giving reasons. Then, each participant filled the pre-experiment questionnaire to collect their demographic information as well as relevant data regarding the content of the experiment such as any previous experience with virtual reality and video games.

Each pair of participants was provided with the necessary instructions to begin the experiment and was equipped with the virtual reality headset in a separated room. As soon as the participants are geared up, they are immersed in the virtual environment. The experiment begins in two distinct virtual rooms where they embody their avatar for two minutes in front of a virtual mirror. Then, they meet each other in another environment dedicated to the collaborative task consisting in completing two puzzles. Participants com- plete the first puzzle on their side using the plan and the parts on their own virtual table. As soon as both participants have completed their first puzzle, they must collaborate to complete the second one following the instructions of their partner who has the corresponding plan on his/her side. The total completion duration of the two puzzles is recorded by the application.

At the end of the experiment, participants complete the questionnaire to assess the sense of body ownership and the attractiveness of the avatar [ZAJ * 15], which is the same for each pair of participants, using seven-point semantic scales. Objective performance data are collected via the application in a CSV (Comma-Separated Values) file. This file contains the completion duration (CD) of the task as well as the speaking duration (SD) of each participant.

Hypotheses

Based on previous work reported in our literature review and to the proposed experimental design, here is a list of hypotheses relative to the impact of anthropomorphism on attractiveness, body ownership and users performance in collaborative tasks:

• H1: Avatars presenting a high level of facial anthropomorphism improve users' sense of body ownership in immersive collaborative virtual environments. • H2: Avatars with more anthropomorphic facial properties are more appealing to users in immersive collaborative virtual environments. • H3: Avatars presenting a high level of facial anthropomorphism enable better communication and performance in collaborative tasks in immersive virtual environments.

Body Ownership

A Kruskal-Wallis Test revealed no significant difference in ownership scores between the three avatar conditions (Figure 5) (p > 0.05). Thus we cannot state that the anthropomorphism level of the three avatars proposed in this experiment impact users' sense of body ownership leading to reject our first hypothesis (H1).

Attractiveness

A Kruskal-Wallis Test revealed a statistically significant difference in avatars' attractiveness scores between the three avatar conditions (1 N = 12: R1, 2 N = 12: R2, 3 N = 12: R3), χ 2 (2, N = 36) = 11.61, p = 0.003 (Figure 6). The R2 group recorded the higher median score (Md = 6.00), while the R3 group recorded a value of 5.50 and the R1 group a value of 4.00. A Mann-Whitney U Test revealed a significant difference in the attractiveness scores of R1 (Md = 4.00, N = 12) and R2 (Md = 6.00, N = 12), U = 27, Z = -2.69, p = 0.008. Another significant difference was observed in the attractiveness scores of R1 (Md = 4.00, N = 12) and R3 (Md = 5.50, N = 12), U = 27, Z = -3.15, p = 0.002. Although we observed no significant difference between the Robot 2 and the Robot 3 conditions, our second hypothesis (H2) seems valid and will be discussed further in the next section.

Results

Data were tested for normality and homogeneity of variance. The Shapiro-Wilk Test revealed that most of the variables were not normally distributed and Levene Test showed that the variances of several variables were not equal (p < 0.05). Therefore, as our data violate parametric tests' assumptions, we used alternative non-parametric tests. Results are considered significant when p < 0.05 (Table 2). Bonferroni's correction was applied to adjust alpha value for post-hoc pairwise comparisons resulting in a significance level set at p < 0.017.

Completion and Speaking Durations

A Kruskal-Wallis Test revealed a statistically significant difference in the completion duration depending on the controlled avatar (1 N = 12: R1, 2 N = 12: R2, 3 N = 12: R3), χ 2 (2, N = 36) = 13.33, p = 0.001 (Figure 7). The R2 group recorded the lower median duration (Md = 443.50 s), while the R1 group recorded a duration of 732.00 s and the R3 group a duration of 596.50 s. A Mann-Whitney U Test revealed a significant difference in the completion duration between R1 (Md = 732.00 s, N = 12) and R2 (Md = 443.50 s, N = 12), U = 8, Z = -3.71, p < 0.001. A trend can be observed in the completion duration between the R1 (Md = 732.00 s, N = 12) and R3 (Md = 596.50 s, N = 12), U = 40, Z = -1.86, p = 0.064.

The speaking duration being obviously linked to the completion duration, we first calculated a relative speaking duration (score between 0 and 100, where 0 means that the participants did not speak and 100 that they spoke for the entire duration of the experiment). A Kruskal-Wallis Test revealed no significant difference in the relative speaking duration between the three avatar conditions (p > 0.05).

According the completion duration of the experiment, it seems that the anthropomorphism level of the three avatar conditions can impact users' performance, especially when comparing the avatar presenting the lower anthropomorphism level (R1) to the others (R2 and R3) which is consistent with our third hypothesis (H3). However, it does not impact the duration of their verbal communication.

Correlations

Using Spearman correlations (Table 3), we unexpectedly observed a strong negative correlation between avatar attractiveness and completion duration, rho = -0.564, n = 36, p < 0.001, the more attractive the avatar the shorter the completion duration. However, ness and performance. This result cannot be explained based on the data we collected and only rises new hypotheses. It is possible that attractiveness led participants to look at each other and to focus on their partner's avatar favoring non-verbal communication and improving their performance. Further studies must be conducted using gaze tracking technologies to analyse if attractiveness increases the time participants spend looking at each other in order to investigate if avatar attractiveness could be a way to improve collaboration in immersive virtual environments.

Limitations

Our results provide guidelines to design avatars for immersive collaborative virtual environments. Nevertheless, it should be noted that the analysis is based on a relatively small sample of 36 participants. Other experiments must be conducted to further investigate the impact of anthropomorphism. Moreover, even if it is a design choice to match most VR applications available to the general public not relying on realistic virtual humans, this experiment focuses on facial properties of robotic characters that do not enable an expressiveness similar to organic models using blend shapes. In addition, several other morphological factors potentially affecting nonverbal communication and interactions such as gestures and animations are not considered in this study. Indeed, the three avatars provide the participants with the same chest as well as the same virtual hands. We encourage developers to design avatars with regards to the proposed tasks as affordance and interaction metaphors can also impact the way users collaborate.

Conclusion

We investigated the impact of avatars' facial anthropomorphism in immersive collaborative virtual environments. Following a between subject design, we analyzed if the sense of body ownership, avatar attractiveness and performance are affected in collaborative tasks.

We observed a very high sense of ownership for each condition with no significant difference leading to the conclusion that the different anthropomorphism levels of the three robotic avatars are too slight to affect ownership compared to bottom-up factors such as visuomotor synchrony. However, the results revealed several significant differences concerning attractiveness and performance as well as a correlation between these two notions. On the one hand, more anthropomorphic facial properties appear to improve attractiveness. On the other hand, participants performed better to complete the collaborative puzzle game with avatars having more anthropomorphic facial properties. We unexpectedly observed a correlation between attractiveness and performance with high level of attractiveness associated with better performance. We hypothesize that higher attractiveness could lead users to focus more on their partner's avatar, which in turn leads to an improved non-verbal communication and therefore to better collaborative performance, but further experiments must be conducted using gaze tracking data to validate this new hypothesis.

Future work

In addition to analysing the link between anthropomorphism, attractiveness and performance, we plan to investigate further the the collected data are not sufficient to explain such results and no mediation analysis can be carried out to test if attractiveness could act as a mediator between anthropomorphism and performance as normality and homogeneity of variance assumptions are not met. This result is discussed further in the next section.

Discussion

Based on our data analysis, we observed several significant differences between the three anthropomorphism conditions (virtual eyes and mouth, physical eyes and virtual mouth, physical eyes and mouth), especially concerning attractiveness and users' performance regarding the task completion. However, we observed no statistically significant d ifference c oncerning t he s ense o f ownership. Therefore, we cannot state about our first h ypothesis (H1). Nevertheless, the sense of ownership is high for each avatar, which means that participants were able to embody every robot independently of their facial properties. We expected high ownership scores for every condition thanks to visuomotor synchrony, which is a critical bottom-up contributor [KS14]. Nevertheless, according to previous experiments, we also expected potential significant differences with higher sense of ownership for avatars presenting higher anthropomorphism levels as human-like similarities could increase the sense of embodiment [WGR * 18, GCHR19]. However, it seems that the differences between our anthropomorphism conditions, only limited to facial properties (same virtual body and hands), are too slight to affect the sense of ownership. Indeed, participants cannot see their own avatar's face as soon as they join the collaborative room (no virtual mirror anymore).

Our results demonstrate that attractiveness levels are significantly higher for both the second condition (physical eyes and virtual mouth) and the third condition (physical eyes and mouth) compared to the first one (virtual eyes and mouth). Participants tend to prefer avatars with more anthropomorphic facial properties, which demonstrate the validity of our second hypothesis (H2). Back to the three criteria of visual fidelity [START_REF] Garau | The Impact of Avatar Fidelity on Social Interaction in Virtual Environments[END_REF], p revious experiments demonstrated that realism is not a good predictor of attractiveness [ZAJ * 15, MBB12] but that truthfulness can improve attractiveness evaluations of virtual characters [START_REF] Gorisse | From robot to virtual doppelganger: Impact of avatar visual fidelity and self-esteem on perceived attractiveness[END_REF]. Based on our results, it seems that anthropomorphism can also positively impact attractiveness of virtual characters, at least concerning their facial properties (eye gaze and mouth type). However, in this context it is important to consider that such evaluations are subjective and, despite the fact that the anthropomorphism levels of the avatars are actually different, artistic design can also impact subjective evaluations of attractiveness.

Objective data revealed that participants performed significantly better using the second condition compared to the first o ne with shorter completion duration. We also observed a trend between the first and the third conditions, the third one allowing for better performance. Overall participants tend to perform better in collaborative tasks using more anthropomorphic avatars. However, the statistical analysis revealed no significant d ifference w hen comparing the relative speaking duration. We argue that more anthropomorphic appearance could favor communication in virtual environments leading to an increase in user performance in collaborative tasks. Unexpectedly, we observed a correlation between attractive-way avatars impact collaboration in immersive virtual environments. We are especially interested to analyse the effect of anthropomorphism on social presence in different tasks. In this experiment we reported a study with an asymmetric collaborative situation. Therefore, we also plan to extend these results to different scenarios and to compare whether the type of task can affect users' sense of co-presence. We will also pursue these investigations using characters with advanced facial expressions such as emotions and advanced labial synchronization.

( a )

 a Robot 1: Virtual eyes and mouth (b) Robot 2: Physical eyes and virtual mouth (c) Robot 3: Physical eyes and mouth

Figure 2 :

 2 Figure 2: Screenshots of the three avatar conditions of the experiment

Figure 3 :

 3 Figure 3: Participants performing the collaborative task.

Figure 4 :

 4 Figure 4: Participants equipped with the virtual reality headset HTC Vive pro and the controllers.

Figure 5 :Figure 6 :

 56 Figure 5: Boxplot of the ownership scores for the three avatars.

Figure 7 :

 7 Figure 7: Boxplot of the completion durations.

Figure 8 :

 8 Figure 8: Boxplot of the relative speaking durations.

Table 1 :

 1 Body ownership and attractiveness questionnaire. Items range from 1 to 7.

	Body ownership
	I felt that the virtual body that I saw when I looked down was my body.
	I felt that the virtual body I saw in the mirror was my body.
	I felt that the virtual body was not me.*
	Attractiveness
	To what extent your avatar seemed attractive to you?
	* reverse scored item.

Table 2 :

 2 Statistical summary of the answers to the post experiment questionnaire (Ownership (O) and Attractiveness (Att)) and of the objective data (Completion Duration (CD) and Relative Speaking Duration (RSD)).

		Robot 1 (R1)	Robot 2 (R2)	Robot 3 (R3)
		x	σ	x	σ	x	σ	p
	O	4.81	1.59	5.31	0.72	4.78	1.07	0.558
	Att	4.25	0.87	5.42	1.24	5.42	0.45	0.003*
	CD	774.50	213.47	473.00	105.98	538.33	156.61	0.001*
	RSD	52.29	10.90	46.25	9.09	47.69	11.00	0.392
	Mean and standard deviation are provided for each condition (R1, R2 and R3). * indicates significant differences.

Table 3 :

 3 Spearman correlation between Ownership (O), Attractiveness (Att), Completion Duration (CD) and Relative Speaking Duration (RSD).

		O	Att	CD	RSD
	Ownership (O)	-	0.129	-0.012	0.123
	Attractiveness (Att)		-	-0.564**	-0.07
	Completion Duration (CD)			-	0.094
	Relative Speaking Duration (RSD)			-
	* p < 0.05 (2-tailed), ** p < 0.01 (2-tailed)
	Completion Duration (s)
	Robot 1	Robot 2	Robot 3

Acknowledgments

First of all, we would like to thank Skyreal for founding this research. We are grateful to the students who initially participated in the prototyping of the experiment. Many thanks also to all the people who provided us with insightful comments and advice.


Vladimir Vitkin

Anton Polishchuk

Daria Zavirukha

Valeria Kurikova

Olga Dymshits

Irina Alekseeva

Svetlana Zapalova

Aleksander Zhilin

Pavel Loiko

Nanosecond Compact Eye-Safe Erbium Lasers with 190 kW Peak Power

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Spinel (MgAl 2 O 4 ) single crystals doped with cobalt ions (Co 2+ ) are known as efficient saturable absorbers (SAs) of eye-safe erbium (Er) laser emitting at 1.5-1.7 µm. Their saturable absorption originates from the 4 A 2 ( 4 F) → 4 T 1 ( 4 F) transition of Co 2+ ions located in tetrahedral (T d ) sites. Recently, Co 2+ -doped spinel transparent polycrystalline ceramics and transparent nanophase glass-ceramics (GCs) were proposed as competitive materials for the singlecrystal technology [START_REF] Loiko | Synthesis, characterization and absorption saturation of Co:ZnAl 2 O 4 (gahnite) transparent ceramic and glass-ceramics: A comparative study[END_REF][START_REF] Vitkin | Passive Qswitching of an Er,Yb:glass laser with Co:Mg(Al,Ga) 2 O 4 -based glass-ceramics[END_REF]. Among them, transparent GCs feature high laser induced damage thresholds (~20 J/cm 2 ) and the possibility to modify the composition of spinel nanophase [START_REF] Loiko | Synthesis, characterization and absorption saturation of Co:ZnAl 2 O 4 (gahnite) transparent ceramic and glass-ceramics: A comparative study[END_REF]. We report on a compact passively-cooled eye-safe Er laser passively Q-switched (PQS) by GC-based SAs suitable for compact range-finders.

The scheme of the laser is shown in Fig. 1(a). The cavity is formed by a concave (RoC = -1.5 m) HR end mirror and a flat output coupler (OC, T OC = 13%). The rod-shaped laser element (Ф1.0 mm × 10 mm) made of Er,Yb:glass is side-pumped by a laser diode array at 940 nm. The passively-cooled laser is housed by a ZrO 2 -coated glass pump chamber with dimensions of only Ф15 mm × 25 mm. In the free-running regime, Fig. 1(b,c), the laser generates ~3.8 ms long pulses with a maximum energy of 40 mJ and a slope efficiency of 17.7%. As SA materials, two transparent GCs based on gallium-containing spinel phases (Mg(Al,Ga) 2 O 4 and γ-Ga 2 O) were selected. They exhibit high GSA cross-sections at ~1.54 µm, Fig. 1(d), determined from the absorption saturation experiments. The uncoated SA is inserted at the Brewster angle between the laser rod and the OC. The initial transmission of the SAs T SA was varied by the heat-treatment regime of the initial glass and by its thickness. After inserting the SA, very stable passive Q-switching was achieved. The laser generated a single giant pulse per each pump pulse (pulse repetition rate: 1 -5 Hz), Fig. 2(a). Using a γ-Co:Ga 2 O 3 based GC saturable absorber with T SA = 85.4%, the pulse duration (FWHM) of 7.2 ns was obtained corresponding to a pulse energy of 1.39 mJ. The peak power thus reached 193 kW. The effect of the small-signal SA transmission on the pulse characteristics was systematically studied, Fig. 2(b,c). The PQS laser exhibited excellent long-term stability (studying >100 repetitive pulses): ±0.02 mJ, ±0.2 ns. No optical damage of the optical elements nor the SAs was observed. The laser wavelength was 1535.2 nm. The measured divergence of the laser beam was Θ x,y = 3.83 and 4.60 mrad, close to the diffraction limit. The developed laser design is suitable for compact range-finders.

Fig. 1

 1 Fig. 1 Diode-side-pumped passively Q-switched compact Er,Yb:glass laser: (a) scheme of the laser, LDlaser diode, HRhighly-reflective mirror, OCoutput coupler, SAsaturable absorber; (b) free-running laser performance; (c) oscilloscope traces of the pump and laser pulses in the free-running regime; (d) ground-state absorption (GSA), σ GSA , cross-sections for the 4 A 2 ( 4 F) → 4 T 1 ( 4 F) Co 2+ transition in T d sites in Mg(Al,Ga) 2 O 4 and γ-Ga 2 O 3 based transparent GCs.

Fig. 2

 2 Fig. 2 Pulse characteristics of the passively Q-switched compact Er,Yb:glass laser: (a) oscilloscope trace of a single Q-switched pulse, γ-Co:Ga 2 O 3 based GC saturable absorber; (b) pulse duration and (c) pulse energy as a function of the initial transmission T SA of GC-based SAs.


Fangxin Yue

Pavel Loiko

Mengting Chen

Josep Maria Serres

Yicheng Wang

Jiang Li

Liza Basyrova

Elena Dunina

Alexey Kornienko

Liudmila

Liudmila Fomicheva

Shibo Dai

Zhenqiang Chen

Ji Eun Bae

Fabian Rotermund

Venkatesan Jambunathan

Antonio Lucianetti

Tomas Mocek

Magdalena Aguiló

Francesc Díaz

Uwe Griebner

Valentin Petrov

Xavier Mateos
email: xavier.mateos@urv.cat

Spectroscopy and diode-pumped laser operation of transparent Tm:Lu3Al5O12 ceramics produced by solid-state sintering

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.

Introduction

Transparent ceramics doped with rare-earth ions (RE 3+ ) represent a promising alternative to the single-crystal development for laser applications [START_REF] Ikesue | Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers[END_REF][START_REF] Lu | Neodymium doped yttrium aluminum garnet (Y 3 Al 5 O 12 ) nanocrystalline ceramicsa new generation of solid state laser and optical materials[END_REF][START_REF] Yagi | Characterizations and laser performances of highly transparent Nd 3+ :Y 3 Al 5 O 12 laser ceramics[END_REF]. Their advantages lie in the technological area, as they offer (i) easier fabrication methods, (ii) lower synthesis temperatures, (iii) size-scalable production, (iv) optical isotropy and (v) the possibility to control the volume of RE 3+ doping or (vi) to fabricate composite structures [START_REF] Ikesue | Ceramic laser materials[END_REF]. Physically, ceramics may offer compositions which are not present in the single-crystal form and allow for higher RE 3+ doping levels. When going from a single-crystal to polycrystalline ceramics, the spectroscopic properties of the RE 3+ ions are typically preserved [START_REF] Lu | Optical properties and highly efficient laser oscillation of Nd:YAG ceramics[END_REF]. A proper fabrication also sustains the thermal and thermo-optical response of the material. As a result, RE 3+ -doped ceramics are of interest for efficient and power-scalable lasers.

So far, the most widespread material for fabrication of transparent ceramics is the cubic (sp. gr. Ia3¯d) yttrium aluminum garnet, Y 3 Al 5 O 12 . The first studies focused on RE:Y 3 Al 5 O 12 transparent ceramics for emission at ~1 μm based on the Nd 3+ [START_REF] Ikesue | Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers[END_REF][START_REF] Lu | Neodymium doped yttrium aluminum garnet (Y 3 Al 5 O 12 ) nanocrystalline ceramicsa new generation of solid state laser and optical materials[END_REF][START_REF] Yagi | Characterizations and laser performances of highly transparent Nd 3+ :Y 3 Al 5 O 12 laser ceramics[END_REF] and Yb 3+ [START_REF] Takaichi | Yb 3+ -doped Y 3 Al 5 O 12 ceramics -A new solid-state laser material[END_REF][START_REF] Dong | Laser-diode pumped heavydoped Yb:YAG ceramic lasers[END_REF] active dopant ions and, more recently, the interest shifted to the ~2 μm spectral range [START_REF] Zhang | Diode-pumped Tm:YAG ceramic laser[END_REF][START_REF] Chen | In-band pumped highly efficient Ho:YAG ceramic laser with 21 W output power at 2097 nm[END_REF][START_REF] Lan | Passive Q-switching of microchip lasers based on Ho:YAG ceramics[END_REF]. The 2-μm laser emission is eye-safe and primarily achieved with Tm 3+ and Ho 3+ doping. The lasers operating at ~2 μm have multiple applications in remote sensing (LIDAR), wind mapping, spectroscopy, range-finding or medicine. They can also be used for nonlinear frequency conversion into the mid-IR [START_REF] Petrov | Frequency down-conversion of solid-state laser sources to the mid-infrared spectral range using non-oxide nonlinear crystals[END_REF]. In particular, the thulium (Tm 3+ ) ion benefits from (i) large Stark splitting of the ground-state ( 3 H 6 ) leading to broadband emission, (ii) strong absorption at ~0.8 μm (the 3 H 6 → 3 H 4 transition) allowing for diode-pumping and (iii) an efficient cross-relaxation (CR) process for adjacent Tm 3+ pairs, 3 H 6 + 3 H 4 → 3 F 4 + 3 F 4 , increasing the pump quantum efficiency up to 2 [START_REF] Honea | 115-W Tm:YAG diode-pumped solid-state laser[END_REF]. Tm 3+ -doped garnets are also known for long upper laser level lifetimes (~10 ms) and emission wavelengths extending beyond 2 μm [START_REF] Stoneman | Efficient, broadly tunable, laser-pumped Tm:YAG and Tm:YSGG cw lasers[END_REF], where the unwanted structured absorption of water in the atmosphere is absent. The latter is in particular relevant for mode-locked (ML) lasers operating at ultrashort pulse durations (broad spectra) with specific applications [START_REF] Pan | Generation of 84-fs pulses from a mode-locked Tm:CNNGG disordered garnet crystal laser[END_REF].

Tm:Y 3 Al 5 O 12 laser ceramics have been previously demonstrated [START_REF] Zhang | Diode-pumped Tm:YAG ceramic laser[END_REF][START_REF] Zou | High-efficiency diode-pumped Tm: YAG ceramic laser[END_REF][START_REF] Wang | Highly efficient Tm:YAG ceramic laser resonantly pumped at 1617 nm[END_REF][START_REF] Gao | Highly efficient 2 μm Tm:YAG ceramic laser[END_REF]. Gao et al. reported on a continuous-wave (CW) diode-pumped Tm:Y 3 Al 5 O 12 ceramic laser delivering 6.05 W at 2016 nm with a slope efficiency of 65% [START_REF] Gao | Highly efficient 2 μm Tm:YAG ceramic laser[END_REF]. Gluth et al. demonstrated a Tm:Y 3 Al 5 O 12 ceramic oscillator ML by a GaSb-based SEmiconductor Saturable Absorber Mirror (SESAM) delivering 3-ps pulses at 2012 nm at a repetition rate of 89 MHz [START_REF] Gluth | GaSb-based SESAM mode-locked Tm:YAG ceramic laser at 2 µm[END_REF].

Another compound in the cubic garnet family, i.e., lutetium aluminum garnet, Lu 3 Al 5 O 12 , is known for its better thermal properties as compared to its yttrium counterpart which is advantageous for the ceramic technology [START_REF] Fu | Fabrication and properties of highly transparent Yb:LuAG ceramics[END_REF][START_REF] Nakao | CW and mode-locked operation of Yb 3+ -doped Lu 3 Al 5 O 12 ceramic laser[END_REF]. Considering Tm 3+ doping, Lu 3 Al 5 O 12 is attractive because of the closeness of the ionic radii of Tm 3+ and Lu 3+ (as compared to Y 3+ ). Studies on Tm:Lu 3 Al 5 O 12 single-crystals exist [START_REF] Barnes | Diode-pumped, room-temperature Tm:LuAG laser[END_REF][START_REF] Scholle | Single mode Tm and Tm,Ho:LuAG lasers for LIDAR applications[END_REF], however, there is a lack of information about such ceramics. Wang et al. reported on a ML Tm:Lu 3 Al 5 O 12 ceramic laser delivering 2.7 ps pulses at 2022 nm; a broad tuning range of 1808-2088 nm was also demonstrated [START_REF] Wang | Thulium doped LuAG ceramics for passively mode locked lasers[END_REF]. Zhou et al. reported on a CW Tm:Lu 3 Al 5 O 12 ceramic laser delivering an output power of 2.64 W at 2016 nm with a slope efficiency of only 35.6% [START_REF] Zhou | Continuous-wave and passively Q-switched Tm 3+ -doped LuAG ceramic lasers[END_REF]. Note that Lu 3 Al 5 O 12 ceramics doped with other RE 3+ ions are also known [START_REF] Luo | Yb:LuAG laser ceramics: a promising high power laser gain medium[END_REF][START_REF] Basyrova | Effect of SiO 2 addition on structural and optical properties of Yb:Lu 3 Al 5 O 12 transparent ceramics based on laser ablated nanopowders[END_REF].

In the present work, we demonstrate the potential of Tm:Lu 3 Al 5 O 12 transparent ceramics for highly-efficient multi-watt laser operation at ~2 μm and study thoroughly their spectroscopic properties, which are of key importance for the development of CW and in particular ML lasers.

Synthesis of ceramics

Tm:Lu 3 Al 5 O 12 transparent ceramics were prepared by solid-state reactive sintering of commercial α-Al 2 O 3 (purity: 99.98%) and Lu 2 O 3 /Tm 2 O 3 (5N) powders, using MgO (5N) and tetraethoxysilane (TEOS, 5N) as sintering aids [START_REF] Wang | Thulium doped LuAG ceramics for passively mode locked lasers[END_REF]. The raw materials were mixed in a stoichiometric ratio of (Lu 0.96 Tm 0.04 ) 3 Al 5 O 12 and ball milled for 12 h with absolute ethyl alcohol as milling medium. Afterwards, we dried the slurry for 2 h at 80 °C in an oven, grounded and sieved it subsequently through a 200-mesh screen. Finally, we calcined it at 800 °C for 1 h to remove organic components. After the preparation, we pressed uniaxially the powders into pellets (diameter: 20 mm) at 50 MPa and cold isostatically pressed (CIP) at 250 MPa. The green-bodies were sintered at 1830 °C for 30 h in a tungsten mesh-heated vacuum furnace. In order to remove the oxygen vacancies, we annealed the samples at 1450 °C for 10 h in air. The Tm 3+ doping level of 4.0 at.% corresponds to N Tm = 5.65×10 20 cm -3 (calculated using a density ρ calc of 6.695 g/cm 3 determined from the XRD data).

The ceramics were transparent and colorless, as shown in Fig. 1. For spectroscopic studies, a sample with a thickness t of 3.08 mm was cut and both surfaces were polished to laser-grade quality.

Characterization of the fabricated ceramics

Structure and morphology

The structure and phase purity of the fabricated transparent ceramics were confirmed by X-ray diffraction (XRD), see Fig. 2 Tm 3+ ions substitute for the Lu 3+ ones in a single type of sites (D 2 symmetry) [START_REF] Gruber | Spectra and energy levels of Tm 3+ :Y 3 Al 5 O 12[END_REF]. The difference in ionic radii of Tm 3+ (0.994 Å) and Lu 3+ (0.977 Å) for VIII-fold coordination by O 2- [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] explains the observed lattice expansion.

The study of the microstructure by Field-Emission Scanning Electron Microscopy (FESEM), Fig. 2(b), reveals a close-packed structure with clean grain boundaries and lack of pores. The grain size distribution was analyzed using the ImageJ software counting >50 grains. The measured grain sizes were multiplied by the shape factor of 1.2. The mean grain size is 21±4 μm.

Raman spectroscopy

The vibronic properties of the fabricated ceramic were studied with Raman spectroscopy, see Fig. 3, showing an unpolarized Raman spectrum for an excitation wavelength of 514 nm. For cubic Lu 3 Al 5 O 12 containing 80 atoms in the unit-cell, the factor-group analysis predicts 97 lattice modes. They are characterized (at k = 0, the center of the Brillouin zone) by the following set of irreducible representations [START_REF] Kaminskii | Stimulated Raman scattering in "garnet" Lu 3 Al 5 O 12 ceramicsa novel host-material for Ln-and TM-lasant ions[END_REF]: Г = 3A 1g + 8E g + 14F 2g + 5A 1u + 5A 2u + 5A 2g + 10E u + 14F 1g + 16F 2u + 17F 1u . Here, 25 lattice modes (A 1g , E g and F 2g ) are Raman-active. In Fig. 3, 14 bands are observed and assigned to the lattice vibrations.

The most intense Raman band at 796 cm -1 (A 1g ) is due to the breathing mode of the [AlO 4 ] tetrahedron [START_REF] Papagelis | Infrared spectroscopy and lattice dynamical calculations of Gd 3 Al 5 O 12 , Tb 3 Al 5 O 12 and Lu 3 Al 5 O 12 single crystals[END_REF]. Its full width at half maximum (FWHM) is 12.7 cm -1 . Other intense bands appear at lower frequencies, at 259 cm -1 (T 2g ) and 374 cm -1 (A 1g ). The maximum phonon energy hν ph for the studied ceramic is 868 cm -1 (T 2g ).

Optical absorption spectroscopy

The transmission spectrum of the ceramic is shown in Fig. 4. At 1.0 μm (out of the absorption of Tm 3+ ions), the transmission T amounts to 82.6% which is close to the theoretical value set by the Fresnel losses, T 0 = 83.6% (assuming a refractive index n = 1.826 [START_REF] Kuwano | Crystal growth and properties of (Lu,Y) 3 Al 5 O 12[END_REF]). This value confirms the very good optical quality of the fabricated ceramic.

The absorption bands are due to Tm 3+ transitions from the ground-state ( 3 H 6 ) to the excitedstates (from 3 F 4 to 1 D 2 ). The absorption cross-sections were calculated from the absorption coefficient α abs according to the equation σ abs = α abs /N Tm . The α abs values, in their turn, were determined from the transmission spectrum, cf. Fig. 4, as α abs = -ln(T/T 0 )/t [cm -1 ] where the thickness t is expressed in cm. For the 3 H 6 → 3 H 4 transition which is used for conventional pumping of Tm lasers, Fig. 5(a), the maximum σ abs is 5.0×10 -21 cm 2 at 787.6 nm and the FWHM of several closely located absorption peaks is 12.4 nm. For the 3 H 6 → 3 F 4 transition, which is spectrally overlapping the ~2 μm emission of Tm lasers, σ abs is 9.5×10 -21 cm 2 at 1631.9 nm, see Fig. 5(b). In the range of the laser emission (2.02 μm), the reabsorption losses σ abs are < 0.04×10 -21 cm 2 .

Optical emission spectroscopy

The stimulated-emission (SE) cross-sections, σ SE , for the 3 F 4 → 3 H 6 transition of Tm 3+ are shown in Fig. 6(a). They was calculated using a combination of the reciprocity method (RM) [START_REF] Payne | Infrared cross-section measurements for crystals doped with Er 3+ , Tm 3+ , and Ho 3+[END_REF] and the Füchtbauer-Ladenburg (F-L) equation [START_REF] Aull | Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections[END_REF]:

, / exp ) ( ) ( ZPL 2 1 abs SE       - - = kT E hc Z Z      (1a) . d ) ( ) ( 8 ) ( rad 2 5 SE  =          W W c n (1b)
In Eq. (1a), Z m are the partition functions of the lower (m = 1) and upper (m = 2) manifolds, calculated to be 3.209 and 1.810, respectively (Z 1 /Z 2 = 1.773), h is the Planck constant, c is the speed of light, λ is the wavelength, k is the Boltzmann constant, T is the temperature (293 K) and E ZPL = 5527 cm -1 (where ZPL stands for the zero-phonon line) is the energy of the transition between the lowest Stark sub-levels of two multiplets. Here, the values of the partition functions and the ZPL energy [START_REF] Morrison | Energy levels and branching ratios of Tm 3+ in ten garnet laser materials[END_REF] are based on the crystal-field calculations, see Section 3.5. In Eq. (1b), ⟨n⟩ = 1.813 is the refractive index of Lu 3 Al 5 O 12 (calculated using the Sellmeier equation [START_REF] Kuwano | Crystal growth and properties of (Lu,Y) 3 Al 5 O 12[END_REF]) at a mean Tm 3+ emission wavelength of ⟨λ⟩ = 1815 nm (determined in the present work), τ rad is the radiative lifetime of the emitting state ( 3 F 4 ) and W(λ) is the luminescence spectrum. The simultaneous use of the two methods allows one to avoid the detrimental effect of reabsorption on the measured W(λ) spectrum and to quantify σ SE at long wavelengths where the RM gives high error due to the exponential term in Eq. 1(a). A reasonable agreement between the two methods is observed for τ rad = 9.8±0.3 ms. To construct the combined SE cross-section spectrum further used for the gain calculations, we have selected the wavelength of 1.88 μm as a borderline. At shorter wavelength, the RM was applied owing to the notable reabsorption and at longer wavelength, we used the F-L equation.

Tm:Lu 3 Al 5 O 12 features a broad emission spanning from 1.61 to 2.06 μm. The maximum σ SE is 2.37×10 -21 cm 2 at 1749 nm (as calculated using the RM). In the long-wavelength spectral range where the laser operation is expected, σ SE is lower, namely, 1.03×10 -21 cm 2 at 2021 nm (the value obtained from the F-L equation). The 3 F 4 → 3 H 6 Tm 3+ lasers operate in a quasi-three-level scheme (exhibiting reabsorption). Thus, the gain at a distinct laser wavelength is quantified as σ gain = βσ SE -(1 -β)σ abs , where β = N 2 ( 3 F 4 )/N Tm is the inversion ratio, Fig. 6(b). Physically, an increase of β indicates an increased level of losses in the laser (e.g., high output-coupling) according to the rule "gain equals the losses". The evolution of the gain spectra with β explains the variation of the laser wavelength when increasing the output coupling ratio. For Tm:Lu 3 Al 5 O 12 , a broad peak at ~2020 nm dominates in the spectra up to at least β = 0.30.

The luminescence decay curve measured at 1950 nm (emitting state: 3 F 4 ) is shown in Fig. 7. It is single-exponential in agreement with a single type of sites for Tm 3+ ions. The luminescence lifetime τ lum = 9.68 ms is close to the estimated τ rad value (9.8±0.3 ms) which indicates weak non-radiative relaxation and quenching of luminescence from the 3 F 4 state in the ceramic.

Judd-Ofelt analysis

To assign the transitions in the absorption spectra, we calculated the Stark splitting for the Tm 3+ multiplets in Lu 3 Al 5 O 12 using crystal-field parameters reported for bulk crystals [START_REF] Morrison | Energy levels and branching ratios of Tm 3+ in ten garnet laser materials[END_REF]. The D 2 group has four one-dimensional irreducible representations Г i (i = 1, 2, 3, 4) and each 2S+1 L J multiplet is split into 2J + 1 singlet Stark components. The energy-level scheme is shown in Fig. 8(a). The energies of the Stark sub-levels for all multiplets from 3 H 6 up to 3 P 2 are also listed in Table 1 (previously reported only for the upper and lower laser levels). The details for the 3 H 6 and 3 F 4 multiplets are shown in Fig. 8(b). The total splitting of the ground-state ( 3 H 6 ) is rather large (ΔE = 777 cm -1 ) defining a possible emission above 2 μm. The 4f-4f transition intensities of Tm 3+ :Lu 3 Al 5 O 12 were analyzed using the Judd-Ofelt (J-O) theory [START_REF] Judd | Optical absorption intensities of rare-earth ions[END_REF][START_REF] Ofelt | Intensities of crystal spectra of rare-earth ions[END_REF]. The squared reduced matrix elements U (k) in absorption and emission were taken from Ref. [START_REF] Walsh | Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm 3+ and Ho 3+ ions in LiYF 4[END_REF]. The magnetic-dipole (MD) contributions for J → J' transitions with ΔJ = 0, ±1 were calculated separately within the Russell-Saunders approximation on wave functions of the Tm 3+ ion under the assumption of a free-ion. More details about the calculation procedure for Tm 3+ can be found elsewhere [START_REF] Zhang | Crystal growth, optical spectroscopy and laser action of Tm 3+ -doped monoclinic magnesium tungstate[END_REF]. The standard J-O theory and its modification (denoted as the modified Judd-Ofelt (mJ-O) theory) [START_REF] Kornienko | Dependence of the line strength of f-f transitions on the manifold energy. II. Analysis of Pr 3+ in KPrP 4 O 12[END_REF][START_REF] Loiko | Spectroscopy of Tb 3+ ions in monoclinic KLu(WO 4 ) 2 crystal: application of an intermediate configuration interaction theory[END_REF] accounting for configuration interaction were used. For both approaches, the electric-dipole (ED) line strengths for a J → J' transition can be written as:

ED (k) calc k k 2,4,6 ( ') . S JJ U = =   (2)
Here, Ω k (k = 2, 4, 6) are the J-O (intensity) parameters. For the standard J-O theory (no configuration interaction), they are constant. In the mJ-O theory, it is assumed that solely the excited configuration with an opposite parity 4f n-1 5d 1 contributes to the configuration interaction, so that the J-O parameters are linear functions of the energies of the two multiplets (E J and E J' ) involved in the transition:

0 k k J J' f [1 2 ( 2 )]. E E E   =  + + - (3)
Here, E f 0 is the mean energy of the 4f n configuration and α ≈ 1/(2Δ), where Δ is associated with the energy of the excited-configuration. In particular, if Δ → ∞, Ω k = constant (the standard J-O theory).

The absorption oscillator strengths were determined from the measured absorption spectra (f Σ exp ) and calculated using the J-O and mJ-O theories (f Σ calc ), as shown in Table 2. Here, the "Σ" superscript stands for the total (ED + MD) value. The latter approach gives much lower root mean square (rms) deviation between f Σ exp and f Σ calc . The corresponding set of parameters -(Ω k ) for the J-O theory and (Ω k and α) for the mJ-O one are given in Table 3.

A direct application of both J-O and mJ-O theories for the description of the transitions (emission) gives a notably underestimated radiative lifetime of the lower-lying excited state ( 3 F 4 ), namely, τ rad = 5.60 ms (J-O) and 6.78 ms (mJ-O). This is a known problem for Tm 3+doped cubic garnets [START_REF] Thomas | Optical spectroscopy of Tm 3+ :YAG transparent ceramics[END_REF].

To support further considerations, we calculated the wave functions of the Tm 3+ multiplets with the same total angular momentum quantum number J = 4, namely, 3 F 4 , 3 H 4 and 1 G 4 , see Table 4. Due to the strong spin-orbit interaction, they form a group of strongly interconnected states [START_REF] Jing | Synthesis, spectroscopy, and efficient laser operation of "mixed" sesquioxide Tm:(Lu,Sc) 2 O 3 transparent ceramics[END_REF]. Indeed, the non-diagonal elements in Table 4 are comparable in magnitude to the diagonal ones. Thus, through the 1 G 4 excited-state of the 4f n configuration, the effect of excited configurations (e.g., 4f n-1 5d 1 ) is transferred to the lower-lying states, 3 F 4 and 3 H 4 . In a recent paper [START_REF] Dunina | Effect of configuration interaction of rare-earth ion states on the intensity of intermultiplet transitions[END_REF], this effect was described in terms of the hypersensitivity of the 3 H 6 → 3 F 4 Tm 3+ transition to the local ligand field. To avoid this problem, the mJ-O theory was applied to all the observed Tm 3+ transitions except 3 H 6 → 3 F 4 to minimize the rms deviation between f Σ exp and f Σ calc . The results are shown in Table 2 (the last column) following the same calculation procedure as described above. The corresponding intensity parameters are Ω 2 = 2.507, Ω 4 = 1.236, Ω 6 = 1.340 [10 -20 cm 2 ] and α = 0.196×10 -4 cm (or Δ = 25510 cm -1 ).

In Table 3, we also provide for comparison the intensity parameters reported for other Tm 3+doped transparent ceramics, i.e., Tm:Y 3 Al 5 O 12 [START_REF] Fei | Spectroscopic properties and laser performance of Tm:YAG ceramics[END_REF] and Tm:(Lu,Sc) 2 O 3 [START_REF] Jing | Synthesis, spectroscopy, and efficient laser operation of "mixed" sesquioxide Tm:(Lu,Sc) 2 O 3 transparent ceramics[END_REF].

By using such intensity parameters, we calculated the probabilities of spontaneous radiative transitions A Σ calc , the luminescence branching ratios B(JJ') and the radiative lifetimes of the excited-states τ rad for Tm 3+ in Lu 3 Al 5 O 12 ceramic, see Table 5. Such an approach gives good agreement between the radiative lifetime of the 3 F 4 state calculated with the mJ-O theory (τ rad = 10.32 ms), its estimation from the calculation of the SE cross-sections by the RM and F-L methods (τ rad = 9.8±0.3 ms), and the reabsorption-free luminescence lifetime (τ lum = 9.68 ms), see Section 3.4. *〈λ〉 -calculated mean emission wavelength, A Σ calcprobability of radiative spontaneous transitions (ED + MD), B(JJ')luminescence branching ratio, A tot and τ radtotal probability of radiative spontaneous transitions (ED+MD) and radiative lifetime of the excited state, respectively. ED and MD stand for electric-dipole and magnetic-dipole transitions, respectively.

Laser operation

Laser setup

Laser operation was achieved in a compact plano-plano (microchip-type) cavity, as shown in Fig. 9(a). It was formed by a flat pump mirror (PM) coated for high transmission (HT) at ~0.79 μm and for high reflection (HR) at 1.80 -2.08 μm, and a set of flat output couplers (OCs) with a transmission T OC = 1.5%-20% at the laser wavelength of ~2.02 μm. The ceramic laser element (t = 3.08 mm, aperture: 5×5 mm 2 ) was kept uncoated. It was mounted in a Cu-holder using In foil for better thermal contact from all four lateral sides. The holder was cooled down to 12 °C by circulating water. Both the PM and OC were placed as close as possible to the laser element resulting in a geometrical cavity length of ~3.1 mm.

As a pump source, we used a fiber-coupled (core diameter: 105 μm, N.A. = 0.22) AlGaAs laser diode (MTLC00031, BWT Beijing Ltd.) emitting up to 30 W of unpolarized output at 792 nm ( 3 H 6 → 3 H 4 transition of Tm 3+ , conventional pumping). Its emission bandwidth was 4.4 nm. The pump radiation was reimaged into the laser element through the PM by a lens assembly (1:1 reimaging ratio, focal length f = 30 mm). The OCs were partially reflective at the pump wavelength (R ≈ 40%), so that the pumping was in double-pass and the total pump absorption at the laser threshold η abs(2-pass) amounted to 33.1±0.5%. The waist of the pump beam in the focus was 2w P ≈ 100 μm.

For passive Q-switching, a transmission-type saturable absorber (SA) was inserted between the laser element and the OC at a minimum separation. It was based on purified arc-discharge single-walled carbon nanotubes (SWCNTs) [START_REF] Loiko | Vibronic thulium laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF]. The SWCNT/PMMA composite film (thickness: ~300 nm) was spin-coated onto an uncoated 1-mm-thick glass substrate. In the small-signal transmission spectrum of the SA, Fig. 9(b), a broad absorption band spanning from 1.6 to 2.2 μm is observed. It is assigned to the first fundamental transition of semiconducting nanotubes (E 11 ) with varying tube diameters between 1.5 and 2.2 nm. At the laser wavelength of ~2.02 μm, the internal small-signal transmission (corrected for the Fresnel losses) T SA was 97.9%. According to our previous studies, the saturation intensity of a similar SWCNT-based SA I sat was 7±1 MW/cm 2 , the fraction of the saturable losses α' S /α' SA = 0.21 (where α' SA = 1 -T SA ), both specified for ns pulse durations [START_REF] Lan | Passive Q-switching of microchip lasers based on Ho:YAG ceramics[END_REF], and the recovery times of the initial absorption are τ rec = 0.25 and 1.16 ps for "fast" and "slow" components, respectively, as determined in a pump-probe experiment [START_REF] Cho | Passive mode-locking of a Tm-doped bulk laser near 2 μm using a carbon nanotube saturable absorber[END_REF].

Continuous-wave laser operation

Continuous-wave laser operation was realized without the SA in the cavity. The input-output power characteristics are shown in Fig. 10(a). The maximum output power reached 3.12 W at 2022-2035 nm with a slope efficiency η of 60.2% (vs. the absorbed pump power, P abs ). The laser threshold was at P abs = 0.25 W and the optical-to-optical efficiency η opt was 18.8% (vs. the pump power incident on the crystal). These characteristics were measured for T OC = 5%. Using T OC > 10%, the output deteriorated probably due to increased upconversion losses and energy-migration to impurities associated with high inversion in the gain medium. Although such effects do not affect the slope efficiency directly, they cause stronger heat loading. For low output coupling (T OC ≤ 5%), a thermal roll-over was observed for P abs > 5.5 W. The power scaling was limited to avoid fracture of the ceramic sample. The laser operated at the fundamental transverse mode, see the inset in Fig. 10(a).

The laser output was unpolarized. The laser emission spectra are shown in Fig. 10(b). They are only weakly dependent on the output coupling, the emission occurred at ~2.02 μm in agreement with the gain spectra, cf. Fig. 6(b).

Passive Q-switching

Q-switching was realized by inserting the SWCNT-SA into the cavity. There existed an upper limit of stable passively Q-switched (PQS) operation, which is ascribed to unwanted heating of the SA by the residual (non-absorbed) pump leading to deterioration of its nonlinear properties. According to the stability of Q-switched operation and the pulse characteristics, a low output coupling was selected (T OC = 3%). The PQS laser delivered a stable pulse train up to P abs ~3.5 W. Above this pump level, irregular multi-pulse behavior was observed. The laser output was unpolarized. The laser performance is presented in Fig. 11. The average output power of the PQS laser P out reached 0.85 W at 2023 nm with η = 27.8%, Fig. 11(a). With respect to the CW performance, the Q-switching conversion efficiency is reduced to η conv = 43.6%. This value is mainly determined by the insertion loss of the SA (Fresnel losses and non-saturable losses of the SWCNT / PMMA film). The laser threshold increased to P abs = 0.95 W for the same reason. The laser emission spectrum, Fig. 11(b), became narrower as compared to the CW operation mode, because of the stronger mode while bleaching the SA.

The pulse duration (FWHM), Δτ, and the pulse repetition frequency (PRF), were measured directly, and the energy of a single Q-switched pulse was calculated as E out = P out /PRF, see Fig. 11(c). The pulse characteristics (duration and energy) were dependent on the pump level which is typical for "fast" SAs such as carbon nanostructures (graphene, SWCNTs) [START_REF] Yasukevich | Modeling of graphene Q-switched Tm lasers[END_REF]. The latter is explained by the different degree of SA bleaching, which depends on the intracavity intensity. With an increase of the pump power, Δτ shortened from 322 to 256 ns and E out increased from 4.8 to 5.6 μJ. The PRF increased nearly linearly, from 37 to 151 kHz. As a result, the highest peak power P peak = E out /Δτ amounted to 22 W.

A typical oscilloscope trace of a single Q-switched pulse is shown in Fig. 11(d). It has a nearly Gaussian temporal shape, revealing a nearly-optimum ratio between the SA modulation depth and the output coupling. The pulse train exhibited relatively weak intensity instabilities, below 15%, as shown in Fig. 11(d). They are attributed to thermal effects in the SA [START_REF] Serres | Tm:KLu(WO 4 ) 2 microchip laser Q-switched by a graphene-based saturable absorber[END_REF].

Conclusion

Thulium-doped Lu 3 Al 5 O 12 transparent ceramics are promising for continuous-wave, Qswitched and mode-locked lasers at ~2 μm. As compared to their yttrium counterpart, Tm:Y 3 Al 5 O 12 , they are expected to offer better thermal properties, easier Tm 3+ doping and advantageous spectroscopic properties (in particular, slightly longer emission wavelength of ~2.02 μm). In the present work, we demonstrated efficient laser operation of a Tm:Lu 3 Al 5 O 12 transparent ceramic. A diode-pumped continuous-wave ceramic laser delivered up to 3.12 W at 2022-2035 nm with a slope efficiency of 60.2% (vs. the absorbed pump power), which is attributed to the good optical quality of the ceramic and the efficient cross-relaxation for Tm 3+ ions. Moreover, we characterized the spectroscopic properties of Tm 3+ in the fabricated Lu 3 Al 5 O 12 ceramic. A method to describe correctly the transition intensities from the lowerlying multiplets with J = 4 ( 3 F 4 ) is proposed. For power scaling and improvement of the slope efficiency, it would be promising to fabricate ceramics with even higher Tm doping (>5 at.%) leading to higher pump absorption and more efficient cross-relaxation among Tm 3+ ions. On the other hand, high doping levels may lead to a decrease of the optical quality and thermal conductivity of ceramics. Thus, a search of an optimum Tm doping is needed. For mode-locked applications, it seems promising to fabricate compositionally "mixed" (Lu,Y) 3 Al 5 O 12 ceramics featuring inhomogeneous broadening of the emission spectra.

Fig. 1 .

 1 Fig. 1. Photograph of a laser-grade-polished Tm:Lu 3 Al 5 O 12 transparent ceramic sample.

  (a). The ceramic sample was finely powdered for the XRD study. The ceramic has a cubic structure similar to that of undoped Lu 3 Al 5 O 12 (ICSD card #23846, sp. gr. Ia3¯d -O 10 h , No. 230) [27]. No traces of other phases are observed in the XRD pattern. The lattice constant is a = 11.91 Å. It is slightly larger than that of undoped Lu 3 Al 5 O 12 (a = 11.90 Å).

Fig. 2 .

 2 Fig. 2. Structure and microstructure of the Tm:Lu 3 Al 5 O 12 ceramic: (a) X-ray powder diffraction (XRD) pattern, black peaks stand for undoped Lu 3 Al 5 O 12 (ICSD card #23846), numbers denote the Miller's indices (hkl); (b) Field-Emission Scanning Electron Microscope (FESEM) image of a fractured surface, the scale bar is 50 μm.

Fig. 3 .

 3 Fig. 3. Unpolarized Raman spectrum of the Tm:Lu 3 Al 5 O 12 ceramic; numbers indicate Raman frequencies in cm -1 .

Fig. 4 .

 4 Fig. 4. Transmission spectrum of a laser-grade-polished 4 at.% Tm:Lu 3 Al 5 O 12 ceramic sample (t = 3.08 mm), green curve -theoretical transmission determined by Fresnel reflections.

Fig. 5 .

 5 Fig. 5. Absorption cross-section, σ abs , of Tm 3+ in the Lu 3 Al 5 O 12 ceramic for (a) the 3 H 6 → 3 H 4 transition and (b) the 3 H 6 → 3 F 4 transition. Arrow in (a) indicates the pump wavelength.

Fig. 6 .

 6 Fig. 6. Stimulated-emission (SE) of Tm 3+ -doped Lu 3 Al 5 O 12 ceramic at ~2 μm ( 3 F 4 → 3 H 6 transition): (a) SE cross-sections, σ SE , calculated using the RM and the F-L equation, and (b) gain cross-section, σ gain , for various inversion ratios β, calculated using a combined SE crosssection spectrum (see the details in the text). Arrow in (a) indicates the laser wavelength.

Fig. 7 .

 7 Fig. 7. Luminescence decay curve for the 4.0 at.% Tm:Lu 3 Al 5 O 12 ceramic: symbolsexperimental data; red linesingle-exponential fit for the luminescence lifetime τ lum .

Fig. 8 .

 8 Fig. 8. Energy-level schemes of Tm 3+ :Lu 3 Al 5 O 12 : (a) energy-level scheme showing the pump and laser transitions, cross-relaxation (CR), radiative (R) and non-radiative (NR) decays; (b) details of the splitting of the upper and lower laser multiplets; green arrow -ZPL transition. The position of the Stark sub-levels is calculated using the crystal-field parameters from [35].

Fig. 9 .

 9 Fig. 9. (a) Scheme of the diode-pumped Tm:Lu 3 Al 5 O 12 (Tm:LuAG) ceramic laser: LDlaser diode, PMpump mirror, OCoutput coupler, SAsaturable absorber; (b) transmission spectrum of the SWCNT-SA (Fresnel losses are subtracted).

Fig. 10 .

 10 Fig. 10. Continuous-wave (CW) diode-pumped Tm:Lu 3 Al 5 O 12 ceramic laser: (a) input-output dependences, ηslope efficiency, insetspatial profile of the laser beam (T OC = 5%, P abs = 5.3 W); (b) typical laser emission spectra measured at P abs = 3.0 W.

Fig. 11 .

 11 Fig. 11. Diode-pumped SWCNT-SA PQS Tm:Lu 3 Al 5 O 12 ceramic laser: (a) input-output dependence, ηslope efficiency; (b) typical laser emission spectrum; (c) pulse duration (FWHM), pulse energy and pulse repetition frequency (PRF) and (d) typical oscilloscope traces of a single Q-switched pulse and the pulse train both measured at P abs = 2.6 W and T OC = 3%. (a,b) contain CW regime data for comparison.

Table 1 . Calculated Stark Splitting of Tm 3+ Multiplets in Lu3Al5O12

 1

	2S+1 LJ E, cm -1
	3 H6	0, 26, 239, 244, 247, 312, 630, 705, 729, 730, 743, 767, 777
	3 F4	5527, 5784, 5847, 5925, 6089, 6174, 6267, 6270, 6295
	3 H5	8374,8385, 8542,8561, 8584, 8586, 8813, 8833, 8868, 8889,8897
	3 H4	12652, 12677, 12777, 12791, 12830, 12987, 13159, 13160, 13186
	3 F3	14673, 14702, 14720, 14753, 14762, 14766, 14766
	3 F2	15259, 15293, 15340, 15442, 15463
	1 G4	20757, 21205, 21221, 21404, 21541, 21736, 21854, 21883, 21884
	1 D2	27954, 27996, 28045, 28055, 28078
	1 I6	34426, 34436, 34438, 34468, 34584, 34677, 34740, 35092, 35092, 35279, 35308, 35387, 35399
	3 P0	35431
	3 P1	36343, 36390, 36464
	3 P2	38009, 38035, 38181, 38450, 38505

Table 2 . Experimental and Calculated Absorption Oscillator Strengths* for Tm:Lu3Al5O12 Ceramic

 2

	Transition 3 H6→ 2S+1 LJ	〈E〉exp, cm -1	n	f Σ exp×10 6 f Σ calc×10 6 (model**) J-O mJ-O	mJ-O***
	3 F4	5831	1.815 1.45	1.672 ED	1.381 ED	0.907 ED
	3 H5	8363	1.822 1.41	1.228 ED + 0.505 MD	1.078 ED + 0.505 MD	0.875 ED + 0.505 MD
	3 H4	12699 1.831 1.94	1.681 ED	1.971 ED	1.952 ED
	3 F2,3	14529 1.836 2.93	2.948 ED	2.868 ED	2.926 ED
	1 G4	21229 1.857 0.76	0.586 ED	0.713 ED	0.730 ED
	1 D2	27871 1.884 2.62	2.506 ED	2.644 ED	2.626 ED
	rms dev.				0.257	0.119	0.026
							Σ exp and f Σ calc -
	experimental and calculated absorption oscillator strengths (ED+MD), respectively. ED and
	MD stand for electric-dipole and magnetic-dipole transitions, respectively.
	**J-O -"standard" Judd-Ofelt model; mJ-O -modified Judd-Ofelt model.
	***Varied oscillator strength of the 3 H 6 → 3 F 4 transition.

*〈E〉 -experimental energy barycenter of the multiplet, n -refractive index, f

Table 3 . Parameters of the "Standard" and Modified Judd-Ofelt Theories for Thulium Ions in Various Ceramic Materials

 3

	Parameter	Tm:Lu3Al5O12		Tm:Y3Al5O12 Tm:(Lu,Sc)2O3
		This work		[43]	[44]
		J-O	mJ-O	mJ-O* J-O	J-O
	Ω2×10 20 , cm 2	1.025	2.164	2.507	0.444	2.429
	Ω4×10 20 , cm 2	1.781	1.511	1.236	1.340	1.078
	Ω6×10 20 , cm 2	0.799	1.039	1.340	0.674	0.653
	α×10 4 , cm	-	0.113	0.196	-	-

*Varied oscillator strength of the 3 H 6 → 3 F 4 transition.

Table 4 . Wave Functions of Tm 3+ Multiplets with J = 4 in Lu3Al5O12

 4

	Multiplet	Energy 〈E〉calc,	Coefficients of wave function for the 2S+1 LJ terms
	[main contribution]	cm -1	3 F4	3 H4	1 G4
	[ 3 F4]	5538	0.7868	-0.2851	0.5474
	[ 3 H4]	12475	0.5300	0.7666	-0.3626
	[ 1 G4]	21025	-0.3162	0.5754	0.7542

Table 5 . Probabilities of the Radiative Spontaneous Transitions* for Tm:Lu3Al5O12 Ceramic

 5

	Excited	Terminal	〈λ〉,	AΣ calc (JJ'),	B(JJ'),	Atot,	τrad,
	state	state	nm	s -1	%	s -1	ms
	3 F4	3 H6	1715	96.9 ED	100	96.9	10.32
	3 H5	3 F4	3949	7.1 ED + 0.2 MD	2.9	255.5	3.91
		3 H6	1196	157.4 ED + 90.8 MD	97.1
	3 H4	3 H5	2306	23.9 ED + 9.1 MD	2.9	1147.3 0.87
		3 F4	1456	102.5 ED + 22.5 MD	10.9
		3 H6	787	989.3 ED	86.2
	3 F2+ 3 F3	3 H4	5464	12.2 ED + 0.3 MD	0.3	3910.3 0.26
		3 H5	1622	550.7 ED	14.1
		3 F4	1150	585.4 ED + 63.6 MD	16.6
		3 H6	688	2698.1 ED	69.0
	1 G4	3 F2+ 3 F3	1493	143.5 ED + 3.5 MD	4.5	3190.0 0.31
		3 H4	1172	385.9 ED + 33.4 MD	13.2
		3 H5	777	1180.8 ED + 134.5 MD 41.2
		3 F4	649	264.3 ED + 10.0 MD	8.6
		3 H6	471	1034.1 ED	32.5

Acknowledgements

P.L. thanks Dr. Olga Dymshits (St. Petersburg, Russia) for the help with the XRD study.

Funding

Spanish Government (MAT2016-75716-C2-1-R (AEI/FEDER, UE), Generalitat de Catalunya (2017SGR755). This work was also supported by the Key research project of the frontier science of the Chinese Academy of Sciences (No. QYZDB-SSW-JSC022).