Pavel Loiko

Esrom Kifle

Lauren Guillemot

Jean-Louis Doualan

Florent Starecki

A Braud

Magdalena Aguiló

Francesc Díaz

Valentin Petrov

Xavier Mateos

Highly efficient 2.3 µm thulium lasers based on a high-phonon-energy crystal: Evidence of vibronic-assisted emissions

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION 2

In recent years, coherent light sources emitting near 2.3 µm in the short-wavelength infrared (SWIR) spectral range have attracted increasing attention. Such emission falls into the atmosphere transparency window with weak water vapor absorption containing at the same time absorption lines of atmospheric pollutants, i.e., hydrogen fluoride (HF), carbon monoxide (CO), methane (CH 4 ), or formaldehyde (H 2 CO).

Consequently, ∼2.3 µm lasers find applications in gas sensing in the atmosphere [1,2] and optical metrology of combustion processes [3]. They are also promising for non-invasive glucose (C 6 H 12 O 6 ) blood measurements [4]. Potentially, ultrafast ∼2.3 µm lasers can be used for further 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].

There exist several possibilities to obtain emission near 2.3 µm from solid-state lasers. Cr 2+ -doped II-IV group materials-zinc chalcogenides (ZnS, ZnSe)-give rise to a broadly tunable laser emission covering the desired wavelength Fig. 1. Energy level scheme of the Tm 3+ ion in the high-phononenergy monoclinic double tungstate crystal KLu(WO 4 ) 2 (after [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]), showing the pump transition (green arrow), laser transitions (red arrows), cross-relaxation (CR), and energy-transfer upconversion (ETU). NR is the non-radiative decay. The equally separated horizontal dashes show the average number of high-energy phonons (hν ph ) needed to bridge the energy-gaps between the multiplets involved in laser emission.

(as compared to other sources emitting in this spectral range) 89 is the availability of pump sources (e.g., AlGaAs laser diodes 90 [START_REF] Yorulmaz | Low-threshold diode-pumped 2.3-µm Tm 3+ : YLF lasers[END_REF] whose emission at ∼0.8 µm well overlaps with an intense 91 and broad 3 H 6 → 3 H 4 Tm 3+ absorption band) and laser gain 92 media (e.g., Tm:LiYF 4 single-crystals [START_REF] Pinto | Tm 3+ :YLF laser continuously tunable between 2.20 and 2.46 µm[END_REF] or Tm:ZBLAN glass 93 fibers [START_REF] El-Agmy | 2.31 µm laser under upconversion pumping at 1.064 µm in Tm 3+ : ZBLAN fibre lasers[END_REF]).

94

The above considerations, however, greatly limited the selec-95 tion of active gain media for bulk ∼2. were reported in [START_REF] Soulard | 2.3 µm Tm 3+ :YLF mode-locked laser[END_REF][START_REF] Canbaz | Kerr-lens mode-locked 2.3-µm Tm 3+ :YLF laser as a source of femtosecond pulses in the mid-infrared[END_REF]. The shortest pulses were achieved by Canbaz et al. (514 fs at 2.30 µm) from a Kerr-lens ML laser operating at a repetition rate of 41.5 MHz [START_REF] Canbaz | Kerr-lens mode-locked 2.3-µm Tm 3+ :YLF laser as a source of femtosecond pulses in the mid-infrared[END_REF]. The slope efficiency in such lasers has been rather low, well below the Stokes (S) limit of η St,L ≈ 34% for Tm:LiYF 4 . Only recently, we showed theoretically [START_REF] Loiko | Efficient Tm:LiYF 4 lasers at ∼2.3 µm: effect of energy-transfer upconversion[END_REF] and reported experimentally using fluoride crystals [START_REF] Loiko | Efficient Tm:LiYF 4 lasers at ∼2.3 µm: effect of energy-transfer upconversion[END_REF][START_REF] Guillemot | Close look on cubic Tm:KY 3 F 10 crystal for highly efficient lasing on the 3 H 4 → 3 H 5 transition[END_REF] that the slope efficiency of Tm lasers operating on the 3 H 4 → 3 H 5 transition can overcome the S limit and potentially approach 2η St,L owing to energy-transfer upconversion (ETU), 3 F 4 (Tm 1 ) + 3 F 4 (Tm 2 ) → 3 H 6 (Tm 1 ) + 3 H 4 (Tm 2 ), which becomes efficient at moderate Tm doping levels and acts against the CR by refilling the upper laser level. We also suggested that this mechanism may act in other Tm 3+ -doped crystals.

Note that other pumping schemes for ∼2.3 µm Tm lasers relying on the photon avalanche mechanism were also proposed, still leading to a relatively low laser efficiency [START_REF] Guillemot | Thulium laser at ∼2.3 µm based on upconversion pumping[END_REF][START_REF] Morova | Upconversion pumping of a 2.3 µm Tm 3+ :KY 3 F 10 laser with a 1064 nm ytterbium fiber laser[END_REF].

Recently, we revisited well-known Tm 3+ -doped oxide crystals (Tm : Y 3 Al 5 O 12 , Tm : YAlO 3 ) regarding their potential for efficient 2.3 µm lasers [START_REF] Guillemot | Watt-level midinfrared continuous-wave Tm:YAG laser operating on the 3 H 4 → 3 H 5 transition[END_REF][START_REF] Guillemot | Continuous-wave Tm:YAlO 3 laser at ∼2.3 µm[END_REF]. We demonstrated a wattlevel output from a Tm : Y 3 Al 5 O 12 laser operating on the 3 H 4 → 3 H 5 transition: 1.07 W at ∼2.19 and 2.32 µm with a slope efficiency of 46.3% [START_REF] Guillemot | Watt-level midinfrared continuous-wave Tm:YAG laser operating on the 3 H 4 → 3 H 5 transition[END_REF]. However, both crystals are known for their relatively long radiative lifetimes of the 3 H 4 state and moderate multi-phonon NR relaxation from this level.

Interestingly, the use of Tm : Y 3 Al 5 O 12 (highest phonon energy of 857 cm -1 ) raised the question of the role of vibronic emission for wavelengths between 2 and 2.3 µm.

In the present work, we demonstrate power-scalable and highly efficient operation on the 3 H 4 → 3 H 5 transition of a Tm laser based on another high-phonon energy oxide host, monoclinic double tungstate, and reveal the effect of the Tm doping concentration on the laser performance. As a material under study, we selected Tm 3+ -doped KLu(WO 4 ) 2 [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. So far, this crystal has been extensively studied for CW [START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF], Q-switched [START_REF] Loiko | Subnanosecond Tm:KLuW microchip laser Q-switched by a Cr:ZnS saturable absorber[END_REF], and fs ML [START_REF] Schmidt | Femtosecond pulses near 2 µm from a Tm:KLuW laser mode-locked by a single-walled carbon nanotube saturable absorber[END_REF] lasers emitting at ∼2 µm. Its spectroscopic features are high absorption and stimulated-emission (SE) cross sections for polarized light, broad and intense emission bands, high quantum yield, and weak concentration-quenching of the luminescence from the 3 F 4 state, and efficient CR [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]. The host matrix also provides nearly athermal behavior for certain crystal cuts, thus allowing for power scaling [START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF]. KLu(WO 4 ) 2 is known as a Raman-active material [START_REF] Kaminskii | Monoclinic tungstates KDy(WO 4 ) 2 and KLu(WO 4 ) 2 -new χ (3) -active crystals for laser Raman shifters[END_REF] with yet higher maximum phonon energy hν ph of ∼907 cm -1 . Thus, the energy-gap law for the multi-phonon NR relaxation postulating that the rate of NR relaxation is weak if E > 4 hν ph ( E is the energy-gap to the lower-lying multiplet) [START_REF] Scheife | Advances in up-conversion lasers based on Er 3+ and Pr 3+[END_REF] is valid for both and KY(WO 4 ) 2 has never been demonstrated.

CRYSTAL GROWTH

The growth of Tm : KLu(WO 4 ) 2 crystals was addressed before [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. Here, we briefly mention the key details. The crystals were grown by the top seeded solution growth slow-cooling (TSSG SC) method from the flux using potassium ditungstate (K 2 W 2 O 7 ) as a solvent [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. An undoped seed oriented along . At the wavelength of ∼2.3 µm, the principal refractive indices calculated using the Sellmeier equations [START_REF] Loiko | Refined orientation of the optical axes as a function of wavelength in three monoclinic double tungstate crystals KRE(WO 4 ) 2 (RE = Gd, Y or Lu)[END_REF] are n p = 1.984, n m = 2.014, and n g = 2.061.

The rectangular laser elements were all oriented for light propagation along the N g axis (N g cut). This is because of two reasons. First, this crystal cut provides attractive thermo-optic properties (weak, positive, and nearly spherical thermal lens [START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF]). Second, it gives access to the polarizations E ||N m and E ||N p corresponding to intense spectral bands both in absorption and emission [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]. The sample thickness (t) and aperture are listed in Table 1. Both input and output facets (N m × N p )

were polished to laser quality and remained uncoated.

NEAR-AND MIR-INFRARED EMISSIONS A. Stimulated-Emission Cross sections

The SE cross sections for the 3 F 4 → 3 H 6 transition (at ∼1.9 µm) of Tm 3+ ions in KLu(WO 4 ) 2 were reported before [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. Here, we mainly focus on thulium emission originating from the 3 H 4 state and suitable for laser operation, i.e., 3 H 4 → 3 F 4 (at ∼1.5 µm) and 3 H 4 → 3 H 5 (at ∼2.3 µm).

We also briefly characterize the 3 F 4 → 3 H 6 transition as it spectrally partially overlaps with the desired SWIR one.

First, polarized luminescence spectra W i (λ), where i = p, m, g represents the polarization index, were measured. As an excitation source, we used a Ti:sapphire laser tuned to ∼802 nm. The spectra at ∼1.5 µm and ∼1.9 µm were measured using an optical spectrum analyzer (OSA, AQ6375B, Yokogawa, spectral bandwidth, SBW = 1 nm). To measure

211

A Glan-Taylor polarizer was employed for polarized studies.

212

The wavelength calibration was performed using an Hg lamp 213 (Schwabe), and the response of the setup was calibrated using 214 a 20 W quartz iodine lamp so that the measured spectra W i (λ) 215 could be calibrated for the spectral response of the setup for the 216 specific polarization yielding the calibrated spectra W i (λ).

217

The SE cross sections, σ SE , were calculated using the 218 Füchtbauer-Ladenburg (F-L) formula [START_REF] Aull | Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections[END_REF],

219 σ i SE (λ) = λ 5 8π n 2 τ rad c W i (λ)B(J J ) (1/3) j = p,m,g λW j (λ)dλ , ( 1
)
where λ is the light wavelength, n is the mean refractive . For each of the considered transitions, we calculated the wavelengths of all the possible purely electronic transitions between the Stark components of the involved multiplets using the reported crystal-field splitting [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]. They are shown as dashes in Fig. 2 and facilitate the assignment of the observed emissions.

For the 3 H 4 → 3 F 4 transition, the emission band spans from

B. Vibronic Contribution

As can be seen from Figs. 2(b) and 2(c), the spectral ranges of purely electronic 3 F 4 → 3 H 6 and 3 H 4 → 3 H 5 transitions do not overlap. However, it is known that all Tm 3+ -doped materials exhibit strong electron-phonon (vibronic) interaction leading to the broadening of their emission bands. For Tm 3+ , this is determined by its location almost in the end of the lanthanide series [START_REF] Ellens | Vibronic transitions of Tm 3+ in various lattices[END_REF][START_REF] Krupke | Optical absorption and fluorescence intensities in several rare-earth-doped Y 2 O 3 and LaF 3 single crystals[END_REF]. Besides the broadening of the emission peaks corresponding to the particular Stark-to-Stark transitions, the

σ S = σ 0 exp(-α S E ), (2a)
σ AS = σ 0 exp(-α AS E ), ( 2b
)
where E is the energy mismatch between the vibronic and 317 the electronic transition, σ 0 is the transition cross section at doping concentration as a lower inversion ratio was needed to ensure the gain needed to compensate for the losses. For small inversion ratios, the gain spectra for the quasi-three-level 3 F 4 → 3 H 6 transition are flat and broad extending beyond 2 µm.

Second, long laser wavelengths were achieved in bulk Tm lasers employing a spectrally selective output coupler (OC) providing high transmission (HT) at <2 µm: Loiko et al. reported on a diode-pumped 3 at. % Tm : KLu(WO 4 ) 2 laser delivering 1.17 W with a slope efficiency of 39% at 2109-2133 nm [START_REF] Loiko | Vibronic thulium 1080 laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF], the longest wavelength achieved so far with this material.

Besides the assignment of this emission to the vibronic mechanism, the authors suggested a resonant mechanism involving low-frequency Raman modes of the host matrix (a possible contribution of CW self-Raman conversion). Note that the use of a similar cavity mirror allowed the authors in [START_REF] Schmidt | Femtosecond pulses near 2 µm from a Tm:KLuW laser mode-locked by a single-walled carbon nanotube saturable absorber[END_REF] to operate a ML Tm : KLu(WO 4 ) 2 laser above 2 µm (at 2037 nm) avoiding the unwanted structured water vapor atmospheric absorption and achieving fs pulse duration.

According to the proposed criterion, the emission at 2109-2133 nm observed in [START_REF] Loiko | Vibronic thulium 1080 laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF] can be in part assigned to the 3 H 4 → 3 H 5 transition (the vibronic contribution). Probably because of the limited reflection band of the cavity mirrors in [START_REF] Loiko | Vibronic thulium 1080 laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF], the authors were unable to achieve laser emission at longer wavelengths corresponding to the electronic 3 H 4 → 3 H 5 transition.

C. Lifetime of the 3 H 4 Multiplet: An Overview

The luminescence dynamics for Tm 3+ ions in KLu(WO 4 ) 2 was studied previously. In this section, we aim to summarize the reported results and to analyze them concerning the targeted 3 H 4 → 3 H 5 transition, i.e., by focusing on the 3 H 4 multiplet.

The intrinsic lifetime τ 30 determined in the limit of a very low Tm concentration (thus not being affected by the CR and energy-migration) is in general shorter than the radiative one because of the multi-phonon NR relaxation [START_REF] Weber | Radiative and multiphonon relaxation of rare-earth ions 1083 in Y 2 O 3[END_REF][START_REF] Layne | Multiphonon relax-1085 ation of rare-earth ions in oxide glasses[END_REF], 1

τ 30 = 1 τ 3rad + W NR , (3a)
382

W NR = C e -α E , ( 3b
)
where W NR is the rate constant (expressed in [s -1 ]) of the multi- 413

The luminescence lifetime of the 3 H 4 state can be represented 414 as a function of the Tm doping concentration (neglecting the 415 energy-migration) [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ∼80% slope efficiency[END_REF][START_REF] Loiko | Stochastic model of energy-transfer proc-1106 esses among rare-earth ions. Example of Al 2 O 3 :Tm 3+[END_REF],

1 τ 3l um = 1 τ 30 + W CR , (4a)
W CR = C CR N 2 Tm . (4b)
Here, W CR is the CR rate constant (expressed in [s The scheme of the laser setup is shown in Fig. 5 cut. The crystals were mounted on a massive passively cooled Cu-holder using a silver thermal paste for better heat removal.

The laser crystals were placed close to the PM leaving only a small air gap (less than 1 mm).

As a pump source, we employed a CW Ti:sapphire laser (3900S, Spectra Physics) delivering up to 3.6 W at the wavelengths of 770-810 nm (tunable output) in the fundamental mode (M 2 ≈ 1). The pump wavelength thus corresponded to decreased with the output coupling from 96.9% (T OC = 0.1%) to 89.4% (T OC = 4%). For all OCs, no colasing at wavelengths below 2 µm (the 3 F 4 → 3 H 6 electronic transition) was observed, verified by spectral measurements in the 1.7-2.4 µm range.

The power characteristics of the laser are shown in Fig. 6. It generated a maximum peak output power of 1.12 W at ∼2.22 and 2.29 µm (multi-color emission) with a slope efficiency η of 69.2% (determined with respect to the absorbed pump power P abs ). The laser threshold was at P th = 0.45 W, and the opticalto-optical efficiency, calculated with respect to the pump power incident on the crystal, η opt , reached 44.4% (all characteristics are specified for T OC = 1.3%). The laser threshold gradually increased with T OC , from 0.28 W for the 0.1% OC up to 0.58 W for the 4% OC. The input-output dependences were nonlinear near the laser threshold. No thermal roll-over or fracture of the crystal was observed up to at least P abs ∼ 2 W.

The true CW laser performance was studied only for the optimum T OC of 1.3%. The input-output dependence was almost identical to that for quasi-CW pumping indicating relatively weak thermal effects for the particular Tm doping level (3 at. % Tm) and output coupling. For the maximum available absorbed pump power P abs of 2.12 W, the CW output power amounted to 1.12 W, as shown by the asterisk in Fig. 6.

The laser generated a linearly polarized output (E ||N m ) with a polarization degree P exceeding 99%. The polarization state was naturally selected by the anisotropy of the gain in agreement with the SE cross section spectra, cf. Fig. 2(c). The laser emission spectra were dependent both on the output coupling and the pump power, Fig. 7. At low pump powers near the threshold, the laser operated at ∼2.29 µm for all the studied OCs. This corresponds to the main maximum in the SE cross section host matrix [START_REF] Loiko | Vibronic thulium 1080 laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF].

584

The mode profile of the Tm laser in the far-field is shown 585 Fig. 9(a). The output beam was nearly circular, which agrees 586 Fig. 8. Crystal-field splitting of the 3 H 4 and 3 H 5 multiplets of Tm 3+ in KLu(WO 4 ) 2 crystal (after [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]) and the assignment of the observed laser transitions. with the weak astigmatism of the thermal lens in N g -cut 587 Tm : KLu(WO 4 ) 2 [START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF]. The 1D intensity profiles in the hori-

η q1 = 1 + W CR (1/τ 30 ) + W CR . (5)
Here, W CR is the CR rate constant defined by Eq. (4b), and 656 C CR is the concentration-independent CR parameter. For 657 high Tm doping, efficient CR may result in η q 1 approaching 658 2 (two-for-one pump process). Thus, the laser slope efficiency 659 may exceed the S limit under lasing conditions setting the upper 660 limit of η < 2η St,L , where η St,L = λ P /λ L and λ P and λ L are 661 the pump and laser wavelengths, respectively. Indeed, very high 662 η q 1 value of 1.98 ± 0.02 was observed in a highly doped 15 at. 663 % Tm : KLu(WO 4 ) 2 laser emitting at ∼1.9 µm [START_REF] Mateos | Efficient micro-lasers based on highly doped monoclinic double tungstates[END_REF]. For the 664 case of 3 at. % Tm doping, Eq. ( 5) yields η q 1 = 1.79, which also 665 explains the high slope efficiency observed in the present work.

666

For the 3 at. % Tm-doped crystal, the round-rip passive cav-667 ity losses were estimated from the Caird analysis [START_REF] Caird | Quantum electronic properties of the 1110 Na 3 Ga 2 Li 3 F 12 :Cr 3+ laser[END_REF] to be L = 668 0.58 ± 0.2%.

669

The higher slope efficiency for the laser operating on the Slightly better laser performance was observed for pumping with E P ||N p : the laser generated 0.42 W at ∼ 2290 nm with η = 25.9% and a laser threshold of P th = 0.30 W. For the second studied pump polarization, the laser threshold slightly increased to P th = 0.32 W, and the output dependence was more nonlinear above it. This led to lower output power (0.35 W) at ∼2292 nm. However, the slope efficiency was almost unchanged (η = 24.7%). All the characteristics are specified for T OC = 1.3%. The pump absorption when pumping in E P ||N p was slightly higher. The total (double-pass) pump absorption at the threshold pump power η abs,L(2-pass) for T OC = 1.3% was calculated to be 96.2% and 92.3% for E P ||N p and E P ||N m , respectively. In Fig. 12, we present the laser excitation spectra for the 1.5 at.% Tm : KLu(WO 4 ) 2 pumped in two polarizations, E P ||N p and E P ||N m , i.e., plots of the (peak) output power versus the pump wavelength λ P . The incident pump power was fixed to P inc = 1.8 W, and it was weakly dependent (within a measurement error of ±5%) on λ P in the 770-820 nm spectral range. The coatings of the PM and OC exhibited flat spectral profiles at these wavelengths. Independent of the pump polarization, the laser polarization was naturally selected to be E ||N m . In Fig. 12, for comparison, we also show the polarized absorption cross section spectra for the 3 symbols, data calculated using Eq. ( 6); violet curve, empirical fit. (c) Output power and slope efficiency for 3 at. % Tm-doped crystal: circles, experimental data on the output power; green line, their linear fit yielding experimental η; red dashed curve, extrapolated output power calculated using Eq. ( 6); blue curve, dP out /dP abs , Eq. ( 7); dashed blue line, the intrinsic slope efficiency η 0 , Eq. ( 8). T OC = 1.3%; λ P = 793.8 nm; pump polarization, E P ||N p . Quasi-CW operation (duty cycle, 1:2). The pump quantum efficiency η q 2 can be evaluated from the input-output dependence according to the following analytical equation [START_REF] Loiko | Efficient Tm:LiYF 4 lasers at ∼2.3 µm: effect of energy-transfer upconversion[END_REF]:

P out = hν L hν P w 2 L w 2 P T OC T OC + L η q2 P abs - T OC hν L π w 2 L 2σ L SE τ 30 . (6)
where P out and P abs are the output laser power and the absorbed pump power, respectively, h is the Planck constant, and ν L and ν P are the laser and pump frequencies, respectively. The results on η q 2 obtained using a round trip loss L = 0.3 ± 0.2% are shown in Fig. 13(c). The L value was taken to be slightly smaller than that estimated in Section 4.C because of the longer laser wavelength and the lack of reabsorption. For all the studied Tm concentrations, the pump quantum efficiency gradually increases with the pump power, and this dependence saturates well above the laser threshold. This can be explained as follows.

In laser operation on the 3 H 4 → 3 H 5 transition, the inversion rate is clamped by the condition "gain equals losses." However, the absolute population density of the 3 F 4 state is not fixed and grows with the pump power. Indeed, direct measurements of the pump absorption under lasing conditions in ∼2.3 µm Tm lasers indicate ground-state bleaching above threshold [START_REF] Loiko | Efficient Tm:LiYF 4 lasers at ∼2.3 µm: effect of energy-transfer upconversion[END_REF].

Thus, the rate of the ETU process, which is proportional to the squared population density of the 3 F 4 state, increases with the pump power. This may be partially responsible for the nonlinear input-output dependences of the laser (another reason is the spatially non-uniform gain). At high pump powers well above the laser threshold, η q 2 reaches a pump-independent value determined by a counteraction of CR and ETU leading to a linear output dependence.

Another observation is that for small Tm doping levels (0.5-1.5 at. %), η q 2 is below unity. Here, η mode is the mode overlap efficiency, and η OC is the output coupling efficiency. As the pump quantum efficiency for the 3 H 4 → 3 H 5 transition η q 2 is pump-dependent, cf. Fig. 13(b), dP out /dP abs is not constant. For high pump powers well exceeding the laser threshold, the power dependence of η q 2 is saturated (η q 2 → η q 2,0 ), so that In Fig. 13(c), we extrapolated the output power of 798 the Tm laser using Eq. ( 6) and fitted the data on the 799 pump quantum efficiency using an empirical formula 800 η q 2 = η q 2,0 * exp[-(P abs -P th )/P 0 ], where P 0 is a free param-801 eter, as shown in Fig. 13(b). The result of this extrapolation 802 is shown by the red dashed curve. Accordingly, we determine 803 dP out /dP abs using Eq. ( 7), as shown by the blue solid curve. 804 dP out /dP abs first increases above the laser threshold and then 805 decreases asymptotically reaching the value of η 0 , which is deter-806 mined by Eq. ( 8). For the considered laser, η 0 = 54.9 ± 3%. [START_REF] Guillemot | Close look on cubic Tm:KY 3 F 10 crystal for highly efficient lasing on the 3 H 4 → 3 H 5 transition[END_REF][START_REF] Muti | Continuous-wave 1113 mid-infrared laser operation of Tm 3+ :KY 3 F 10 at 2.3 µm[END_REF], BaY 2 F 8 [START_REF] Muti | Tunable 1116 continuous-wave laser operation of Tm 3+ :BaY 2 F 8 near 2.3 µm[END_REF]) and oxide (Y 3 Al 5 O 12 [START_REF] Guillemot | Watt-level midinfrared continuous-wave Tm:YAG laser operating on the 3 H 4 → 3 H 5 transition[END_REF], 820 YAlO 3 [START_REF] Guillemot | Continuous-wave Tm:YAlO 3 laser at ∼2.3 µm[END_REF]56]) crystals. Among these results, we selected only 821 those relying on laser-pumping at ∼0.8 µm (to the 3 H 4 state, 822 conventional pump scheme). For this, typically, a Ti:sapphire 823 laser has been used as a pump source. The best results selected 824 from publications on the topic are summarized in Table 3 high An important parameter of the laser host crystal to be included in the comparison is the thermal conductivity κ.

η 0 = dP out dP abs P abs P th = η St,L η mode η OC η q2,0 . (8)
Its mean value for KLu(WO 4 ) 2 is κ = 3.12 Wm -1 K -1 [58]. This value is lower than for other crystals considered in Table 3. Thus, thermal management of Tm lasers based on this crystalline host is very important.

Note that for pumping in the same absorption band of Tm 3+ ( 3 H 6 → 3 H 4 ), AlGaAs laser diodes can be also used [START_REF] Wang | High 1132 efficiency nanosecond passively Q-switched 2.3 µm Tm:YLF laser 1133 using a ReSe 2 -based saturable output coupler[END_REF][START_REF] Kifle | In-band pumping of Tm:LiYF 4 channel waveguide: a power scaling strategy for ∼2 µm waveguide lasers[END_REF]. The main issues for diode-pumped ∼2.3 µm Tm lasers (as compared to those pumped by high-brightness sources such as bulk or fiber lasers) are the following: (i) higher laser thresholds, (ii) the key role of optimized mode-matching between the pump and laser radiation preventing the appearance of higherorder modes and colasing at ∼1.9 µm, and (iii) more serious thermal effects in the active element.

CONCLUSION

To conclude, solid-state lasers based on Tm 3+ -doped materials and operating on the 3 H 4 → 3 H 5 transition are excellent candidates for highly efficient coherent light sources in the short-wave infrared spectral range and, in particular, at ∼2.3 µm. Contrary to well-established models, they are rather tolerant to such key parameters of the gain media as their phonon spectra and Tm doping levels. This is due to the relatively complex physical nature of the 3 H 4 → 3 H 5 laser scheme affected by both CR and ETU between neighboring Tm 3+ ions. We prove that highly efficient lasing at ∼2.3 µm (with a slope efficiency exceeding the S limit) can be achieved even in high-phonon energy Tm 3+doped crystals at moderate doping levels leading to a notable self-quenching of the upper laser level by CR. An evidence of a two-for-one pump process associated with the ETU refilling the upper laser level and probably with the gain at the vibronic sideband of the 3 F 4 → 3 H 6 transition has been provided. A compact Tm : KLu(WO 4 ) 2 laser generated a watt-level output at ∼2.22 and 2.29 µm (multi-color emission) with a slope efficiency of 69.2%-a record-high for this type of lasers. Thus, it can be expected that other Tm 3+ -doped oxide crystals may be also of practical importance for ∼2.3 µm lasers by providing better power scaling or other laser wavelengths.

Research Article

We also extend the understanding of the physical nature 879 of emission at wavelengths lying between the 3 H 4 → 3 H 5 880 and 3 F 4 → 3 H 6 electronic transitions. First, we determined 881 the SE cross sections for Tm 3+ ions in KLu(WO 4 ) 2 , which 882 reached 1.78 × 10 -20 cm 2 at 2289 nm for the former transi-883 tion representing the highest value among all the Tm 3+ -doped 884 materials (crystals, ceramics, and glasses) studied so far. We 885 were able to assign multiple observed laser lines lying between 886 2.14 and 2.30 µm to electronic transitions occurring between 887 the Stark sub-levels of the 3 H 4 and 3 H 5 multiplets. We also 888 showed that vibronic transitions bridge the gap between the

the 3 H

 3 4 and 3 F 4 states [Fig.1(a)]. So far, ∼2.3 µm lasing from Tm : KLu(WO 4 ) 2 or its Tm 3+ -doped isomorphs KGd(WO 4 ) 2

  the [010] direction was used to start the growth. The growth was performed in Pt crucibles using K 2 CO 3 , WO 3 , Lu 2 O 3 , and Tm 2 O 3 reagents. The concentration of Tm 3+ ions was 0.5, 1.5, or 3.0 at. %. The temperature gradient in the solution was ∼1 K/cm, the rotation speed of the seed was 40 rpm, and the cooling rate was 0.1-0.3 K/h. The crystals had a slight paleyellow coloration due to the Tm 3+ doping. The actual Tm 3+ doping concentration N Tm in the crystals was determined by electron probe microanalysis (EPMA); see Table 1. Tm : KLu(WO 4 ) 2 belongs to the monoclinic crystal class (sp. gr. C 6 2h -C 2/c , No. 15). The lattice constants for 3 at. % Tm doping are a = 10.576 Å, b = 10.215 Å, c = 7.487 Å, and the monoclinic angle β = 130.68 • [14]. This crystal is optically biaxial. Its optical indicatrix was deeply characterized before [31,37]. Briefly, the three optical indicatrix axes (N p , N m and N g ) are selected according to the convention n p < n m < n g for the principal refractive indices, and are oriented as follows: the N p axis is parallel to the b axis (the C 2 symmetry axis), and the N m and N g ones are lying in the a-c plane (⊥ C 2 , the mirror plane). The angle N c g = 18.5 • , measured outside the monoclinic angle β [31]

Fig. 2 .

 2 Fig. 2. Stimulated-emission (SE) cross sections, σ SE , for (a) 3 H 4 → 3 F 4 , (b) 3 F 4 → 3 H 6 , and (c) 3 H 4 → 3 H 5 transitions of Tm 3+ in monoclinic KLu(WO 4 ) 2 for light polarizations E ||N p , N m and N g , calculated using the F-L formula, Eq. (1). Vertical dashes indicate all possible purely electronic transitions between the Stark sub-levels of the involved multiplets.

Fig. 3 .

 3 Fig. 3.Electron-phonon coupling bridges the gap between the 3 F 4 → 3 H 6 and 3 H 4 → 3 H 5 electronic transitions of Tm 3+ in monoclinic KLu(WO 4 ) 2 crystal: a semi-logarithmic plot of the stimulated-emission, σ SE , and absorption, σ abs , cross sections for the3 F 4 ↔ 3 H 6 and 3 H 4 → 3 H 5 transitions for light polarization E ||N m . Symbols, experimental data; lines, exponential fits to the phonon sidebands of the spectral bands, Eq. (2). Vertical dashes indicate the purely electronic transitions between the Stark sub-levels of the involved multiplets. Black vertical dashed line indicates the wavelength of equal σ SE for the two transitions.

  318the photon energy corresponding to the electronic transition, and the factors α S and α AS depend on the host material. For 320 Tm : KLu(WO 4 ) 2 , we obtain the material-dependent fac-321 tors α S = 10.0 ± 0.7 × 10 -3 cm -1 and α AS = 14.5 ± 1.5 × 322 10 -3 cm -1 . The wavelength at which the SE cross sections for 323 both transitions are equal is λ eq = 2104 ± 10 nm.Thus, the gap between the 3 F 4 → 3 H 6 and 3 H 4 → 3 H 5 electronic transitions of Tm 3+ in KLu(WO 4 ) 2 is bridged by vibronic transitions. The performed analysis allowed us to propose a criterion for the attribution of emissions within this gap. All the emissions with wavelengths exceeding λ eq will be assigned as such related to the 3 H 4 → 3 H 5 transition (either of electronic or vibronic nature), and all the emissions at shorter wavelengths to the 3 F 4 → 3 H 6 one.Let us discuss previously obtained results on Tm : KLu(WO 4 ) 2 lasers in light of this criterion. Typically, bulk lasers based on this crystal operated at a wavelength of ∼1.94 µm, e.g., Serres et al. reported on a diode-pumped 3 at. % Tm-doped laser delivering multi-watt output at 1946 nm[START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF]. This wavelength is close to the longest wavelength of the 3 F 4 → 3 H 6 purely electronic transition.Longer wavelengths were achieved under two circumstances.First, highly doped crystals provided emission above 2 µm using low output coupling and without any spectrally selective elements: Mateos et al. reported a 0.59 W output power at 2005-2045 nm with a slope efficiency of 51% for 15 at. % Tm doping[START_REF] Mateos | Efficient micro-lasers based on highly doped monoclinic double tungstates[END_REF]. Such wavelengths clearly represent vibronic emission. This behavior was mainly induced by the high Tm 3+

Fig. 4 .

 4 Fig. 4. (a) Rate constants of multi-phonon non-radiative relaxation W NR versus the energy-gap to the lower-lying state E for various excited states of rare-Earth ions in monoclinic double tungstate crystals: circles, data from[START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF][START_REF] De Mendívil | Judd-Ofelt analysis and transition probabilities of Er 3+ 1089 doped KY 1-x-y Gd x Lu y (WO 4 ) 2 crystals[END_REF][START_REF] Pujol | Crystalline structure and optical spectroscopy of 1093 Er 3+ -doped KGd(WO 4 ) 2 single crystals[END_REF][START_REF] Pujol | Emission cross sections and spectroscopy of Ho 3+ laser channels 1097 in KGd(WO 4 ) 2 single crystal[END_REF]; red line, fit using Eq. (3b); red circle, estimation for the 3 H 4 Tm 3+ state. (b) Luminescence lifetimes of the 3 H 4 Tm 3+ state in monoclinic double tungstate crystals: symbols, data from[START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF][START_REF] Demidovich | Optical characterization of Yb,Tm:KYW crystal con-1101 cerning laser application[END_REF][START_REF] Güell | Blue luminescence in Tm 3+ -doped KGd(WO 4 ) 2 single 1104 crystals[END_REF]; red curve, fit using Eq. (4a); horizontal dashed lines, estimations of the radiative lifetime (this work and[START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]).

  383 phonon NR relaxation, which depends on the energy-gap to 384 the lower-lying state E and the maximum phonon energy 385 hν ph , and C and α are characteristic constants for the material. 386 C has the meaning of a NR rate 3 constant in the limit of zero 387 energy-gap ( E → 0), and α = -ln(ε)/(hν ph ), where ε is the 388 ratio between the probabilities of m-phonon and m-1-phonon 389 relaxation. 390 In Fig. 4(a), we analyzed the W NR values calculated by com-391 paring the radiative and intrinsic lifetimes of various excited 392 states of several rare-Earth ions in several KRE(WO 4 ) 2 393 crystals [14,47-49] considering their very close phonon 394 spectra. The experimental data on W NR are well fitted with 395 Eq. (3b) yielding the following best-fit material parameters: 396 C = 2.14 ± 2 × 10 8 s -1 and α = 2.90 ± 0.1 × 10 -3 cm. 397 These parameters reasonably agree with those estimated by de 398 Mendivil et al. [47]. 399 Regarding the 3 H 4 Tm 3+ state, according to the Judd-400 Ofelt analysis by Silvestre et al. [14], the radiative lifetime 401 τ 3 rad = 0.203 ms. This obviously contradicts the lumines-402 cence lifetime measured by the same authors for the low doped 403 sample (0.5 at. % Tm), τ 3l um = 0.230 ms [14], which can 404 be approximately taken as the intrinsic one. The application 405 of Eq. (3b) with the material parameters determined above 406 yields W NR = 2.2 ± 1 × 10 3 s -1 and, accordingly, τ 3 rad about 407 0.47 ms. The difference between this value and the one obtained 408 from the Judd-Ofelt calculations can be explained by the error 409 in the latter. At the moment, we are unable to clarify this dis-410 crepancy, and further analysis is needed (e.g., by employing the 411 modified Judd-Ofelt theory accounting for the configuration 412 interaction).

Fig. 5 .

 5 Fig. 5. (a) Scheme of the Tm laser operating on the 3 H 4 → 3 H 5 transition: λ/2, half-wave plate; P, Glan-Taylor polarizer; FL and CL, focusing and collimating lenses, respectively; PM, pump mirror; OC, output coupler; F, bandpass filter. (b) and (c) Total (double-pass) pump absorption under non-lasing conditions η abs,NL(2-pass) for the studied laser crystals. The pump polarization is (b) E P ||N p and (c) E P ||N m .

the 3 H 6 → 3 H 4

 3634 Tm 3+ transition. The incident pump power was adjusted using a half-wave plate and a Glan-Taylor polarizer oriented in such a way that the pump polarization corresponded to E P ||N p or E P ||N m in the crystal. The pump beam was expanded using a homemade telescope (reimaging ratio, 1:2) and focused into the crystal using an achromatic lens (focal length, f = 60 mm). A mechanical chopper (frequency, 20 Hz; duty cycle, 1:2) was introduced in the beam path to ensure quasi-CW pumping reducing the heat loading in the crystal. The pump spot radius in the focus w P was 40 ± 10 µm (at the 1/e 2 level, as measured by the optical knife method), and the calculated confocal parameter of the pump beam 2z R exceeded 10 mm (in the crystal). The radius of the laser mode in the crystal was calculated by the ABCD-method accounting for the positive thermal lens to be w L = 40-44 ± 5 µm (slowly decreasing with the pump power). Thus, relatively good mode-matching was observed.For each crystal, first, we measured pump absorption under non-lasing (NL) conditions in a single-pass. The measurements were done for the pump wavelengths of 793.8 and 802.1 nm corresponding to the polarizations E P ||N p or E P ||N m , respectively. Then, the second pass of the pump was taken into account leading to the total value η abs,NL(2-pass) (it does not include Fresnel losses at the uncoated crystal surfaces). The decreasing η abs,NL(2-pass) value with the incident pump power, as shown in Figs. 5(b) and 5(c), represents the effect of groundstate bleaching (absorption saturation). The absorption under lasing (L) conditions was estimated from the η abs,NL(2-pass) value for each OC at the threshold pump power. To separate the 3 H 4 → 3 H 5 laser emission from the residual (non-absorbed) pump, we used a bandpass filter (FB2250-500, Thorlabs). The spectra of the laser emission were measured using an OSA (AQ6375B, Yokogawa; resolution, 0.2 nm). The pump wavelength was determined using another OSA (Ando AQ6315-E; resolution, 0.1 nm). The laser beam profile in the far-field was captured using a pyroelectric camera (PY-III-HR-C-A, Ophir). The beam quality factors M 2 x ,y were measured by an ISO-standard method using a single spherical CaF 2 lens ( f = 100 mm) placed after the OC. In addition to the laser experiment on the 3 H 4 → 3 H 5 transition, we studied the performance of the 3.0 at. % Tm-doped crystal on the 3 F 4 → 3 H 6 transition. For this, the same setup was used, only the cavity mirrors were replaced. The flat PM provided HT (T = 97.4%) at ∼0.79 µm and HR at 1.87-2.30 µm, and the concave OCs (RoC = -100 mm) provided T OC of 0.5%-15% at 1.90-2.08 µm. The OCs provided relatively HT of T > 70% at the pump wavelength, so that the pumping was in a single-pass in this case.

Fig. 6 .

 6 Fig. 6. Input-output dependences for the Tm laser pumped at 793.8 nm (E P ||N p ) and operating on the 3 H 4 → 3 H 5 transition in the quasi-CW mode (duty cycle, 1:2); η, slope efficiency. Tm doping, 3 at. %. The asterisk indicates the maximum power obtained in true CW regime (T OC = 1.3%).

Fig. 7 .

 7 Fig. 7. Emission spectra from the thulium laser (3 at. % Tm) operating on the 3 H 4 → 3 H 5 transition at different absorbed pump powers P abs . Output coupling: (a) 0.1%, (b) 0.7%, (c) 1.3%, and (d) 4.0%. The laser polarization is E ||N m .

Fig. 9 .

 9 Fig. 9. Spatial characteristics of the output of the Tm laser operating on the 3 H 4 → 3 H 5 transition. (a) 1D intensity profiles in the horizontal (x , ||N m ) and vertical (y , ||N p ) directions: symbols, experimental data; curves, Gaussian fits; inset, 2D mode profile in the far-field. (b) Evaluation of the beam quality factors M 2 x ,y . Tm doping, 3 at.%. T OC = 1.3%; P abs = 0.8 W. The laser polarization (E ||N m ) is horizontal.

Fig. 10 .

 10 Fig. 10. Tm laser pumped at 793.8 nm (E P ||N p ) and operating on the 3 F 4 → 3 H 6 transition in quasi CW mode (duty cycle, 1:2): (a) input-output dependences; η, slope efficiency; the output dependence for the laser operating on the 3 H 4 → 3 H 5 transition is given for comparison; (b) typical laser emission spectra measured at P abs = 0.5 W. The laser polarization is E ||N m . Tm doping, 3 at. %.

670 3 H 4 Fig. 11 .

 3411 Fig. 11. Effect of the pump polarization (E P ||N m and E P ||N p ) on (a) 3 H 4 → 3 H 5 laser performance; η, slope efficiency. (b) Laser emission spectra captured at P abs = 1.1 W for 1.5 at. % Tm : KLu(WO 4 ) 2 . Quasi-CW operation (duty cycle, 1:2). The laser polarization is E ||N m .

Fig. 12 .

 12 Fig. 12. Laser excitation spectra (output power versus pump wavelength) for the Tm laser operating on the 3 H 4 → 3 H 5 transition for pump polarization (a) E P ||N m and (b) E P ||N p . The absorption cross sections, σ abs , for the 3 H 6 → 3 H 4 Tm 3+ transition are shown for comparison. Quasi-CW operation (duty cycle, 1:2). P inc = 1.8 W. Tm doping, 1.5 at. %.

  H 6 → 3 H 4 Tm 3+ transition. For E P ||N p , laser emission was observed when varying the pump wavelength in the 781.2-807.6 nm range and for E P ||N m -in the 773.1-812.7 nm range. The shape of the laser excitation spectra matched well that of the polarized absorption spectra. E. 3 H 4 → 3 H 5 Transition: Effect of the Doping Concentration A summary of the laser experiments on the 3 H 4 → 3 H 5 Tm 3+ transition with the 0.5, 1.5, and 3.0 at. % Tm 3+ -doped crystals performed with polarized pump (E P ||N p and E P ||N m ) is presented in Table 2. The input-output dependences measured using the same output coupling (T OC = 1.3%) and pump polarization (E P ||N p ) are compared in Fig. 13(a). With increasing the Tm doping concentration, the slope efficiency of the laser η greatly increased from 10.7% (0.5 at. % Tm) to 69.2% (3.0 at. % Tm), so that the maximum slope efficiency Research Article

Fig. 13 .

 13 Fig.[START_REF] Shterengas | High-power 2.3-µm GaSb-based linear laser array[END_REF]. Effect of doping concentration on the performance of Tm lasers operating on the 3 H 4 → 3 H 5 transition: (a) input-output dependences, η, slope efficiency. (b) Pump quantum efficiency η q 2 : symbols, data calculated using Eq. (6); violet curve, empirical fit. (c) Output power and slope efficiency for 3 at. % Tm-doped crystal: circles, experimental data on the output power; green line, their linear fit yielding experimental η; red dashed curve, extrapolated output power calculated using Eq. (6); blue curve, dP out /dP abs , Eq. (7); dashed blue line, the intrinsic slope efficiency η 0 , Eq. (8). T OC = 1.3%; λ P = 793.8 nm; pump polarization, E P ||N p . Quasi-CW operation (duty cycle, 1:2).

  For the medium doping of 3 at. % Tm, it approaches 1.8 ± 0.1, which explains the observed high laser efficiency. Moreover, with increasing Tm concentration, the maximum pump quantum efficiency gradually increases. It seems that the positive effect of ETU on the performance of ∼2.3 µm lasers based on Tm : KLu(WO 4 ) 2 crystals is enhanced with the Tm doping concentration faster than the negative effect of CR. Let us discuss the definition of the slope efficiency of a Tm laser operating on the 3 H 4 → 3 H 5 transition. By definition, η = dP out /dP abs . If the input-output dependence is linear within a certain range of pump powers, this will lead to a constant η value. By applying this definition to Eq. (6), we achieve dP out dP abs = η St,L η mode η OC η q2 (P abs ) + d η q2 dP abs P abs . (7)

807 9 )

 9 Note that this value is almost not sensitive to the round trip 808 passive loss used for the calculations. η 0 can be further improved 809 under the condition of η mode and η OC both approaching unity 810 (excellent mode-matching and very low round trip intracavity 811 losses), so that 812 η 0 ≤ 2η St,L . (This equation represents an upper limit for the slope efficiency 813 of a Tm laser operating on the 3 H 4 → 3 H 5 transition and repre-814 sents an ideal two-for-one pump process. 815 F. 3 H 4 → 3 H 5 Transition: Comparison with Other 816 Hosts 817 So far, CW laser operation on the 3 H 4 → 3 H 5 transition has 818 been achieved in very few Tm 3+ -doped fluoride (LiYF 4 [25], 819 KY 3 F 10

  doping level, the maximum phonon frequency 826 of the host matrix hν ph , the spectroscopic properties at the laser 827 wavelength, and the CW laser performance. 828 The Tm : KLu(WO 4 ) 2 crystal features the highest maximum 829 phonon frequency (907 cm -1 ) among the crystals intended for 830 ∼2.3 µm Tm lasers. It also provides the highest SE cross section 831 for the 3 H 4 → 3 H 5 transition in polarized light, owing to the 832 strong polarization-anisotropy of spectroscopic properties of 833 this monoclinic crystal, and relatively short radiative lifetime of 834 the upper laser level. Moreover, we report on the highest output 835 power and slope efficiency ever achieved from a laser-pumped 836 ∼2.3 µm Tm laser using a 3.0 at. % Tm : KLu(WO 4 ) 2 crystal.The slope efficiency (69.2%) almost approaches the limit set by 2 times the S efficiency, highlighting the very efficient ETU in this material.

889 3 H 4

 34 → 3 H 5 and 3 F 4 → 3 H 6 electronic transitions leading 890 to a non-vanishing SE cross section and, potentially, optical 891 gain within this spectral range. Based on these studies, we were 892 able to explain previous findings on vibronic Tm lasers. Our 893 results indicate that Tm 3+ -doped monoclinic double tungstate 894 crystals may provide a continuously tunable laser emission over 895 an ultra-broad spectral range of about 1.7-2.5 µm. 896 We highlight the suitability of Tm 3+ -doped monoclinic dou-897 ble tungstates for fs ML lasers at ∼2.3 µm based on their broad 898 emission spectra (bandwidth exceeding 30 nm, not affected by 899 the inversion rate). Another relevant conclusion of our work 900 is the possible contribution of 3 H 4 → 3 H 5 and 3 F 4 → 3 H 6 901 related vibronic emissions to the very broad emission spectra 902 of ML thulium lasers extending beyond 2 µm, observed so 903 far in several crystals [61,62]. This should be clarified further, 904 e.g., by comparing the resonant Raman and vibronic gain in 905 such materials. 906 Further power scaling of monoclinic double tungstate-based 907 ∼2.3 µm Tm lasers can be realized in several ways, i.e., (i) by 908 using other pump sources, such as laser diodes at ∼0.8 µm 909 (for the conventional pump scheme), Er Raman fiber lasers 910 emitting at ∼1.6 µm (in-band pumping [63]) or Yb fiber lasers 911 at ∼1 µm (upconversion pumping [64], which would require 912 the measurements of the excited-state absorption spectra); or 913 (ii) by using short highly doped samples (5-15 at. % Tm) for 914 better pump absorption, pump and laser mode overlap, and 915 high slope efficiency. The latter approach will require a rate-916 equation modeling of the Tm 3+ system involving the ETU and 917 energy-migrations rate constants, which are still unknown for 918 monoclinic double tungstates. The power scaling will raise the 919 question of the fractional heat loading under laser operation on 920 the 3 H 4 → 3 H 5 transition. Finally, as Tm 3+ -doped monoclinic

  LiYF 4 lasers operating on the 3 H 4 → 3 H 5 transition

3 µm Tm lasers from 96 the point of view of the host matrix (only low-phonon energy 97 crystals, e.g., fluorides) and the Tm doping level (preferably low, 98 to prevent self-quenching of the 3 H 4 lifetime). Thus, in most of 99 the previous studies, mainly Tm:LiYF 4 crystals with relatively 100 low doping levels were studied (see, e.g., [20,21]). 101 Pinto et al. reported on a CW Tm : LiYF 4 laser delivering 0.22 W at 2.30 µm with a slope efficiency of 15% and achieved a wavelength tuning between 2.20 and 2.46 µm [21]. ML Tm:

Table 1 .

 1 Parameters of the Thulium-Doped Laser Elements

Doping, at. % N Tm , 10 20 cm -3 t, mm Aperture, mm 2

	0.5	0.35	9.30 (N

g ) 2.56(N m ) × 3.12(N p ) 1.5 1.14 5.97 (N g ) 3.72(N m ) × 4.10(N p ) 3.0 2.41 4.91 (N g ) 3.73(N m ) × 4.09(N p )

  1.38 to 1.52 µm (according to the calculated electronic transitions) and the maximum σ SE = 2.11 × 10 -20 cm 2 at 1483 nm for the light polarization E ||N m . For the 3 F 4 → 3 H 6 transition, the emission band is much broader due to the relatively large total Stark splitting of the ground-state ( 3 H 6 ), and it spans from 1.67 to 1.95 µm (the electronic transitions), while the vibronic tail of the emission band extends beyond ∼2 µm. The maximum σ SE reaches 3.57 × 10 -20 cm 2 at 1842 nm for E ||N m . The 3 F 4 → 3 H 6

	transition represents a quasi-three-level laser scheme with
	reabsorption. Thus, the laser emission is typically achieved at
	longer wavelengths. In particular, σ SE = 0.91 × 10 -20 cm 2
	at 1946 nm for E ||N m . At this emission wavelength, the
	anisotropy of the SE cross sections is expressed by the ratios
	σ SE (m) : σ SE ( p) = 3.7 and σ SE (m) : σ SE (g ) = 11. This imposes
	the emission to be linearly polarized in Tm : KLu(WO 4 ) 2 lasers.
	The determined σ SE values agree with those calculated by the
	reciprocity method [31].
	Finally, for the transition of interest in this work, namely
	3 H 4 → 3 H 5 , the emission band is also rather broad and
	spans from 2.14 to 2.53 µm (the electronic transitions).
	The laser wavelength for this quasi-four-level laser scheme
	is simply determined by the SE cross section spectra. The
	maximum σ SE is 1.78 × 10 -20 cm 2 at 2289 nm, and the cor-
	responding emission bandwidth λ em (determined as the
	full width at half-maximum, FWHM) is 32.1 nm for E ||N m .
	The anisotropy of the SE cross sections is weaker than for
	the 3 F 4 → 3 H 6 transition, i.e., σ SE (m) : σ SE ( p) = 1.7 and
	σ SE (m) : σ SE (g ) = 2.5; however, it is enough to ensure natural
	selection of the laser polarization. The determined SE cross
	section for the 3 H 4 → 3 H 5 transition is higher than in any previously studied Tm 3+ -doped fluoride or oxide crystal, and
	is assigned to the strong polarization-anisotropy of the optical
	properties in Tm : KLu(WO 4 ) 2 , and in part, to the relatively
	short radiative lifetime of the emitting state ( 3 H 4 ). Indeed, for
	the most widespread crystal for ∼2.3 µm lasers, Tm:LiYF 4 , σ SE reaches 0.57 × 10 -20 cm 2 at 2305 nm, and λ em is 25.8 nm
	for π -polarized light [25]. Considering the relatively broad
	emission band, Tm : KLu(WO 4 ) 2 appears to be attractive for
	ML lasers at ∼2.3 µm.

  -1 ]), and C CR

	418
	419	is the concentration-independent CR parameter (expressed
	420	in [cm 6 s -1 ]). In Fig. 4(b), we summarize the luminescence
	421	lifetimes of the 3 H 4 multiplet of Tm 3+ ions reported for
	422	KLu(WO 4 ) 2 and its isomorph crystals [14,50,51]. In this
	423	analysis, we accounted for the different cation density per
	424	1 at. % doping in different crystals. As can be seen, for differ-
	425	ent host-forming cations in the monoclinic double tungstate
	426	crystals, the 3 H 4 lifetime of the dopant ones (Tm 3+ ) follows
	427	nearly the same trend. The fitting of the experimental data using
	428	Eq. (4) yields the following parameters: τ 30 = 0.24 ± 0.01 ms
	429	and C CR = 2.70 ± 0.15 × 10 -37 cm 6 s -1 . These values are in
	430	reasonable agreement with those published in [18].
	431	The use of Eq. (4a) with the determined best-fit τ 30 and C CR
	432 433	parameters yields τ 3l um = 222, 130, and 50 µs for the 0.5, 1.5, and 3.0 at.%Tm 3+ -doped KLu(WO 4 ) 2 crystals, respectively.
	434	4. LASER PERFORMANCE
	435	A. Laser Setup

Table 2 .

 2 Output Characteristics a of Thulium Lasers at , pump wavelength (polarization given in brackets); P out , peak output power; P th , laser threshold; η, slope efficiency versus P abs ; λ L , laser wavelength; η opt , optical-to-optical efficiency. T OC = 1.3%.

	∼2.3 µm
	Tm, at. %	λ P , nm P out , W η, % P th , W λ L , nm η opt , %
	0.5	793.8 (N p ) 0.17 10.7 0.28 2290-2293	6.9
	1.5	793.8 (N p ) 0.42 25.9 0.30 2288-2290 17.6
		802.1 (N m ) 0.35 24.7 0.32 2291-2292 14.4
	3.0	793.8 (N p ) 1.12 69.2 0.45 2218-2223, 44.4
		2290-2294
		802.1 (N m ) 1.02 67.7 0.44 2214-2219, 40.5
		2289-2293

a λ P

  well exceeded the S limit, η St,L = 35.8%. Let us discuss this (Tm 1 ) + 3 H 6 (Tm 2 ) → 3 F 4 (Tm 1 ) + 3 F 4 (Tm 2 ),

		where values below unity are governed by CR (assuming no
		ETU) and values above unity indicate efficient ETU.
	730
	731	behavior.
	732	Recently, we developed a model describing Tm lasers
	733	operating on the 3 H 4 → 3 H 5 transition [25]. It is based on
	734	accounting for two key energy-transfer processes affecting
	735	the population of the upper laser level ( 3 H 4 ), namely the
	CR, 3 H 4 736
	737	and the reverse process of ETU, 3 F 4 (Tm 1 ) + 3 F 4 (Tm 2 ) →
	738	3 H 6 (Tm 1 ) + 3 H 4 (Tm 2 ). The CR depopulates the upper laser
	739	level while the ETU brings the ions back using the metastable
	740	3 F 4 state as a "reservoir" of electronic excitations. Thus, contrary
	741	to the ∼1.9 µm laser transition, ETU plays a positive role for the
	742	∼2.3 µm lasers, while the CR is a detrimental effect. The pump
	743	quantum efficiency η q 2 , defined as the number of electronic excitations to the 3 H 4 level per number of absorbed pump pho-
	745

744

tons at ∼0.8 µm, can thus vary in the range of 0 < η q 2 < 2,

Table 3 .

 3 Summary a of Laser-Pumped Thulium Lasers Operating on the 3 H 4 → 3 H} 5 Transition Reported So Far SE , peak stimulated-emission cross section at ∼2.3 µm; τ 30 , intrinsic lifetime of the 3 H 4 state; λ P , pump wavelength; P th , laser threshold; P out , output power; η, slope efficiency; λ L , laser wavelength.Best results selected from multiple publications on the same crystal.

	Crystal

b Tm, at. % hν ph , cm -1 σ SE , 10 -20 cm 2 τ 30 , ms λ P , nm P th , W P out , W η, % λ L , µm b c This work.

Vol. 38, No. 1 / January 2021 / Journal of the Optical Society of America B

F

(Tm 1 ) + 3 F 4 (Tm 2 )[START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ∼80% slope efficiency[END_REF][START_REF] Loiko | Stochastic model of energy-transfer proc-1106 esses among rare-earth ions. Example of Al 2 O 3 :Tm 3+[END_REF],

Vol. 38, No. 1 / January 2021 / Journal of the Optical Society of America B

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disordered garnet crystal laser," Photon. Res. 6, 800-804 (2018).

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F. Rotermund, Y. J. Cho, P. Loiko, X. Mateos, U. Griebner, and V.

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Funding. French Agence Nationale de la Recherche (ANR) (LabEx 924 EMC3 (ANR-10-LABX-09-01), SPLENDID2 (ANR-19-CE08-0028)); 925 European Community (European project "NOVAMAT"); Spanish 926 Government, MINECO (MAT2016-75716-C2-1-R (AEI/FEDER,UE), 927 PID2019-108543RB-I00); Generalitat de Catalunya (2017SGR755).