Esrom Kifle

Pavel Loiko

Lauren Guillemot

Jean-Louis Doualan

Florent Starecki

Alain Braud

Ammar Hideur

Patrice Camy
email: patrice.camy@ensicaen.fr

Design and modelling of a passively Q-switched diode-pumped Thulium laser at 2.3 μm

Keywords: diode-pumped laser, thulium ions, passive Q-switching, mid-infrared, laser transition. 1. Introduction

We report on a diode-pumped Tm:LiYF4 laser operating on the 3 H4 → 3 H5 transition (at ~2.3 μm) passively Q-switched by a Cr 2+ :ZnSe saturable absorber. This laser delivers a maximum average output power of 130 mW at 2304.6 nm with a nearly diffraction limited beam, a linear polarization (π) and no colasing at ~1.9 μm. The corresponding pulse characteristics (duration / energy) are 1.24 μs / 3.6 μJ at a repetition rate of 36 kHz. By power scaling under quasi-CW pumping, even shorter pulse durations of 870 ns and higher pulse energies of 6.1 μJ are achieved. The performance of the laser is simulated using a model of a quasi-four-level gain medium and a "slow" saturable absorber showing a good agreement with the experiment. The effect of the thermal lens of the saturable absorber on the pulse characteristics is discussed.

reported on 0.71 μs / 97 μJ pulses [START_REF] Wang | High efficiency nanosecond passively Q-switched 2.3 μm Tm:YLF laser using a ReSe2-based saturable output coupler[END_REF]. However, the stability of the pulse train was low and secondary pulses were observed. Moreover, the practical applications of such SAs are very limited due to their low stability.

In the present work, we report on a diode-pumped Tm:LiYF4 laser at ~2.3 μm PQS by Cr 2+ :ZnSe and delivering very stable pulsed output without any colasing at ~1.9 μm. The performance of the laser is modelled showing good agreement with the experiment.

Experimental 2.1. Laser set-up

The scheme of the laser set-up is shown in Fig. 1. For the laser experiments, we have selected a simple (linear) nearly hemispherical cavity to reduce the cavity roundtrip time and to shorten the Q-switched pulses. The cavity was formed by a flat pump mirror (PM) coated for high transmission (HT, T = 94.4%) at 0.78 µm and for high reflection (HR) at 2.12 -2.50 µm and two concave output couplers (OCs) with a radius of curvature (RoC) of -100 mm and a transmission TOC of 0.7% and 1.3% (±0.2%) at 2.18 -2.35 µm. The OCs provided HT (T > 90%) at ~1.9 µm to suppress the oscillations at the competitive high-gain 3 F4 → 3 H6 transition while no special coatings were provided for the PM.

As a gain material, we used tetragonal lithium yttrium fluoride crystal, Tm:LiYF4. The laser element was cut for light propagation along the crystallographic a-axis (a-cut) giving access to both principal light polarizations (π and σ). The actual doping level determined by inductively coupled plasma mass spectrometry (ICP-MS) was 3.5 at.% Tm corresponding to the ion density NTm of 4.83×10 20 cm -3 . The laser element had a cylindrical shape (diameter: Ф8.5 mm, thickness: t = 8.1 mm). Both faces were polished to laser-grade quality and antireflection (AR) coated at ~0.78 µm. The crystal was mounted on a massive Cu-holder from one of the faces leaving an opening in the centre using a silver paint for better heat removal. The holder was passively cooled. The crystal was placed close to the PM with a separation of ~5 mm. The geometrical length of the cavity was ~100 mm.

As a pump source, we used a CW fiber-coupled AlGaAs laser diode (DILAS, fiber core diameter: 105 µm, numerical aperture, N.A.: 0.22) emitting up to 20 W at ~788 nm (the 3 H6 → 3 H4 transition of Tm 3+ ions). The output from the laser diode was unpolarized and the measured emission bandwidth (FWHM) was ~3 nm. The estimated beam quality factor M 2 was ~45 (a nearly "top-hat" pump beam profile). The pump beam was collimated with an AR coated achromatic lens (focal length: f = 50 mm). The pump radiation was focused into the laser element through the PM using another AR-coated achromatic lens with f = 60 mm. The pump spot size (radius) in the focus was measured by the optical knife method to be wP = 78±10 μm (at the 1/e 2 level). To provide quasi-CW pumping, a mechanical chopper was inserted between the FL and CL (pulse duration: ~5 ms, duty cycle: 1:4).

The OCs provided high reflectivity at the pump wavelength. However, due to the strong pump divergence, the back-reflected pump was focused behind the crystal almost not contributing to the population inversion in the laser element. The absorbed pump power Pabs was calculated assuming single-pass pumping. The pump absorption under non-lasing (NL) conditions, ηabs,NL = Pabs/Pinc (Pincthe incident pump power) was estimated from the pump-transmission experiment. Then, the pump absorption under lasing (L) conditions was determined from the ηabs,NL value at the threshold pump power. It amounted to 53.3% (TOC = 0.7%) and 51.8% (TOC = 1.3%). The laser crystal was partially bleached.

A band-pass filter (FB2250-500, Thorlabs) was used to separate the laser emission from the residual (non-absorbed) pump. The spectra of laser emission were measured with an optical spectrum analyzer (OSA, AQ6375B, Yokogawa). The mode profile of the laser beam in the far-field was captured using a pyroelectric camera (PY-III-HR-C-A, Ophir) using a spherical uncoated CaF2 lens (f = 100 mm) placed after the OC. The temporal behavior of the laser emission was studied using a fast InGaAs photodetector (model UPD-5N-IR2-P, rise time: <200 ps) and an 8 GHz digital oscilloscope (DSA70804B, Tektronix).

Saturable absorber

As a saturable absorber (SA) material, we have selected Cr 2+ -doped chalcogenides (ZnS and ZnSe). In both materials, the chromium ions replaces for the Zn 2+ ones in tetrhedral (Td) sites giving rise to high ground-state absorption (GSA) cross-sections, σGSA, owing to the 5 T2 → 5 E( 5 D) Cr 2+ transition, weak excited-state absorption (ESA), low non-saturable losses and relatively fast recovery time τrec [START_REF] Mirov | Progress in mid-IR Cr 2+ and Fe 2+ doped II-VI materials and lasers[END_REF][START_REF] Podlipensky | Cr 2+ :ZnSe and Co 2+ :ZnSe saturable-absorber Q switches for 1.54-µm Er:glass lasers[END_REF]. The σGSA spectra for Cr 2+ -doped ZnS and ZnSe materials (measured in this work) are shown in Fig. 2(a). As one can see, the absorption band of chromium ions in ZnSe is red-shifted by about 75 nm as compared to its ZnS counterpart. Thus, Cr 2+ :ZnSe is more suitable for passive Q-switching of mid-IR lasers because of the higher GSA cross-sections. For Cr 2+ :ZnSe at the laser wavelength of 2.30 μm, σGSA is estimated from the measured GSA spectrum to be 0.024 ± 0.01×10 -18 cm 2 . Although this value is much lower that the peak one, 0.98×10 -18 cm 2 at 1.76 μm, it still provides a reasonable saturation fluence, FS = (hνL)/σGSA = 3.6 ± 1 J/cm 2 , where h is the Planck constant and νL is the laser frequency. For Cr 2+ :ZnSe, the ratio σGSA/σESA is <0.04 [START_REF] Podlipensky | Cr 2+ :ZnSe and Co 2+ :ZnSe saturable-absorber Q switches for 1.54-µm Er:glass lasers[END_REF] and τrec = 5.4 μs [START_REF] Mirov | Progress in Cr 2+ and Fe 2+ doped mid-IR laser materials[END_REF].

The SA fabricated from Cr 2+ :ZnSe had a cylindrical shape (Ф12 mm, t = 1.0 mm). Both its surfaces were polished with good parallelism and coated for HT (T >90%) at 2.0-2.3 μm. The calculated mean Cr 2+ concentration was 2.2×10 18 cm -3 . The small-signal (unsaturated) absorption due to the Cr 2+ ions at the laser wavelength of 2.30 μm α'SA was 0.5% (recalculated from the value specified at 1.76 μm). The optical losses originating from the polycrystalline ZnSe material α'loss were about 1.8% (measured using a spectrophotometer), so that the smallsignal transmisison TSA = 1 -α'SAα'loss ≈ 97.6%.

To ensure passive Q-switching of the laser, the SA was inserted between the PM and the laser element at normal incidence. The air gap between the PM and the SA was ~1 mm. The SA was mounted on an Al-holder and passively cooled. The Cr 2+ ions in Td sites do not exhibit absorption at the pump wavelength of 0.78 μm, so that the SA heating by the pump was weak and provided mainly by the backgroung absorption of the host material. This position of the SA almost in the waist of the laser mode (the calculated radius of the laser mode on the SA was 106±6 μm) ensured its deep bleaching as compared to location between the crystal and the OC. The latter option may reduce the local heating of the SA, however, we did not manage to achieve stable passive Q-switching in this geometry probably because of insufficient intracavity fluence.

Results and Discussion

Continuous-wave laser

To improve the thermal management of the laser (namely, to reduce the excessive heating of the passively cooled gain medium and the SA which may lead to serious Qswitching instabilities), the CW pumping was applied until an absorbed pump power Pabs of ~6.8 W. Above this power, the pumping was in quasi-CW regime.

Prior to the PQS experiment, we briefly characterized the laser performance without the SA in the cavity. The laser generated temporally stable output without instabilities or relaxation oscillations. Under CW pumping, the output power reached 0.63 W at 2302-2307 nm with a slope efficiency η of 14.3% (vs. the absorbed pump power) and a laser threshold of Pth = 1.39 W (for TOC = 1.3%), Fig. 3(a). A very similar performance was observed for TOC = 0.7%. The input-output dependences for both OCs were slightly nonlinear near the laser threshold and thus the fit yielding the slope efficiency was performed for pump powers well above Pth.

For quasi-CW pumping, the output dependences well matched those measured in the CW regime (for Pabs <6.8 W) indicating weak thermal effects. Further increase of the pump power from the laser diode lead to a maximum average output power of 0.35 W (instantaneous peak power: 1.41 W) with higher η = 20.8%, Fig. 3(b). The optical-to-optical efficiency ηopt (vs. the average incident pump power) reached 7.5% (all the values are specified for TOC = 1.3%). For TOC = 0.7% under quasi-CW pumping, the laser performance was slightly inferior. These experiments confirm the possibilities for further power scaling if providing, e.g., active cooling of the laser element and SA.

The laser output was linearly polarized (E || c, π-polarization) and the polarization state was naturally selected by the anisotropy of the gain. The spectra of laser emission were weakly dependent on TOC being centred at ~2.30 μm, Fig. 4(a,b), well matching the main peak in the stimulated-emission (SE) cross-section, σSE, spectra for the 3 H4 → 3 H5 transition of Tm 3+ ions in LiYF4 (the corresponding σSE value is 0.57×10 -20 cm 2 at 2305 nm in πpolarization [START_REF] Loiko | Efficient Tm:LiYF4 lasers at ~2.3 μm: Effect of energytransfer upconversion[END_REF]). For CW operation (in the free-running regime, i.e., without any spectrally selective elements in the cavity), the spectra of laser emission were relatively broad spanning from 2302 to 2308 nm. This is ascribed to a relatively broad gain bandwidth of Tm:LiYF4 (25.8 nm [START_REF] Loiko | Efficient Tm:LiYF4 lasers at ~2.3 μm: Effect of energytransfer upconversion[END_REF]).

Passively Q-switched laser: Power scaling

When inserting the SA into the laser cavity, very stable passively Q-switched operation was achieved. First, we studied the power transfer characteristics and the spectra of the PQS laser. We observed in this regime that the output coupling had a notable effect on the laser performance. Under CW pumping, for TOC = 1.3%, the maximum average output power reached 130 mW at 2304.6 nm with η = 3.7% and a laser threshold of 3.24 W, Fig. 3(a). For smaller TOC = 0.7%, the laser generated only 49 mW at 2304.7 nm with η = 1.4% and a slightly lower threshold of 3.03 W. The increase of the laser threshold and the reduction in the slope efficiency as compared to the CW regime of operation is clearly related to the insertion loss of the SA (in particular, the background scattering loss of ZnSe and the losses at the dielectric coatings). Indeed, the Q-switching conversion efficiency with respect to the CW regime ηconv amounted to 20.6% (TOC = 1.3%) and 8.0% (TOC = 0.7%).

The possibility for further power scaling of the PQS laser was also demonstrated under quasi-CW pumping, Fig. 3(b). For the best-performing TOC = 1.3%, the average output power reached 89 mW with η = 5.0% and a Q-switching conversion efficiency ηconv = 25.3%. It should be noticed that it was possible to operate the PQS laser under CW pumping at the expense of increased intensity instabilities in the Q-switched pulse train.

The typical spectra of the PQS laser are shown in Fig. 4. For both output couplers, the spectra were notably narrowed as compared to the CW regime which is related to competition of longitudinal modes bleaching the SA resulting in the filtering of some of them.

Both in the CW and PQS operation regimes, no colasing on the 3 F4 → 3 H6 transition (at ~1.9 μm) was observed.

The PQS laser generated a nearly-circular beam and the 1D intensity profiles in the horizontal (x) and vertical (y, || c-axis) directions were well fitted with a Gaussian distribution (goodness of the fit: R 2 > 0.99). The measured beam quality factors M 2 x,y were below 1.4. The spatial characteristics of the laser beam and their evaluation were similar to those described in the previous work [START_REF] Kifle | Watt-level diode-pumped thulium lasers around 2.3 µm[END_REF].

Passively Q-switched laser: Pulse characteristics

Under CW pumping, the laser generated a continuous train of Q-switched pulses. The pulse duration (FWHM) Δτ and the pulse repetition frequency (PRF) were measured directly and the pulse energy was calculated, Eout = Pout/PRF, where Pout is the average output power. Under quasi-CW pumping, the laser generated regular bunches of pulses containing hundreds of pulses. The energy of an individual pulse was calculated as Eout = 4Pout/PRF (for a duty cycle 1:4).

The pulse characteristics (duration and energy) of the PQS Tm:LiYF4 laser are shown in Fig. 5. They exhibited a dependence on the pump power. For TOC = 1.3% near the laser threshold, Δτ = 3.6 μs, then it shortened with increasing the pump power and stabilized at 1.16±0.2 μs. Nanosecond pulses (~870 ns) were achieved at intermediate power levels. For TOC = 0.7%, a similar behavior was observed while slightly longer pulse durations were obtained (stabilized at 1.30±0.15 μs). Concerning the pulse energy, it slightly increased with the pump power and reached a maximum value of 6.1 μJ and 3.5 μJ for TOC = 1.3% and 0.7%, respectively.

The pulse repetition frequency PRF of the PQS laser gradually increased with the pump power, Fig. 6, namely from 4.4 to 58.7 kHz (for TOC = 1.3%) and from 4.0 to 52.7 kHz (for TOC = 0.7%).

The typical oscilloscope traces of single Q-switched pulses from the PQS Tm:LiYF4 laser are shown in Fig. 7. Here, we present the pulse corresponding to the maximum CW pump level (Pabs = 6.7 W) and the shortest pulse observed at higher pump power of Pabs ~8 W.

The pulses have a nearly Gaussian temporal shape. In Fig. 9(a,b), we present the typical oscilloscope traces of the pulse trains observed under CW pumping for the two studied output couplers. They confirm good stability of the PQS operation with intensity instabilities <7% and the r.m.s. pulse-to-pulse timing jitter of <5%. The PQS laser operated for tens of minutes without a noticeable deterioration of the output performance and Q-switching instabilities (for the range of pump powers applied for CW pumping). The Q-switching instabilities for the used laser design are mainly attributed to the heating of the SA by the pump radiation. In Fig. 9(c), we show a typical regular bunch of pulses under quasi-CW pumping.

Passively Q-switched laser: Simulation

Cr 2+ :ZnSe represents a "slow" saturable absorber for PQS mid-infrared lasers. This is because its recovery time of initial absorption (τrec = 5.4 μs [START_REF] Mirov | Progress in Cr 2+ and Fe 2+ doped mid-IR laser materials[END_REF]) that corresponds to the lifetime of the 5 T2( 5 D) Cr 2+ state is longer than the characteristic time of formation of a single Q-switched pulse. For the designed laser with pulse durations of about ~1 μs, this condition is still satisfied. There exist a criterion for "slow" SA passive Q-switching [30]:

L g GSA L SE SA 1. A X A   =  (1)
Here, σ L GSA is the GSA cross-section of the SA and σ L SE is the SE cross-section of the gain medium (both at the laser wavelength), and Ag and ASA are the mode areas in the gain medium and the SA, respectively. Physically, the parameter X compares the saturation of the gain medium and the SA. If X >> 1, the SA is deeply bleached and a weak dependence of pulse energy and duration on the pump power is observed, corresponding to generation of "giant" pulses. For the designed laser, X = 6.1 > 1 (this small value explains the variation of the pulse characteristics in Fig. 5).

The pulse energy and duration and the PRF were calculated using the model of a quasifour-level gain medium (the 3 H4 → 3 H5 Tm 3+ transition) and a "slow" SA (Cr 2+ :ZnSe) developed by Zhang et al. [START_REF] Zhang | Optimization of Cr 4+ -doped saturable-absorber Q-switched lasers[END_REF]. The main equations are given in Appendix A. The parameters of the cavity and the spectroscopic characteristics of the gain medium and the SA are listed in the text.

The results of the modelling are shown in Fig. 9 for the pulse duration and energy which are treated in the model as pump-independent values and in Fig. 6 (as curves) for the PRF which is pump-dependent. Let us first describe Fig. 9 where the parameters are calculated as a function of the output coupling (TOC = 0.1 -7%) for several values of the saturable loss α'SA ranging between 0.35% and 0.95%. The best agreement between the experiment and the model is observed for α'SA = 0.55% which agrees with the estimation from the transmission spectra (Section 2.2).

From Fig. 9(a), one can see that, for saturable losses α'SA > 0.55%, the model predicts first a weak dependence of the pulse duration on the output coupling and then an abrupt rise of Δτ. With increasing the saturable loss α'SA, the range of TOC values within which relatively short Q-switched pulses are expected becomes broader. As for the pulse energy, there exist an optimum output coupling leading to a maximum pulse energy at a given α'SA. For higher saturable loss, this maximum shifts towards higher transmissions of the OC. For TOC = 1.3%, the model predicts a pulse energy / duration of 4.8 μJ / 2.0 μs which reasonably agrees with the experiment. Moreover, Fig. 9(b) indicates that this output coupling is nearly optimum for the employed SA.

The pulse repetition frequency as a function of the pump power was also calculated for the two studied OCs, see the curves in Fig. 6. The model well describes the observed increase of the PRF with the pump power. For TOC = 1.3% and Pabs = 6.7 W (the upper limit for CW pumping), it predicts a PRF of 33.8 kHz which agrees well with the experimental value (35.8 kHz).

During the PQS operation, no damage to the SA nor to the gain medium was observed. The intracavity axial peak fluence on the SA, calculated assuming a Gaussian spatial profile of the laser mode were Fin = 4.73 and 5.06 J/cm 2 for TOC = 1.3% and 0.7%, respectively. These values are exceeding the calculated saturation fluence of the SA FS, so that it is deeply bleached. Besides, the determined Fin values are below the LIDT for zinc chalcogenides (e.g., LIDT = 6.0 ± 0.5 J/cm 2 for Cr 2+ :ZnS for ns pulses [START_REF] Loiko | Saturable absorption properties at 1.54 µm of Cr 2+ :ZnS prepared by thermal diffusion at hot isostatic pressing[END_REF]).

Thermal lensing of the saturable absorber

The pump absorption in the SA (Cr 2+ :ZnSe) may induce a thermal lens [START_REF] Song | Thermal influence of saturable absorber in passively Q-switched diode-pumped cw Nd:YAG/Cr 4+ :YAG laser[END_REF][START_REF] Sennaroglu | Continuous-wave power transmission and thermal lensing of a saturable absorber subject to excited-state absorption[END_REF] which, in its turn, affects the size of the laser mode and the pulse characteristics of the PQS laser. For thin elements longitudinally pumped by a "top-hat" pump beam, the optical (refractive) power of the thermal lens D = 1/f is expressed as [START_REF] Chénais | On thermal effects in solid-state lasers: The case of ytterbium-doped materials[END_REF]:

SA abs inc SA SA 2 P , 2 P D w    = (2a) SA d / d ( 1)(1 ) . n T n    = + - + (2b)
Here, η SA abs ≈ 3.3% is the absorption of the SA at the pump wavelength, Fig. 2(b), which is not saturated, Pinc is the incident pump power, wP ~ 450±100 μm is the pump spot radius on the SA (calculated using the ABCD formalism), κ = 17.8 Wm -1 K -1 is the thermal conductivity [START_REF] Sankar | On the thermal and optical properties of ZnSe and doped ZnSe crystals grown by PVT[END_REF], dn/dT = 5.34×10 -5 K -1 is the thermo-optic coefficient, n = 2.438 is the refractive index at 2.30 μm [START_REF] Marple | Infrared thermooptic coefficient measurement of polycrystalline ZnSe, ZnS, CdTe, CaF2, and BaF2, single crystal KCl, and glass[END_REF]36], α = 7.8×10 -6 K -1 [START_REF] Browder | Thermal expansion data for eight optical materials from 60 K to 300 K[END_REF] is the coefficient of thermal expansion and ν = 0.28 is the Poisson ratio of the SA material (ZnSe). Equation 2(b) represents the term χSA = 6.74×10 -5 K -1 which is called the "generalized" thermo-optic coefficient and it determines the sign of the thermal lens (positive). In Eq. (2b), we neglect the contribution of the photo-elastic effect which is relatively weak in cubic materials. Although the absorption in the SA is weak, the relatively large "generalized" thermo-optic coefficient of ZnSe may induce strong thermal lens.

For comparison, we also estimated the thermal lens of the diode-pumped laser crystal (Tm:LiYF4) [START_REF] Chénais | On thermal effects in solid-state lasers: The case of ytterbium-doped materials[END_REF]:

abs h,L inc AE AE 2 P . 2 P D w    = (3)
We used the same equation, only the factor of η SA abs was replaced by ηabsηh,L, and ηabs = 51.8% is the pump absorption under lasing conditions (TOC = 1.3%) and ηh,L = 22.5% is the fractional heat loading under lasing (L) conditions. The ηh,L value was estimated from the following considerations: the heat generation for a ~2.3 μm laser originates mostly from the multi-phonon non-radiative relaxation from the lower laser level ( 3 H4) to the metastable state ( 3 F4). The latter manifold is mostly depopulated via radiative decay and this process does not generate heat. Thus, the fractional heat loading can be estimated as:

𝜂 h,L ≈ 1 - ℎ𝜈 L(2.3 μm) +ℎ〈𝜈 lum 〉 (1.9 μm) ℎ𝜈 P , (4)
where νL and νP are the laser and pump frequencies, respectively, and <νlum> is the mean luminescence frequency (corresponding to <λlum> = 1824 nm for Tm:LiYF4). Finally, we achieve ηh ≈ 22.5%. This value reasonably agrees with the previously reported results for a Tm:YAG laser operating on the 3 H4 → 3 H5 transition, ηh = 30-35% well above the laser threshold [START_REF] Kifle | Watt-level diode-pumped thulium lasers around 2.3 µm[END_REF]. The uncertainty in the estimation of the fractional heat loading is the main source of error in evaluating the thermal lens of the laser crystal. Other material parameters are as following: <κ> = 5.13 Wm -1 K -1 [START_REF] Aggarwal | Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, LiYF4, LiLuF4, BaY2F8[END_REF] and χAE = -2.3×10 -6 K -1 (specified for an a-cut crystal and π-polarization) [39].

The optical power of the thermal lens is pump-dependent, so that it is convenient to calculate the so-called sensitivity factor [START_REF] Loiko | Polarization anisotropy of thermal lens in Yb:KY(WO4)2 laser crystal under high-power diode pumping[END_REF]

: inc d . d D M P = ( 5
)
For the SA (Cr 2+ :ZnSe) and the active element (Tm:LiYF4), MSA = 0.096 m -1 /W and MAE = -1.37 m -1 /W, respectively. Thus, the thermal lens in these two optical elements has different sign (it is positive in the SA and negative in the laser crystal). The thermal lens induced in the laser crystal is much stronger than that formed in the SA. Consequently, the thermal lens of the laser crystal is mainly responsible for the mode formation in the laser cavity. Figure 10 presents the radii of the fundamental transverse mode in the center of the SA and the laser crystal as a function of the incident pump power calculated using the ABCD formalism and the determined M-factors of the thermal lenses. The mode radius in the laser crystal is weakly dependent on the pump power. However, the thermal lens of the laser crystal induces an increase of the mode radius on the SA, from ~100 μm at the laser threshold of the PQS laser up to ~112 μm at high pump powers. This will cause less deep bleaching of the SA and can partially explain the difference between the measured and calculated pulse characteristics.

As is it clear from Fig. 10, the thermal lens of the SA has a minor effect on the mode in the PQS laser cavity.

Discussion

In Table 1, we summarize the results on PQS Tm lasers operating on the 3 H4 → 3 H5 transition reported so far. In all the previous studies [START_REF] Canbaz | 2.3-μm Tm 3+ :YLF laser passively Q-switched with a Cr 2+ :ZnSe saturable absorber[END_REF][START_REF] Wang | High efficiency nanosecond passively Q-switched 2.3 μm Tm:YLF laser using a ReSe2-based saturable output coupler[END_REF][START_REF] Huang | High power simultaneous dual-wavelength CW and passively-Q-switched laser operation of LD pumped Tm:YLF at 1.9 and 2.3 µm[END_REF], Tm:LiYF4 crystals were used as gain media and two types of SAs were employed, i.e., Cr 2+ :ZnSe ("slow" SA, the same as in the present work) and few-atomic layer ReSe2 ("fast" SA).

The present work represents the first diode-pumped thulium laser operating solely at ~2.3 μm (without colasing at ~1.9 μm) and generating very stable regular trains of pulses at relatively high repetition rates of tens of kHz. In terms of the average output power, we also report on the best results as compared to the studies were Cr 2+ :ZnSe SAs were employed [START_REF] Canbaz | 2.3-μm Tm 3+ :YLF laser passively Q-switched with a Cr 2+ :ZnSe saturable absorber[END_REF][START_REF] Huang | High power simultaneous dual-wavelength CW and passively-Q-switched laser operation of LD pumped Tm:YLF at 1.9 and 2.3 µm[END_REF].

Canbaz et al. reported on a Tm:LiYF4 / Cr 2+ :ZnSe laser [START_REF] Canbaz | 2.3-μm Tm 3+ :YLF laser passively Q-switched with a Cr 2+ :ZnSe saturable absorber[END_REF], however, employing a diffraction-limited pump (a Ti:Sapphire laser) limiting its applications. Moreover, the average output power was low (27 mW at 2309 nm) and no information allowing to assess the pulse train stability was provided.

Huang et al. studied a similar laser with diode-pumping [START_REF] Huang | High power simultaneous dual-wavelength CW and passively-Q-switched laser operation of LD pumped Tm:YLF at 1.9 and 2.3 µm[END_REF] which however exhibited simultaneous laser emission at 1.88 μm and 2.31 μm. This affected the stability of the PQS operation because pulse groups with a varying number of individual pulses (between few and 10 pulses) were observed.

Wang et al. employed few-atomic layer ReSe2 SA in a diode-pumped Tm:LiYF4 laser [START_REF] Wang | High efficiency nanosecond passively Q-switched 2.3 μm Tm:YLF laser using a ReSe2-based saturable output coupler[END_REF]. Few-atomic layer materials are of little practical use as they have limited stability under long-term operation. However, such SAs provide much lower insertion losses as compared to crystals doped with TM ions [START_REF] Lan | Passive Q-switching of microchip lasers based on Ho:YAG ceramics[END_REF], so better power scaling capabilities are expected. In [START_REF] Wang | High efficiency nanosecond passively Q-switched 2.3 μm Tm:YLF laser using a ReSe2-based saturable output coupler[END_REF], the PQS laser generated irregular bunches of pulses; moreover, the presented oscilloscope traces indicated a possible CW component in the laser emission. Thus, the reported high pulse energy cannot be interpreted as a single-pulse energy.

Conclusion

To conclude, we report on the first diode-pumped passively Q-switched Thulium laser operating on the 3 H4 → 3 H5 transition (without colasing at ~1.9 μm) and generating very stable regular trains of ~1 μs-long single Q-switched pulses at high repetition rates of about few tens of kHz. This is due to (i) a combination of the gain material (Tm:LiYF4) highly suitable for lasing at ~2.3 μm and the saturable absorber (Cr 2+ :ZnSe) ensuring reasonable saturation fluence at this laser wavelength; (ii) the use of spectrally-selective cavity mirrors suppressing the unwanted lasing at ~1.9 μm; (iii) a compact cavity design ensuring short cavity roundtrip time and deep bleaching of the SA. Passive Q-switching of ~2.3 μm Tm lasers is a complicated task due to the relatively short upper laser level ( 3 H4) lifetime (e.g., only 156 μs for 3.5 at.% Tm:LiYF4 as used in the present work), low gain for the 3 H4 → 3 H5 transition and a strong competition with the high-gain 3 F4 → 3 H6 one.

Further improvement of the pulse characteristics of the Tm:LiYF4 / Cr 2+ :ZnSe lasers seems to be possible by optimization of the cavity design. The use of an L-shaped cavity may simultaneously provide deep bleaching of the SA, eliminate its heating by the residual pump and ensure large mode area in the gain material leading to higher pulse energies. Going to a microchip-type design will result in generation of much shorter pulses of few tens of ns whilst at the expense of the low pulse energy. At a glance, better energy storage capabilities are expected with Tm:LiYF4 crystals with lower doping leading to weaker self-quenching of the upper laser lifetime. However, as it was shown [START_REF] Loiko | Efficient Tm:LiYF4 lasers at ~2.3 μm: Effect of energytransfer upconversion[END_REF], higher doping levels enhance the performance of ~2.3 μm Tm lasers due to the energy-transfer upconversion. Thus, the search of an optimum doping level for PQS laser operation is needed.

              -- -- -                 = (A2)
Here, h is the Planck constant, νL is the laser frequency, AAE is the mode area in the active element and ℓ is its length, σ L SE is the SE cross-section at νL, γ is the inversion reduction factor, ROC is the reflectivity of the OC, tr = 2ℓ'/c is the cavity roundtrip time, ℓ' is the cavity optical length and c is the speed of light, α = σGSA/(γσ L SE) is a factor concerning the saturation of the active element and the SA, and nt0, ni, nt and nf are determined from the following equations:

2 OC SA 0 L SE ln( ) ln( ) , 2 t R T L n   -+ = - (A3) 2 OC SA L SE ln( ) ln( ) , 2 i R T L n  - = -+ (A4) 00 1, t t t t i i i i n n n n n n n n     +-      = (A5) 00 1 1 ln 1 0. f f f t t i i i i i n n n nn n n n n n             -+ -- - =                   (A6)
Here, δ = σESA/σGSA and σESA is the ESA absorption cross-section of the SA, TSA is the initial (small-signal) transmission of the SA at νL, and L is the roundtrip passive loss. Here, n is the instantaneous population inversion density: niits initial value at the start of Q-switching, nt its value at the moment of maximum power and nfits final value. The parameter nt0 has a meaning of nt when α → ∞. The pulse repetition frequency (PRF) is:

th 3lum ( ) (1 ) / 2 1 PRF= , 1 B / B   -+ - (A7) 1 1 , f a i n f n    = - -   (A8)
where τ3lum is the upper laser level ( 3 H4) lifetime, B is the volumetric pump rate into the upper laser level, Bth = ni/τ3lum is the threshold pump rate, fa is the Boltzmann occupation factor of the upper laser level. These equations correspond to the condition B > 2Bth and describe high repetition rate lasers. P outaverage output power, λ Llaser wavelength, ηslope efficiency, η conv -Q-switching conversion efficiency, Δτpulse duration, E outpulse energy, PRFpulse repetition frequency. b TS -Ti:Sapphire laser, LDlaser diode. c Total energy for a bunch of pulses. d Quasi-CW pumping with a duty cycle of 1:4.

List of figure captions

Figure 1 .

 1 Figure 1. Scheme of the diode-pumped Tm:LiYF 4 laser Q-switched by the Cr 2+ :ZnSe SA: LDlaser diode, CL and FLcollimating and focusing lens, respectively, PMpump mirror, SAsaturable absorber, OCoutput coupler, Fcut-off filter.

Figure 2 .

 2 Figure 2. Saturable absorber: (a) Ground-state absorption cross-sections, σ GSA , for Cr 2+ ions in ZnS and ZnSe materials; (b) Small-signal intrinsic transmission (T SA ) spectrum (subtracting the effect from the coatings) of the Cr 2+ :ZnSe SA (t = 1.0 mm). The arrows in (a,b) indicate the pump (0.79 μm) and laser (2.30 μm) wavelengths.

Figure 3 .

 3 Figure 3. Input-output dependences for the CW and Cr 2+ :ZnSe PQS diodepumped Tm:LiYF 4 lasers: (a) CW pumping, (b) quasi-CW pumping (duty cycle: 1:4), ηslope efficiency.

Figure 4 .

 4 Figure 4. Typical spectra of laser emission for the CW and Cr 2+ :ZnSe PQS diode-pumped Tm:LiYF 4 lasers: (a) T OC = 0.7%, (b) T OC = 1.3%. P abs ~ 6 W. The laser polarization is π.

Figure 5 .

 5 Figure 5. Pulse characteristics: (a) duration (FWHM) and (b) energy for the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA.

Figure 6 .

 6 Figure 6. Pulse repetition frequency for the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA: symbolsexperimental data, curvesmodelling.

Figure 7 .

 7 Figure 7. Oscilloscope traces of single Q-switched pulses from the diodepumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA (the pulses observed at the maximum CW pump power of P abs = 6.7 W and the shortest pulses are shown): (a) T OC = 1.3%, (b) T OC = 0.7%.

Figure 8 .

 8 Figure 8. Oscilloscope traces of pulse trains from the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA: (a,b) CW pumping, (a) T OC = 1.3%, P abs = 5.45 W, (b) T OC = 0.7%, P abs = 6.23 W; (c) quasi-CW pumping, T OC = 1.3%, P abs = 8.27 W.

Figure 9 .

 9 Figure 9. Simulation of (a) the pulse duration and (b) the pulse energy for the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA: curvescalculated dependences of the pulse characteristics on the transmission of the output coupler T OC for various values of the saturable loss α' SA , symbolsexperimental data.

Figure 10 .

 10 Figure 10. Simulation of the radius of the fundamental transverse mode in the center of the SA (Cr 2+ :ZnSe) and laser crystal (Tm:LiYF 4 ) in the diodepumped PQS laser: solid curvesaccounting for the thermal lenses in both elements, dashed curvesaccounting only for the thermal lens of the laser crystal. Vertical line: laser threshold for T OC = 1.3%.

Figure 1 .

 1 Figure 1. Scheme of the diode-pumped Tm:LiYF 4 laser Q-switched by the Cr 2+ :ZnSe SA: LDlaser diode, CL and FLcollimating and focusing lens, respectively, PMpump mirror, SAsaturable absorber, OCoutput coupler, Fcut-off filter.

Figure 2 .

 2 Figure 2. Saturable absorber: (a) Ground-state absorption cross-sections, σ GSA , for Cr 2+ ions in ZnS and ZnSe materials; (b) Small-signal intrinsic transmission (T SA ) spectrum (subtracting the effect from the coatings) of the Cr 2+ :ZnSe SA (t = 1.0 mm). The arrows in (a,b) indicate the pump (0.79 μm) and laser (2.30 μm) wavelengths.

Figure 3 .

 3 Figure 3. Input-output dependences for the CW and Cr 2+ :ZnSe PQS diodepumped Tm:LiYF 4 lasers: (a) CW pumping, (b) quasi-CW pumping (duty cycle: 1:4), ηslope efficiency.

Figure 4 .

 4 Figure 4. Typical spectra of laser emission for the CW and Cr 2+ :ZnSe PQS diode-pumped Tm:LiYF 4 lasers: (a) T OC = 0.7%, (b) T OC = 1.3%. P abs ~ 6 W. The laser polarization is π.

Figure 5 .

 5 Figure 5. Pulse characteristics: (a) duration (FWHM) and (b) energy for the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA.

Figure 6 .

 6 Figure 6. Pulse repetition frequency for the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA: symbolsexperimental data, curvesmodelling.

Figure 7 .

 7 Figure 7. Oscilloscope traces of single Q-switched pulses from the diodepumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA (the pulses observed at the maximum CW pump power of P abs = 6.7 W and the shortest pulses are shown): (a) T OC = 1.3%, (b) T OC = 0.7%.

Figure 8 .

 8 Figure 8. Oscilloscope traces of pulse trains from the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA: (a,b) CW pumping, (a) T OC = 1.3%, P abs = 5.45 W, (b) T OC = 0.7%, P abs = 6.23 W; (c) quasi-CW pumping, T OC = 1.3%, P abs = 8.27 W.

Figure 9 .

 9 Figure 9. Simulation of (a) the pulse duration and (b) the pulse energy for the diode-pumped Tm:LiYF 4 laser PQS by a Cr 2+ :ZnSe SA: curvescalculated dependences of the pulse characteristics on the transmission of the output coupler T OC for various values of the saturable loss α' SA , symbols experimental data.

Figure 10 .

 10 Figure 10. Simulation of the radius of the fundamental transverse mode in the center of the SA (Cr 2+ :ZnSe) and laser crystal (Tm:LiYF 4 ) in the diodepumped PQS laser: solid curvesaccounting for the thermal lenses in both elements, dashed curvesaccounting only for the thermal lens of the laser crystal. Vertical line: laser threshold for T OC = 1.3%.

Table 1 .

 1 Output characteristics a of passively Q-switched ~ 2.3 μm Tm:LiYF 4 lasers reported so far.

	Pump b SA	P out ,	λ L ,	η,	η conv ,	Δτ,	E out ,	PRF,	Ref.
			mW	nm	%	%	μs	μJ	kHz
	TS	Cr 2+ :ZnSe 27	2309	~4	~18	1.3	13	2.1	[22]
	LD	Cr 2+ :ZnSe 77 +	2306 +	~6	6.9	4	3.1	24.8	[27]
			202	1880
	LD	ReSe 2	486	2306	9	42.3 0.72 97.2 c	5.0	[23]
	LD	Cr 2+ :ZnSe 130	2304.6 3.7	20.6 1.24 3.6	36.1	This
			89 d	2304.6 5.0	25.3 1.30 6.1	59.2	work
	a

Acknowledgements

This work was supported by French Agence Nationale de la Recherche (ANR) through the LabEx EMC3 (ANR-10-LABX-09-01), SPLENDID2 (ANR-19-CE08-0028), and the European project "NOVAMAT" co-funded by the Normandy County Council and the European Union within the framework of the Operational Program ERDF/ESF 2014-2020.

Among the SAs based on transition-metal ions, Fe 2+ -doped ZnSe may be a good candidate for PQS of ~2.3 μm lasers due to its broadband absorption centered at ~3.1 μm and featuring high GSA cross-sections.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A

Expressions for calculating the pulse characteristics of a continuously-pumped PQS ~2.3 μm Thulium laser (after [START_REF] Zhang | Optimization of Cr 4+ -doped saturable-absorber Q-switched lasers[END_REF]). The pulse energy Eout and the peak power Ppeak (the pulse duration: Δτ = Eout/Ppeak) are:


Liza Basyrova

Pavel Loiko

Roman Maksimov

Vladislav Shitov

Josep Maria Serres

Uwe Griebner

Valentin Petrov

Magdalena Aguiló

Francesc Díaz

Xavier Mateos
email: xavier.mateos@urv.cat

Comparative study of Yb:Lu 3 Al 5 O 12 and Yb:Lu 2 O 3 laser ceramics produced from laser-ablated nanopowders

Keywords: garnets, sesquioxides, optical ceramics, laser operation

We present a comparative study of two Lu-based oxide ceramics doped with Yb 3+ ions, namely Yb:Lu3Al5O12 (garnet) and Yb:Lu2O3 (sesquioxide), promising for thin-disk lasers. The ceramics are fabricated using nanopowders of 3.6 at.% Yb:Lu2O3 and Al2O3 produced by laser ablation: Yb:Lu3Al5O12 -by vacuum sintering at 1800 °C for 5 h with the addition of 1 wt% TEOS as a sintering aid, and Yb:Lu2O3by vacuum pre-sintering at 1250 °C for 2 h followed by Hot Isostatic Pressing at 1400 °C for 2 h under Ar gas pressure of 207 MPa. The comparison includes the structure, Raman spectra, transmission, optical spectroscopy and laser operation. The crystal-field splitting of Yb 3+ multiplets is revealed for Lu3Al5O12. A continuous-wave (CW) Yb:Lu3Al5O12 ceramic microchip laser generates 5.65 W at 1031.1 nm with a slope efficiency of 67.2%. In the quasi-CW regime, the peak power is scaled up to 8.83 W. The power scaling for the Yb:Lu2O3 ceramic laser is limited by losses originating from residual coloration and inferior thermal behavior.

Introduction

Transparent ceramics are fully dense single-phase polycrystalline materials containing μm-sized grains and featuring high light transmission in a broad spectral range [START_REF] Wang | Transparent ceramics: Processing, materials and applications[END_REF][START_REF] Ikesue | Ceramic laser materials[END_REF]. High transmission is ensured by: (i) very small porosity, (ii) absence of a second phase at the grain boundariesnegligible difference of the optical properties between the grains and their boundaries, (iii) high quality grain boundaries, (iv) small grain size with narrow and spatially uniform size distribution, (v) isotropic lattice structure and (vi) high surface quality. Under such conditions, transparent ceramics are of interest for fabrication of photonic elements. [START_REF] Serres | Microchip laser operation of Yb-doped gallium garnets[END_REF].7% [START_REF] Fu | Fabrication and properties of highly transparent Yb:LuAG ceramics[END_REF]. Pirri et al. demonstrated a highly-doped 10 at.% Yb:Lu3Al5O12 ceramic laser diode-pumped at 936 nm delivering 6.0 W at 1030 nm with a slightly higher slope efficiency of 52% [25]. Yb:Lu3Al5O12 ceramic thin-disk lasers are also known: Nakao et al. developed such a thin-disk laser with an output power of 166 W and a slope efficiency of 72.2% [START_REF] Nakao | Yb 3+ -doped ceramic thin-disk lasers of Lu-based oxides[END_REF].

Recently, we proposed a novel approach to fabricate transparent Yb:Lu3Al5O12 ceramics by using laser-ablated Yb:Lu2O3 and Al2O3 nanopowders and tetraethoxysilane (TEOS) as a sintering additive [START_REF] Basyrova | Effect of SiO2 addition on structural and optical properties of Yb:Lu3Al5O12 transparent ceramics based on laser ablated nanopowders[END_REF]. It allowed us to reduce the synthesis temperature down to 1800 °C while maintaining the good optical quality of the ceramics.

In the present work, we report on efficient and power-scalable diode-pumped operation of transparent Yb:Lu3Al5O12 ceramics fabricated using laser-ablated nanoparticles by employing a compact (microchip-type) laser design. For comparison, we also studied Yb:Lu2O3 ceramics produced from the corresponding laser-ablated nanopowder. The structural, optical and spectroscopic properties of the two ceramics are compared.

Synthesis of ceramics

For the fabrication of the Yb 3+ -doped ceramics, we used Yb:Lu2O3 and Al2O3 nanopowders (mean particle size: 34 nm and 29 nm, respectively) synthesized by laser ablation and subsequent sedimentation [START_REF] Basyrova | Effect of SiO2 addition on structural and optical properties of Yb:Lu3Al5O12 transparent ceramics based on laser ablated nanopowders[END_REF][START_REF] Kijko | Sintering of transparent Yb-doped Lu2O3 ceramics using nanopowder produced by laser ablation method[END_REF]. This approach allowed us to produce nanopowders with a narrow particle size distribution which has a positive effect on the transparency of ceramics.

To fabricate Yb:Lu3Al5O12 garnet ceramics, both nanopowders were used. To achieve a stoichiometric Al/(Yb + Lu) ratio corresponding to (Yb0.036Lu0.964)3Al5O12 composition, the nanopowders were converted into the cubic phase by calcining at 900-1200 °C for 3 hours (h) in air. The calcined powders were weighed and mixed by ball milling in ethyl alcohol for 48 h with an addition of 1 wt% of TEOS (Si(OC2H5)4) as a sintering aid. After drying, the mixture was compacted into a cylindrical pellet by uniaxial static pressing at 200 MPa. The obtained compact powder was sintered at 1800 °C for 5 h in a vacuum furnace with graphite heaters at a residual gas pressure of 10 -3 Pa. The as-sintered blue-colored ceramic disk (diameter: Ф = 14 mm, thickness: t = 2 mm) was annealed in air at 1300 °C for 5 h to remove the coloration originating from oxygen vacancies and Yb 2+ species appearing in oxygendeficient atmosphere [START_REF] Basyrova | Effect of SiO2 addition on structural and optical properties of Yb:Lu3Al5O12 transparent ceramics based on laser ablated nanopowders[END_REF][START_REF] Ma | Spectral and laser properties of Yb:LuAG transparent ceramics fabricated by tape casting method[END_REF]. As a result, a transparent and colorless sample was obtained, Fig. 1.

The formation of SiO2-rich liquid phase during sintering of Yb:Lu3Al5O12 ceramics with the addition of TEOS promotes mass transfer and densification enabling almost porefree microstructure using conventional vacuum sintering. However, the complete elimination of pores in sesquioxides is difficult because the conventional sintering usually requires high temperatures for full densification, which often results in grain-entrapped pores due to a rapid grain growth at the final stage of sintering. One of the approaches to avoid the breakaway of pores from the grain boundaries is based on the reduction of the sintering temperature by using pressure-assisted densification methods such as Hot Isostatic Pressing (HIP). Consequently, to fabricate the Yb:Lu2O3 ceramics, the laser-ablated Yb:Lu2O3 nanopowder was compacted by uniaxial dry-pressing at 200 MPa and then pre-sintered under vacuum at 1250 °C for 2 h. The pre-sintered sample was subjected to a capsule-free post-HIP step under an Ar gas pressure of 207 MPa at a temperature of 1400 °C for 2 h.

The obtained Yb:Lu2O3 ceramic disk with dimensions similar to those for Yb:Lu3Al5O12 was transparent but had a deep-brown coloration. The latter is assigned to oxygen vacancies forming during HIP in the oven with graphite heaters (forming reducer conditions). To remove the coloration, the ceramic was annealed in air. We studied the effect of annealing temperature and duration on the sample transmission, Fig. 2. For this, we used a similar Yb:Lu2O3 sample obtained by vacuum pre-sintering at 1400 °C for 1 h followed by HIP at 1500 °C for 2 h. For the annealing temperature of 1200 °C with increasing the treatment time from 1 to 10 h, the in-line transmission of the ceramic disk T0 gradually increases from 75.5% to 77.7% (at the wavelength of 1.10 μm) which is well above the transmission for the as-HIPed ceramics (T0 = 71.1%). Further increase of this time above 10 h does not improve the sample transmission. However, the annealing at 1300 °C for 1 h results in a notable drop of T0. A similar effect was observed previously in [START_REF] Rhodes | Loss and recovery of transparency in pressure-consolidated Lu3Al5O12[END_REF] and was assigned to the intense growth of nm-sized pores at ambient pressure and temperature high enough to activate the solid-phase processes. Thus, the sample used for the laser studies was annealed at 1200 °C for 10 h in air, see Fig. 1. It maintained a weak grey-brown coloration.

The drop in the transmission in the visible spectral range for annealed Yb:Lu2O3 ceramics (and, respectively, its residual coloration) may be explained as follows. First, it can originate from the presence of sub-μm and nm sized pores. According to the Rayleigh law, the scattering intensity is proportional to the squared volume of the defect and inverse proportional to λ 4 . Considering that the content of scattering centers detected using optical microscopy is relatively low (see Section 2.2), we conclude that the scattering centers with characteristic diameter above 2 μm cannot be responsible for the considerable decrease in light transmission at short wavelengths. Second, the coloration can be caused by impurity ions. We analyzed the impurity composition of the Yb:Lu2O3 ceramic by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) indicating the following uncontrolled impurities: transition-metal elements -Mn and Ti (both ~12 ppm) and rare-earth ones -Gd and Tb (both ~10 ppm) and Ho (7 ppm). Further discussion of the evidence for the presence of Tb 3+ species in the ceramics is presented in Section 3.2.

The doping level for both ceramics is the same, 3.6±0.4 at.%, determined by the composition of the Yb:Lu2O3 nanoparticles analyzed using ICP-MS, while the ion density NYb is different, namely 5.1×10 20 cm -3 for Yb:Lu3Al5O12 (measured density: ρ = 6.70 g/cm 3 ) and 10.2×10 20 cm -3 for Yb:Lu2O3 (ρ = 9.41 g/cm 3 ).

For the spectroscopic studies, the disks were double-sided polished to laser-grade quality.

Experimental

The structure and the phase purity of the two ceramics were studied by X-ray powder diffraction (XRD) analysis using a Shimadzu XRD-6000 diffractometer and Cu Kα radiation with a Ni filter.

The distribution of scattering centers (μm-sized pores) through the depth of the ceramic disks was analyzed by direct counting using an optical microscope (Olympus BX51TRF). The selected disk volume (577×433×50 μm 3 ) was in-depth scanned starting from one sample surface and moving down reaching the opposite surface with a step of 50 μm by changing the position of the focus. The spatial resolution of the microscope was ~2 μm, so that smaller pores than this size were not visualized.

The microstructure of a fractured surface of both ceramics was studied by Scanning Electron Microscopy (SEM) using a MERLIN SEM microscope (Carl Zeiss), Fig. 5. The SEM images were analyzed with the ImageJ software counting >100 grains and a shape factor of 1.2 was applied.

The room temperature (RT, 293 K) in-line transmission spectra of annealed and lasergrade polished ceramic disks were measured using a Shimadzu UV-3600 spectrophotometer. The luminescence spectra were measured with an optical spectrum analyzer (AQ6370B, Yokogawa) using a Ti:Sapphire laser tuned to 976 nm as an excitation source. For the lowtemperature (LT, 6 K) absorption and luminescence studies, we used a cryostat (SU 12, Oxford Instruments Ltd.) with helium-gas close-cycle flow.

The luminescence decay curves were measured at RT for powdered samples to avoid the effect of radiation trapping. We used a 1/4 m monochromator (Oriel 77200), an InGaAs detector and an 8 GHz digital oscilloscope (DSA70804B, Tektronix). The luminescence was excited by the output of a ns optical parametric oscillator (Horizon, Continuum) tuned to 970 nm.

The RT Raman spectra were measured with a Renishaw inVia confocal Raman microscope using a ×50 Leica objective (N.A. = 0.75). The excitation was at 488 nm (Ar + ion laser line) and the spectral resolution was ~1 cm -1 .

Characterization of ceramics 4.1 Structure and microstructure

The X-ray powder diffraction patterns of ceramics are shown in Fig. 3. Both ceramics are of single-phase nature. The Yb:Lu3Al5O12 ceramic exhibits a cubic structure identical to that of undoped Lu3Al5O12 (International Centre for Diffraction Data, ICDD card #73-1368, sp. gr. Ia3¯d -O 10 h, No. 230). The lattice constant is a = 11.912 Å. The Yb 3+ ions in Lu3Al5O12 replace the host-forming Lu 3+ cations in a single type of sites (symmetry: D2, coordination number (C.N.) by oxygen: VIII) and their ionic radii are RYb = 0.985 Å and RLu = 0.977 Å [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. This difference determines a slight increase of the lattice parameter a with respect to undoped Lu3Al5O12 (a = 11.90 Å).

The Yb:Lu2O3 ceramic is also cubic (sp. gr. Ia3¯ -T 7 h, No. 206) and possesses the socalled bixbyite ((Mn,Fe)2O3-type) or C-type structure [START_REF] Guzik | Structural investigations of Lu2O3 as single crystal and polycrystalline transparent ceramic[END_REF] of undoped Lu2O3 (ICDD card #76-0162). In the bixbyite structure, there are two crystallographic sites for RE 3+ ions replacing the Lu 3+ cations (symmetry: C2 and C3i, C.N. by oxygen: VI). The optical properties are mainly determined by the majority of ions residing in the C2 sites (for the C3i site, the electric-dipole transitions are forbidden due to inversion symmetry) [START_REF] Kränkel | Rare-earth-doped sesquioxides for diode-pumped high-power lasers in the 1-, 2-, and 3-μm spectral range[END_REF]. The Yb 3+ ions in Lu2O3 have lower coordination than in garnets (Lu3Al5O12) and shorter Yb|Lu -O interatomic distances leading to a stronger crystal field. The lattice constant for the Yb:Lu2O3 ceramics is a = 10.401 Å, slightly larger compared to undoped Lu2O3 (a = 10.391 Å).

The results on the distribution of scattering centers (μm-sized pores) through the depth of the ceramic disks are shown in Fig. 4. The very high content of scattering centers near one of the surfaces is explained by the polishing quality (pre-polish prior to the actual laser-gradepolish). The mean concentration of μm-sized pores Xpore is 9.8 ppm for Yb:Lu3Al5O12 and 3.5 ppm for Yb:Lu2O3 ceramics.

The SEM images of a fractured surface of both ceramics are shown in Fig. 5. The Yb:Lu3Al5O12 ceramics exhibited a close-packed microstructure with relatively large grains (mean size: Dgrain = 14 μm), clean grain boundaries and a very low content of sub-μm sized pores. The grain size distribution was similar over different parts of the ceramic disk. For the Yb:Lu2O3 ceramics, much smaller grains were observed with Dgrain = 0.4 μm. The ceramics also featured a close-packed structure. The difference in the mean grain size is related mainly to the different sintering temperature.

Optical spectroscopy

The in-line transmission spectra of annealed and laser-grade polished Yb:Lu3Al5O12 and Yb:Lu2O3 ceramic disks recalculated to the same thickness t of 1.0 mm are shown in Fig. 6. They are compared with the upper limit of transmission set by the Fresnel losses.

For the Yb:Lu3Al5O12 ceramic disk at the wavelength of 1.10 μm (out of the Yb 3+ absorption), the measured low-signal transmission was T0 = 83.0%, which is very close to the theoretical limit, TFr = 83.7% (calculated for a refractive index n = 1.824 [START_REF] Kuwano | Crystal growth and properties of (Lu,Y)3Al5O12[END_REF]). The ceramics also exhibited excellent transparency in the visible with the UV absorption edge at ~230 nm. For the Yb:Lu2O3 ceramic disk, T0 = 81.3% at 1.10 μm, cf. with TFr = 81.5% corresponding to a refractive index n = 1.909 [START_REF] Zelmon | Temperaturedependent Sellmeier equations for rare-earth sesquioxides[END_REF]. For this ceramic sample, the absorption in the visible gradually decreased reaching the UV absorption edge at ~270 nm.

The room temperature (RT, 293 K) absorption cross-sections for Yb 3+ were calculated from the absorption coefficient, σabs = αabs/NYb, where αabs = -ln(T0/TFr)/t. For Yb:Lu3Al5O12, at the zero-phonon line (ZPL, i.e., the transition between the lowest Stark sub-levels of Yb 3+ multiplets), σabs is 0.63×10 -20 cm 2 at 968.4 nm, see Fig. 7(a). The full width at half maximum (FWHM) of the absorption peak is 3.9 nm. A broad (FWHM > 20 nm) and structured absorption band is observed at shorter wavelengths with a maximum at 936.3 nm. For Yb:Lu2O3, σabs = 1.77×10 -20 cm 2 for the ZPL at 976.2 nm with a FWHM of 3.3 nm.

The RT stimulated-emission (SE) cross-sections, σSE, were calculated using the reciprocity method (RM) [START_REF] Payne | Infrared cross-section measurements for crystals doped with Er 3+ , Tm 3+ and Ho 3+[END_REF]:

1 ZPL SE abs 2 / ( ) ( ) exp , Z hc E Z kT      -   = -     (1a) exp( / ). m m m k k k Z g E kT = -  (1b)
Here, h is the Planck constant, c is the speed of light, λ is the light wavelength, k is the Boltzmann constant, T is the crystal temperature, EZPL is the ZPL energy, and Zm are the partition functions of the lower (m = 1) and the upper (m = 2) multiplets, g m k (assumed to be 1) is the degeneracy of the sub-level with the number k and the energy E m k measured from the lowest sub-level of each multiplet. The Stark splitting for Yb 3+ :Lu3Al5O12 was determined from low-temperature (LT) spectroscopy, and for Yb 3+ :Lu2O3was taken from [START_REF] Guyot | Assignment of Yb 3+ energy levels in the C2 and C3i centers of Lu2O3 sesquioxide either as ceramics or as crystal[END_REF]. The resulting SE cross-section spectra are shown in Fig. 7(a),(c).

In the long-wavelength part of the SE cross-section spectrum, the application of the RM leads to high uncertainty, so 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] was additionally employed. We used the following values of the radiative lifetime of the 2 F5/2 state giving a good agreement between the two methods: τrad = 1.01 ms (Yb:Lu3Al5O12) and 0.805 ms (Yb:Lu2O3) which agrees well with previous studies [START_REF] Brenier | Growth, spectroscopic, and laser properties of Yb 3+ -doped Lu3Al5O12 garnet crystal[END_REF][START_REF] Peters | Crystal growth by the heat exchanger method, spectroscopic characterization and laser operation of high-purity Yb:Lu2O3[END_REF].

For Yb:Lu3Al5O12, the maximum σSE is 2.46×10 -20 cm 2 at a wavelength of 1030.2 nm which is longer than the ZPL transition. For Yb:Lu2O3, the maximum σSE is 1.65×10 -20 cm 2 at 976.2 nm (the ZPL). At longer wavelengths, where the laser operation is expected, the SE cross-sections are lower, namely 0.86×10 -20 cm 2 at 1033.0 nm.

The Yb 3+ ion represents a quasi-three-level laser scheme with reabsorption. The gain cross-sections, σgain = βσSE -(1 -β)σabs, are thus calculated to conclude about the expected laser wavelengths. Here, β = N2( 2 F5/2)/NYb is the inversion ratio (N2 is the fraction of Yb 3+ ions in the upper laser level). The gain spectra are shown in Fig. 7(b),(d). For Yb:Lu3Al5O12, the spectra are only weakly dependent on the inversion level showing a maximum at ~1030 nm and a gain bandwidth (FWHM) of 6.7 nm for β = 0.20. For Yb:Lu2O3, at small inversion ratios, β < 0.10, the local peak at ~1080 nm dominates in the spectra and for higher inversion ratios, another peak at 1033 nm appears. The gain bandwidth is 14.7 nm for β = 0.20.

The crystal-field splitting for Yb 3+ :Lu3Al5O12 ceramics was determined using the LT (6 K) absorption and luminescence studies, as shown in Fig. 8(a),(b). The spectra were interpreted using the Raman spectra (see Fig. 10) to assign the phonon sidebands (marked by "hν"). Each 2S+1 LJ multiplet splits into J + 1/2 components numbered as i = 0..3 ( 2 F7/2, ground-state) and j' = 0'..2' ( 2 F5/2, excited-state). As a result, we determined the following set of energy levels: 0, 602, 643 and 764 cm -1 ( 2 F7/2), 10333, 10643 and 10908 cm -1 ( 2 F5/2), Fig. 8(c). Thus, EZPL = 10333 cm -1 and the partition functions Z1 = 1.122 and Z2 = 1.277, so that Z1/Z2 = 0.879. The determined Stark splitting is close to that reported previously for highly-doped (15 at.%) Yb:Lu3Al5O12 single-crystal, i.e., 0, 600, 635 and 762 cm -1 ( 2 F7/2), 10330, 10645 and 10900 cm -1 ( 2 F5/2) [START_REF] Brenier | Growth, spectroscopic, and laser properties of Yb 3+ -doped Lu3Al5O12 garnet crystal[END_REF].

For both studied ceramics, the decay curves are clearly single-exponential, Fig. 9, corresponding to the luminescence lifetimes τlum = 1.01 ms (for Yb:Lu3Al5O12) and 0.74 ms (for Yb:Lu2O3).

The RT Raman spectra are shown in Fig. 10. The cubic garnet structure of Lu3Al5O12 gives rise to 25 Raman-active modes (irreducible representations: 3A1g + 8Eg + 14F2g) [START_REF] Kaminskii | Stimulated Raman scattering in "garnet" Lu3Al5O12 ceramics-a novel hostmateriel for Ln-and TM-lasant ions[END_REF]. The most intense band at 374 cm -1 assigned as A1g (FWHM = 11 cm -1 ) is due to the rotation of the [AlO4] tetrahedral unit. The second intense mode at 796 cm -1 (also A1g, FWHM = 14 cm -1 ) is due to the breathing mode of the [AlO4] tetrahedrons. The maximum phonon energy is 869 cm -1 . The cubic sesquioxide structure of Lu2O3 has 22 Raman-active modes (4Ag + 4Eg + 14Fg) [START_REF] Todorov | Raman spectroscopy and lattice dynamical calculations of Sc2O3 single crystals[END_REF]. The most prominent band at 389 cm -1 (FWHM = 11 cm -1 ) is ascribed to the Ag + Fg vibrations and the maximum phonon energy is ~610 cm -1 .

Laser operation 5.1 Laser set-up

For the laser experiments, we fabricated two rectangular ceramic elements with the following dimensions: Yb:Lu3Al5O12 (t = 2.75(z) mm, aperture: 3.18(x)×1.50 mm 2 ) and Yb:Lu2O3 (t = 1.07(z) mm, aperture: 2.5(x)×2.5 mm 2 ), where x denotes an arbitrary direction lies in the plane of the ceramic disk and z-axis is orthogonal to it, respectively, cf. Fig. 1. Their input and output facets were polished to laser-grade quality and remained uncoated. The elements were wrapped in an Indium foil and mounted in a Cu-holder for better heat removal from all four lateral sides. The holder was cooled by circulating water (12 °C). The elements were placed in a compact (microchip-type) laser cavity formed by a flat pump mirror (PM) providing high transmission (HT) at ~0.97 μm and high reflectance (HR) at 1.02-1.23 μm, and a set of flat output couplers (OCs) with a transmission TOC = 0.5%-10% at 1.02-1.10 μm, Fig. 11. The PM and the OC were placed close to the laser element so that the geometrical cavity length was close to the element thickness. The mode stabilization in a plano-plano cavity was provided by the positive thermal lens in both materials.

The pump source was a fiber-coupled (N.A. = 0.22, fiber core diameter: 105 μm) InGaAs laser diode (LD) emitting up to 54 W of unpolarized output at 968 nm (emission linewidth: 1.5 nm, M 2 ≈ 37). Thus, the pumping was at the ZPL of Yb 3+ ions in Lu3Al5O12 ceramics. This approach (compared to pumping at 936 nm [25]) has the advantage of reduced heat load. The pump was reimaged into the ceramic by an antireflection (AR) coated 1:1 lens assembly (f = 30 mm) leading to a pump spot diameter 2wP ≈ 100 μm and a confocal parameter 2zR ≈ 1 mm (in the gain element). The OCs provided high reflection at the pump wavelength (R > 90%), so that the pumping was in a double-pass increasing the total pump absorption. The latter was determined from pump-transmission measurements at the laser threshold, ηabs(2 passes) = 25.5±1% (for Yb:Lu3Al5O12) and 19.9±1% (Yb:Lu2O3). It was possible to operate the diode in quasi-CW regime by electronic modulation of the driving current.

The size of the laser mode in the ceramic laser element 2wL was calculated using the ABCD formalism accounting for the thermal lens to be 55±7 μm (for Yb:Lu3Al5O12) and 47±5 μm (for Yb:Lu2O3).

The laser output was separated from the residual pump using a long-pass filter (FEL1000, Thorlabs). The spectra were measured using a spectrometer (APE, WaveScan; 800-1600 nm).

Laser performance

First, we studied the performance of the Yb:Lu3Al5O12 ceramics limiting the absorbed pump power to Pabs < 5 W, Fig. 12(a). Under such conditions, we did not observe any thermal effects (e.g., roll-over in the output dependence) when operating the laser in true CW regime. For the highest available output coupling (TOC = 10%), the laser generated 2.72 W at 1031.1 nm with a slope efficiency η = 67.2%. The optical-to-optical efficiency ηopt vs. the pump power incident on the ceramic element was only 15.0%, mostly because of the limited pump absorption. The laser threshold slightly increased with the output coupling, from Pth = 0.30 W (for TOC = 0.5%) to 0.45 W (for TOC = 10%).

The laser spectra were weakly dependent on the output coupling, Fig. 12(b). The laser oscillation occurred at ~1030 nm in agreement with the gain spectra, Fig. 7(b). The laser emission was unpolarized. The multi-line structure of the emission spectra is due to etalon (Fabry-Perot) effects at the interfaces of the laser element / cavity mirrors.

The Yb:Lu3Al5O12 ceramic laser operated in the fundamental transverse mode. The example profile of the laser mode (measured using TOC = 10%) in the far-field is shown in Fig. 11(b). It is nearly circular. For Pabs < 5 W, the beam profile was weakly dependent on the pump level.

The performance of the Yb:Lu3Al5O12 ceramic laser for TOC = 10% was analyzed using the model of a quasi-three-level gain medium [START_REF] Serres | Microchip laser operation of Yb-doped gallium garnets[END_REF] yielding a double-pass intracavity loss L of 4.1%. This value is lower than the Fresnel losses at the uncoated surfaces of the laser element as it was polished with a good parallelism thus acting as a Fabry-Perot etalon. Thus, the coefficient of passive losses δloss = 0.076±0.05 cm -1 .

For the Yb:Lu2O3 ceramics, we limited the absorbed pump power to Pabs < 2 W. The laser generated a maximum output power of 0.59 W at 1080-1084 nm with η = 38.0% and the optical-to-optical efficiency ηopt of 5.8% (TOC = 5%). The laser threshold gradually increased with the output coupling, from Pth = 0.22 W (for TOC = 0.5%) to 0.48 W (for TOC = 10%). A reduction in the laser threshold for small output coupling, as compared to the Yb:Lu3Al5O12 laser is due to the smaller thickness of the Yb:Lu2O3 laser element. A thermal roll-over was observed in the output dependences for Pabs > 2 W. The emission occurred at ~1080 nm for low TOC ≤ 5% and the laser wavelength experienced a blue-shift to 1036 nm for higher TOC, in agreement with the gain spectra, Fig. 7(d).

A notable reduction in the slope efficiency for the Yb:Lu2O3 laser as compared to its garnet counterpart is mainly attributed to non-optimum mode-matching owing to the shorter cavity and thermal lens. To confirm this, we designed a hemispherical laser cavity with a concave (radius of curvature: -50 mm) output coupler. The calculated size of the laser mode in the ceramic element for this cavity geometry amounted to 55±5 μm, i.e., much closer to the pump spot size. The CW output power reached 1.0 W at 1083 nm with η = 68.0% and a laser threshold of 0.28 W, see Fig. 12(c). Still, we were unable to avoid the thermal roll-over at Pabs > 2 W. The analysis of the laser performance yielded a double-pass loss L of 1.6% corresponding to δloss = 0.077±0.05 cm -1 (i.e., almost the same as for the garnet ceramics). Thus, the difference in the power scaling capabilities for the two ceramics is mainly related to their different thermal behavior. One should also consider much longer emission wavelength for the Yb:Lu2O3 ceramics leading to higher fractional heat loading, ηh ≈ 1 -λP/λL = 10.6% (cf. with 6.1% for Yb:Lu3Al5O12).

Subsequently the pump power for the Yb:Lu3Al5O12 ceramic micro-laser was increased to the maximum available from the laser diode, Fig. 13(a). It corresponded to Pabs = 13.7 W. In the CW regime, the laser generated 5.65 W. As a result of the thermal roll-over in the input-output dependence for Pabs > 5 W, ηopt dropped to 10.5%. To reduce the heat loading, the laser was operated in quasi-CW regime with different duty cycles (from 1:1.5 to 1:3). The duration of the rectangular pump pulses was 1 ms in all cases. With increasing the time interval between the pump pulses, the peak output power increased and the input-output dependence became linear reaching maximum values of Pout,peak = 8.83 W and η = 66.9%, respectively, almost reproducing the slope of the true CW performance in the low-power regime.

To improve the thermal management of the ceramic laser, we also fabricated a slabshaped Yb:Lu3Al5O12 element with a thickness of 3.18(x) mm and aperture of 1.0(z)×2.75 mm 2 . Cooling was provided at the two large-area lateral faces. The pump absorption in the slab slightly increased to 28.8±1% (2 passes). The input-output characteristics of the microslab ceramic laser are shown in Fig. 13(b) and compared with those for the microchip design. In the CW regime, the mini-slab laser generated 5.0 W at 1031.2 nm with improved η = 78.8% (fitting the linear part of the output dependence), a laser threshold of 0.58 W and ηopt = 15.0% (TOC = 10%). Still, a thermal roll-over was observed for Pabs above ~6 W. We assign the improved slope efficiency to better mode-matching and probably weaker thermal lens in the laser element owing to its better cooling.

Note that the cut of the ceramic laser element (i.e., the propagation direction of the laser) of the micro-laser was orthogonal to the plane of the ceramic disk (|| z-axis) while the cut of the slab element was lying on the plane of the disk (|| x-axis, see Fig. 1). No deterioration of the laser performance is observed in the latter case, indicating good uniformity of the ceramic disk in the radial direction and highlighting its suitability for laser applications. Transparent ceramics fabricated on the basis of cubic materials exhibit no anisotropy of optical properties. However, one may observe anisotropy of pore distribution in the ceramic disk (and, consequently, the related anisotropy of scattering losses) under synthesis conditions when the pores are predominantly removed along one direction, e.g., when using hot (uniaxial) pressing or spark plasma synthesis. The lack of such effects for the studied ceramics was confirmed by analyzing the distribution of scattering centers and the grain size distribution across the ceramic disks (the difference was within the measurement error).

Discussion

The present work reports the first CW laser operation of Yb:Lu3Al5O12 and Yb:Lu2O3 ceramics obtained from laser-ablated nanoparticles.

Regarding previously reported Yb:Lu3Al5O12 lasers based on single-crystals and ceramics, cf. Table 1, we obtained one of the best results in terms of output power (CW and quasi-CW operation) and slope efficiency, with highly compact (microchip-type) laser geometries. Microchip Yb:Lu3Al5O12 lasers were reported by Dong et al. using 5 at.% Yb doped single-crystals delivering a maximum CW output power of 1.63 W at 1030 nm with η = 72%. Much better output performance is achieved in the present work with the new ceramic material.

Using Yb:Lu2O3 ceramics, multi-watt CW laser output has been previously reported by other researchers, e.g., Sanghera et al. demonstrated a diode-pumped 10 at.% Yb:Lu2O3 laser delivering ~16 W at 1080 nm with η = 74% [START_REF] Sanghera | 10% Yb 3+ -Lu2O3 ceramic laser with 74% efficiency[END_REF]. However, a much larger pump spot size (as compared to the present work) was used thus reducing the localized heat release.

Let us discuss the reasons for the thermal roll-over observed for the Yb:Lu2O3 ceramic laser. The thermal conductivity of Yb:Lu2O3 ceramics is high (κ = 13.9 Wm -1 K -1 for 3 at.% Yb doping [START_REF] Nakao | Yb 3+ -doped ceramic thin-disk lasers of Lu-based oxides[END_REF]) and is weakly dependent on the Yb doping level [START_REF] Peters | Growth and spectroscopy of ytterbium doped sesquioxides[END_REF]; moreover, it is higher than that for Yb:Lu3Al5O12 [START_REF] Nakao | Yb 3+ -doped ceramic thin-disk lasers of Lu-based oxides[END_REF]. This difference would compensate for the higher fractional heat load in Yb:Lu2O3 originating from the longer emission wavelength. As determined in the present work, the passive losses in both materials at the laser wavelength are very close. Thus, another mechanism should be the reason.

It was suggested that the interaction of Yb 3+ laser-active ions with uncontrolled rareearth impurities such as Tb 3+ , Ho 3+ or Dy 3+ may affect the output performance of Yb ceramic lasers [25,[START_REF] Peters | Growth and spectroscopy of ytterbium doped sesquioxides[END_REF]. Such ions are always present in the Yb2O3 and Lu2O3 raw materials. In addition, Yb 2+ ions may play a similar role and act as quenching centers for Yb 3+ . Typically, Yb 2+ ions formed during the synthesis in oxygen-deficient conditions are completely removed after annealing in air unless a charge compensation is present by a tetravalent impurity center such as Tb 4+ . Terbium is polyvalent and Tb 4+ species can be formed during the oxidizing annealing preventing complete removal of Yb 2+ . Indeed, an unwanted energy transfer from Yb 3+ ions to such impurity centers will lead to additional heat generation.

To clarify this issue, we measured the luminescence spectra of Yb 3+ -doped ceramics under excitation in the blue, Fig. 14(a), using the Renishaw inVia confocal Raman microscope. For the Yb:Lu2O3 ceramics, we observed intense characteristic emissions of Tb 3+ ions owing to the 5 D4 → 5 FJ (J = 5 ... 0) transitions in addition to Yb 3+ emission at ~1 μm which was at least one order or magnitude more intense. The spectral shape of the Yb 3+ luminescence well matched the one observed under near-IR excitation. Although Tb 3+ does not exhibit energy-levels being resonant in energy with the excited-state of Yb 3+ (the energy of the metastable Tb 3+ state 5 D4 is ~20500 cm -1 whereas the energy of the Yb 3+ excited-state 2 F5/2 is ~10000 cm -1 ), the bidirectional energy-transfer (ET) between these ions is known. It involves Yb 3+ -Yb 3+ ion pairs exhibiting an excited-state with an energy 2E( 2 F5/2) ~20000 cm - 1 leading either to cooperative sensitization (2Yb 3+ → Tb 3+ ET) [START_REF] Pandey | Influence of Li + codoping on visible emission of Y2O3:Tb 3+ , Yb 3+ phosphor[END_REF] or cooperative downconversion (Tb 3+ → 2Yb 3+ ET) [START_REF] Yuan | Energy transfer mechanisms in Tb 3+ , Yb 3+ codoped Y2O3 downconversion phosphor[END_REF]. The latter process is observed in our case.

Furthermore, we analyzed the effect of the form of the sesquioxide material on the Tb 3+ → 2Yb 3+ ET by comparing the luminescence spectra of three materials: a commercial Lu2O3 powder, an Yb:Lu2O3 nanopowder produced by laser ablation, sedimentation and calcination, and an Yb:Lu2O3 ceramic, Fig. 14(b). Almost no Yb 3+ emission is observed in the commercial (undoped) powder. In the visible, apart from the rare-earth ion impurity emissions, broad bands originating from defect states appear. For the nanopowder, both kinds of visible emissions are suppressed while the ~1 μm emission appears suggesting weak ET. Finally, for the ceramic, the Yb 3+ emission is enhanced by an order of magnitude and the visible emissions are further diminished indicating much stronger ET.

For the Yb:Lu3A5O12 ceramics, Fig. 14(a), similar Tb 3+ emissions are observed but the ~1 μm Yb 3+ luminescence is much weaker due to cooperative down-conversion. The latter suggests weaker effect of terbium impurity on Yb 3+ laser performance. The rare-earth ion density in sesquioxides is higher than in garnets (for the same at.%) which explains the higher content of Tb in Yb:Lu2O3. It is known that cooperative energy-transfer processes are particularly strong in sesquioxides [START_REF] Yuan | Energy transfer mechanisms in Tb 3+ , Yb 3+ codoped Y2O3 downconversion phosphor[END_REF]. Thus, Tb 3+ species directly act as quenching centers. Tb 4+ species are formed during annealing serving as charge compensators for Yb 2+ ions but also acting as strong quenching centers. As a consequence the presence of Tb 3+ and Tb 4+ may be responsible for the observed thermal roll-over and explains the coloration of the fabricated Yb:Lu2O3 ceramics.

Conclusions

We presented a detailed comparative study of the microstructure, optical, vibronic and spectroscopic properties, and diode-pumped laser performance of two Yb-doped Lu-based oxide transparent ceramics, namely Yb:Lu3Al5O12 (garnet) and Yb:Lu2O3 (sesquioxide). These ceramics were synthesized using the same nanopowders (Yb:Lu2O3 and Al2O3) produced by laser ablation by two different methods: solid-state reaction synthesis at 1800 °C for 5 h with a presence of a sintering aid (1 wt% TEOS) and vacuum pre-sintering followed by HIP at 207 MPa / 1400 °C for 2 h, respectively. The use of different methods was dictated by the different microstructure evolution of these materials during sintering (concerning the pore formation) and it led to a notable difference in the mean grain size: 14 and 0.4 μm for Yb:Lu3Al5O12 and Yb:Lu2O3, respectively. Both ceramics exhibited low content of μm-sized pores, a close-packed structure, high transmission at ~1.1 μm approaching the theoretical one, and relatively low passive losses at the Yb 3+ laser wavelength.

Efficient continuous-wave laser operation under diode-pumping at 968 nm is achieved with both ceramics. The Yb:Lu3Al5O12 ceramic outperformed its sesquioxide counterpart: a compact (microchip-type) laser generated 5.65 W at 1031.1 nm with a slope efficiency of 67.2% (fitting the linear part of the output dependence) and a laser threshold of 0.45 W and in the quasi-CW regime, the peak power was scaled up to 8.83 W (limited only by the available pump power). For the Yb:Lu2O3 ceramic laser, the power scaling was limited (the CW output power reached 1.0 W at 1083 nm with η = 68.0%) by the thermo-optic effects which are assigned to stronger heat dissipation due in part to the longer laser wavelength and in part to the impurity Tb 3+ ions and possibly Yb 2+ ions charge-compensation by Tb 4+ species. These optical centers also determined a weak brown coloration of the Yb:Lu2O3 ceramics.

Further power scaling of compact lasers based on both Lu-based oxide ceramics seems to be possible via several routes: (i) improvement of the ceramic quality by eliminating the effect of terbium impurity responsible for the formation of Tb 3+ and Yb 2+ centers, e.g., by purification of the nanopowders; (b) alleviating thermal effects using larger pump spot size or employing other geometries of the laser element providing more efficient cooling (e.g., slabshaped, as already demonstrated in the present work for Yb:Lu3Al5O12 ceramics); (iii) using higher Yb doping levels up to 10 at.% for better pump absorption efficiency.

The developed Yb:Lu3Al5O12 ceramics are promising for thin-disk lasers and amplifiers at ~1 μm.

List of figure captions

Figure 1 .

 1 Figure 1. Photograph of Yb:Lu3Al5O12 (left) and Yb:Lu2O3 (right) ceramic disks after annealing.

Figure 2 .

 2 Figure 2. Effect of the annealing temperature and duration on the transmission of an Yb:Lu2O3 ceramic disk (thickness: t = 1.0 mm).

Figure 3 .

 3 Figure 3. X-ray powder diffraction (XRD) patterns of (a) Yb:Lu3Al5O12 and (b) Yb:Lu2O3 ceramics, numbers denote the Miller's indices (hkl). Blue barspositions of the diffraction peaks for cubic Lu3Al5O12 and Lu2O3 phases.

Figure 4 .

 4 Figure 4. In-depth distribution of scattering centers in (a) Yb:Lu3Al5O12 (t = 1.75 mm) and (b) Yb:Lu2O3 (t = 1.4 mm) ceramics.

Figure 5 .

 5 Figure 5. Scanning Electron Microscopy (SEM) images of the fracture surface of (a) Yb:Lu3Al5O12 and (b) Yb:Lu2O3 ceramics, insets: grain size distributions.

Figure 6 .

 6 Figure 6. Low-signal transmission spectra of Yb:Lu3Al5O12 and Yb:Lu2O3 ceramic disks (t = 1.0 mm), dashed curves -calculated Fresnel losses.

Figure 7 .

 7 Figure 7. Room temperature spectroscopy of Yb 3+ in (a,b) Lu3Al5O12 and (c,d) Lu2O3 ceramics: (a,c) absorption, σabs, and stimulated-emission (SE), σSE, cross-section spectra for the 2 F5/2 ↔ 2 F7/2 transition; (b,d) gain cross-sections, σgain = βσSE -(1 -β)σabs, where β = N2( 2 F5/2)/NYb is the inversion ratio and N2 is the population of the upper laser level.

Figure 8 .

 8 Figure 8. Low-temperature (6 K) spectroscopy of Yb 3+ in Lu3Al5O12 ceramics: (a) absorption spectrum, (b) luminescence spectrum, λexc = 976 nm. "hν"phonon sidebands; (c) Stark splitting of Yb 3+ multiplets: i = 0..3 and j' = 0'..2' number the Stark sub-levels, values indicate their energy in cm -1 , Z1(2) are the partition functions for the lower (upper) multiplets.

Figure 9 .

 9 Figure 9. Room temperature luminescence decay curves of Yb 3+ in (a) Lu3Al5O12 and (b) Lu2O3 ceramics measured for powdered samples (plotted in a semi-log scale), symbols: experimental data, lines: their exponential fits, λexc = 970 nm, λlum = 1050 nm.

Figure 10 .

 10 Figure 10. Room temperature Raman spectra of (a) Yb:Lu3Al5O12 and (b) Yb:Lu2O3 ceramics, numbers denote the Raman frequencies in cm -1 . λexc = 488 nm.

Figure 11 .

 11 Figure 11. (a) Scheme of the compact diode-pumped ytterbium ceramic laser: LDlaser diode, PMpump mirror, OCoutput coupler; (b) Typical profile of the output laser mode for the Yb:Lu3Al5O12 ceramic laser.

Figure 12 .

 12 Figure 12. Low-power diode-pumped laser performance of (a,b) 3.6 at.% Yb:Lu3Al5O12 and (c,d) 3.6 at.% Yb:Lu2O3 ceramics (microchip laser geometry): (a,c) input-output dependences, ηslope efficiency; (b,d) typical laser emission spectra measured at Pabs = 4 W. In (c), the results for a hemispherical cavity are shown for comparison. The laser emission is unpolarized.

Figure 13 .

 13 Figure 13. Thermal effects in the diode-pumped 3.6 at.% Yb:Lu3Al5O12 ceramic lasers: (a) CW and quasi-CW performance of the microchip laser; (b) Comparison of the CW performance of the microchip laser and the mini-slab laser, ηslope efficiency, TOC = 10%.

Figure 14 .

 14 Figure 14. (a) Luminescence spectra of Yb:Lu3Al5O12 and Yb:Lu2O3 ceramics under excitation in the blue. The spectra are normalized with respect to the visible emission. For the Yb:Lu2O3 ceramic, the ~1 μm luminescence is divided by a factor of 10; (b) Luminescence spectra of a commercial Lu2O3 powder, laser-ablated and calcined Yb:Lu2O3 nanopowder, and Yb:Lu2O3 ceramic.

Table 1 .

 1 Output characteristics a of Yb:Lu3Al5O12 crystalline and ceramic lasers.

	Material	Doping, at.% λP, nm	Pth, W Pout, W	η, %	λL, nm	Ref.
	Crystal	12	970	0.75	0.17 CW	~15	1078	[24]
	Crystal	5	940	0.15	1.63 CW	72	1030	[42]
	Crystal	10	968	0.5	3.0 CW	35	1048	[43]
			936	0.5	11.8 qCW	82	1046	[43]
	Ceramics 3.6	968	0.45	5.65 CW	67.2	1031	b

Acknowledgments 13 This work was supported by the Spanish Government (project No. MAT2016-75716-C2-1-R (AEI/FEDER,UE)); Generalitat de Catalunya (project No. 2017SGR755); Government of the Russian Federation (state task project No. 0389-2016-0002 (2018-2020)); RFBR (Grant No. 19-03-00855). The authors gratefully acknowledge Vyacheslav V. Platonov and Egor V. Tikhonov from IEP UrB RAS for providing Yb:Lu2O3 and Al2O3 nanopowders. L. B. thanks Mikhail Baranov from ITMO University for the help with the SEM studies.

Declaration of competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. [START_REF] Tokurakawa | Continuous wave and mode-locked Yb 3+ :Y2O3 ceramic thin disk laser[END_REF]


Liza Basyrova
email: liza.basyrova@ensicaen.fr

Pavel Loiko

Gurvan Brasse

Abdelmjid Benayad

Jean-Louis Doualan

Alain Braud

Patrice Camy

Highly-Doped Er:LiYF 4 Waveguiding Epitaxial Films for ~2.7 µm Laser Sources

Single-crystalline oriented highly-doped 9.6 at.% Er 3+ :LiYF 4 waveguiding thin films (30-50 µm) are grown by Liquid Phase Epitaxy. Their polarized spectroscopic properties are studied. The maximum stimulated-emission cross-section is 1.61×10 -20 cm 2 at 2720 nm for π-polarization.

Erbium (Er 3+ ) ions are well-known due to their mid-IR emission at ~2.7 µm owing to the 4 I 11/2 → 4 I 13/2 transition. ~2.7 µm Er lasers are of practical importance for medicine, infrared countermeasures, spectroscopy and pumping of midinfrared OPOs. The difficulty in developing ~2.7 µm Er lasers is the self-terminating nature of the 4 I 11/2 → 4 I 13/2 transition. It is typically overcome by using high Er doping levels [START_REF] Stoneman | Efficient resonantly pumped 2.8-μm Er 3+ :GSGG laser[END_REF]. Among the gain media for mid-IR Er lasers, fluoride crystals have attracted a lot of attention. For example, Er 3+ -doped yttrium lithium fluoride (LiYF 4 ) crystal was successfully employed in ~2.7 µm lasers [START_REF] Hubert | Emission properties, oscillator strengths and laser parameters of Er 3+ in LiYF 4 at 2.7 μm[END_REF].

Waveguide lasers emitting in the near-and mid-IR are of interest for the development of compact ultrafast oscillators [START_REF] Khurmi | Ultrafast pulse generation in a mode-locked Erbium chip waveguide laser[END_REF]. Few results concerning ~2.7 µm waveguide lasers have been already reported [START_REF] Lancaster | Efficient 2.9 μm fluorozirconate glass waveguide chip laser[END_REF]. Rare-earth-doped LiYF 4 is well-known for fabrication of active waveguides by Liquid Phase Epitaxy (LPE) [START_REF] Loiko | Watt-level Tm:LiYF 4 channel waveguide laser produced by diamond saw dicing[END_REF]. However, so far, Er 3+ :LiYF 4 active layers were not fabricated. In the present work, we aimed to grow highly Er 3+ -doped LiYF 4 singlecrystalline oriented waveguiding films and to study their spectroscopic properties relevant for ~2.7 µm laser operation.

Er 3+ :LiYF 4 thin-films were grown on (001)-oriented bulk undoped LiYF 4 substrates by LPE using a batch with a composition of 73 mol% LiF -27 mol% (YF 3 + ErF 3 ); LiF was used as a solvent also entering into the composition of the solute. The growth temperature was 729.5 -730.5 °C and the growth duration was 45 min. The Er 3+ doping level in the flux was 11 at.% and the segregation coefficient for Er 3+ ions K Er was 0.88. The thickness of the films was in the range 30 -50 µm (growth rate: 0.7-1.1 µm/min). The structure (cubic, sp. gr. C 6 4h -I4 1 /a) and orientation of the films were confirmed by single-crystal XRD. The film composition was studied by EDX. The absorption cross-section, σ abs , spectra for transitions of Er 3+ ions from the ground-state 4 I 15/2 to the excited-states 4 I 13/2 , 4 I 11/2 and 4 I 9/2 are shown in Fig. 2(a) for the available σ-polarization. For the most common pump transition ( 4 I 15/2 → 4 I 11/2 ), σ abs = 0.46×10 -20 cm 2 at 972.3 nm and the absorption bandwidth (FWHM) is 6.2 nm. For the 4 I 15/2 → 4 I 9/2 one, σ abs is much lower, ~0.05×10 -20 cm 2 at 781 nm, but the absorption band is broader.

The stimulated-emission (SE) cross-sections, σ SE , for the 4 I 11/2 → 4 I 13/2 transition in emission were calculated using the Füchtbauer-Ladenburg (F-L) equation, Fig. 2(b), based on the polarized luminescence spectra and using a radiative lifetime τ rad = 6.7 ms and a luminescence branching ratio β = 15% determined from the Judd-Ofelt theory. As the considered transition has both electric-dipole (ED) and magnetic-dipole (MD) contributions, three polarization states were considered: σ (E ⊥ c, k ⊥ c), α (E ⊥ c, k || c) and π (E || c, k ⊥ c) -LiYF 4 is optically uniaxial with the optical axis parallel to the c-axis. The maximum σ SE is 1.61×10 -20 cm 2 at 2720 nm and at longer wavelengths where the laser operation is expected (owing to the ESA), it is 0.69×10 -20 cm 2 at 2812 nm (both values correspond to π-polarization).

The crystal-field splitting of the multiplets involved in the ~2.7 µm laser transition ( 4 I 11/2 and 4 I 13/2 ) is revealed using LT (12 K) spectroscopy, Fig. 2(c). The luminescence lifetimes τ lum of different multiplets of Er 3+ ions (from 4 I 13/2 to 4 S 3/2 + 2 H 11/2 ) were systematically studied, Fig. 3. For the levels involved in the ~2.7 µm laser transition, τ lum ( 4 I 11/2 ) = 2.71 ms and τ lum ( 4 I 13/2 ) = 8.36 ms. The fabricated films exhibit a positive refractive index contrast, Δn = n filmn substrate ≈ 2×10 -3 owing to the effect of Er 3+ dopant ions. The waveguiding properties of the films are confirmed by coupling the pump radiation at 972 nm from a Ti:sapphire laser. The waveguide laser experiments are in progress.

To conclude, highly-doped single-crystalline oriented Er 3+ :LiYF 4 thin-films (thickness: up to 50 µm) of high optical quality are grown on bulk LiYF 4 substrates by LPE. They exhibit intense mid-IR emission at ~2.7 µm and weak quenching of the 4 I 11/2 lifetime, as well as waveguiding properties. Er 3+ :LiYF 4 epitaxial films are promising for mid-IR waveguide lasers. Further work will focus on laser experiments and adjustment of the Er 3+ doping level in order to optimize energy-transfer processes populating the upper laser level.

Figure 1 (

 1 a) shows an optical image of a polished end-facet of the Er 3+ :LiYF 4 /LiYF 4 epitaxy. The film / substrate interface is clear, there are no cracks nor secondary phases in the film. The film thickness, t = 38±2 µm, is nearly constant over the substrate area deep in the flux. The morphology of the as-grown top surface reveals smooth "hills and valleys" landscape and crystallized residual LiF solvent which is typical for LPE films, Fig. 1(b).

Fig. 1 .

 1 Fig. 1. (a) Optical microscope image of the polished end-facet of the Er 3+ :LiYF 4 / LiYF 4 epitaxy after cleaning the residual solvent; (b) Confocal microscope image (interferometric regime, reflection mode, λ = 405 nm) of the as-grown top surface of the film.

Fig. 2 .

 2 Fig. 2. Spectroscopy of 9.6 at.% Er 3+ :LiYF 4 LPE films: (a) absorption cross-sections, σ abs , for the 4 I 15/2 → 4 I 9/2 , 4 I 11/2 and 4 I 13/2 transitions (σ-polarization), (b) stimulated-emission, σ SE , cross-sections for the 4 I 11/2 → 4 I 13/2 transition, light polarizations: π, σ and α; (c) crystalfield splitting for the 4 I 11/2 and 4 I 13/2 multiplets of Er 3+ ions resolved at 12 K.

Fig. 3 .

 3 Fig. 3. (a) Luminescence decay curves for emissions from the 4 I 13/2 and 4 I 11/2 states of Er 3+ ions in the 9.6 at.% Er 3+ :LiYF 4 epitaxial film, λ exc = 960 nm; (b) summary of the measured luminescence lifetimes τ lum for Er 3+ multiplets.


Pavel Loiko
email: pavel.loiko@ensicaen.fr

Ludovic Gauthier-Manuel

Gurvan Brasse

Alain Braud

Abdelmjid Benayad

Patrice Camy

Efficient Broadly Tunable Waveguide Lasers in Yb 3+ :CaF 2 Produced by Deep Diamond Saw Dicing

High-aspect-ratio ridge waveguides (propagation losses: 0.13±0.05 dB/cm) were fabricated in Yb 3+ :CaF2 by diamond-saw-dicing. The waveguide laser generated 723 mW at 1029-1051 nm with a slope efficiency of 76.0%; wavelength tuning between 1009-1072 nm was achieved.

Ytterbium (Yb 3+ ) doped calcium fluoride (CaF2) is an attractive laser material [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]. The host matrix provides high thermal conductivity (~9.7 Wm -1 K -1 ), isotropic thermal expansion, negative thermal lensing and low refractive index (n = 1.429 at ~1 µm). CaF2 can be easily doped with Yb 3+ and it features strong ion clustering already at low doping levels (above 0.1 at.%) resulting in significant inhomogeneous broadening of spectral bands (a glassy-like spectroscopic behavior) [START_REF] Petit | Spectroscopy of Yb 3+ :CaF2: From isolated centers to clusters[END_REF]. The smooth and broad gain spectra of Yb 3+ :CaF2 determine its potential for broadband wavelength tuning and especially generation of femtosecond pulses in mode-locked oscillators at ~1 µm [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].

So far, little attention was paid to the development of Yb 3+ :CaF2 waveguide (WG) lasers [START_REF] Loiko | Ytterbium calcium fluoride waveguide laser[END_REF][START_REF] Ren | Switchable single-dual-wavelength Yb,Na:CaF2 waveguide lasers operating in continuous-wave and pulsed regimes[END_REF]. Ren et al. fabricated buried channel WGs in Yb 3+ ,Na + :CaF2 by ultrafast laser inscription and achieved 174 mW at ~1.01 µm with an opticalto-optical efficiency of 45.3% [START_REF] Ren | Switchable single-dual-wavelength Yb,Na:CaF2 waveguide lasers operating in continuous-wave and pulsed regimes[END_REF]. In the present work, we report on highly-efficient and wavelength-tunable WG lasers fabricated using diamond saw dicing [START_REF] Loiko | Watt-level Tm:LiYF4 channel waveguide laser produced by diamond saw dicing[END_REF] of bulk Yb 3+ :CaF2 crystals.

High aspect ratio (height: 200 µm, width: 10-50 µm) surface channel (ridge) WGs were produced in a bulk 4.5 at.% Yb 3+ :CaF2 crystal by "deep" diamond saw dicing, Fig. 1(a). The guides exhibited no chipping at the facets nor cracks, as well as good verticality of the side walls. The r.m.s. surface roughness of the latter studied using a confocal microscope in an interferometric mode was 0.5 nm, Fig. 1(b). The WG propagation loss δloss increased for narrower guides, from 0.17 dB/cm for the 50 μm wide guide up to 0.52 dB/cm for the 10 μm wide one (for vertical polarization, at 0.91 µm).

The laser operation was studied in the continuous-wave (CW) regime using a plano-plano cavity. It was formed by a pump mirror (PM) coated for HT at 0.88-0.99 μm and for HR at 1.02-1.20 μm, and a set of output couplers (OCs) having a transmission TOC in the range of 2% -50% at 1.0-1.1 μm. The Yb 3+ :CaF2 sample containing the WGs was mounted on a Cu-holder and it was passively cooled. As a pump source, we employed a CW Ti:Sapphire laser emitting at 979.5 nm in the fundamental mode (M 2 ≈ 1) with linear polarization (vertical). Its output was focused using a spherical CaF2 lens (f = 40 mm). For the 40 µm wide WG, the pump coupling efficiency ηcoupl was 74.2%. With increasing the output coupling, the pump absorption under lasing conditions ηabs,L decreased from 92.7% (TOC = 1%) to 68.2% (TOC =50%). The laser performance of the 40 μm wide guide for the pump wavelength of 979.5 nm corresponding to the zerophonon-line of Yb 3+ ions in CaF2 is shown in Fig. 2(a,b). The laser generated a maximum output power of 723 mW at 1029-1051 nm with a slope efficiency η of 76.0% (vs. the absorbed pump power) and a laser threshold of 165 mW (for TOC = 20%). The maximum optical-to-optical efficiency vs. the pump power incident on the crystal ηopt was 38.9%. With increasing the output coupling, the laser threshold gradually increased, from 52 mW (TOC = 1%) to 394 mW (TOC = 50%). No lasing was achieved when pumping into the bulk area of the sample. With increasing the output coupling, the central emission wavelength experienced a slight blue-shift, from ~1048 nm (TOC = 1%) to ~1029 nm (TOC = 50%), Fig. 2(a). The observed laser efficiencies were analyzed using the Caird approach, i.e., with the formula 1/η = 1/η0(1 + 2γ/γOC) where γ is the loss coefficient and γOC is the output-coupling loss, yielding the intrinsic slope efficiency η0 of 75.0±4% and δloss of 0.13±0.05 dB/cm, Fig. 2(с). The laser mode was localized near the top part of the guide and it was elliptical, Fig. 2(d). The measured beam quality factors were M 2 x = 1.05±0.05 and M 2 y = 1.3±0.1. To demonstrate wavelength tuning of the Yb 3+ :CaF2 WG laser, the flat OC was replaced by a concave one (RoC = -100 mm) with TOC = 2% resulting in a nearly hemispherical cavity. As a tuning element, we used an uncoated quartz birefringent plate with the optical axis lying in the plane of the plate. It was placed at the Brewster angle near the output facet of the sample. A continuous wavelength tuning between 1009.2 and 1072.4 nm was demonstrated, Fig. 3. This corresponded to a tuning range of ~63 nm. The maximum of the tuning curve was observed at ~1052 nm corresponding to an output power of 118 mW. To conclude, deep diamond saw dicing is a powerful approach to fabricate ridge WGs in bulk Yb 3+ :CaF2 crystals. Such guides ensure low propagation losses (down to 0.13±0.05 dB/cm at ~1 μm), small surface roughness and good verticality of the side walls and the lack of cracking / chipping. No post-processing polishing is required for the ridges. The combination of good thermal properties of CaF2 with the broadband emission of Yb 3+ ions determine the power scaling capabilities of deep-diced Yb 3+ :CaF2 WG lasers, as well as the broadband wavelength tuning. The fabricated guides are promising for compact mode-locked oscillators at ~1 μm operating at high repetition rates (GHz-range).

Fig. 1 .

 1 Fig. 1. (a) Confocal laser microscopy image of an end-facet of a 4.5 at.% Yb 3+ :CaF2 sample containing ridge waveguides, bright field, reflection mode, λ = 405 nm; (b) roughness profile for one of the WG side walls (diced); (c) photograph of the waveguide laser: PMpump mirror, OCoutput coupler, FL and CLfocusing and collimating lenses, respectively; (d) top view photograph of the pumped guide.

Fig. 2 .

 2 Fig. 2. Laser performance of the deep-diced Yb 3+ :CaF2 waveguide (width: 40 μm): (a) input-output dependences, ηslope efficiency; (b) typical spectra of laser emission measured at maximum Pabs; (c) Caird analysis of propagation losses; (d) near-field profile of the laser mode, TOC = 20%, Pabs ~ 0.5 W. Pump polarization: vertical, λp = 979.5 nm. In (c), white lines mark the air / crystal interfaces.

Fig. 3 .

 3 Fig. 3. Tunable deep-diced Yb 3+ :CaF2 ridge waveguide laser (WG width: 40 μm): (a) tunability curve, TOC = 2%, Pabs = 1.25 W, the gain cross-section, σg, spectra for several inversion ratios β = N2( 2 F5/2)/NYb are shown for comparison; (b) typical spectra of laser emission from the tunable laser; the spectrum for the free-running laser is shown for comparison.