Pavel Loiko

Daniel Rytz

Sebastian Schwung

Patrick Pues

Thomas Jüstel

Jean-Louis Doualan

Patrice Camy
email: patrice.camy@ensicaen.fr

Watt-level europium laser at 703 nm

come

During the past years, there is a great interest for the development of visible solid-state lasers based on such rare-earth ions as Pr 3+ , Tb 3+ , Dy 3+ , Sm 3+ or Eu 3+ [1].

Trivalent Europium ions (Eu 3+ , electronic configuration: [Xe]4f 6 ) are featuring multi-color emissions in the visible (orange, red and deep red) due to transitions from the metastable 5 D0 state to a group of lower-lying 7 FJ (J = 0...6) energy-levels ( 7 F0 is the ground-state), Fig. 1. Among them, the 5 D0 → 7 F2 transition at ~612 nm is typically the most intense one which determines the use of Eu 3+ ions as activators of red phosphors with high color purity [2] for applications in white LEDs [3,4]. The metastable 5 D0 state exhibits a relatively long lifetime (in the ms-range) and weak non-radiative relaxation even in high-phonon-energy matrices leading to high luminescence quantum yields [4]. Intense absorption bands of Eu 3+ ions in the blue and UV allow for their efficient excitation, e.g., by GaN diodes. The Eu 3+ ions are also known as structural markers [5], as the 5 D0 → 7 F2 transition of purely electric-dipole nature is a hypersensitive one (its intensity depends on the site symmetry and its distortion).

At a glance, Eu 3+ ions appear attractive for the development of low-threshold red lasers with a quasi-four-level scheme. However, to date, only few studies were dedicated to Eu lasers. The first laser action in Eu 3+ (at the 5 D0 → 7 F2 transition) was achieved in 1963 by Chang using a Eu:Y2O3 single-crystal cooled to 77 K to reduce the thermal population of the lower laser level [6]. In 2004, Park et al. demonstrated room-temperature (RT) stimulated-emission at 620 nm in Eu 3+ -doped semiconductor GaN thin-films on sapphire [7,8]. In 2007, Nakamura et al. reported on RT lasing from polymer films containing Eu 3+ complexes [9]. In 2011, Bagayev et al. achieved pulsed RT lasing (at the 5 D0 → 7 F4 transition) in a Eu:KGd(WO4)2 single-crystal [10]. Shortly after that, quasi continuous-wave (CW) and CW operation of this crystal and its isomorph, Eu:KY(WO4)2, were obtained [11,12].

So far, the best result achieved with a highly-doped (25 at.%) Eu:KGd(WO4)2 crystal comprised a peak output power of 54 mW at 702.3 nm with a slope efficiency of ~4.6% [11]. The authors developed a frequency-doubled Nd laser at 533.6 nm (pumping into the short-living 5 D1 state, Fig. 1) suffering from thermo-optic problems. Recently, lasing in Eu 3+ -doped LiYF4 was demonstrated leading to still low output of 15 mW at 701.9 nm with a similar slope efficiency [13]. A frequency-doubled 393.5 nm Ti:Sapphire laser (pumping into the higher-lying 5 L6 state, Fig. 1) was used, however, such pumping leads to stronger heat loading and may induce color centers in oxide crystals. The main difficulty for power scaling of Eu lasers in [11,13] was the selection of an appropriate pump source. The Eu 3+ transitions in absorption falling in the visible and UV spectral ranges ( 7 FJ → 5 DJ', 5 LJ', 5 GJ') are spin-forbidden and their intensities are weak [14]. The corresponding spectral linewidths are also narrow. Thus, for achieving high pump absorption, one must adjust precisely the pump wavelength (~0.1 nm) or ensure very high Eu 3+ doping.

In the present work, we aimed at reconsidering Eu 3+ ions for efficient and power-scalable continuous-wave RT lasers operating in the deep red spectral range. For that, as a gain material, we have used the KEu(WO4)2 crystal and as a pump source -a commercial high-power 532 nm laser. This compound belongs to the crystal family of monoclinic double tungstates (MDTs) KRE(WO4)2 which are known as excellent host matrices for doping with rare-earth ions [15]. Their advantages are the following: (i) long RE 3+ -RE 3+ interatomic distances leading to weak luminescence quenching; (ii) high doping concentrations up to stoichiometric (100 at.%) compositions; (iii) strong polarization anisotropy of absorption and stimulated-emission spectra [14] and (iv) suitable thermo-optical properties for certain crystal cuts [16] (nearly athermal behavior). These properties are particularly interesting for the stoichiometric KEu(WO4)2 crystal.

The single crystal of KEu(WO4)2 was grown by the Top-Seeded Solution Growth method [17] using potassium ditungstate (K2W2O7) as a solvent. The starting reagents were K2CO3, WO3 and Eu2O3 (4N purity) taken according to the solute : solvent mass ratio of 1:5. The growth started at 1228 K. A [010] seed crystal was used. The as-grown crystal, Fig. 2 First, we studied polarized spectroscopic properties of Eu 3+ ions in K(Y1-xEux)(WO4)2 crystals. The absorption cross-section, σabs, spectra for the 7 F0, 1 → 5 D1 transitions in the green are shown in Fig. 3(a). For Eu 3+ ions, due to the small energy separation between the lower-lying multiplets 7 F1, 2 and the ground-state 7 F0, the former ones are thermally populated at RT. For transitions from the 7 F1 state, the maximum σabs is 1.71×10 -20 cm 2 at 534.2 nm and the corresponding absorption bandwidth (full width at half maximum, FWHM) is only 0.6 nm (for E || Nm). The measurements were done for a KY0. 8Eu0.2(WO4)2 crystal to avoid saturation of the detector.

The stimulated-emission (SE) cross-section, σSE, spectra for the 5 D0 → 7 F2 and 5 D0 → 7 F4 transitions are shown in Fig. 3(b). They were calculated using the Füchtbauer-Ladenburg (F-L) equation assuming a radiative lifetime of the 5 D0 state τrad = 0.49 ms [17] and the luminescence branching ratios B(JJ') = 83.7% (0 → 2) and 12.8% (0 → 4) [14]. For the latter transition, the maximum σSE is 1.11×10 - 20 cm 2 at 702.4 nm and the emission bandwidth (FWHM) is ~1 nm (for E || Nm). The σSE spectra exhibit a significant anisotropy which is a prerequisite for linearly polarized laser emission.

The RT luminescence decay curve from the 5 D0 state of Eu 3+ ions in KEu(WO4)2 is single-exponential with a lifetime τlum of 0.479 ms, see Fig. 3(c). Almost no reduction of the lifetime is observed as compared to the crystal containing 20 at.% Eu. The lifetime of the 5 D1 pump level was estimated from the luminescence risetime to be ~4 µs. The parallelepipedic laser element from the KEu(WO4)2 crystal had the dimensions of 4.75(Np)×5.07(Nm)×5.21(Ng) mm 3 . All six faces were polished and remained uncoated. The element was oriented for light propagation along the Ng optical indicatrix axis (Ng-cut). This cut provides access to polarizations E || Nm and E || Np and ensures nearly athermal behavior (i.e., weak and positive thermal lens). A linear laser cavity was composted of a flat pump mirror (PM) providing a transmission T = 86.0% at 532 nm and high reflection (HR, R >99.5%) at 595-710 nm and a set of output couplers (OCs) having a transmission TOC at 703 nm in the range of 0.3% -4.3%. Two cavity geometries were used: (i) a hemispherical cavity was terminated by a concave OC (radius of curvature of -50 mm) with the crystal placed near the PM at a ~1 mm airgap; (ii) the plano-plano cavity contained flat PM and OC placed as close as possible to the crystal, Fig. 4. The radii of the laser mode in the crystal were calculated using the ABCD method and they amounted to 55±5 μm and 40±5 μm, respectively. The laser crystal was mounted on a passively cooled Cu-holder using silver paste for better heat removal. As a pump source, we used a green laser (Verdi G series, Coherent) emitting up to 9 W of linearly polarized emission at 532.1 nm (linewidth: <0.1 nm) in the fundamental mode (M 2 ≈ 1). This corresponded to pumping into the 5 D1 Eu 3+ state, Fig. 3(a). The pump was focused into the crystal using an achromatic lens (AC254-X-A series, Thorlabs) coated for high transmission (HT, T > 99.5%) at 532 nm. Lenses with the focal lengths f in the range of 50 -100 mm were tested. The pump polarization in the crystal corresponded to E || Nm. The measured pump absorption, ηabs = 59.5±0.5%, was weakly dependent on the pump power. The pumping was in a single pass. The pump was modulated using a chopper (frequency: 25 Hz, duty cycle: 1:4, pump pulse duration: ~10 ms) for quasi-CW operation.

The laser output was filtered from the residual pump using a long-pass filter (FEL600, Thorlabs). The laser emission spectra were measured using an optical spectrum analyzer (OSA, Ando AQ6315-E). The temporal behavior of the laser output was studied using a fast InGaAs photodetector (UPD-5N-IR2-P) and an 8 GHz digital oscilloscope (DSA70804B, Tektronix).

At first, the optimum focusing lens was selected employing a hemispherical cavity and the available OC (TOC = 4.3%). The best performance was achieved for f = 75 mm (pump spot size: 2wP = 75±5 μm, measured by the optical knife method at the 1/e 2 level). The laser generated a maximum peak output power of 0.532 W at 703 nm with a slope efficiency η of 34.1% (vs. the absorbed pump power) and a laser threshold Pth of 565 mW, Fig. 5(a). The use of lenses with shorter focal lengths (f = 50 -60 mm) leading to smaller pump spot sizes resulted in reduced thresholds (412 mW for f = 50 mm) whilst with lower η attributed to poorer mode-matching. Longer f of 100 mm resulted in a rapid increase of the threshold to 722 mW. Thus, the 75 mm lens was selected.

Due to the availability of mirrors, the effect of the output coupling on the laser performance was studied in a plano-plano cavity, Fig. 5(b). The laser operation in such a cavity is possible due to the positive thermal lens expected for Ng-cut KEu(WO4)2 crystal, similarly to other MDTs. The Eu laser generated a maximum peak output power of 1.11 W at 703 nm with a slope efficiency of 43.2% and a laser threshold of 183 mW (for TOC = 2.4%). At the maximum incident pump power of 4.70 W, the optical-to-optical conversion efficiency ηopt amounted to 23.6%. The achieved η value was lower than the Stokes efficiency under lasing conditions, ηSt, L = λP/λL = 75.7%, indicating a further room for improvement. The inputoutput dependence was linear up to at least 4.70 W of the incident pump power. Further power scaling was limited to avoid the risk of thermal fracture of the passively cooled crystal. With reducing TOC from 4.3% to 0.3%, the laser threshold gradually decreased from 285 mW to only 64 mW. Such a low laser threshold is due to the quasi-four level laser scheme of the 5 D0 → 7 F4 transition. The laser emission was linearly polarized; the polarization state (E || Nm) was naturally selected by the anisotropy of the gain, cf. Fig. 3(b). The laser wavelength (~703 nm) was weakly dependent on TOC, see Fig. 6(a). The crystal-field splitting of the 5 D0 and 7 F4 Eu 3+ multiplets revealed at low temperature (6 K) is shown in Fig. 6(b). For C2 sites, each 2S+1 LJ multiplet with integer J will be split into 2J+1 sub-levels. The observed laser emission wavelengths are assigned to electronic transitions 0' ( 5 D0) → 4, 5 and 6 ( 7 F4). The multi-peak spectral behavior is due to the etalon effects at the crystal / mirror interfaces.

True CW operation was also studied. The incident pump power was limited to ~1 W. Using the smallest TOC = 0.3%, the maximum output power reached 162 mW in good agreement with the quasi-CW regime, Fig. 5(b).

A typical oscilloscope trace of the CW laser is shown in Fig. 7(a). The CW regime was established within ~1 ms after switching on the pump. The slow intensity variations are due to instabilities in the pump green laser.

The typical profile of the laser mode in the far-field (plano-plano cavity) measured at the maximum CW output power is shown in Fig. 7(b). The corresponding 1D intensity profiles were well fitted with the Gaussian distribution. The beam is slightly elliptic, and it is extended along the Np axis. This is assigned to the astigmatism of the thermal lens in Ng-cut MDT crystals [16]. The measured beam quality factors M 2 x,y slightly increased with the pump power from ~1.1 near the laser threshold up to ~2 -2.5 at full power. In our experiments, the coatings of the cavity mirrors supported potential laser oscillations at the 5 D0 → 7 F2 transition. However, despite higher SE cross-sections, lasing at this transition was not observed. We suggest two main reasons for that: (i) reabsorption related to transitions from the thermally populated state 7 F2 leading to quasi-three-level laser scheme and increased threshold and (ii) possible excited-state absorption from the metastable 5 D0 state (e.g., spin-allowed transition to the higher-lying 5 F4 excited-state which is estimated to occur at ~612 nm).

To conclude, we report on the first watt-level, highly efficient and low-threshold room-temperature Europium laser operating at the 5 D0 → 7 F4 transition. It delivers 1.11 W at ~703 nm (falling in the deep-red spectral range) with a slope efficiency of 43.2% and a linear polarization. The laser threshold as low as 64 mW is also achieved utilizing the advantage of the quasi-four-level laser scheme. These output characteristics represent record values for any Eu lasers reported so far. This advance is based on the use of a stoichiometric KEu(WO4)2 crystal ensuring high absorption in the green and very weak luminescence quenching. Further power scaling in true CW regime seems feasible by appropriate thermal management of the crystal (e.g., active cooling). Further work should focus on revealing the possibility of RT laser operation at other Eu 3+ transitions in the red (~0.62 µm, 5 D0 → 7 F2) and deep red (~0.75 µm and ~0.81 µm, 5 D0 → 7 F5, 6). In the former case, ESA measurements are required.

Disclosures. The authors declare no conflicts of interest.

Fig. 1 .

 1 Fig. 1. The scheme of energy-levels of Eu 3+ ions showing possible pump and laser transitions. NR -non-radiative relaxation. The crystal-field splitting corresponds to KY(WO4)2.

  (a), was pink colored due to Eu 3+ ions. KEu(WO4)2 is monoclinic (sp. gr. C 6 2h -C2/c, No. 15), its lattice constants are a = 1069.88(7) Å, b = 046.87(5) Å, c = 760.47(5) Å and β = 130.774(4)°. Eu 3+ ions are residing in a single type of sites with the C2 symmetry and VIII-fold oxygen coordination. According a single-crystal X-ray diffraction study, there are no vacancies in the Eu 3+ site. No signs of Eu 2+ species were observed as well. Thus, the Eu 3+ ion density was calculated to be NEu = 61.55×10 20 cm -3 using the measured density of 7.07 g/cm3 .Monoclinic KEu(WO4)2 is optically biaxial. Its optical properties are described in the optical indicatrix frame {Np, Nm, Ng}. The Np axis is parallel to the b-axis (C2 symmetry axis) and the other two axes are lying in the a-c plane, Fig.2(b). The angle Ng ^ c = 18.5°, measured outside of the monoclinic angle β.

Fig. 2 .

 2 Fig. 2. (a) Photograph of the as-grown KEu(WO4)2 crystal (length: 40 mm, weight: 61 g, growth direction: along [010]); (b) the scheme of its optical orientation: Np, Nm, Ng -optical indicatrix axes, a, b, ccrystallographic axes.

Fig. 3 .

 3 Fig. 3. Spectroscopy of Eu 3+ ions in monoclinic K(Y1-xEux)(WO4)2 crystals: (a) polarized absorption cross-sections, σabs, for the 7 F0, 1 → 5 D1 transition (x = 0.2); (b) polarized stimulated-emission cross-sections, σSE, for the 5 D0 → 7 F2, 4 (x = 1); (c) luminescence decay from the 5 D0 state (x = 0.2 and 1). In (a), the spectrum of the pump green laser is shown for comparison.

Fig. 4 .

 4 Fig. 4. Scheme of the compact KEu(WO4)2 laser: L -achromatic focusing lens, PM -pump mirror, OC -output coupler, F -cut-off filter.

Fig. 5 .

 5 Fig. 5. Input-output dependences for the KEu(WO4)2 laser operating on the 5 D0 → 7 F4 transition: (a) effect of the focal length of the focusing lens f, hemispherical cavity, TOC = 4.3%; (b) effect of the output coupling TOC, plano-plano cavity, f = 75 mm. Ng-cut crystal. Quasi-CW regime, duty cycle: 1:4. Orange circle -true CW operation, TOC = 2.4%.

Fig. 6 .

 6 Fig. 6. (a) Typical spectra of laser emission from the KEu(WO4)2 laser (plano-plano cavity). The laser polarization is E || Nm; (b) crystal-field splitting of the 5 D0 and 7 F4 Eu 3+ multiplets, arrow -the laser transition.

Fig. 7 .

 7 Fig. 7. KEu(WO4)2 laser (true CW operation): (a) typical oscilloscope trace of laser emisison; (b) photograph of the laser mode on a screen in the far-field (plano-plano cavity, TOC = 0.3%).


Anna Volokitina

Pavel Loiko

Anatoly Pavlyuk

Josep Maria Serres

Ezzedine Sami Slimi

Ben Salem

Esrom Kifle

Uwe Griebner

Valentin Petrov

Li I Wang

Ben Ezzedine

Salem

Weidong Chen

Rosa Maria Solé

Magdalena Aguiló

Francesc Díaz

Xavier Mateos
email: xavier.mateos@urv.cat

Spectroscopy and efficient laser operation of cleaving Yb:KY(MoO 4 ) 2 crystal

Introduction

Cleavage is the property of crystalline materials to split along certain crystallographic planes. The simplest case is basal or pinacoidal cleavage when this happens along only a single plane. It may result from a weaker bond strength or larger lattice spacing perpendicular to the plane, and it is frequently observed in crystals with a regular location of atoms forming "layers". As a result, crystalline plates with continuous, smooth and flat faces, both strictly parallel to the so-called cleavage plane are easily obtained. An example of a cleaving mineral is mica showing perfect (or even "eminent") cleavage. Crystals with perfect cleavage can cleave without leaving any rough surface (mirror-quality) [START_REF] Zhu | Growth, spectral properties, and laser demonstration of Yb 3+ :BaGd 2 (MoO 4 ) 4 cleavage crystal[END_REF]. Cleavage is used for identification of minerals. It is also useful for chipping of wafers of semiconductor crystals (e.g., silicon).

Laser crystals exhibiting perfect cleavage along a crystallographic plane are known [START_REF] Zhu | Growth, spectral properties, and laser demonstration of Yb 3+ :BaGd 2 (MoO 4 ) 4 cleavage crystal[END_REF][START_REF] Chen | Laser emission from unprocessed cleavage microchip[END_REF][START_REF] Volokitina | Laser operation of cleaved single-crystal plates and films of Tm:KY(MoO 4 ) 2[END_REF]. On the one hand, this complicates their mechanical processing (cutting and polishing). On the other hand, it can turn out to be a useful feature for applications where thin laser elements with a large aperture and good parallelism / optical quality of the faces are required. Moreover, this simplifies fabrication of laser elements, especially for soft crystals. Two examples are the microchip and thin-disk lasers. In particular, a microchip laser consists of a thin (typically, few hundred μm thick) gain medium placed in a simple plano-plano cavity without air gaps, leading to a highly-compact and monolithic design (optionally, one or both of the cavity mirrors are coated on the crystal faces) [START_REF] Zayhowski | Microchip lasers[END_REF]. Note a positive thermal lens of the gain material for stabilizing the laser mode of microchip lasers is an important requirement [START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF]. This robust design is almost insensitive to misalignment and leads to low intracavity losses, low laser threshold, good cavity stability and very short cavity roundtrip time beneficial for achieving sub-ns pulses in passively Q-switched lasers [START_REF] Loiko | Sub-nanosecond Yb:KLu(WO 4 ) 2 microchip laser[END_REF].

So far, only few crystals doped with rare-earth ions (RE 3+ ) such as Nd 3+ , Yb 3+ or Tm 3+ showing perfect cleavage have been applied for lasers in the near-IR, cf. Table 1. These include borates (LaB 3 O 6 ) [START_REF] Chen | Continuous-wave laser characteristics of a Nd 3+ :LaB 3 O 6 cleavage microchip and the influence of thermal effects[END_REF], phosphates (YPO 4 and LuPO 4 ) [START_REF] Liu | Spectroscopic properties and continuouswave laser operation of Yb:LuPO 4 crystal[END_REF][START_REF] Zhang | Efficient laser operations of unprocessed thin plate of Nd:YPO 4 crystal[END_REF] and molybdates (BaGd 2 (MoO 4 ) 4 ) [START_REF] Chen | 805-nm diode-pumped continuous-wave 2-µm laser performance of Tm 3+ :BaGd 2 (MoO 4 ) 4 cleavage plate[END_REF]. Other cleaving crystals were proposed as potential laser materials (e.g., CsGd(MoO 4 ) 2 ) [START_REF] Zhao | Spectra and energy levels of a layered Yb 3+ :CsGd(MoO 4 ) 2 crystal with perfect cleavage: a candidate for microchip lasers[END_REF] but no laser operation has been reported so far. Yb 3+ -doped materials are known for efficient laser operation at ~1 μm on the 2 F 5/2 → 2 F 7/2 electronic transition. The Yb 3+ ion can be easily pumped by commercially available high-power InGaAs laser diodes emitting at ~0.96-0.98 μm [START_REF] Liu | Power scaling of a continuous-wave and passively Q-switched Yb:KLu(WO 4 ) 2 laser end-pumped by a high-power diode[END_REF]. It also exhibits a simple energy level scheme eliminating parasitic energy-transfer processes. In-band pumping of Yb 3+ leads to high pump Stokes efficiency, and, thus, reduced heat load and slope efficiencies up to ~80% [START_REF] Loiko | Microchip Yb:CaLnAlO 4 lasers with up to 91% slope efficiency[END_REF]. Moreover, as compared to Nd 3+ , Yb 3+ shows larger Stark splitting of the ground-state ( 2 F 7/2 ) and, consequently, broader emission at ~1 μm, beneficial for broadly tunable and mode-locked lasers. Liu et al. reported on a diode-pumped Yb:LuPO 4 laser based on a (100)-oriented unprocessed as-grown crystal plate delivering 1.61 W at 1036-1040 nm with a slope efficiency of 75% [START_REF] Liu | Spectroscopic properties and continuouswave laser operation of Yb:LuPO 4 crystal[END_REF]. Zhu et al. used cleaved plates of Yb:BaGd 2 (MoO 4 ) 4 and produced a similar output power (1.16 W at 1046-1054 nm) albeit with much lower slope efficiency (20%) [START_REF] Zhu | Growth, spectral properties, and laser demonstration of Yb 3+ :BaGd 2 (MoO 4 ) 4 cleavage crystal[END_REF]. Among the host crystals for Yb 3+ doping, complex tungstates and molybdates are attracting a lot of attention. Their advantages include: (i) high attainable Yb 3+ doping concentrations; (ii) weak luminescence quenching, (iii) low non-radiative relaxations and luminescence quantum yields approaching unity, (iv) polarized, intense and broad absorption and emission bands at 1 μm, and (v) Raman activity. A prominent example is the crystal family of monoclinic double tungstates with chemical formula KLn(WO 4 ) 2 , where Ln = Gd, Y or Lu [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF][START_REF] Lagatsky | Diode-pumped CW lasing of Yb:KYW and Yb:KGW[END_REF]. Efficient continuous-wave [START_REF] Liu | Power scaling of a continuous-wave and passively Q-switched Yb:KLu(WO 4 ) 2 laser end-pumped by a high-power diode[END_REF][START_REF] Serres | Prospects of monoclinic Yb:KLu(WO 4 ) 2 crystal for multi-watt microchip lasers[END_REF], passively Q-switched [START_REF] Loiko | Sub-nanosecond Yb:KLu(WO 4 ) 2 microchip laser[END_REF] and especially mode-locked [START_REF] Griebner | Passively mode-locked Yb:KLu(WO 4 ) 2 oscillators[END_REF][START_REF] Pekarek | Diode-pumped gigahertz femtosecond Yb:KGW laser with a peak power of 3.9 kW[END_REF] Yb:KLn(WO 4 ) 2 lasers are known. Thin-disk lasers based on these materials were also demonstrated using thin bulk or epitaxial samples [START_REF] Brunner | 240-fs pulses with 22-W average power from a mode-locked thin-disk Yb:KY(WO 4 ) 2 laser[END_REF][START_REF] Rivier | Thin-disk Yb:KLu(WO 4 ) 2 laser with single-pass pumping[END_REF].

Compared to the above mentioned potassium double tungstates, their double molybdate (DMo) counterparts with chemical formula KLn(MoO 4 ) 2 have been barely studied. One example of the DMo crystal family is potassium yttrium double molybdate, KY(MoO 4 ) 2 [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF][START_REF] Chen | Polarized spectral characteristics of Nd 3+ : KY(MoO 4 ) 2 crystal with perfect cleavage planes: a promising microchip gain medium[END_REF][START_REF] Loiko | Efficient continuous-wave in-band pumped Nd:KY(MoO 4 ) 2 laser[END_REF]. It is orthorhombic and exhibits an interesting layered structure together with a lowsymmetry site for the RE ions (C 2 ) leading to a strong anisotropy of the optical properties as well as to the natural cleavage habit [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF]. The structure and vibronic properties of undoped KY(MoO 4 ) 2 have been reported [START_REF] Klevtsova | X-ray structural study of the double molybdate KY(MoO 4 ) 2[END_REF][START_REF] Hanuza | Polarized Raman and infrared spectra of a multilayer KY(MoO 4 ) 2 crystal[END_REF]. The RE 3+ site symmetry was revealed using Eu 3+ as a structural probe [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF]. Very recently, we achieved laser operation in cleaved singlecrystalline plates and thin films of Tm:KY(MoO 4 ) 2 [START_REF] Volokitina | Laser operation of cleaved single-crystal plates and films of Tm:KY(MoO 4 ) 2[END_REF]. A crystal-plate laser generated 0.88 W at 1840-1905 nm with a slope efficiency of 65.8%. The concept of the thin-film laser using cleaved Nd:KY(MoO 4 ) 2 was first proposed [START_REF] Kaminskii | Ribbon and sheet miniature crystal laser[END_REF] by Kaminski et al.

In the present work, we demonstrate laser operation of a Yb:KY(MoO 4 ) 2 crystal, for the first time to the best of our knowledge, by using its perfect cleavage feature.

Crystal growth

The Yb:KY(MoO 4 ) 2 compound melts at ~1243 K. The single crystals were grown by the Low Temperature Gradient (LTG) Czochralski method [START_REF] Borovlev | Progress in growth of large sized BGO crystals by the low-thermal-gradient Czochralski technique[END_REF]. As raw materials, we used Y 2 O 3 (purity: 5N), Yb 2 O 3 (4N), MoO 3 (4N) and K 2 CO 3 (5N) taken according to the composition 95-93mol% KY 0.97 Yb 0.03 (MoO 4 ) 2 solute -5-7 mol% K 2 Mo 3 O 10 solvent assuming substitution of Y 3+ ions by the Yb 3+ dopants (3 at.% Yb). The potassium trimolybdate (K 2 Mo 3 O 10 ) was added to the melt to prevent its partial dissociation resulting in the formation of yttrium oxomolybdate (Y 2 MoO 6 ) and, thus, to stabilize the growth process [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF]. The raw materials were mixed and placed in a Pt crucible. It was heated up to ~1320 K in air and kept at this temperature for 2-3 hours to homogenize the melt. Then, it was cooled to ~1240 K (the temperature where the growth started). A [100]-oriented seed from an undoped KY(MoO 4 ) 2 was used. It was rotated at 20 rpm, the pulling rate was 1-2 mm/h and the cooling rate was ~2 K/day. The temperature gradient in the melt was below 3 K/cm (in the vertical direction). After completing the growth, the crystal was removed from the melt and slowly cooled down to room temperature (RT, 293 K). No annealing was applied. More details can be found elsewhere [START_REF] Volokitina | Laser operation of cleaved single-crystal plates and films of Tm:KY(MoO 4 ) 2[END_REF][START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF]. The as-grown crystals were transparent and colorless, Fig. 1. They had a cylindrical shape with an elliptic cross-section with the semiaxes oriented along the [010] and [001] directions. Neither cracks nor inclusions were observed. The crystals showed an easy cleavage along the (100) plane (orthogonal to the growth direction). The orientation of the [010] and [001] axes was determined by single-crystal X-ray diffraction.

The actual Yb 3+ doping concentration was determined by Energy Dispersive X-ray (EDX) spectroscopy to be N Yb = 2.3±0.5×10 20 cm -3 (~3.0 at.% Yb), so that the segregation coefficient for Yb 3+ doping K Yb = N crystal /N melt was close to unity.

Crystal structure

Rietveld refinement

The structure and phase purity of the 3 at.% Yb:KY(MoO 4 ) 2 was confirmed by X-ray powder diffraction (XRD), Fig. 2(a). The measurements were carried out in a θ-θ Bragg Brentano configuration using a Siemens D-5000 powder X-ray diffractometer with Cu Kα (1.5406 Å) radiation. The XRD pattern was recorded in a 2θ range from 10° to 65°, a step size of 0.02° and a step time of 16 s. The crystal belongs to the orthorhombic class (sp. gr. Pbna -D 14 2h , centrosymmetric point group 2/m). Note that we use the non-conventional space group (the standard one is Pbcn, No. 60), following the early publications [START_REF] Klevtsova | X-ray structural study of the double molybdate KY(MoO 4 ) 2[END_REF][START_REF] Kaminskii | Stimulated emission from KY(MoO 4 ) 2 -Nd 3+ crystal laser[END_REF]. The unit cell parameters refined using the Le Bail method are: a = 18.212(2) Å, b = 7.9343(6) Å, c = 5.0705( 5) Å (number of the formula units in the unit-cell Z = 4). The obtained R-factors were R wp = 6.44% and R exp = 5.19% (the reduced χ-squared value χ 2 = (R wp /R exp ) 2 = 1.54). The calculated volume of the unit cell V is 732.7(1) Å 3 and the crystal density ρ calc = 4.083 [START_REF] Loiko | Sub-nanosecond Yb:KLu(WO 4 ) 2 microchip laser[END_REF] g/cm 3 . The structure from [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF] was taken as the starting one for the refinement. The fractional atomic coordinates were refined by the Rietveld method using the TOPAS software, see the results in Table 2, with the fixed unit cell parameters obtained by the Le Bail's method and considering the (100) preferred orientation. For this refinement, R wp = 8.90% and R exp = 5.19% (χ 2 = 2.94). Figure 2 shows the Rietveld refinement plot with the observed, calculated and difference patterns. No other phases except the orthorhombic one are found in the pattern. The min / max residual electron densities are -0.6 e/Å 3 and +0.1 e/Å 3 , respectively. The unit-cell parameters are slightly smaller than those for undoped KY(MoO 4 ) 2 , a = 18.23 Å, b = 7.95 Å, c = 5.07 Å [START_REF] Klevtsova | X-ray structural study of the double molybdate KY(MoO 4 ) 2[END_REF]. In KY(MoO 4 ) 2 , the Yb 3+ ions substitute for the Y 3+ ones in a single type of crystallographic sites (Wyckoff symbol: 4c, site symmetry: C 2 , coordination number (C.N.): VIII). The corresponding ionic radii are R Yb = 0.985 Å and R Y = 1.019 Å for VIII-fold oxygen coordination [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF], explaining the observed decrease of the lattice constants. The closeness of the ionic radii of Yb 3+ and Y 3+ , the existence of the orthorhombic stoichiometric KYb(MoO 4 ) 2 phase [START_REF] Frolova | Crystal-field effects on the thermodynamic properties of the KLn(MoO 4 ) 2 isostructural compounds[END_REF] and the homovalent doping mechanism also explain the observed K Yb ≈ 1.

Using the refined atomic coordinates, the structure of Yb:KY(MoO 4 ) 2 is illustrated in Fig. 2(b,c). The corresponding interatomic distances are listed in Table 3. The C.N. for Mo 6+ cations is 4+1: a distorted tetrahedral coordination (with 4 closely located oxygens, with the Mo -O distances lying in the range 1.644(8) -1.847(6) Å and 1 more distant oxygen at 2.5735 Å). For K + , the C.N. is 6+4, defined in a similar manner. The closest 6 oxygens are at 2.742(1) -2.759(6) Å, while the other oxygens are at 3.335(2) -4.223(0) Å. Such a coordination behavior is common for tungstates and molybdates with a C.N. of W (or Mo) of V or VI, where the cationanion distances may vary in a broad range, so that a formal definition of the C.N. is not possible [START_REF] Klevtsova | X-ray structural study of the double molybdate KY(MoO 4 ) 2[END_REF]. For the distorted [Y|YbO 8 ] polyhedra (bicapped octahedra), the bond lengths are in the range 2. The shortest Y|Yb -Y|Yb distance is 3.973 Å (along the b-axis, in the layer plane). It is relatively long and similar to that (Y -Y) in the monoclinic KY(WO 4 ) 2 crystal (4.06 Å) [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF]. This distance determines the weak cross-talk of Yb 3+ ions (weak concentration quenching of luminescence) along the a-axis (orthogonal to the layer plane), 9.45 Å. The coefficients of thermal expansion (CTE) of Yb:KY(MoO 4 ) 2 were calculated from the temperature dependence of the lattice constants determined by high-temperature powder XRD. For the XRD studies in the temperature range of 300-550 K, we used a temperature chamber (HTK10). The heating rate was 0.17 K/s with a delay of 300 s before each measurement. The 2θ angle varied from 10º to 70º with a step size of 0.03º and a step time of 5 s. The relative evolution of the unit cell parameters with temperature is shown in Fig. 3. The linear thermal expansion tensor (α ij ) in abc frame was obtained from the slopes of the linear fits shown in Fig. 3. Thus, (α ij ) is: The thermal conductivity of KY(MoO 4 ) 2 is unknown but it is expected to be higher in the layer plane. By mechanical cleavage orthogonal to the crystal growth direction (along the (100) plane), we produced single-crystalline plates of Yb:KY(MoO 4 ) 2 with a thickness (t) as thin as 100 μm. They were studied by Scanning Electron Microscopy (SEM) using a MERLIN microscope (Carl Zeiss). Under bending, the plates exhibited an elastic deformation along the [010] axis and broke with the fracture edge running parallel to the [001] axis, Fig. 4(a). This SEM image shows multiple "steps" parallel to the (100) cleavage plane. Both surfaces of the cleaved plates had mirror-quality. No polishing was applied to them. The SEM study in the μm-scale revealed dark flower-like defects, Fig. 4(b); however, the concentration of these defects was low. The clean aperture of the obtained crystal-plates was >1 cm 2 . They contained no macroscopic cracks.

Distances (Å) [Y|Yb]O 8 [Mo]O 4+1 [K]O 6+4 Y|Yb -O4 = 2.

Raman spectra

Molybdate crystals are known as efficient Raman-active materials. Thus, Yb:KY(MoO 4 ) 2 can serve for self-frequency Raman conversion. The RT polarized Raman spectra were measured using a confocal Raman microscope (Renishaw inVia) equipped with an ×50 objective, an edge filter and an Ar + ion laser (488 nm). A cleaved crystal plate (a-cut) was used and the excitation / collection geometries were a(mn)a, where m, n = b, c (according to Porto's notations).

The Raman spectra are shown in Fig. 5. They are strongly polarized with the most intense Raman response in the a(bb)a geometry. The observed bands are classified into three groups of vibrations [START_REF] Volokitina | Eu 3+ :KY(MoO 4 ) 2 : A novel anisotropic red-emitting material with a layered structure[END_REF][START_REF] Hanuza | Polarized Raman and infrared spectra of a multilayer KY(MoO 4 ) 2 crystal[END_REF]. The low-frequency range, 80-272 cm -1 , contains translational (T') and rotational (R') modes of the K, Y|Yb and Mo cations. Internal bending vibrations (δ) of the oxygen bridged [MoO 4 ] tetrahedra are observed in the intermediate frequency range, 315-435 cm -1 . The high-frequency range, 726-944 cm -1 , contains intense stretching vibrations (ν) of these tetrahedra. The gap in the Raman spectra (500-700 cm -1 ) is due to the relatively weak oxygen linkage of the [MoO 4 ] tetrahedra in the layer plane. This feature is similar to the one found in scheelite (CaWO 4 ) type double tungstate and molybdate crystals with isolated [WO 4 ] tetrahedra [START_REF] Macalik | Polarized Raman spectra of the oriented NaY(WO 4 ) 2 and KY(WO 4 ) 2 single crystals[END_REF].

The most intense Raman mode is at 865 cm -1 with a width at half maximum (FWHM) of 18.8 cm -1 . The maximum phonon energy hν max is 944 cm -1 .

Optical spectroscopy

Optical absorption

Orthorhombic KY(MoO 4 ) 2 is an optically biaxial crystal. Only a mean value of its refractive index is known, <n> ≈ 1.95. KY(MoO 4 ) 2 shows a strong birefringence, Δn = 0.018 -0.087 [START_REF] Kulakova | Acoustooptical and elastic properties of laminated KY(MoO 4 ) 2 crystals[END_REF]. The optical indicatrix axes coincide with the crystallographic axes. We will denote the principal light polarizations as E || a, b and c.

The absorption spectra were measured using a Varian CARY-5000 spectrophotometer (0.3-2 μm) and a FTIR spectrometer Bruker Tensor 27 (2-7 μm). A Glan-Taylor prism was used for polarization-resolved studies.

The transmission spectrum of a ~1 cm-thick 3 at.% Yb:KY(MoO 4 ) 2 crystal sample is shown in Fig. 6(a) revealing a transparency range from 0.33 to 3.4 μm (extending up to 5 μm to some extent). The structured absorption at longer wavelengths is related to the ν vibrations of the MoO 4 tetrahedra. The infrared cut-off is due to the 2ν 1 overtone peak of the [MoO 4 ] 2- group fundamental vibration. The absorption cross-sections in Yb:KY(MoO 4 ) 2 are lower than those for the monoclinic Yb:KY(WO 4 ) 2 crystal: σ abs = 10.8×10 -20 cm 2 at 981.0 nm corresponding a narrower FWHM of 4.0 nm (for light polarization E || N m ) [START_REF] Mateos | Indiummodified Yb:KLu(WO 4 ) 2 crystal: Growth, spectroscopy and laser operation[END_REF].

The optical bandgap of Yb:KY(MoO 4 ) 2 was evaluated with the Tauc plot, i.e, by plotting (α abs ×E ph ) 2 vs. the photon energy E ph = h(c/λ). The intersection of the linear fit of the obtained plot with the horizontal axis yields E g = 3.72 eV (the wavelength of the UV absorption edge is ~330 nm).

Luminescence: spectra and lifetime

The polarized luminescence spectra were measured using an optical spectrum analyzer (OSA, Hamamatsu, AQ6373) and a Glan-Taylor polarizer. The stimulated-emission (SE) crosssections, σ SE , for i-th polarization (i = a, b, c) were calculated from the measured luminescence spectra calibrated for the spectral response of the set-up W'(λ) using the Füchtbauer-Ladenburg (F-L) formula [START_REF] Aull | Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections[END_REF]:

5 SE 2 rad ,, 3 ' ( ) ( ) , ' ( )d 8 i i i i a b c W W n c          = =   ( 2
)
where λ is the wavelength, <n> ≈ 1.95 is the refractive index, c is the speed of light in vacuum and τ rad = 458 μs is the radiative lifetime of the emitting level ( 2 F 5/2 ), see below. The results are shown in Fig. 7(a). For Yb:KY(MoO 4 ) 2 , the maximum σ SE amounts to 3.70×10 -20 cm 2 at 1008.0 nm and the emission bandwidth (FWHM) Δλ em is 37.0 nm for the high-gain light polarization E || b. The emission spectra are also strongly polarized, as expressed by the ratios σ SE (b) : σ SE (c) = 3.9 and σ SE (b) : σ SE (a) = 6.0 at ~1.01 μm. These high ratios are a prerequisite for linearly polarized laser emission. Note that (100)-oriented crystal plates give access to the preferable light polarization E || b. Compared to its monoclinic double tungstate counterpart, Yb:KY(WO 4 ) 2 , for which σ SE = 3.2×10 -20 cm 2 at 1021.9 nm with Δλ em = 30.2 nm for E || N m [START_REF] Mateos | Indiummodified Yb:KLu(WO 4 ) 2 crystal: Growth, spectroscopy and laser operation[END_REF], Yb:KY(MoO 4 ) 2 provides higher SE cross-sections and broader emission bandwidth. These are attractive features for broadly tunable and ultrashort-pulse lasers at ~1 μm.

For the Yb 3+ ion, exhibiting reabsorption at the laser wavelength, the spectral behavior of the laser depends on the output-coupling losses via the rate of inversion in the gain medium, expressed by the inversion ratio β = N 2 ( 2 F 5/2 )/N Yb , where N 2 is the population of the upper level ( 2 F 5/2 ) and N 1 + N 2 = N Yb . Thus, the gain cross-sections, σ gain = βσ SE -(1 -β)σ abs , are calculated to predict the possible laser wavelengths for different β. The gain spectra for light polarization E || b are shown in Fig. 7(b). For small β < 0.03, the gain spectra are very flat and broad extending from ~1040 nm to 1100nm. For intermediate inversion ratios 0.05 < β < 0.10, a local peak in the spectra appears at ~1039 nm. For even higher inversion ratios, another maximum at a shorter wavelength of ~1019 nm is observed. For β = 0.15, the gain bandwidth Δλ g is 33.0 nm in agreement with the luminescence studies.

The luminescence decay curve of the sample was measured using an InGaAs photodetector under ns pulse excitation from an optical parametric oscillator (Horizon, Continuum) tuned to 930 nm, a 1/4 m monochromator (Oriel 77200) and an 8 GHz oscilloscope (DSA70804B, Tektronix). A thin (~30 μm) cleaved film was used to avoid the effect of radiation trapping. The decay curve plotted in a semi-log scale, Fig. 7(c), is singleexponential in agreement with a single type of Yb 3+ sites. The luminescence decay time τ lum = 458 μs is longer than that of monoclinic Yb:KY(WO 4 ) 2 crystals (τ lum = 231 μs [START_REF] Mateos | Indiummodified Yb:KLu(WO 4 ) 2 crystal: Growth, spectroscopy and laser operation[END_REF]).

Crystal-field splitting

For Yb 3+ ions in C 2 sites, each 2S+1 L J multiplet is split into J + 1/2 Stark sub-levels which are numbered as 0...3 for the ground-state ( 2 F 7/2 ) and 0'...2' for the excited-state ( 2 F 5/2 ). To resolve their energies, we measured the unpolarized absorption and luminescence spectra at low temperature (LT, 6 K) using an Oxford Instruments Ltd. cryostat (model SU 12) with heliumgas close-cycle flow. The results are shown in Fig. 8. The LT spectra were interpreted accounting for the Raman spectra in order to assign the possible vibronic sidebands.

The zero-phonon line (ZPL) is the transition between the lowest Stark sub-levels of both multiplets, designated as 0 ↔ 0'. It is observed at 10246 cm -1 corresponding to the wavelength of 976.0 nm (at 6 K). The full set of energy-levels of Yb 3+ :KY(MoO 4 ) 2 is 2 F 7/2 = (0, 315, 411, 601) cm -1 and 2 F 5/2 = (10246, 10440, 10749) cm -1 , see Fig. 9(a), showing the energy-level scheme and the wavelengths of the electronic transitions in absorption and emission. In particular, the emission peak at ~1007 nm corresponding to the maximum SE cross-sections is assigned to the 0' → 1 transition. The partition functions for the lower (m = 1) and upper (m = 2) manifolds are Z 1 = 1.397 and Z 2 = 1.469 (the ratio Z 1 /Z 2 = 0.951). The determined crystal-field splitting is different from that in monoclinic Yb:KY(WO 4 ) 2 for which 2 F 7/2 = (0, 169, 407, 568) cm -1 and 2 F 5/2 = (10187, 10476, 10695) cm -1 [START_REF] Lagatsky | Diode-pumped CW lasing of Yb:KYW and Yb:KGW[END_REF]. In particular, the total Stark splitting of the ground-state, ΔE( 2 F 7/2 ), is larger for Yb:KY(MoO 4 ) 2 (601 cm -1 ), which explains the broadband emission properties of this material. Previously, for the isostructural KYb(MoO 4 ) 2 , it was pointed out that even at LT, the spectra of the Yb 3+ ion revealed a strong electron-phonon coupling [START_REF] Frolova | Crystal-field effects on the thermodynamic properties of the KLn(MoO 4 ) 2 isostructural compounds[END_REF]. Thus, the assignment of the Stark levels was complicated. The following splitting for the ground-state ( 2 F 7/2 ) was proposed: (0, 240, 460, 460) cm -1 . This poorly agrees with our data.

For all RE ions, the barycenter energy of any isolated 2S+1 L J 4f n multiplet depends linearly on the barycenter energy of any other isolated multiplet. This relation is expressed by the barycenter plot [START_REF] Haumesser | Spectroscopic and crystal-field analysis of new Yb-doped laser materials[END_REF], Fig. 9(b). The determined barycenter energies <E( 2 F 5/2 )> and <E( 2 F 7/2 )> agree well with the linear fit to this plot, expressed by the equation E( 2 F 5/2 ) = 10166.6 + 0.997×E( 2 F 7/2 ) cm -1 , where E 0 = 10166.6 cm -1 denotes the energy of the Yb 3+ excited-state for a free-ion. This confirms the correctness of the constructed energy-level scheme.

Laser operation

Laser set-up

The active elements for the laser experiments were fabricated by mechanical cleavage of the 3 at.% bulk Yb:KY(MoO 4 ) 2 crystal along the (100) plane. In this way, we produced a thin cleaved crystal-plate with a thickness t = 286 μm and a high uniformity of ±2 μm over the clear aperture. No post-cleavage treatment (e.g., polishing) was applied to both surfaces which remained uncoated. The crystal orientation corresponded to light propagation along the a-axis (a-cut) which is beneficial for the pump absorption providing access to light polarizations E || b and E || c with higher σ abs values, Fig. 6(b).

For laser experiments, we selected a plano-plano (microchip) laser cavity, Fig. 10, formed by a flat pump mirror (PM) coated for high transmission (HT) at ~0.97 μm and for high reflection (HR) at 1.02-1.2 μm, and a set of flat output couplers (OCs) with a transmission at the laser wavelength T OC of 0.5%-10%. Both cavity mirrors were gently pressed towards the crystal-plate resulting in a nearly monolithic design. The geometrical cavity length L cav nearly equaled the crystal-plate thickness t. The whole stack (cavity mirrors and crystal-plate) was passively cooled. As a pump source, we employed an InGaAs fiber coupled laser diode (fiber core diameter: 105 μm; numerical aperture (N.A.): 0.22) emitting unpolarized output at a central wavelength of ~968 nm. The pump was collimated and focused into the crystal through the PM using a lens assembly (reimaging ratio: 1:1, focal length: f = 30 mm). The pump spot diameter 2w P in the focus was 100±10 μm. The crystal-plate was pumped in a double-pass, as all the used OCs provided reflection at the pump wavelength, R ≈ 90%. The total pump absorption in two passes was estimated from the small-signal value accounting for the Fresnel losses at the uncoated crystal surfaces and amounted to 9.4%. In one pass, η abs,0 = 1exp(-<σ abs >N Yb t) = 4.8%, where <σ abs > = 0.75×10 -20 cm 2 is the polarization-averaged absorption cross-section. This value does not account for the ground-state bleaching but at the same time it does not overestimate the laser slope efficiency. Due to the small leakage of the residual pump through the OC, it was difficult to estimate the pump absorption under lasing conditions.

A long-pass filter (FEL1000, Thorlabs) separated the laser output and the residual pump. The laser emission spectra were measured with an accuracy of ±0.2 nm.

Laser performance

Laser operation was achieved for all the employed OCs. The CW input-output dependences of the diode-pumped microchip cleaved crystal-plate Yb:KY(MoO 4 ) 2 laser are shown in Fig. 11(a). For the 1% OC, the laser generated a maximum output power of 0.81 W at 1021-1044 nm with a high slope efficiency (η) of 76.4% vs. the absorbed pump power P abs . The laser threshold P th was as low as 56 mW whilst the optical-to-optical efficiency (vs. the pump power incident on the crystal) η opt was rather low, 7.0%, owing to the low pump absorption in the thin crystal. With increasing the output coupling, the laser threshold gradually increased, from 55 mW for T OC = 0.5% to 143 mW for T OC = 10%. The input-output dependences were linear for all the OCs. The absorbed pump power in the crystal-plate P abs was limited to below 1.1 W in order to avoid thermal fracture of the passively cooled crystal. The laser spectra were modulated by etalon (Fabry-Perot) effects showing two wavelength separations, Δλ 1 = 1.0±0.1 nm and Δλ 2 = 6.2±0.5 nm. The smaller one is attributed to the etalon effect of the crystal itself and the larger oneto the residual small airgap between the crystal and one of the cavity mirrors. The free spectral range (FSR) of the Fabry-Perot etalon with a thickness t and a refractive index n at normal incidence is Δλ FSR ≈ λ 2 /(2nt) which yields 0.95 nm for the crystal (t = 286 μm and <λ> = 1030 nm). The thickness of the equivalent airgap is ~90 μm. The roughly 20 nm broad laser spectra originated from the large gain bandwidth of Yb 3+ in KY(MoO 4 ) 2 .

The laser operation in the plano-plano cavity indicated a positive thermal lens for a-cut Yb:KY(MoO 4 ) 2 . Positive thermal lens was observed also for monoclinic Yb:KY(WO 4 ) 2 crystal [START_REF] Loiko | Polarization-anisotropy of thermal lens in Yb:KY(WO 4 ) 2 laser crystal under high-power diode pumping[END_REF] and ascribed to the counteraction of negative thermo-optic coefficients dn/dT [START_REF] Loiko | Thermo-optical properties of pure and Ybdoped monoclinic KY(WO 4 ) 2 crystals[END_REF] and the positive thermal expansion. Negative dn/dT values were also measured for tetragonal double molybdates [START_REF] Loiko | Thermooptical properties of uniaxial NaT(XO 4 ) 2 laser host crystals, (where T = Y, La, Gd or Bi and X = W or Mo)[END_REF]. Note that for Yb:KY(MoO 4 ) 2 , the largest coefficient of linear thermal expansion (38.3×10 -6 K -1 ) is along the a-axis which may explain the positive thermal lens for the present crystal cut.

Conclusion

To conclude, we report on the growth, structure refinement by the Rietveld method, polarized room-temperature spectroscopy and crystal-field splitting (at 6 K), and first laser operation of Yb 3+ -doped potassium yttrium double molybdate, Yb:KY(MoO 4 ) 2 . Its layered crystal structure dictates a strong polarization-anisotropy of the transition cross-sections for the Yb 3+ dopant and a perfect natural cleavage habit along the (100) plane. Mechanically cleaved thin crystal films and plates with a thickness as thin as tens of μm can be directly applied as gain medium for laser operation. We report on a watt-level output from a diode-pumped microchip 3 at.% Yb:KY(MoO 4 ) 2 crystal-plate laser operating with a high slope efficiency (76.4%) almost approaching the Stokes limit. Highly Yb 3+ -doped KY(MoO 4 ) 2 crystal plates and films (e.g., up to 10 at.%, as obtained in our preliminary growth experiments) are attractive for short-pulse (sub-ns) passively Q-switched microchip lasers, as well as thin-disk lasers.

Fig. 1 .

 1 Fig. 1. A photograph of as-grown 3 at.% Yb:KY(MoO 4 ) 2 crystals. The growth direction is along the [100] crystallographic axis.

Fig. 2 .

 2 Fig. 2. (a) Rietveld analysis of the RT X-ray powder diffraction (XRD) pattern of a 3 at.% Yb:KY(MoO 4 ) 2 crystal, the numbers denote the Miller's indices (hkl) for the sp. gr. Pbna; (b,c) Illustration of the layered structure of the Yb:KY(MoO 4 ) 2 crystal: (b) three-dimensional view, (c) a projection of the a-c plane. Black rectangle denotes the unit-cell.

  26(2) -2.74(3) Å. The belts of edge-sharing [Y|YbO 8 ] polyhedra run along the b-axis. Along the c-axis, they are separated by an empty polyhedron which is sharing 4 edges with four [MoO 4 ] tetrahedra. Each Mo-tetrahedron connects two translationally identical belts of Y-polyhedra and, simultaneously, it connects the corners of two adjacent Y-polyhedra (within the belt). Thus, the multi-layer structure of Yb:KY(MoO 4 ) 2 is determined by [Y|Yb(MoO 4 ) 2 ] layers (lying in the b-c plane) formed by [MoO 4 ] tetrahedra and [Y|YbO 8 ] polyhedra and containing cavities, as well as zigzag K +layers separating two neighboring [Y|Yb(MoO 4 ) 2 ] layers. The zigzag K + -layers are more loose than the [Y|Yb(MoO 4 ) 2 ] ones. Moreover, the latter are separated by a relatively large a/2 spacing of 9.106 Å. This determines the natural cleavage along the (100) plane.

  261(2) ×2 Mo -O3 =1.784(6) ×1 K -O1 = 2.742(1) ×2 Y|Yb -O3 = 2.348(0) ×2 Mo -O4 = 1.847(6) ×1 K -O1' = 2.759(6) ×2 Y|Yb -O2 = 2.418(9) ×2 Mo -O2 = 1.644(8) ×1 K -O2 = 2.756(2) ×2 Y|Yb -O4' = 2.743(1) ×2 Mo -O1 = 1.708(7) ×1 K -O2' = 3.335(2)×1 Y|Yb -Y|Yb = 3.973(2) ×2 a Mo -O4 = 2.5735 ×1 K -O1'' = 3.587(6) ×2 Y|Yb -Y|Yb = 5.071(5) ×2 b K -O3 = 4.223(0) × 1 a,b The shortest Y|Yb -Y|Yb distances are added for comparison. a Along the b-axis. b Along the c-axis (sp. gr. Pbna).

Fig. 3 .

 3 Fig. 3. Relative thermal evolution of the unit cell parameters of 3 at.% Yb:KY(MoO 4 ) 2 with the temperature up to 550 K.

  the volumetric thermal expansion, α vol = α a + α b + α c is 67.1×10 -6 K -1 . The anisotropy of the thermal expansion in Yb:KY(MoO 4 ) 2 is relatively strong, as expressed by the ratios α a : α b = 1.64 and α a : α c = 7.15. The thermal expansion in KY(MoO 4 ) 2 is stronger than in its double tungstate counterpart. Indeed, for KY(WO 4 ) 2 , α a = 8.4, α b = 2.0 and α c* = 19.8 [10 -6 K -1 ] [32].

Fig. 4 .

 4 Fig. 4. Scanning Electron Microscope (SEM) images of a cleaved single-crystal plate of 3 at.% Yb:KY(MoO 4 ) 2 : (a) the fracture edge of the plate running along the c-axis, the a-axis is vertical; (b) the plate surface parallel to the (100) plane showing flower-like defects.

Fig. 5 .

 5 Fig. 5. RT Raman spectra of the 3 at.% Yb:KY(MoO 4 ) 2 crystal for the a(mn)a, m, n = b, c geometries (Porto's notations), λ exc = 488 nm, numbers indicate the peak frequencies in cm -1 .

Fig. 6 .

 6 Fig. 6. RT absorption properties of a 3 at.% Yb:KY(MoO 4 ) 2 crystal: (a) unpolarized transmission spectrum of a ~1 cm-thick (100)-oriented crystal plate; (b) absorption crosssection, σ abs , spectra for light polarizations E || a, b, c. The arrow indicates the pump wavelength used in the laser experiments; (c) Tauc plot for the evaluation of the optical bandgap (E g ), E phphoton energy. The absorption at ~1 μm originates from the 2 F 7/2 → 2 F 5/2 transition of Yb 3+ ions. It is analyzed in Fig. 6(b) in terms of absorption cross-sections, σ abs = α abs /N Yb (α abs -absorption coefficient) for the principal light polarizations E || a, b, c. The absorption spectra exhibit strong polarization anisotropy. The maximum σ abs is 1.77×10 -20 cm 2 at 977.1 nm and the

Fig. 7 .

 7 Fig. 7. Emission properties of Yb 3+ :KY(MoO 4 ) 2 : (a) stimulated-emission (SE) cross-sections, σ SE , for light polarizations E || a, b and c. The arrow indicates the observed laser wavelength; (b) gain cross-sections, σ gain = βσ SE -(1 -β)σ abs , β = N 2 ( 2 F 5/2 )/N Yb is the inversion ratio, the light polarization is E || b; (c) luminescence decay curve for a cleaved film, λ exc = 930 nm, λ lum = 1030 nm, symbols: experimental data, line: single-exponential fit.

Fig. 8 .

 8 Fig. 8. Absorption and luminescence spectra of Yb 3+ :KY(MoO 4 ) 2 plotted vs. the energy difference (E ph -E ZPL ), where E ph = h(c/λ) is the photon energy and E ZPL = 10246 cm -1 is the zero-phonon line (ZPL) energy, measured at LT (6 K) and RT (293 K) with unpolarized light. For LT emission spectra, λ exc = 976 nm. Electronic transitions are indicated as i ↔ j', phonon sidebandsas hν.

Fig. 9 .

 9 Fig. 9. (a) Crystal-field splitting of the Yb 3+ ion in the KY(MoO 4 ) 2 crystal (site symmetry: C 2 ), Z 1(2) are the partition functions for the ground-and excited-state, respectively, arrows indicate the transitions in absorption / emission at 6 K; (b) barycenter plot [37] for the Yb 3+ ion showing the position of Yb:KY(WO 4 ) 2 and Yb:KY(MoO 4 ) 2 crystals (blue circles).

Fig. 10 .

 10 Fig. 10. Scheme of the diode-pumped 3 at.% Yb:KY(MoO 4 ) 2 cleaved crystal-plate microchip laser: LDlaser diode, PMpump mirror, OCoutput coupler.

Fig. 11 .

 11 Fig. 11. Diode-pumped Yb:KY(MoO 4 ) 2 cleaved crystal-plate microchip laser: (a) input-output dependences, ηslope efficiency; (b) typical laser emission spectra measured at P abs = 1.0 W. The laser polarization is E || b.Typical laser emission spectra are shown in Fig.11(b). The spectra experienced a blueshift with the increase of the output coupling: from 1020-1051 nm for T OC = 0.5% to 1012-1020 nm for T OC = 10%. This is due to the quasi-three level nature of the Yb 3+ laser transition 2 F 5/2 → 2 F 7/2 exhibiting reabsorption. The observed spectral behavior agrees with the gain spectra for E || b, Fig.7(b). The laser output was linearly polarized (E || b) naturally selected by the anisotropy of the gain.The laser spectra were modulated by etalon (Fabry-Perot) effects showing two wavelength separations, Δλ 1 = 1.0±0.1 nm and Δλ 2 = 6.2±0.5 nm. The smaller one is attributed to the etalon effect of the crystal itself and the larger oneto the residual small airgap between the crystal and one of the cavity mirrors. The free spectral range (FSR) of the Fabry-Perot etalon with a thickness t and a refractive index n at normal incidence is Δλ FSR ≈ λ 2 /(2nt) which yields 0.95 nm for the crystal (t = 286 μm and <λ> = 1030 nm). The thickness of the equivalent airgap is ~90 μm. The roughly 20 nm broad laser spectra originated from the large gain bandwidth of Yb 3+ in KY(MoO 4 ) 2 .

Table 1 . Laser Performance a of RE 3+ -doped Cleaving Crystals

 1 P out -output power, λ L -laser wavelength, η -slope efficiency, P th -laser threshold.

	Crystal	Plane	t, mm	P out , W	λ L , nm	η, %	P th , W	Ref.
	Nd:LaB 3 O 6	(101)	0.5	0.53	1060	49	~0.03	[7]
	Nd:YPO 4	(010)	0.6	2.16	1063	56.4	0.22	[9]
	Nd:BaGd 2 (MoO 4 ) 4	(010)	1.1	0.70	1061	51	<0.01	[14]
	Yb:LuPO 4	(100)	0.3	1.61	1036-1040 75	0.17	[8]
	Yb:BaGd 2 (MoO 4 ) 4	(010)	4.0	1.16	1046-1054 20	5.8	[1]
	Yb:KY(MoO 4 ) 2	(100)	0.29	0.81	1021-1044 76.4	0.06	This work
	Tm:KY(MoO 4 ) 2	(100)	0.70	0.88	1840-1905 65.8	0.21	[3]
	Tm:BaGd 2 (MoO 4 ) 4 (010)	1.6	0.35	1905-1921 49	0.1	[10]

a t -thickness,

Table 2 . Fractional Atomic Coordinates (x, y, z), Occupancy Factors (O.F.) and Temperature Factors (Biso) for 3 at.% Yb:KY(MoO4)2 (Space Group Pbna)

 2

	Atom	Wyckoff symbol	x	y	z	O.F.	B iso
	K	4c	0.2713(4)	0.25	0	1	2.6(3)
	Y	4c	0.5060(2)	0.25	0	0.97	0.94(1)
	Yb	4c	0.5060(2)	0.25	0	0.03	0.94(1)
	Mo	8d	0.1014(1)	-0.0163(3)	0.0204(6)	1	0.83(8)
	O1	8d	0.1885(6)	0.531(2)	0.102(2)	1	1.6(2)
	O2	8d	0.1001(1)	0.834(2)	0.245(2)	1	1.6(2)
	O3	8d	0.1039(1)	0.164(2)	0.230(2)	1	1.6(2)
	O4	8d	0.4716(7)	-0.034(4)	0.2804(2)	1	1.6(2)

Table 3 . Selected Interatomic Distances in 3 at.% Yb:KY(MoO4)2

 3

Acknowledgments

P. L. thanks Ms. Liza Basyrova for the help with the SEM studies.

Funding

Russian Foundation for Basic Research (19-32-90199); Spanish Government (MAT2016-75716-C2-1-R (AEI/FEDER,UE)); Catalan Government (2017 SGR 755), National Natural Science Foundation of China (61975208, 51761135115, 61875199, 61850410533), Deutsche Forschungsgemeinschaft (PE 607/14-1).

Disclosures

The authors declare no conflicts of interest.