text:
Fabien Méry
email: fabien.mery@onera.fr

Jean-Luc Godard

Guillaume Arnoult

Philippe Bardoux

Christophe François

Maxime Forte

Estelle Piot

HIGH-SPEED WIND-TUNNEL INVESTIGATION OF MAJOR AERODYNAMIC CHALLENGES FOR HLFC TECHNOLOGY

Reduction of the specific consumption of aircraft would lead to substantial economic and environmental benefits. A promising technique consists in reducing skin friction drag by delaying the laminar-turbulent transition point as far aft as possible, particularly on the wings, in order to obtain lower friction coefficient in the presence of laminar flow. This can be achieved by Hybrid Laminar Flow Control (HLFC) technology. This paper presents the aerodynamic design of a largescale HLFC wing model for experiments that will be conducted in ONERA's S1MA wind-tunnel. The wing model is designed to investigate the major aerodynamic challenges that must be tackled to enable the development of HLFC airfoils: assessment in transonic flow conditions of the wing drag reduction due to HLFC suction, surface tolerance requirements on a HLFC wing and investigation of Attachment Line Contamination.

INTRODUCTION

Over the last decades, all civil aircraft manufacturers have made great efforts to reduce aircraft drag. The long-term aim of this operation is to reduce the specific consumption of aircraft, which would lead to substantial economic and environmental benefits. A promising technique consists in reducing skin friction drag by delaying the laminar-turbulent transition point as far aft as possible, particularly on the wings, in order to obtain lower friction coefficient in the presence of laminar flow. ONERA scientists have investigated this concept, called "laminarity", for more than three decades (see for instance some recent references [START_REF] Methel | An experimental study on the effects of positive surface defects on the laminar-turbulent transition of a sucked boundary layer[END_REF][START_REF] Hue | Wind Tunnel and CFD investigations focused on transition and performance predictions of laminar wings[END_REF][START_REF] Beguet | Modeling of transverse gaps effects on boundary-layer transition[END_REF][START_REF] Fiore | Characterization of a highly efficient chevron-shaped anti-contamination device Exp[END_REF][START_REF] Forte | Research activities of ONERA on laminar airfoils in the framework of JTI Clean Sky SFWA-ITD: transition control Greener Aviation[END_REF][START_REF] Forte | Research activities of ONERA on laminar airfoils in the framework of JTI Clean Sky SFWA-ITD: transition prediction[END_REF][START_REF] Thibert | The A320 Laminar Fin Programme[END_REF][START_REF] Reneaux | Overview on Drag Reduction Technologies for Civil Transport Aircraft[END_REF]. In the frame of the HLFC-Win project, funded by the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme, AERNNOVA, DLR, ONERA and SONACA are working jointly with AIRBUS on the development and evaluation of Hybrid Laminar Flow Control technology (HLFC) for large passenger aircraft 1 . More precisely, the target application is a long-range aircraft wing. Some major aerodynamic challenges that must be tackled to enable the development of HLFC airfoils are: assessment of the wing drag reduction due to HLFC suction; assessment of robustness of advanced suction systems under transonic flow conditions; surface tolerance requirements on a HLFC wing; investigation of Attachment Line Contamination. Within the HLFC-Win project, ONERA is setting-up wind-tunnel investigations for addressing them. Especially, a largescale HLFC wing model is being prepared for experiments to be conducted at the end of 2022 in ONERA's S1MA wind-tunnel, under transonic conditions (Mach  0.83) and at a high Reynolds number (unitary Re  11.10 6 m -1 ). In the paper, we present the aerodynamic design of this large-scale wing model and we explain how it will address the challenges listed previously.

PRESENTATION OF THE AERO-SHAPE

The high-speed wind-tunnel model was designed starting from an AIRBUS reference airplane shape. The airplane half-span is 29 m roughly. Airfoils suited for HLFC technology were considered only in the outer wing, for spanwise positions over 16 m. The airplane design point corresponds to a Mach number equal to 0.83 and a lift coefficient of 0.50. Firstly, a parametric study was done to select the model scale and the airplane wing portion to be represented by the wind-tunnel model. Then a more detailed aerodynamic design was done with high fidelity methods and the so-called ONERA-S1MA shape was selected from this design work. Different computations have been done on this shape to investigate the effects of flow conditions, of boundary layer suction and of the wind-tunnel walls. A variant of this shape with a leading edge sweep angle increased by 20° (ie up to a value of 52°) has also been calculated to analyse the leading edge contamination phenomenon and the associated attachment line transition control.

Model scale selection

The main objectives of the aerodynamic design of the model are:

- which is calculated from the leading edge sweep angle, the leading edge radius and from the flow conditions.

The kinematic viscosity *  is computed at a reference temperature T* which can be estimated from an empirical relationship:

T*=Te+A(Tw-Te) + B(Taw-Te) where Te is the boundary layer edge temperature, Tw is the wall temperature and Taw is the adiabatic wall (recovery) temperature. A=0.1 and B=0.6 are empirical constants [START_REF] Poll | Boundary layer transition on the windward face of space shuttle during re-entry[END_REF]. The variation of R * along the span is plotted in Figure 1 for different model scales (colored lines) and compared to what would be obtained for the airplane scale in flight (black line). As the objective is here to have contamination in 1/3 inner wing, that is with R* over 250 [START_REF] Arnal | Laminarity and laminar-turbulent transition control[END_REF][START_REF] Poll | Some Aspects of the Flow near a Swept Attachment Line with Particular Reference to Boundary Layer Transition[END_REF], and having airfoils suited for HLFC technology in the 2/3 outer wing, that is spanwise positions over 16 m, a model scale of 0.40 was finally selected. With this value, the model will represent the airplane wing portion between spanwise positions 13.50 and 24.75 m (see Figure 2).

Model aerodynamic design

The model aerodynamic design was performed with the elsA software (Airbus-Safran-ONERA property), solving RANS equations [START_REF] Cambier | The ONERA elsA CFD software: input from research and feedback from industry[END_REF]. The k-ω turbulence model was used for these computations. The transition location predictions were done with criteria integrated in the software: the so-called AHD criterion for Tollmien-Schlichting instabilities and the so-called C1 criterion for crossflow instabilities [START_REF] Cliquet | Application of Laminar-Turbulent Transition Criteria in Navier-Stokes Computations[END_REF]. These criteria give only approximate values in case of suction..

The design was done for a Mach number equal to 0.83 and an angle of attack equal to 5.0°. The calculations were done in the S1MA WT conditions, with a Reynolds number equal to 11 millions per meter roughly. An extended laminar flow was desired mainly on the suction side of the wing. The model design was done without modifying the wing planform, and in particular the leading edge sweep angle was kept equal to 32°. Different geometrical modifications of the initial wing shape were introduced with in-house tools and an analysis of each shape was done with RANS computations:

-Wing global thickness modification; -Wing twist modifications; -Airfoil camber modifications; -Local modifications of the airfoils, in particular to modify the thickness or the leading edge radius.

From the analysis of the different shapes, the so-called ONERA-S1MA shape was selected. It was the best compromise to reach the aerodynamic design objectives. Although the pressure distributions do not fully match with the airplane ones, the shape is not too far from the airplane one and it allows a good similarity for the study of technological aspects, with in particular a suction system and its integration close to what could be done on the airplane. The main geometrical characteristics of this shape are:

-Portion of the airplane wing between spanwise positions 13.50 and 24.75 m; -Scale 0.40 (1 / 2.50); -Model span 4.5 m; -Mean Aerodynamic Chord 1.9658 m; -Reference surface 8.5976 m 2 ; -Wing planform unchanged; -Wing twist unchanged; -Airfoils thickness increased by +10%; -Local modification of the wing tip to have a smooth shape.

AERODYNAMIC ASSESSMENT OF ONERA-S1MA SHAPE

Variation of angle of attack at Mach number 0.83

The pressure distributions at the design Mach number 0.83 obtained for different angle of attacks are displayed in Figure 3. These computations are performed with boundary layer suction and transition prediction using the criteria. It is applied from position x/c equal to 1.5% on the pressure side of the wing to x/c equal to 20.0% on the suction side. For angles of attack below 4.0°, the suction velocity is equal to 0.3 m/s from 1.5% (pressure side) to 1.5% (suction side), then equal to 0.2 m/s from x/c equal to 1.5% to 5.0% and equal to 0.1 m/s from x/c equal to 5.0% to 20.0%. For angles of attack over 5.0°, a constant suction velocity equal to 0.5 m/s is applied from x/c equal to 1.5% (pressure side) to x/c equal to 20.0% (suction side).

The pressure distributions are typical of the ones observed for a HLFC wing. A strong acceleration is present at the leading edge on the suction side, followed by a region with a decrease of velocities, where boundary layer suction would be applied, and followed by an extended region where the flow is accelerated and where no suction is applied. The extended supersonic region ends with a shock wave, at 80% of the chord roughly. The decrease of velocity in the upstream part of the airfoils allows limited Mach numbers upstream of the shock wave. Nevertheless, the shock wave is quite strong whatever the angle of attack considered, between 2.0° and 6.0°. For angle of attack 6.0° an upstream and weak shock wave is observed, that could be a concern to maintain the boundary layer laminar.

Section Y= 1.0m

Section Y=2.2m

Section Y= 3.0m

Section Y= 3.8m It is possible to evaluate the contamination Reynolds number R * from the pressure distributions calculated in the region of the stagnation line. Results are shown in Figure 4. For the different angles of attack investigated, the value of R * is over 250 along the whole span of the wing. It means that the contamination phenomenon is present on the whole wing. For spanwise positions under 1.0 m, ie the region in which contamination phenomenon will be specifically looked at, R * is higher than 330. R * is slightly higher for a higher angle of attack.

Influence of wind-tunnel walls

The S1MA test section is very large (approximately 8m of diameter), so even a wing model of this size can easily be placed there, as shown by the sketch in Figure 5 . The installation of the model in the wind tunnel test section creates a blockage effect and it has for consequence an increase of the flow velocities around the model. The isobar lines on the wing suction side, shown in Figure 6, illustrate this phenomenon. For the Mach number 0.83 and the angle of attack 2.0°, an increase of the velocities is observed in the supersonic region on the wing suction side and it has for consequence an increase of the shock wave intensity with a slightly more downstream position. A very slight increase of the velocities is observed on the wing pressure side. Similar tendencies are observed for the Mach number 0.83 and the angle of attack 5.0° but with some differences. On the wing pressure side, the walls effects are of higher intensity than for the angle of attack 2.0°. On the wing suction side, a boundary layer separation is present at the trailing edge and in a large portion of the wing. It generates an upstream displacement of the shock wave that is located upstream of its position without wind tunnel wall at mid span of the wing. Nevertheless, the velocities in the supersonic region remain higher for the case with wind tunnel walls than without wall.

Influence of increased leading edge sweep

In order to investigate the leading edge contamination phenomenon and to obtain high values of the Reynolds number R*, over 600, it decided that the model should be rotated by 20° during the wind-tunnel tests: the leading edge sweep angle would be changed from 32° to 52°. With such a rotation, the model planform and airfoils remain unchanged. Different computations of this new shape have been performed, for the Mach number 0.83 and different angles of attack. For the angle of attack of 2.0°, the increase of sweep angle leads to an important modification of the pressure distributions on the model. As expected, the velocities on the wing and especially on the suction side are strongly reduced, and there is no more acceleration of the flow and no more shock wave.

Of course these new pressure distributions are no more adapted to hybrid laminar flow control but this configuration will not be tested for this purpose but only for the study of leading edge contamination. Similar phenomena are observed for the Mach number 0.83 and the angle of attack 5.0°. The flow velocities are reduced when the sweep angle is increased, the flow is no more supersonic on the suction side of the model and there is no more shock wave. On the main part of the wing suction side, the velocities are decreasing along the chord. The isobar lines on the wing suction side, shown in Figure 8, confirm these observations, in particular the disappearance of the supersonic region.

ANALYSIS OF THE BOUNDARY-LAYER TRANSITION

Boundary layer computations have been performed using the 3C3D boundary layer code [START_REF] Houdeville | Three-dimensional boundary layer calculation by a characteristic method[END_REF]. The boundary layer calculation is fed by the 3D external flow around the wing obtained in the fully turbulent RANS calculations. In order to model the transition onset, the parabola method is used [START_REF] Perraud | Automatic transition predictions using simplified methods[END_REF]. This method is compatible with the introduction of the suction. The parabola method enables to tackle with both Tollmien-Schlichting (TS) and crossflow (CF) instabilities. As it is an envelop method (ΨCF,max=88.5°, ΨTS,max=40°, Fmax=50000Hz, 100 frequencies), in the S1MA conditions the N threshold value for transition is taken at 8 for both CF and TS instabilities. The boundary layer suction distribution was specifically adjusted to ensure a maximum laminar extent while being compliant with the flow rate limits of the suction system that will be installed inside the model. Two main configurations have been simulated :

uniform suction: 0.5 m/s from -1.5% up to 20% chordwise variable suction: 0.45m/s from -1.5% up to 0.3% chordwise, suction rate 0.30m/s from 0.3% up to 5% and suction rate 0.15 m/s from 5% up to 20%

In order to have some inputs for an accurate calibration of the N threshold during the wind tunnel tests, an NLF area has been kept on the model. This NLF area will be obtained for a non-nominal flow condition. Thus, the HLFC area extents from 1m up to 3.5m spanwise only. In particular, AERNNOVA is maturating the technology for manufacturing the variable porosity perforated sheets; the S1MA model will be equipped with such panels.

Results presented in Figure 10 also show that with this aerodynamic condition and for this wing design, it is important to suck at a quite high rate close to the leading edge in order to control the CF instabilities since they are the most amplified (compared to the TS instabilities). It must be pointed out that the uniform suction configuration (0.5 m/s on all the suction area) guarantees the same laminar extent. This configuration is therefore considered as a maximum design point in the design activities of the suction piping system inside the model.

SURFACE TOLERANCE INVESTIGATION

The ONERA-S1MA model is also designed so that surface tolerance investigation can be performed. There is indeed a lack of experimental data to validate and calibrate the models of allowable surface tolerance at the downstream edge of a suction panel, especially under transonic conditions. Therefore a surface defects device will be installed on the model, as shown in Figure 11. The dashed lines correspond to the value of the gap dimensions regarding the boundary layer displacement thickness computed at the target flow conditions in the wind tunnel. Several pins defects will also be created.

The dimensions of the surface defects will be automatically changed during the wind tunnel run and so it enables to do some parametric study during the same run. Each device has an actuator and a sensor which enables to accurately control the dimensions achieved by the defect (gap depth or pin height or depth).

CONCLUSION

As part of the HLFC-Win project, included in the Large Passenger Aircraft initiative funded by the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme, ONERA is leading the activities devoted to Wind Tunnel Tests. These tests will enable a verification of several aerodynamic assumptions made to develop the HLFC concept for a wing and the associated Ground Based Demonstrator prepared by the HLFC-Win partners, as an enabler to reach TRL4 at the end of the project. ONERA S1MA wind tunnel will be used to test a largescale wing model representative of the outer part of a long-range aircraft under transonic conditions (Mach ~0.83; unitary Reynolds number~11.10 6 m -1 ). The aerodynamic design of this model was presented in this paper. This is a wing model of 4.5 meters span with a mean aerodynamic chord of 2 meters. The sweep angle can be changed in order to increase the leading edge Reynolds number achieved by the model, and therefore allow investigation on the leading edge contamination phenomenon, and its control by wall suction. A surface defects device was also designed in order to study surface tolerance downstream of the suction panels. The model is being manufactured by the consortium COMPACT, composed of ARA, IBK and Meca-Ouest. The wind tunnel tests will be performed in the winter 2022/2023.

  To have during the wind-tunnel tests (WTT) Reynolds numbers as close as possible to flight ones; -To have contamination in at least 1/3 inner span of model; -To have in the 2/3 outboard span airfoils suited for HLFC. In addition, there are several constraints for the model: to have a maximum model span of 4.5 m and a root chord length of 2.0 m roughly, and to have maximum aerodynamic loads acceptable for the wind-tunnel (WT) set-up. The ratio between the Reynolds numbers expected during the wind-tunnel tests and the airplane flight, as a function of the scale of the WT model, is given in

A

  parametric analysis was also done on the leading edge contamination Reynolds number R *

Figure 1 .

 1 Figure 1. Contamination Reynolds number R * versus wing span for different model scales

Figure 2 .

 2 Figure 2. Airplane wing portion corresponding to the S1MA wing model

Figure 3 .

 3 Figure 3. Pressure distributions on ONERA-S1MA shape for Mach number 0.83 and different angles of attack: 2.0° (black line), 4.0° (red line), 5.0° (green line) and 6.0° (blue line).

Figure 4 .

 4 Figure 4. Contamination Reynolds number R * for Mach number 0.83 and different angles of attack: 2.0° (green line), 4.00 (black line), 5.0° (orange

Figure 5 .

 5 Figure 5. Sketch of the ONERA-S1MA model in the test section.

Figure 6 . 7 Figure 7 .

 677 Figure 6. Isobar lines on suction side for Mach number 0.83. Model installed in the S1MA test section (left column) or in free field (right column). Computations obtained foe an angle of attack of 2.0° (upper line) or 5.0° (bottom line).

Figure 8 .

 8 Figure 8. Isobar lines on suction side for models with sweep angles 32° (top) and 52° (bottom). Computations for Mach number 0.83 and angle of attack 5.0°

Figure 9 .

 9 Figure 9. Contamination Reynolds number R * for model with sweep angle 32° (red line) or 52° (blue line). Computations for Mach number 0.83 and different angles of attack: 2.0° (top) and 5.0° (bottom).

Figure 10 .

 10 Figure 10. Boundary layer results for Mach number 0.83 and angle of attack 5.0°. Variable suction configuration. Top: Map of the transition on the suction side of the model. Bottom: Plot of the N-factors growth (TS in red, CF in blue) at the spanwise location materialized by the purple line on the transition map figure.

Figure 10 presents

 10 Figure 10 presents the results of the boundary layer transition analysis and highlights that the variable suction configuration enables to have a laminar extent up to the shock location. This configuration has been selected in order to minimize the suction rate. The chordwise change of the suction rate is made possible by the use of suction panels that have a variable porosity, mounted on three suction chambers only in the

Figure 11 .

 11 Figure 11. Implantation of the surface defects device

Figure 12 .

 12 Figure 12. Gap definition based on Beguet et al [3]. The gap depth (h) ranges from 0 down to 2.5 mm, the gap width (b) is equal to 4.5, 6 or 7.5 mm.

Figure 12

 12 Figure 12 proposes an extract from Beguet et al. paper.The dashed lines correspond to the value of the gap dimensions regarding the boundary layer displacement thickness computed at the target flow conditions in the wind tunnel. Several pins defects will also be created. The dimensions of the surface defects will be automatically changed during the wind tunnel run and so it enables to do some parametric study during the same run. Each device has an actuator and a sensor which enables to accurately control the dimensions achieved by the defect (gap depth or pin height or depth).

Table

Table 1 . Ratio between WTT and flight Reynolds numbers, according to the scale of the wind tunnel model.

 1

	1.
	Scale	1.0	1 / 1.772 = 0.564	1 / 2.125 = 0.471	1 / 2.50 = 0.400	1 / 2.765 = 0.362
	Re (WTT) / Re (flight)	177%	100%	83%	71%	64%

ACKNOWLEDGMENTS

This work was funded by the European Union within the frame of the HLFC-WIN project. This project is part of the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme (Grant agreements CS2-GAM-2018-LPA-AMD-807097-38 and CS2-GAM-2020-LPA-AMD-945583-11).

 [START_REF] Methel | An experimental study on the effects of positive surface defects on the laminar-turbulent transition of a sucked boundary layer[END_REF]Grant agreements No. CS2-GAM-2018-LPA-AMD-807097-38 and CS2-GAM-2020-LPA-AMD-945583-11


domain: spi phys

text:
Bastien Beaumont

Pierre Bourdon

Alexandre Barnini

Louanne Kervella

Thierry Robin

Julien Le Gouët

High efficiency holmium-doped triple-clad fiber laser at 2120 nm

Keywords: Holmium, fiber laser, high power

We developed a new holmium-doped triple-clad fiber (Ho-3CF), reducing the clad diameter to improve the overlap between pump and doped-core, and the holmium concentration to reduce the influence of ion clustering on the laser efficiency. We illustrate here the performance of this fiber in a laser oscillator configuration. The laser emission is centered at 2.12 µm by a fiber Bragg grating, and the active fiber is pumped in the clad by a 1.94 µm thulium-doped fiber laser. The slope efficiency reaches 60 %, for a maximum signal power of 62 W delivered on a quasi single spatial mode (M 2 =1.2). To the best of our knowledge, this slope efficiency is the highest reported for a high power clad-pumped fiber laser emitting at a wavelength higher than 2.1 µm. We also analyze experimentally the impact of the pump Numerical Aperture (NA), at the input of the Ho-3CF, on the laser efficiency. Finally, we use our numerical simulation to comment on the best choice of pump wavelength.

I. INTRODUCTION

H IGH power lasers are required in many applications like defence systems, LIDAR, or free-space optical telecommunications. Considering a continuous regime of several kilowatts, the laser systems must be transportable, eye-safe for the operators, and able to concentrate all the power in a specific spot. Those system specifications are equivalent to require a compact laser, robust to vibrations and temperature variations, with high electro-optical efficiency (typically>20%), emitting at a wavelength higher than 1.5 µm (for atmospheric transmission and eye-safety) in a single spatial mode (generally gaussian), and low heat generation. In addition narrow linewidth amplification must be possible, to allow coherent beam combining of several laser sources.

To date, the highest laser power reported with all these criteria is on the order of the kW, and has been obtained with thulium (Tm) doped fibers [START_REF] Ehrenreich | 1kW, all-glass Tm:fiber laser[END_REF], [START_REF] Anderson | 1.1 kW, beam combinable thulium doped all-fiber amplifier[END_REF]. However for laser emission beyond 2.1 µm, the power of this type of fiber source might be limited by the thermal load caused by the exothermic crossrelaxation pumping process [START_REF] Jackson | Cross relaxation and energy transfer upconversion processes relevant to the functioning of 2 µm Tm3+-doped silica fibre lasers[END_REF]. Another approach, similar to the ubiquitous erbium:ytterbium codoped fibers, consists in adding Tm sensitizing ions in an holmium (Ho) doped fiber [START_REF] Allain | High-efficiency CW thuliumsensitised holmium-doped fluoride fibre laser operating at 2.04 µm[END_REF], [START_REF] Motard | Diffraction limited 195-W continuous wave laser emission at 2.09 µm from a Tm 3+ , Ho 3+codoped single-oscillator monolithic fiber laser[END_REF]. The downside of this approach lies mainly in the difficulty of optimizing simultaneously the two dopant concentrations, and in managing the thermal load.

Another promising approach consists in pumping an Hodoped fiber close to the absorption peak of the laser transition Bastien Beaumont, Pierre Bourdon and Julien Le Gouët are with Office national d'études et de recherches aérospatiales (ONERA) in Palaiseau, France Alexandre Barnini, Louanne Kervella and Thierry Robin are with iXblue Photonics in Lannion, France e-mail: julien.le_gouet@onera.fr.

with several Tm-doped fiber lasers, which are pumped themselves by multimode fiber coupled laser diodes. An optical efficiency of about 40% has already been demonstrated with a record signal power of 407 W in a monolithic architecture [START_REF] Hemming | A monolithic cladding pumped holmium-doped fibre laser[END_REF]. The efficiency reached about 50% in the lower power regime (< 200 W). In these experiments, the holmium-doped triple-clad fiber had a silica clad diameter of 118 µm [START_REF] Simakov | A cladding-pumped, tunable holmium doped fiber laser[END_REF].

We demonstrated a similar efficiency, reaching a laser signal of 90 W with a fiber with two-fold larger clad diameter, corresponding to a four-fold lower overlap between pump beam and active core [START_REF] Le Gouët | Realization and simulation of high-power holmium doped fiber lasers for long-range transmission[END_REF]. This result illustrated the high optical quality of the glass, with low holmium clustering and hydroxyl (OH -) concentration, which are the main contributions to the propagation losses in this type of fiber [START_REF] Humbach | Analysis of OH absorption bands in synthetic silica[END_REF], [START_REF] Wang | Effects of ion clustering and excited state absorption on the performance of ho-doped fiber lasers[END_REF].

In this paper, we present the results that we obtained in laser oscillator configuration with a new Ho-doped triple-clad fiber, with a reduced clad diameter of 105 µm, obtained by an improved fabrication process. In the first part, we detail the fiber properties and the experiment setup. In the second part, we present our results with this new fiber and comment on our pump coupling method. In the last part, we discuss about the choice of pump wavelength for the high power applications.

II. FIBER FABRICATION AND LASER SETUP

The setup of the clad-pumped Ho-doped fiber oscillator is presented on Figure 1. The pump beam is provided by a continuous-wave Tm-doped fiber laser from IPG Photonics (TLR-200) emitting at 1.94 µm with 120 W maximum power on a gaussian spatial mode. The output of the fiber laser is an integrated collimator. We couple the pump beam into a standard multimode silica fiber (MMF) with core/clad diameters 105/125µm and numerical aperture NA=0.22, using an AR coated dry-silica lens with focal length 100 mm. Each MMF is an input port of a 2x1 combiner, which exits on an identical output MMF.

The holmium-doped fiber has a triple-clad structure, very similar to the fiber described in [START_REF] Le Gouët | Realization and simulation of high-power holmium doped fiber lasers for long-range transmission[END_REF]. Its main novelty lies in the new geometry, with a reduced diameter of the silica clad, now at 105 µm flat-to-flat instead of 250 µm and an outer diameter of 145 µm for the fluorinated clad. The pumping clad diameter now fits the core diameter and NA of the standard MMF used in the combiner. Compared to our previous fiber, the surface ratio between active core and pump beam is thus increased by a factor of almost 6. An interesting point of comparison is the all-fiber laser from DSTG, which produced more than 400 W at 2120 nm. The fiber there had core and clad diameters of 18 µm and 112 µm respectively [START_REF] Hemming | A monolithic cladding pumped holmium-doped fibre laser[END_REF]. The doping/pump surface ratio in our fiber is 40% higher.

The interest of the reduced clad diameter, in addition with the useful fitting with a 105/125/0.22 MMF, is that the pump beam is absorbed on a shorter length, for identical core diameter and holmium concentration ρ Ho . As long as the main propagation loss are caused by holmium-independent mechanisms (such as OH bond absorption [START_REF] Humbach | Analysis of OH absorption bands in synthetic silica[END_REF]), it is interesting to maintain a high concentration ρ Ho . However, a high concentration of holmium can lead to the formation of ion clusters, which affect the amplification efficiency through the well-known mechanism of Pair Induced Quenching (PIQ) [START_REF] Wang | Effects of ion clustering and excited state absorption on the performance of ho-doped fiber lasers[END_REF], [START_REF] Delevaque | Modeling of pair-induced quenching in erbium-doped silicate fibers[END_REF]. In a fiber with low propagation loss (e.g. with low OH content), it can become more interesting to reduce the concentration of rare-earth ions, which implies a longer fiber, however compensated by a lower fraction of ions in clusters.

Owing to our fabrication method, the concentration of hydroxyl groups OH is very low. In the previous fiber, we estimated from the clad attenuation that the OH concentration was approximately 0.04 pm. Since we did not modify the fabrication process of the core, we assume that the hydroxyl concentration is of the same order of magnitude in our new fiber, i.e. much lower than the 1 ppm reported in the Nufern fiber developed for the DSTG demonstrations [START_REF] Hemming | A monolithic cladding pumped holmium-doped fibre laser[END_REF], [START_REF] Simakov | A cladding-pumped, tunable holmium doped fiber laser[END_REF]. Therefore we decided to reduce significantly the holmium concentration in the core, in order to reduce accordingly the fraction of ions in pairs. On the other hand, we did not modify notably the aluminum concentration, to preserve the solvation of the remaining holmium ions.

By cut-back measurement in the Ho-3CF core at λ peak = 1950 nm, we find an absorption α Ho (λ peak ) = 43 ± 1 dB/m for the fundamental optical mode. In the meantime, we measured the chemical composition across the core with an electron micro-probe and energy or wavelength dispersive spectroscopy (EDS and WDS), depending on the atoms. As shown on Figure 2, the average holmium concentration ρ Ho in the fiber core is close to 3 10 25 /m 3 . On a single-clad Ho-doped fiber with similar core composition, we measured a fraction of clustered ions 2k = 15 ± 1% for a holmium concentration of about 4 10 25 /m 3 [START_REF] Le Gouët | Realization and simulation of high-power holmium doped fiber lasers for long-range transmission[END_REF]. Assuming that the fraction 2k is proportional to ρ Ho in this range, we estimate that 2k ≃ 11% in our new Ho-3CF. As a comparison, the linear absorption was close to 70 dB/m at 1950 nm in the Ho-doped fiber used in the famous work from DSTG [START_REF] Hemming | A monolithic cladding pumped holmium-doped fibre laser[END_REF], and the fraction of clustered ions was later estimated by numerical simulation to 2k ≃ 30% [START_REF] Wang | Numerical modeling of in-band pumped Ho-doped silica fiber lasers[END_REF].

As for the peak absorption cross-section for the 5 I 8 -5 I 7 transition in our alumino-silica host, we measure it in the fiber core from the usual formula:

σ abs (λ peak ) = α Ho (λ peak ) ρ Ho .Γ(λ peak )
where Γ(λ peak ) is the overlap between the optical mode guided in the core and the active region. The usual Marcuse formula yields a mode diameter 2w mode = 23 µm. Given the active core diameter D core = 20 µm, we thus find an overlap mode/doping Γ(λ peak ) = 80%. The resulting value is σ abs (λ peak ) = 4.1 10 -25 m 2 , in good agreement with our previous measurement in a similar host [START_REF] Le Gouët | Realization and simulation of high-power holmium doped fiber lasers for long-range transmission[END_REF].

Fig. 2. Profile of the holmium concentration across the fiber core, obtained by electron micro-probe and an EDS detector. The dotted line represents the refractive index profile in the core (see Fig. 4).The red lines correspond approximately to the guiding core of the fiber.

The MMF of the combiner output is spliced to a 5 m passive 3CF, coiled with a diameter D c ≃ 8 cm to guarantee an optimal filling of the numerical aperture of the following Ho-3CF. The passive 3CF has essentially the same dimensions as the holmium doped fiber, except that it has no pedestal and that the F-doped silica layer is not octagonal.

After this pump-mixing fiber, we splice the fiber Bragg grating (FBG) that provides the spectral selectivity at the laser wavelength. The FBG is realized by imprinting a phase mask in the core of a sample of passive 3CF. It exhibits a high reflectivity (HR) of 99% at 2.12 µm, with a spectral linewidth of about 1 nm. We tested the FBG in two versions, with and without high power packaging, and measured the same results with both samples. In our setup, where the FBG is simply in contact with the optical table, we did not detect any heating at this point of the fiber when injecting the maximal pump power of 110 W in the fiber laser.

Finally, the low reflectivity of the output coupler of the laser oscillator cavity is obtained either by the Fresnel reflection of a straight cleave on the Ho-doped fiber (R=3%), or by another FBG imprinted on another sample of passive 3CF. At the fiber laser output, we collimate the signal and residual pump beams, and separate them with a dichroic mirror (HR at 2.12µm, AR at 1.94µm).

III. LASER EFFICIENCY

In order to estimate the Ho-3CF optimal length in terms of laser optical efficiency, we use our numerical simulation. Considering approximate values in the simulation for holmium concentration, interaction cross-sections, cluster rate, attenuation (OH groups, silica), and FBG specifications, we find an optimum length close to 8 m. We then precise the Ho-3CF optimal length for laser efficiency by cutback method. Experimentally, we reach an optical-optical efficiency of 60% for a 9 m fiber, and obtain 62 W at 2120 nm for 106 W pump power (see Figure 3).

The laser efficiency is thus improved compared to the previous state of the art of about 50% for clad-pumped allfiber lasers at 2120 nm [START_REF] Hemming | A monolithic cladding pumped holmium-doped fibre laser[END_REF], [START_REF] Le Gouët | Realization and simulation of high-power holmium doped fiber lasers for long-range transmission[END_REF]. As mentioned above, this performance results from two notable achievements in the fiber fabrication process. First, the ability to realize a complex structure (core/pedestal/silica/fluorinated silica) in a reduced diameter, which allows a better overlap between pump beam and active region compared to our previous work. Second, the low OH concentration in the fiber allows the reduction of the holmium concentration, to reduce the effect of PIQ while maintaining the background attenuation low enough to preserve the laser efficiency. Interestingly, our first measurement showed a higher efficiency for a slightly shorter optimal length of Ho-3CF, across the same range of pump power. At first, we were coupling the pump beam into a 3 m long standard MMF (105/125/0.22) that was spliced to the passive 3CF containing the FBG. In this configuration, the laser efficiency was close to 65% for an optimal length of about 8 m.

Then we prepared the experiment to couple a second pump laser, and replaced the MMF by the 1 m long input port of the bundle presented above (Fig. 1). With this modified coupling setup, we found that the efficiency was notably lower (about 62%), even though we were already taking into account the pump loss in the combiner. We finally identified the coupled pump beam NA as the cause of the efficiency difference, and thus made sure to fill the pump clad NA (using longer passive MMF, reduced coiling diameter...). The laser efficiency of 60% corresponds to the configuration with the maximal NA.

It should be noted that the pump beam in the clad of the Ho-3CF is neither gaussian nor flat-top, so the concept of an absolute beam diameter that would define the numerical aperture is not relevant. In order to determine the NA values at the fiber input, we thus measure the second moment diameter D 4σ of the far field image of the beam, and assume that the value NA=0.22 corresponds to the maximum value of D 4σ that can be delivered.

IV. REFRACTIVE INDEX PROFILE AND BEAM QUALITY

We also checked the beam quality of the output signal, as the measurement of the refractive index across the Ho-3CF diameter revealed a shape quite distinct from the ideal flat step profile (see Figure 4). The beam parameter measurement yielded a surprising good value of M 2 = 1.2 ± 0.1 for the two orthogonal directions. It should be noted however that the M 2 value could be notably degraded (up to 1.9 in one of the directions) by tightening slightly the Ho-3CF. This sensitivity of the beam quality to the fiber coiling or position may be due to the uneven index profile of the fiber core. Ongoing work consists in fabricating a core host matrix based on a co-doping of aluminum and phosphorus, to test an approach that already showed interesting results with other rare-earths such as erbium [START_REF] Likhachev | Effect of the AlPO_4 join on the pump-to-signal conversion efficiency in heavily Er-doped fibers[END_REF], [START_REF] Jebali | 264 W output power at 1585 nm in Er-Yb codoped fiber laser using in-band pumping[END_REF], ytterbium [START_REF] Liu | 3 kW 20/400 Yb-Doped Aluminophosphosilicate Fiber with high stability[END_REF], or neodymium [START_REF] Barnini | Low numerical aperature large-mode-area neodymiumdoped fibers fabricated by SPCVD and ASD for laser operation near 920nm[END_REF]. Indeed, this type of host offers low molar refractivity composition, and the possibility to reduce the refractive index of the rare-earth-doped core, which could eventually allow the suppression of the pedestal.

V. ON THE PUMP WAVELENGTH

In several recent communications [START_REF] Tench | Novel highly efficient inband pump wavelengths for Ho-doped fiber amplifiers[END_REF]- [START_REF] Tench | Performance Benefits of 1860 nm vs. 1940 nm Pumping of Holmium-doped Fibres with Significant Ion Pairing[END_REF], the choice of a pump wavelength at higher energy (typically around 1850 nm) has been presented as an innovative advantageous approach, as compared to the 1950 nm wavelength used in lasers dedicated to high power [START_REF] Hemming | A monolithic cladding pumped holmium-doped fibre laser[END_REF], [START_REF] Le Gouët | Realization and simulation of high-power holmium doped fiber lasers for long-range transmission[END_REF], [START_REF] Friebele | Ho-doped fiber for high energy laser applications[END_REF]- [START_REF] Holmen | Holmium-doped fiber amplifier for pumping a ZnGeP 2 optical parametric oscillator[END_REF]. Here we propose a brief analysis of the interests and drawbacks of these wavelength, based on numerical simulations.

For rare-earth ions, infrared optical transitions are available between electronic energy states that contain themselves several Stark shifted substates. As it is well-known, pumping towards the highest energy states can convert an apparent two-level system into a quasi three-level system [START_REF] Desurvire | Erbium-Doped Fiber Amplifiers: Principles and Applications[END_REF], [START_REF] Paschotta | Ytterbium-doped fiber amplifiers[END_REF]. A higher population inversion and better gain can thus be obtained by pumping at wavelengths shorter than the peak absorption λ peak , where the probability of emission is also at its maximum. This is exactly the case for a fiber short enough to avoid pump depletion, and where the population inversion remains almost constant.

Let us consider now the spectral variation of the saturation intensity I sat = hν/ [τ.(σ abs + σ em )], where τ is the excited state lifetime and σ abs and σ em are the absorption and emission cross-sections [START_REF] Saleh | Modeling of gain in erbium-doped fiber amplifiers[END_REF]. As a consequence of the highest absorption and emission at λ peak (about 976 nm for Yb, 1530 nm for Er, 1950 nm for Ho), I sat reaches its lowest value for this wavelength. For example, I sat is higher by a factor of 6 at 920 nm compared to 976 nm in an Yb-doped fiber, and a factor of almost 10 at 1850 nm compared to 1950 nm in Ho-doped fiber. Therefore, for a high pump intensity I pump (compared to I sat at any wavelength), the pump beam will bleach the fiber on a longer section if it is set at λ peak , and thus provide population inversion on a longer section, and finally higher gain integrated over the fiber.

We illustrate this aspect by two examples: first the corepumped fiber amplifier described in [START_REF] Tench | Novel Highly Efficient In-Band Pump Wavelengths for Medium Slope Efficiency Holmium-Doped Fiber Amplifiers[END_REF], but without ion clustering, and second the clad-pumped high power laser oscillator reported above (taking clusters into account). On Figure 5 we present the corresponding results of our numerical simulation for the signal and pump powers (straight and dotted lines respectively), for a pump beam at 1850 or 1940 nm (red and blue lines).

Although hypothetical, the case of the holmium-doped fiber without ion clustering is interesting, as it brings to a conclusion that differs from the cited works [START_REF] Tench | Novel highly efficient inband pump wavelengths for Ho-doped fiber amplifiers[END_REF]- [START_REF] Tench | Performance Benefits of 1860 nm vs. 1940 nm Pumping of Holmium-doped Fibres with Significant Ion Pairing[END_REF]. As detailed above, a given pump power saturates more efficiently the holmium ions at 1940 nm (close to λ peak ) than at 1850 nm. Even though the maximum population inversion is lower for 1940 nm pumping, it is provided on a longer path, which eventually results in a higher output signal. For the parameters mentioned in [START_REF] Tench | Novel Highly Efficient In-Band Pump Wavelengths for Medium Slope Efficiency Holmium-Doped Fiber Amplifiers[END_REF], but taking into account the Ho ion pairs, our simulation confirms the results presented in the cited article.

Finally, the example of clad-pumped high power laser reminds that shifting the pump wavelength out of the absorption peak requires to increase the fiber length. In particular, since the Ho 3+ absorption is about 5 times lower at 1850 than at λ peak , the optimal fiber laser would be almost 5 times longer at 1850 nm in absence of any fiber loss. This has several negative Fig. 5. Numerical simulation of the laser signal (straight lines) and pump powers (dotted lines), for a pump beam at 1850 nm (red) or at 1940 nm (blue). Top: amplifier described in [START_REF] Tench | Novel Highly Efficient In-Band Pump Wavelengths for Medium Slope Efficiency Holmium-Doped Fiber Amplifiers[END_REF] for a hypothetical Ho 3+ -doped fiber without ion clustering (2k=0). Bottom: fiber laser oscillator in the configuration reported above. consequences: first, in copropagative pumping, the population inversion is high at the very beginning of the fiber, and becomes depleted long before the output, so there is less gain available towards the fiber end. In a real fiber laser, various propagation losses (multi-phonon transitions, OH -absorption, pair-induced quenching...) contribute to reducing the optimal length and the maximum power. Therefore, the shorter the fiber and the less affected the output power, which comes as an advantage again of pumping at 1940 nm instead of 1850 nm. In addition, in the context of narrow-linewidth high power laser amplifiers, nonlinear effects such as Stimulated Brillouin Scattering are more limiting for longer fiber length. The same arguments are also valid for Yb or Er-doped fibers for example, which explains why most high power fiber sources are pumped at the absorption peak of the laser transition [START_REF] Jebali | 264 W output power at 1585 nm in Er-Yb codoped fiber laser using in-band pumping[END_REF], [START_REF] Yu | Diode-pumped narrow linewidth multi-kilowatt metalized Yb fiber amplifier[END_REF], [START_REF] Hawkins | Kilowatt power scaling of an intrinsically low Brillouin and thermo-optic Yb-doped silica fiber[END_REF]. As a conclusion, defining a systematic judicious choice of pump wavelength seems difficult, as it depends on the specific configuration of the laser.

VI. CONCLUSION

By modifying the fabrication process of our holmiumdoped fiber, we managed to reduce the diameter of the silica clad down to 105 µm, instead of 250 µm for the previous successful realization. Thanks to a better overlap between pump and active core, a lower holmium concentration and non-saturable absorption by PIQ, we achieve a signal power of 62 W at 2120 nm, with a slope efficiency of 60% considering the pump power at 1940 nm. We believe that this is the highest value reported so far for a clad-pumped single-mode continuous-wave holmium-doped fiber laser. We also report on the influence of the pump numerical aperture at the fiber input on the laser efficiency. Finally, we use our numerical simulation to show why the pump wavelength should be set to the peak holmium absorption for a high-power clad-pumped fiber laser.

Fig. 1 .

 1 Fig. 1. Setup of the clad-pumped holmium-doped fiber laser, relying on a single-mode thulium-doped fiber laser pump at 1940 nm.

Fig. 3 .

 3 Fig.3. Output powers for the signal (red dots) and residual pump (blue), for the optimal fiber length of 9 m, as a function of the coupled pump power. The dashed line is a linear fit with a slope of 60%.

Fig. 4 .

 4 Fig. 4. Absolute variation of the refractive index profile (RIP) of the holmiumdoped alumino-silicate fiber across the pedestal (65 µm diameter) and core (20 µm diameter), compared to the pure silica clad refractive index.

ACKNOWLEDGMENT

The authors are thankful to the french defense direction DGA for financial support.