Nonlinear Optics and Quantum Optics, Vol. 41, pp. 9–18 Reprints available directly from the publisher Photocopying permitted by license only

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Thermal Conductivity Measurement of Ytterbium doped Sesquioxides at Low Temperature V. Cardinali1 , E. Marmois1 , B. Le Garrec1 and G. Bourdet2 1 Commissariat

à l’Energie Atomique, Département Lasers de Puissance, B.P.2, 33114 Le Barp, France Email: [email protected] 2 Laboratoire pour l’Utilisation des Lasers Intenses, UMR, 7605, Ecole Polytechnique, 91128 Palaiseau Cedex, France Received: June 24, 2009. Accepted: October 25, 2009.

In this paper, we investigate laser performances of ytterbium doped Y2 O3 ceramics at room and at cryogenic temperatures. We show that at low temperature, laser performances are improved by leading experimental comparative studies of the laser performance of Yb:Y2 O3 : at room temperature, we have found 230 mJ, corresponding to a slope efficiency less than 20%, while at 77 K, we have obtained 570 mJ, corresponding to a slope efficiency of nearly 40%, in free running regime at 1 Hz with a 10 at. % doped Yb:Y2 O3 ceramic. Room temperature measurements, using both “Flash Laser” and “Hot Disk” methods, lead to thermal conductivity values of ytterbium doped Y2 O3 ceramics of 6.26 W/m.K and 5.27 W/m.K respectively. Keywords: Ytterbium, sesquioxides, ceramics, oscillator laser performances, thermal conductivity, cryogenic temperature.

INTRODUCTION High average power laser chains are intensively studied for Inertial Confinement Fusion applications that require high repetition rate and high beam quality. Nowadays, neodymium doped glass is the most commonly used laser material for solid-state lasers as, for example, on the National Ignition Facility (NIF) in the USA and for the Laser MegaJoule (LMJ) in France. Heat generation in solid-state media represents the main limiting feature for this type of lasers [1, 2]. It induces thermal distortions of the beam

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wave-front and perturbs the quality of the focused spot, preventing the use of high repetition rates. Diode-pumped solid-state lasers (DPSSL) have shown a very important breakthrough in high power laser technologies due to their high repetition rate which is essential for power production. In particular, ytterbium doped sesquioxides are acknowledged to be very promising solutions for high average power solid-state lasers [3]. The high melting temperatures of single crystal sesquioxides (∼2400◦ C) have always presented a limitation for the production of these materials. On the contrary, elaboration of transparent ceramics only requires to reach the sintering temperature of the material (∼1700◦ C), which allows to make ceramics of high optical quality and large dimensions. Sesquioxides represent very promising solutions for high average power solid-state lasers, mainly due to their thermal conductivity which is higher than e.g. that one of the widely used yttrium aluminium garnet (YAG). It is known that operating the laser medium at low temperature should lead to higher thermal conductivities than at room temperature. At 77 K, the thermal conductivity of undoped YAG is greater than 70 W/m.K, between 300 K and 77 K, the value of the thermooptic coefficient decreases of about a factor twelve while the value of the thermal expansion coefficient decreases by four [4]. Following the Callaway model [5], we expect the thermal conductivities of sesquioxides to reach their maximum between 10 and 100 K. But polycrystalline materials have a lower thermal conductivity than single crystals in this range of temperatures [6]. In this paper, we investigate ceramic performances of ytterbium doped Y2 O3 as a laser material at different temperatures. We have also measured its thermal conductivity at room temperature.

LASER DESIGN Ytterbium ions are known to present three main advantages compared to neodymium ions: – The electronic scheme of the ytterbium ion is made of only two electronic levels (see Fig. 1). Therefore, it is impossible to have an absorption of the excited states, an up-conversion and a concentration quenching. – The quantum defect ηQ measures the amount of pump power that is dissipated as heat and reads: ηQ = 1 −

λpump λlaser

(1)

The ytterbium quantum defect is low compared to the neodymium quantum defect. Quantum defects depend of the laser host materials. As an example,

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Thermal Conductivity Measurement of Y2 O3 Sesquioxides at Low Temperature 11

(a)

(b)

FIGURE 1 Electronic schemes of neodymium (a) and ytterbium (b) in YAG host materials.

in a Y3Al5 O12 (YAG) host material, when pumping the 1–6 transition and for laser emission on the 5–3 transition, the ytterbium quantum defect is approximately of 9% against approximately 24% for the 4 F3/2 -4 I11/2 transition, in neodymium. Therefore, the energy lost by heat dissipation inside the material is reduced. – The excited state lifetime of the ytterbium ion is three times longer than that of the neodymium ion (1 ms against 250 µs for Nd) and best energy storage can be obtained in the case of ytterbium ion. At room temperature, a Yb doped laser is a quasi-three level system in which the terminal level of the laser transition is close to the fundamental level. However, it has been shown that at low temperature [7], the system acts as a four level system and at high temperature, the system acts as a three level system. Cryogenic cooling and experimental set-up In our experiment, in order to improve the thermo-optic properties of our laser materials, we have decided to work at cryogenic temperature by using a JANIS® cryostat, model ST-100. The ceramic is set on a copper holder (see Fig. 2). The thermal contact between the laser disk and the copper holder is ensured by a 127 µm thick pure indium foil. A XRP-60S dewar (Cryodiffusion®) feeds the cryostat with liquid nitrogen. With this system, the temperature of the laser material goes down to 77 K. The cryostat has a thermal resistance that allows fixing the temperature of the cryostat to the desired temperature. The cryostat has also two thermocouples: the first gives the temperature inside the cryostat, and the second gives the temperature of the laser material. We have used a 20 mm diameter, 2 mm thick disk of 10 at. % ytterbium doped sesquioxide of yttrium, Y2 O3 . The ceramic used in our experiment has

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been supplied by Konoshima Chemical Co., Japan. The front side of the disk is anti-reflection coated from 900 nm to 1100 nm and the rear side is highly reflective coated from 900 nm to 1100 nm. The disk is pumped with a laser diode stack (Jenoptik Laserdiode®) made from 25 microlenses collimated diode bars. The stack can deliver 1ms pump pulses with a repetition rate of 1 to 10 Hz. The laser diode energy and wavelength depend on the current (from 0 to 100 A) and on the temperature of the cooling liquid (from 10◦ C to 40◦ C) going through them. Taking into account these two parameters, the laser diode wavelength can vary from 930 nm to 945 nm and a maximum energy of 2.3 J can be reached for a 100 A current, a pump pulse of 1 ms with a repetition rate of 1 Hz and a cooling liquid temperature of 10◦ C. The pump radiation is focused on the disk in an elliptical spot using a system of lenses shown on Fig. 2. The diameter at 1/e2 of the pump spot is 2.5 mm in

FIGURE 2 Experimental set up.

FIGURE 3 3D and 2D representations of the pump spot for a cooling liquid temperature of 20◦ C, a current of 30 A, a pump pulse of 1 ms with a repetition rate of 10 Hz. The intensity scale is from 0 to 30 kW/cm2 .

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the horizontal direction and of 1.3 mm in the vertical direction (Fig. 3). The maximum energy deposited in the sample reaches 1.55 J for a temperature of the cooling system of 40◦ C, a pump pulse of 1 ms with a repetition rate of 1 Hz and a laser diode current of 100 A. This corresponds to a maximum pump intensity of 121.5 kW/cm2 . Taking into account the transmission of the cryostat window, we have in reality, obtained an energy of 1.53 J corresponding to an intensity of 119.7 kW/cm2 . The angle between the pump radiation and the cavity laser is of 30◦ (Fig. 2). The laser cavity is made of the high reflective coating laser disk and of a plane output coupler with a 95, 80 or 70% reflectivity. The cavity length is of 40 cm and is stabilized with a spherical lens of 10 m focal length set at the centre of the cavity. Oscillator performances The output energy obtained versus pump energy has been measured for various values of the copper holder temperature. The results are summarized on Fig. 4 and on Table 1.

Output Energy (mJ)

600 500 400 300 200

77 K Coupler 70% 120 K 170 K 220 K 295 K Coupler 95%

100 0 0

200

400

600

800

1000

1200

1400

1600

Pump Energy (mJ)

FIGURE 4 Output energy versus pump energy for a 2 mm thick 10 at. % doped Yb:Y2 O3 disk for 77 K, 120 K, 170 K, 220 K and 295 K. Cooling liquid temperature of laser diodes is 40◦ C, pump pulse duration is of 1 ms with a repetition rate of 1 Hz.

T

Output Coupler

Slope

Pump Threshold

77 K 120 K 170 K 220 K 295 K

70% 70% 70% 70% 95%

39.3% 37.8% 31.3% 24.4% 17.8%

95.5 mJ 114.2 mJ 133.6 mJ 302.6 mJ 151.7 mJ

TABLE 1 Slope efficiencies and pump thresholds corresponding to the curves shown on Fig. 4

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FIGURE 5 Emission spectrum of Yb:Y2 O3 oscillator versus laser disk temperature.

By optimizing both the reflectivity of the output coupler and the wavelength emitted by the laser diodes [7], we have obtained a maximum output energy of 570 mJ with a slope efficiency of 39.3% for a Yb:Y2 O3 disk cooled at 77 K, with a 70% reflectivity output coupler and a pump wavelength centred at 943 nm, corresponding to a cooling liquid temperature of 40◦ C. We find that there is no laser emission at 295 K with an output reflectivity of 70%, a cooling liquid of 40◦ , a pump pulse of 1 ms and a repetition rate of 1 Hz. We see that the slope efficiency increases when the temperature of the copper holder decreases. This can be explained by an increase of the emission cross section of the material when the temperature decreases [8]. Besides, the pump threshold is lower at low temperature than at room temperature. Indeed, at low temperature, the thermal population of the lower-laser-level is strongly reduced and the reabsorption phenomenon almost disappears. We have also measured the emission laser wavelength for different temperatures of the copper holder (Fig. 5). The results have been obtained for a laser diode cooling liquid temperature of 40◦ C, a pump pulse of 1 ms with a repetition rate of 1 Hz and an output coupler reflectivity of 95%. At room temperature, we have found that Yb:Y2 O3 worked at the wavelength of 1076 nm which corresponds to the first sublevel of the 2 F5/2 manifold to the fourth sublevel of the 2 F7/2 manifold transition (the 5–4 transition). At cryogenic temperature, the emission wavelength shifts to 1030 nm which corresponds to the first sublevel of the 2 F5/2 manifold to the third sublevel of the 2F 7/2 manifold transition (the 5–3 transition).

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We can see that the laser emission shifts towards short wavelengths at low temperatures. For high temperatures, the gain is greater at 1076 nm than at 1030 nm. Even if the emission cross section is lower at 1076 nm than at 1030 nm, reabsorption is lower at 1076 nm than at 1030 nm: the thermal population of the level 3 is higher than the one of the level 4. In this case, we have a three level laser system. When the temperature decreases, Stark sublevels are less populated and reabsorption phenomena are reduced. Therefore, at low temperature, the favoured transition is 5–3. We have a four level laser system.

THERMAL CONDUCTIVITY MEASUREMENT “Flash” method We first measured the thermal conductivity κ with the well known “flash” method at room temperature. This method consists in illuminating the front face of the material with a pulse laser. The temperature of the material increases and is recorded at the rear face of the material as a function of time. The thermal diffusivity is determined by using the Parker equation [9]; it depends on the thickness of the sample L and on the time at which the thermogram reaches half of the maximum temperature (t1/2 ): β = 1.38

L2 π 2t

(2)

1/2

Thermal conductivity is deduced from the measured value of the thermal diffusivity, using the following equation: κ = ρβCp

(3)

Here ρ represents the density, Cp is the specific heat and β is the value of the thermal diffusivity measured with the “flash” method. Thermal diffusivity has been measured by the LEMTA (Laboratoire d’Energétique et de Mécanique Théorique Appliquée, Nancy, France) at room temperature on Y2 O3 10% doped ytterbium sample. The thermal diffusivity β is 2.7428.10−6 m2 .s−1 . The density ρ of the material [10] is 5035 kg.m−3 and the heat capacity [11] Cp is 453.54 J.kg −1 .K−1 . The thermal conductivity of 10 at. % Yb:Y2 O3 room temperature is obtained from equation (3) and is 6.26 W/m.K ± 10%. “Hot disk” method This technique allows a direct measurement of the thermal conductivity of the material. The probe is a double spiral of nickel metal between two insulating kapton layers. The sensor is placed between two identical pieces of the sample to be measured. During the measurement, a current passes through the nickel

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FIGURE 6 Thermal conductivity of Yb:Y2 O3 as a function of the doping level in at.

and creates an increase of temperature. The heat generated dissipates on either sides of the sample. Thermal conductivity of the material is determined by recording the temperature versus the time response in the sensor. The thermal diffusivity and the heat capacity are estimated from these results. Thermal conductivity on a 10 at. % Yb:Y2 O3 disk has been made by Neotim society (Albi, France) at room temperature. Thermal conductivity is 5.27 W/m.K ± 5%. The thermal conductivity value measured by the “hot disk” method is lower than the one calculated by the “flash” method. Two disks of 10 at. % Yb:Y2 O3 with 3 mm and 4 mm thickness have been used to measure the thermal conductivity with the “hot disk” method. However, the “hot disk” method needs to have two identical samples with the same thickness. Besides, we have estimated the penetration depth of the heat in the material. It is of 3.11 mm. This value is close to the thickness of the sample. Therefore, thicker and identical materials would be more appropriate for this method. In the literature, we found a thermal conductivity value for undoped Y2 O3 ceramic of 13 W/m.K at room temperature [12]. Thermal conductivity decreases when the doping level increases because of the disorder created in the crystal by introducing foreign ions: phonons are slowed down [13]. According to Ref. 13, there is a simple model that can predict the thermal conductivity of doped crystals [7, 13]. This model shows that the thermal conductivity of Yb doped Y2 O3 decreases with the doping level. Fig. 6 illustrates the results of the model up to 20 at. %, leading to a thermal conductivity of 7 W/m.K in our case (10 at. % Yb:Y2 O3 ). So far, by taking into account the

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experimental errors, our results from both methods are in good agreement with the computed value. Thermal conductivity is also a function of temperature. Ref. 12 illustrates the temperature dependence: the value of the thermal conductivity of an undoped Y2 O3 ceramic at 298 K is multiplied by a factor four at a temperature of 90 K. In our case, we expect the thermal conductivity to reach a maximum value between 10 and 100 K.

CONCLUSION By using two different methods, the “flash” method and the “hot disk” method, the thermal conductivities of a 10 at. % Yb:Y2 O3 ceramic has been found to be of 6.26 and of 5.27 W/m.K at room temperature respectively. We plan to use the “hot disk” method for future measurements at cryogenic temperatures. We will perform thermal conductivity measurement with both undoped and doped Y2 O3 ceramic. Among sesquioxides, scandia Sc2 O3 and lutetia Lu2 O3 are also good candidates for laser operation at high Yb3+ doping level (10%). There are few values concerning their thermal conductivities. Most of the time, either the material’s temperature or the doping level is not known at all. We will thus perform thermal conductivity measurements on Sc2 O3 and Lu2 O3 ceramics for both undoped and 10 at. % ytterbium doped at room and cryogenic temperatures.

REFERENCES [1] Koechner, W. Thermal lensing in a Nd:YAG laser rod. Applied Optics 9(11) (1970), 2548–2553. [2] Fan, T. Heat generation in Nd:YAG and Yb:YAG. IEEE J. of Quantum Electronics 29(6) (1993), 1457–1459. [3] Le Garrec, B., Bourdet, G. and Cardinali, V. Comparison of potential ceramic gain media. to be published in Fusion Science and Technology. [4] Brown, D. The promise of Cryogenic Solid-State Lasers. IEEE J. Sel. Topics Quantum Electron. 11(3) (2005), 587–599. [5] Numazawa, T., Arai, O., Hu, Q. and Noda, T. Thermal conductivity measurements for evaluation of crystal perfection at low temperatures. Meas. Sci. Technol. 12 (2001), 2089– 2094. [6] Yagi, H., Yanagitani, T., Numazawa, T. and Ueda, K. The physical properties of transparent Y3Al5 O12 elastic modulus at high temperature and thermal conductivity at low temperature. Ceram. Inter, 2006. [7] Casagrande, O. Theoretical and experimental study of an Yb-doped solid-state laser either single crystal or ceramic for high average power generation. PhD Thesis, Ecole Polytechnique, Paris (in French), 2007. [8] Garcia, A., Guillen, F., Jubera, V., Le Garrec, B. and Cardinali, V. Emission and absorption spectra of ytterbium doped ceramic sesquioxides: Sc2 O3 , Y2 O3 and Lu2 O3 . Poster Presented at ICL’O8 Conference, Lyon, France, 2008.

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[9] Parker, W., Jenkins, W., Butler, C. and Abbot, G. Flash method of determining thermal diffusivity, heat capacity and thermal conductivity. J. Appl. Phys. 32(9) (1961), 1679–1684. [10] Laversenne, L. Nouvelle méthode de chimie combinatoire pour l’optimisation des propriétés spectroscopiques des ions terres rares laser Yb3+ , Er3+ et Ho3+ dans des fibres monocristallines de sesquioxydes réfractaires M2 O3 (M = Y, Sc, Lu, Gd). PhD Thesis, Université Claude Bernard, Lyon, (in French), 2002. [11] Leitner, J., Chuchvalec, P., Sedmidubsky, D., Strejc, A. and Abrman P. Estimation of heat capacities of solid state mixed oxides. Thermochimica Acta 395(1–2–3) (2002), 27–46. [12] Fan, T., Ripin, D., Aggarwal, R., Ochoa, J., Chann, B., Tilleman, M. and Spitzberg, J. Cryogenic Yb3+-Doped solid-State Lasers. IEEE J. Sel. Topics Quantum Electron. 13(3) (2007), 448–459. [13] Gaume, R., Viana, B., Vivien, D., Roger, J.-P. and Fournier, D.Asimple model for prediction of thermal conductivity in pure and doped insulating crystals. Applied Physics Letters 83(7) (2003), 1355–1357.

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