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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 20712–20722
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Thermal and laser properties of Yb:LuAG for kW thin disk lasers

Kolja Beil, Susanne T. Fredrich-Thornton, Friedjof Tellkamp, Rigo Peters, Christian Kränkel, Klaus Petermann, and Günter Huber  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 20712-20722 (2010)
http://dx.doi.org/10.1364/OE.18.020712


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Abstract

Thin disk laser experiments with Yb:LuAG (Yb:Lu3Al5O12) were performed leading to 5 kW of output power and an optical-to-optical efficiency exceeding 60%. Comparative analyses of the laser relevant parameters of Yb:LuAG and Yb:YAG were carried out. While the spectroscopic properties were found to be nearly identical, investigations of the thermal conductivities revealed a 20% higher value for Yb:LuAG at Yb3+-doping concentrations of about 10%. Due to the superior thermal conductivity with respect to Yb:YAG, Yb:LuAG offers thus the potential of improved performance in high power thin disk laser applications.

© 2010 OSA

1. Introduction

In the last two decades the thin disk laser [1

1. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable Concept for Diode-Pumped High-Power Solid-State Lasers,” Appl. Phys. B 58, 365–372 (1994).

] has been proven to be a suitable laser design for multi-kW output power with high beam quality [2

2. A. Giesen and J. Speiser, “Fifteen Years of Work on Thin-Disk Lasers: Results and Scaling Laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007). [CrossRef]

]. To exploit the advantages of the thin disk laser, the thickness of the gain medium needs to be as low as possible for efficient heat removal. Therefore, high doping concentrations are required to allow for sufficient absorption.In addition, a high thermal conductivity is necessary to improve the heat transport to the heat sink. Up to now Yb3+-doped Y3Al5O12 (Yb:YAG) is the gain material of choice for most commercial applications: the Yb3+-ion exhibits a small quantum defect and a simple two-manifold energy level structure, avoiding detrimental loss processes like upconversion, cross relaxation, and excited state absorption, thus allowing high doping concentrations. In combination with the relatively strong coupling of the electronic 4f-4f-transitions to the phonons of the host lattice [3

3. A. Ellens, H. Andres, M. L. H. ter Heerdt, R. T. Wegh, A. Meijerink, and G. Blasse, “Spectral-line-broadening study of the trivalent lanthanide-ion series. II. The variation of the electron-phonon coupling strength through the series,” Phys. Rev. B 55(1), 180–186 (1997). [CrossRef]

], which leads to broad absorption lines, this laser ion is highly suitable for efficient high power diode laser pumping. Even though there is a rapid progress in the development of new, more efficient host materials for the Yb3+-ion, e. g. the sesquioxides [4

4. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]

], YAG is still preferred in commercial applications due to the possibility to grow large crystals in reproducible and very good optical quality by the well established Czochralski-technique. Furthermore, most of the newly developed Yb3+-doped gain materials for thin disk laser applications [5

5. C. Kränkel, R. Peters, K. Petermann, P. Loiseau, G. Aka, and G. Huber, “Efficient continuous-wave thin disk laser operation of Yb:Ca4YO(BO3)3 in EIIZ and EIIX orientations with 26 W output power,” J. Opt. Soc. Am. B 26(7), 1310–1314 (2009). [CrossRef]

7

7. C. R. E. Baer, C. Kränkel, O. H. Heckl, M. Golling, T. Südmeyer, R. Peters, K. Petermann, G. Huber, and U. Keller, “227-fs pulses from a mode-locked Yb:LuScO3 thin disk laser,” Opt. Express 17(13), 10725–10730 (2009). [CrossRef] [PubMed]

] are pumped at the zero phonon line around 975 nm, whereas Yb:YAG is pumped at a much broader absorption band around 940 nm. Using e.g. the sesquioxides in commercial applications will thus require the implementation of new pump diodes and new coating structures, optimized for the different pump wavelength, not to mention the challenges of the crystal growth [8

8. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Crystal growth by the heat exchanger method, spectroscopic characterization and laser operation of high-purity Yb:Lu2O3,” J. Cryst. Growth 310(7-9), 1934–1938 (2008). [CrossRef]

].

In contrast, Yb3+-doped Lu3Al5O12 (Yb:LuAG), which is examined in this work, is an alternative to Yb:YAG that would not require substantial changes in commercial applications as it has nearly identical optical properties compared to Yb:YAG and can be pumped at a similar wavelength with the same pump source. Like Yb:YAG, Yb:LuAG can also be simply fabricated by the Czochralski-technique. But compared to Yb:YAG, where the Yb3+-ion of the atomic mass 173 g/mol substitutes an Y3+-ion of the atomic mass 89 g/mol, LuAG provides Lu3+-sites (mass 175 g/mol) for the dopant ion. This very low mass difference of the dopant and the substituted ion leads to a low phonon scattering rate [9

9. P. G. Klemens, “Thermal Resistance due to Point Defects at High Temperatures,” Phys. Rev. 119(2), 507–509 (1960). [CrossRef]

]. Thus, at high doping concentrations which are necessary for efficient thin disk laser operation, the thermal conductivity of Yb:LuAG is expected to be higher than that of Yb:YAG, even though the latter provides a better thermal conductivity for the undoped host [10

10. G. A. Slack and D. W. Oliver, “Thermal Conductivity of Garnets and Phonon Scattering by Rare-Earth Ions,” Phys. Rev. B 4(2), 592–609 (1971). [CrossRef]

12

12. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

]. A similar approach led to the development of many other very suitable host materials for the Yb3+-ion containing lutetium instead of yttrium, e.g. LuVO4 [13

13. J. Liu, V. Petrov, H. Zhang, J. Wang, and M. Jiang, “High-power laser performance of a-cut and c-cut Yb:LuVO4 crystals,” Opt. Lett. 31(22), 3294–3296 (2006). [CrossRef] [PubMed]

], KLu(WO4)2 [14

14. G. Palmer, M. Schultze, M. Siegel, M. Emons, U. Bünting, and U. Morgner, “Passively mode-locked Yb:KLu(WO4)2 thin-disk oscillator operated in the positive and negative dispersion regime,” Opt. Lett. 33(14), 1608–1610 (2008). [CrossRef] [PubMed]

], LiLuF4 [15

15. A. Bensalah, Y. Guyot, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Spectroscopic properties of Yb3+:LuLiF4 crystal grown by the Czochralski method for laser applications and evaluation of quenching processes: a comparison with Yb3+:YLiF4,” J. Alloy. Comp. 380(1-2), 15–26 (2004). [CrossRef]

], and also Lu2O3 [4

4. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]

].

2. Fabrication, spectroscopic and thermal investigations

2.1 Crystal growth

Table 1. Structural and thermal properties of YAG, LuAG, and YbAG

table-icon
View This Table

For the determination of the Yb3+-concentration dependency of the thermal conductivity Yb:LuAG crystals of different Yb3+-doping concentrations were grown. In addition, two high quality 10% and 15% (with respect to the dodecahedral site) Yb3+-doped LuAG crystals were grown for laser experiments. By scanning electron microscopy with energy dispersive X-ray spectrometry (SEM/EDS) the Yb3+-distribution coefficient of both crystals was determined to be 1.0. This indicates a more homogeneous doping concentration in contrast to YAG, which exhibits a distribution coefficient of 1.1 to 1.2.

2.2 Spectroscopic investigations

Fluorescence lifetime measurements applying the pinhole method [27

27. H. Kühn, S. T. Fredrich-Thornton, C. Kränkel, R. Peters, and K. Petermann, “Model for the calculation of radiation trapping and description of the pinhole method,” Opt. Lett. 32(13), 1908–1910 (2007). [CrossRef] [PubMed]

,28

28. C. Kränkel, D. Fagundes-Peters, S. T. Fredrich, J. Johannsen, M. Mond, G. Huber, M. Bernhagen, and R. Uecker, “Continuous wave laser operation of Yb3+:YVO4,” Appl. Phys. B 79, 543–546 (2004). [CrossRef]

] resulted in 965 µs and 985 µs for the 10% and 15% doped Yb:LuAG, respectively. The value for the 10% doped crystal is lower than the value of 1317 µs for the same material reported by Brenier et al. [17

17. A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]

]. It is assumed that in [17

17. A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]

] reabsorption effects led to increased values for the measured lifetime, which are eliminated by the pinhole method. For the 15% Yb3+-doped crystal the corresponding value of 830 µs reported by Brenier et al. is much lower than the presented data above. In this case the explanation can probably be found in the lower purity of the crystals in [17

17. A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]

], which led to quenching of the fluorescence lifetime [16

16. D. Fagundes-Peters, N. Martynyuk, K. Lünstedt, V. Peters, K. Petermann, G. Huber, S. Basun, V. Laguta, and A. Hofstaetter, “High quantum efficiency YbAG-crystals,” J. Lumin. 125(1-2), 238–247 (2007). [CrossRef]

]. The lifetimes in this work obtained by the pinhole method are very similar to the 951 µs reported for Yb(16.5%):YAG investigated with the same method [27

27. H. Kühn, S. T. Fredrich-Thornton, C. Kränkel, R. Peters, and K. Petermann, “Model for the calculation of radiation trapping and description of the pinhole method,” Opt. Lett. 32(13), 1908–1910 (2007). [CrossRef] [PubMed]

].

The absorption cross sections were determined from transmission spectra of Yb(10%):LuAG and Yb(7%):YAG [29

29. K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, “Rare-earth-doped sesquioxides,” J. Lumin. 87–89, 973–975 (2000). [CrossRef]

] measured with a Varian CARY 5000 spectrophotometer with a spectral resolution of 0.6 nm. For the determination of the emission cross sections, fluorescence spectra were recorded with a Fourier-transform spectrometer (Equinox 55, Bruker Optik GmbH, Germany) at a resolution of 0.5 cm−1. As the results of the Füchtbauer-Ladenburg method [30

30. P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3(1), 125–132 (1986). [CrossRef]

] are influenced by reabsorption in the short wavelength range and the reciprocity method [31

31. D. E. McCumber, “Einstein Relations Connecting Broadband Emission and Absorption Spectra,” Phys. Rev. 136, A954–957 (1964). [CrossRef]

] results in a weak signal to noise ratio in the longer wavelength range, a combination of the resulting spectra was used to avoid both effects. In this way, reliable values for the emission cross sections σem over the whole emission bandwidth of the Yb3+-ion were obtained.

As the ratio of the partition functions Zu and Zl is needed, the reciprocity relation requires the exact knowledge of the energetic positions of the three Stark energy levels of the upper 2F5/2 and the four Stark levels of the lower 2F7/2 multiplet of the Yb3+-ion:
σem(ν)=σabs(ν)ZlZuexp(EZPLhνkT),
(1)
where σabs is the absorption cross section at frequency ν, EZPL the energy of the zero phonon line (energy difference between the lowest Stark levels of the two multiplets), h the Planck constant, k the Boltzmann constant, and T the temperature. In garnets like Yb:YAG or Yb:LuAG the Stark levels are difficult to identify due to several additional lines in the low temperature spectra and many different values for their energetic positions can be found in the literature [17

17. A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]

,32

32. R. A. Buchanan, K. A. Wickersheim, J. J. Pearson, and G. F. Herrmann, “Energy Levels of Yb3+ in Gallium and Aluminum Garnets. I. Spectra,” Phys. Rev. 159(2), 245–251 (1967). [CrossRef]

35

35. G. A. Bogomolova, L. A. Bumagina, A. A. Kaminskii, and B. Z. Malkin, “Crystal field in laser garnets with TR3+ ions in the exchange charge model,” Sov. Phys. Solid State 19 (1977).

]. To obtain comparable spectra, the Stark level energies for Yb3+ in YAG and LuAG given in [17

17. A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]

] were used, as these were determined under the same conditions for both materials. The resulting room temperature absorption and emission cross section spectra for Yb:YAG and Yb:LuAG are shown in Fig. 1
Fig. 1 (Color online) Comparison of the absorption and emission cross sections of Yb:YAG and Yb:LuAG. The different scaling of the y-axis for the upper and lower graph should be noted.
, where the vertical line marks the changeover between the results of the reciprocity and the Füchtbauer-Ladenburg method. As expected, due to the similarity of both cubic Ia3¯d host materials (see Tab. 1) the spectra of the materials are nearly identical.

The absorption maximum of Yb:YAG at 941 nm with a cross section of 8.20 × 10−21 cm2 is about 14% higher than the absorption maximum of Yb:LuAG at 940 nm (7.22 × 10−21 cm2). However, this difference becomes less important when considering the emission bandwidth of high power laser diodes. A convolution of the absorption spectra of Yb:YAG and Yb:LuAG with a Gaussian curve simulating the emission spectrum of a high power laser diode revealed that for a realistic bandwidth of 5 nm the effective maximum absorption only differs by about 5%. It has to be mentioned, that in this case the highest absorption in Yb:LuAG is obtained for a center wavelength of 938 nm, whereas for Yb:YAG it remains at 941 nm. However, both pump wavelengths can be covered with standard Yb:YAG laser diodes by temperature tuning of about 10 K [36

36. J. Kawanaka, H. Nishioka, N. Inoue, and K. Ueda, “Tunable continuous-wave Yb:YLF laser operation with a diode-pumped chirped-pulse amplification system,” Appl. Opt. 40(21), 3542–3546 (2001). [CrossRef]

].

In contrast, the emission cross section at the laser wavelength around 1030 nm is about 20% higher for Yb:LuAG (σem = 2.59 × 10−20 cm2) than for Yb:YAG (σem = 2.14 × 10−20 cm2). This results in a slightly lower threshold for Yb:LuAG which contributes to a good pump light absorption, because the bleaching at the pump wavelength is less pronounced than in case of Yb:YAG. Also, the extractable gain for the laser wavelength in Yb:LuAG is higher, allowing for a higher transmission of the output coupling mirror which makes the resonator more tolerant with respect to intracavity losses.

2.3 Thermal conductivity

The thermal conductivity κ of a solid state material is given by the relation
κ=cpρα,
(2)
where cp is the specific heat capacity, ρ is the density and α is the thermal diffusivity. While the specific heat capacity and the density exhibit a nearly linear change with increasing doping concentration, the dependency of the thermal diffusivity on the doping concentration is more complicated. In insulator materials like oxide crystals the heat transport occurs mainly via phonon propagation due to the lack of mobile conduction band electrons, which provide the main contribution to heat transport in metals. For the undoped crystals LuAG and YAG as well as for YbAG, which results from a complete substitution of the Lu3+- and Y3+-ions, respectively with Yb3+-ions, the crystal order is high. This results in a low phonon scattering rate and thus in a high thermal diffusivity. In contrast, a doped crystal exhibits a certain degree of disorder, leading to a decrease in thermal diffusivity with increasing Yb3+-doping concentration [12

12. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

,26

26. F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser Demonstration of Yb3Al5O12 (YbAG) and Materials Properties of Highly Doped Yb:YAG,” IEEE J. Quantum Electron. 37(1), 135–144 (2001). [CrossRef]

]. One can intuitively understand that the disorder due to Yb3+-doping is larger in the YAG lattice than in the LuAG lattice due to the very large mass difference between Y3+-ions and Yb3+-ions (see Tab. 1). Thus, despite the fact that for the undoped YAG the thermal diffusivity (and also the thermal conductivity) is higher than for LuAG, this is not necessarily the case for higher Yb3+-concentrations.

To evaluate the Yb3+-concentration dependency of the thermal conductivity in Yb:LuAG and Yb:YAG the thermal diffusivities at room temperature were measured for crystals with different doping concentrations using an ai-Phase Mobile 1 (ai-Phase CO, Ltd., Japan) which is based on the temperature wave analysis [37

37. J. Morikawa, C. Leong, T. Hashimoto, T. Ogawa, Y. Urata, S. Wada, M. Higuchi, and J. Takahashi, “Thermal conductivity/diffusivity of Nd3+ doped GdVO4, YVO4, LuVO4, and Y3Al5O12 by temperature wave analysis,” J. Appl. Phys. 103, 063522 (2008). [CrossRef]

]. According to the Neumann-Kopp rule [38

38. E. S. R. Gopal, Specific Heats at Low Temperatures (Plenum Press, New York, 1966).

], the specific heat capacities for the examined doping concentrations were linearly interpolated from literature values for undoped YAG, LuAG and YbAG (see Tab. 1). The shift of the density due to a linear change of the lattice constant with increasing Yb3+-concentration [11

11. Y. Kuwano, K. Suda, N. Ishizawa, and T. Yamada, “Crystal growth and properties of (Lu,Y)3Al5O12,” J. Cryst. Growth 260(1-2), 159–165 (2004). [CrossRef]

,39

39. X. Xu, Z. Zhao, P. Song, G. Zhou, J. Xu, and P. Deng, “Structural, thermal, and luminescent properties of Yb-doped Y3Al5O12 crystals,” J. Opt. Soc. Am. B 21(3), 543–547 (2004). [CrossRef]

] and the mass difference of Yb3+ and the substituted ion were also taken into account. The resulting thermal conductivities obtained from Eq. (2) are shown in Fig. 2
Fig. 2 (Color online) Dependency of thermal conductivity κ of Yb:LuAG and Yb:YAG on the Yb3+-doping concentration. Due to the nearly identical cation densities in both materials (see Tab. 1), identical percentage-values correspond to very similar Yb3+-densities. Symbols represent the measured data while the curves represent the fits according to Eq. (3).
.

If the thermal conductivities for the undoped (κ0) and 100% doped (κ100) material are known, the doping concentration dependency of the thermal conductivity κ can be calculated by the following equation [9

9. P. G. Klemens, “Thermal Resistance due to Point Defects at High Temperatures,” Phys. Rev. 119(2), 507–509 (1960). [CrossRef]

]:
κ=κmχTεarctan(εχT),
(3)
with the abbreviations
ε=c(1c)(msmd)2(cms+(1c)md)2    and    κm=(1c)κ0+cκ100, (4,
5)
where χ is a constant describing the strength of the phonon scattering, T is the temperature, c is the doping concentration, ms is the mass of the substituted ion (Y3+ or Lu3+), and md is the mass of the dopant ion (Yb3+). With fixed κ0 and κ100 the fit is in good agreement with the measured data (see Fig. 2).

The measurements presented in Fig. 2 show, that indeed the room temperature thermal conductivity of undoped YAG (9.5 W/(m·K)) is by about 20% higher than for undoped LuAG (7.7 W/(m·K)). However, according to the fit, κ becomes already equal for both materials at an Yb3+-concentration of about 3% due to a much stronger decrease with Yb3+-concentration in Yb:YAG. For an Yb3+-concentration of 10%, which is a typical doping concentration used in thin disk lasers, both the fit and the experimental data result in a 20% higher thermal conductivity for Yb:LuAG (7.4 W/(m·K)) than for Yb:YAG (6.1 W/(m·K)). Fan et al. have defined the thermo-optic figure of merit FOM [40

40. T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-Doped Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007). [CrossRef]

]:
FOM=κχQL|dn/dT|    with    χQL=λlasλpump1, (6,
7)
where λlas is the laser and and λpump the pump wavelength, respectively. For Yb(10%):LuAG this FOM-value is 10% higher in comparison to Yb(10%):YAG.

It has to be mentioned, that at a measurement error of just 5% for the thermal diffusivity, the data shown in Fig. 2 are about 10% lower than previously reported thermal conductivities for Yb:YAG with comparable doping concentrations [12

12. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

,26

26. F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser Demonstration of Yb3Al5O12 (YbAG) and Materials Properties of Highly Doped Yb:YAG,” IEEE J. Quantum Electron. 37(1), 135–144 (2001). [CrossRef]

,41

41. R. Gaumé, B. Viana, D. Vivien, J.-P. Roger, and D. Fournier, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. 83(7), 1355–1357 (2003). [CrossRef]

]. Although an accurate determination of the thermal conductivity is difficult (cf. Tab. 1), e. g. due to the uncertainty of cp, it cannot be excluded that this is a general issue of the temperature wave method compared to the more common laser-flash method [42

42. W. J. Parker, R. J. Jenkins, C. P. Butler, and G. L. Abbott, “Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity,” J. Appl. Phys. 32(9), 1679–1684 (1961). [CrossRef]

]. However, the ratios between the Yb:LuAG and Yb:YAG values should not be affected.

3. Laser experiments

3.1 Theoretical considerations

For comparison of 10% Yb3+-doped LuAG and YAG, internal losses of 0.1% and pump intensities of 6 kW/cm2 at a pump wavelength of the 940-nm-peak are assumed, which are typical values for such simulations [44

44. K. Contag, Modellierung und numerische Auslegung des Yb:YAG Scheibenlasers (PhD-thesis, IFSW, University of Stuttgart, 2002).

]. Figure 3a
Fig. 3 (Color online) (a) Theoretical values for the maximum optical-to-optical efficiencies of Yb(10%):LuAG and Yb(10%):YAG in dependence of the thickness of the disk according to the zero-dimensional model [43]. (b) Average heating of the disk (ΔTav) with reference to the cooling temperature for pump intensities between 4 kW/cm2 and 10 kW/cm2 for Yb:LuAG and Yb:YAG at their respective optimum disk thicknesses extracted from Fig. 3a. All fit parameters are given in the graphs.
shows the optical-to-optical efficiency for an output coupling transmittance of 3%. The rise of the optical-to-optical efficiency with increasing disk thickness is based on the improvement of the absorption efficiency. Due to the effect of reabsorption at the laser wavelength, the laser threshold is also increasing with the disk thickness and becomes dominant at thicker disks decreasing the optical-to-optical efficiency. This results in an optimum thickness of 185 µm for Yb(10%):YAG. Because of the slightly lower absorption efficiency at this pump wavelength, the optimum thickness of 200 µm for Yb(10%):LuAG is a bit larger . But as shown in Fig. 3a, in the range from about 160 µm to 230 µm the efficiency is just varying by about 0.5% or less. In this region Yb(10%):LuAG and Yb(10%):YAG can be considered having practically the same optical-to-optical efficiency. For both optimum disks the fraction of absorbed pump power after 24 pump light passes is calculated to be higher than 98.8%. As the quantum defect and Yb3+-densities can be considered identical in Yb:LuAG and Yb:YAG (see Tab. 1), the thermal load is almost the same for both materials.

3.2 Experimental results

The disks, prepared with different thicknesses around the optimum values, had an anti-reflective coating for the pump and the laser wavelength on their front side. On their backside, being mounted onto a water-cooled copper heat sink a highly reflective coating for the pump and the laser wavelength was applied.

For the demonstration of the first thin disk laser operation with Yb:LuAG, a commercial thin disk laser pump head (TGSW Stuttgart, Germany) aligned for 24 pump passes through the active medium was used. A 600 µm fiber-coupled laser diode (JENOPTIK Laserdiode GmbH, Germany) which was imaged onto a 1.2 mm pump spot on the disk served as pump source. In these experiments the diode emission wavelength was tuned by adapting the cooling temperature to match the absorption of Yb:LuAG at 938 nm. The multimode I-cavity was formed simply by the HR-backside of the disk and one curved output mirror.

In Fig. 4a
Fig. 4 (Color online) (a) Input-output characteristics of Yb:LuAG and Yb:YAG with similar disk thicknesses in comparison. (b) Measured slope efficiencies of a 200 µm thick Yb:LuAG disk for different output coupler transmissions between 0.4% and 4.0% with 1.2 mm pump spot diameter and 40 W of incident pump power.
the laser characteristics of Yb:LuAG and Yb:YAG disks with nearly identical doping concentrations and thicknesses, pumped with the same laser diode at their respective optimum pump wavelengths are presented. The materials exhibit a very similar laser performance with slope efficiencies of more than 70% and an identical optical-to-optical efficiency of 62% for each disk.Although the thickness of the Yb:LuAG disk is lower than the optimum value of 200 µm, no remarkable difference in efficiency is expected as can be seen in Fig. 3a. This comparison demonstrates that Yb:LuAG is very well suited as alternative gain material to Yb:YAG in the thin disk laser setup. For higher power experiments, where heat removal is crucial, Yb:LuAG is expected to benefit more from its better thermal conductivity.

Figure 4b shows the dependency of the slope efficiency on the transmission TOC of the output coupling mirror at the laser wavelength for a Yb(10%):LuAG disk of 220 µm thickness. It can be seen that the best results in this power region were obtained for TOC between 1.5% and 3.5%. This crystal also delivered the highest slope efficiency of all examined Yb:LuAG disks with 72% at TOC = 2.2%.

To prove the suitability of Yb:LuAG for output powers in the kW-regime, first high power experiments were performed at Trumpf Laser GmbH & Co. KG. The 11% Yb3+-doped crystals were grown, prepared, and mounted under the same conditions (and by the same suppliers) as the standard Yb:YAG crystals usually used in commercially available Trumpf-Lasers. In Fig. 5
Fig. 5 (Color online) Comparable input-output characteristics and optical-to-optical efficiencies of Yb:LuAG and Yb:YAG for optimized Yb:YAG laser operation (courtesy of Trumpf Laser GmbH & Co. KG).
the laser characteristics of the Yb:LuAG and the Yb:YAG disks are shown, obtained using a thin disk laser setup, which was optimized for Yb:YAG. Both materials delivered maximum optical-to-optical efficiencies of more than 60%, comparable to the results in the low power experiments and output powers of 5.0 kW and 5.4 kW for Yb:LuAG and Yb:YAG, respectively.

As mentioned in the spectroscopic investigations section the optimum pump wavelength for Yb:LuAG would be 938 nm (see Fig. 1). However, in these initial experiments the cooling temperature of the pump diode laser was adjusted to perfectly fit the absorption of Yb:YAG at 941 nm at the maximum pump power of 9.2 kW. As a consequence, the emission wavelength of the diode laser shifted from shorter wavelengths to this value while increasing the pump power. Obviously, the optimum pump wavelength for Yb:LuAG is reached at a pump power around 4 kW (see Fig. 5), where the highest optical-to-optical efficiency for this material was obtained. The drop in efficiency for higher incident pump powers is thus attributed to a wavelength drift to even longer wavelengths and is not caused by a thermal rollover. Further experiments with a pump wavelength optimized for Yb:LuAG are in progress.

Nevertheless, it can be seen that the maximum optical-to-optical efficiency of Yb:LuAG of 61.9% is slightly higher than the maximum for Yb:YAG of 60.7%. From this fact it can be deduced that with an optimized pump wavelength, Yb:LuAG has the potential to deliver higher efficiencies and output powers.

4. Conclusion

This paper reports on the first thin disk laser operation with Yb:LuAG as gain material and presents a detailed analysis of the relevant laser parameters in comparison to Yb:YAG. While the spectroscopic properties of both materials are shown to be very similar, investigations of the thermal properties reveal a 20% higher thermal conductivity of Yb:LuAG at the typical doping concentrations used in thin disk lasers. Theoretical calculations suggest, that this should allow for higher pump power densities and thus higher laser output powers in kW-thin disk lasers, where heat removal is crucial.

Compared to other high efficiency thin disk laser materials as for example the Yb-doped sesquioxides [4

4. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]

] which are pumped at their zero phonon line around 975 nm, a major advantage of Yb:LuAG is its pump wavelength of 938 nm. This pump wavelength allows for the use of the same pump diodes and coatings like for the established Yb:YAG which is typically pumped at 940 nm.

In first thin disk laser experiments, with an output power of 25 W at 71% slope efficiency Yb(10%):LuAG delivered very similar laser properties compared to Yb(10%):YAG. Subsequent high power thin disk laser experiments performed at Trumpf Laser GmbH & Co KG did not yet demonstrate the advantage of Yb:LuAG, since the pump wavelength was adjusted for Yb:YAG in these experiments. However, the maximum optical-to-optical efficiency was even slightly higher for Yb:LuAG, promising a superior performance compared to Yb:YAG when operated the adequate pump wavelength. The maximum output power of 5 kW obtained in these experiments represents the highest that has ever been obtained with this material.

Acknowledgements

We thank the BMBF (contract no. 13N 8382) and the Joachim Herz Stiftung for their financial support. Furthermore, we would like to thank Trumpf Laser GmbH & Co. KG for performing the high power laser experiments and the accreditation to publish these data. We also thank Dr. H.-J. Bernhardt (Institute of Geology, Mineralogy and Geophysics, Bochum) for performing the EDS-measurements and Dr. D. Klimm (Institut für Kristallzüchtung, Berlin) for providing experimental and theoretical data for our thermal conductivity measurements.

References and links

1.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable Concept for Diode-Pumped High-Power Solid-State Lasers,” Appl. Phys. B 58, 365–372 (1994).

2.

A. Giesen and J. Speiser, “Fifteen Years of Work on Thin-Disk Lasers: Results and Scaling Laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007). [CrossRef]

3.

A. Ellens, H. Andres, M. L. H. ter Heerdt, R. T. Wegh, A. Meijerink, and G. Blasse, “Spectral-line-broadening study of the trivalent lanthanide-ion series. II. The variation of the electron-phonon coupling strength through the series,” Phys. Rev. B 55(1), 180–186 (1997). [CrossRef]

4.

R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]

5.

C. Kränkel, R. Peters, K. Petermann, P. Loiseau, G. Aka, and G. Huber, “Efficient continuous-wave thin disk laser operation of Yb:Ca4YO(BO3)3 in EIIZ and EIIX orientations with 26 W output power,” J. Opt. Soc. Am. B 26(7), 1310–1314 (2009). [CrossRef]

6.

C. Kränkel, J. Johannsen, R. Peters, K. Petermann, and G. Huber, “Continuous-wave high power laser operation and tunability of Yb:LaSc3(BO3)4 in thin disk configuration,” Appl. Phys. B 87(2), 217–220 (2007). [CrossRef]

7.

C. R. E. Baer, C. Kränkel, O. H. Heckl, M. Golling, T. Südmeyer, R. Peters, K. Petermann, G. Huber, and U. Keller, “227-fs pulses from a mode-locked Yb:LuScO3 thin disk laser,” Opt. Express 17(13), 10725–10730 (2009). [CrossRef] [PubMed]

8.

R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Crystal growth by the heat exchanger method, spectroscopic characterization and laser operation of high-purity Yb:Lu2O3,” J. Cryst. Growth 310(7-9), 1934–1938 (2008). [CrossRef]

9.

P. G. Klemens, “Thermal Resistance due to Point Defects at High Temperatures,” Phys. Rev. 119(2), 507–509 (1960). [CrossRef]

10.

G. A. Slack and D. W. Oliver, “Thermal Conductivity of Garnets and Phonon Scattering by Rare-Earth Ions,” Phys. Rev. B 4(2), 592–609 (1971). [CrossRef]

11.

Y. Kuwano, K. Suda, N. Ishizawa, and T. Yamada, “Crystal growth and properties of (Lu,Y)3Al5O12,” J. Cryst. Growth 260(1-2), 159–165 (2004). [CrossRef]

12.

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

13.

J. Liu, V. Petrov, H. Zhang, J. Wang, and M. Jiang, “High-power laser performance of a-cut and c-cut Yb:LuVO4 crystals,” Opt. Lett. 31(22), 3294–3296 (2006). [CrossRef] [PubMed]

14.

G. Palmer, M. Schultze, M. Siegel, M. Emons, U. Bünting, and U. Morgner, “Passively mode-locked Yb:KLu(WO4)2 thin-disk oscillator operated in the positive and negative dispersion regime,” Opt. Lett. 33(14), 1608–1610 (2008). [CrossRef] [PubMed]

15.

A. Bensalah, Y. Guyot, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Spectroscopic properties of Yb3+:LuLiF4 crystal grown by the Czochralski method for laser applications and evaluation of quenching processes: a comparison with Yb3+:YLiF4,” J. Alloy. Comp. 380(1-2), 15–26 (2004). [CrossRef]

16.

D. Fagundes-Peters, N. Martynyuk, K. Lünstedt, V. Peters, K. Petermann, G. Huber, S. Basun, V. Laguta, and A. Hofstaetter, “High quantum efficiency YbAG-crystals,” J. Lumin. 125(1-2), 238–247 (2007). [CrossRef]

17.

A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]

18.

J. L. Caslavsky and D. J. Viechnicki, “Melting behaviour and matastability of yttrium aluminium garnet (YAG) and YAlO3 determined by optical differential thermal analysis,” J. Mater. Sci. 15(7), 1709–1718 (1980). [CrossRef]

19.

H. Okamoto, “The Ir-Re (Iridium-Rhenium) System,” J. Phase Equilibria 13(6), 649–650 (1992). [CrossRef]

20.

F. Euler and J. A. Bruce, “Oxygen coordinates of compounds with garnet structure,” Acta Crystallogr. 19(6), 971–978 (1965). [CrossRef]

21.

A. A. Kaminskii, Laser Crystals: Their Physics and Properties (Springer Verlag, Heidelberg, 1990).

22.

T. B. Coplen, “Atomic Weights of the Elements 1999 Technical Report,” Pure Appl. Chem. 73(4), 667–683 (2001). [CrossRef]

23.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Heidelberg, Germany, 1999).

24.

D. Klimm, data from FactSage 5.3 (personal communication, 2009).

25.

N. P. Padture and P. G. Klemens, “Low Thermal Conductivity in Garnets,” J. Am. Ceram. Soc. 80(4), 1018–1020 (1997). [CrossRef]

26.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser Demonstration of Yb3Al5O12 (YbAG) and Materials Properties of Highly Doped Yb:YAG,” IEEE J. Quantum Electron. 37(1), 135–144 (2001). [CrossRef]

27.

H. Kühn, S. T. Fredrich-Thornton, C. Kränkel, R. Peters, and K. Petermann, “Model for the calculation of radiation trapping and description of the pinhole method,” Opt. Lett. 32(13), 1908–1910 (2007). [CrossRef] [PubMed]

28.

C. Kränkel, D. Fagundes-Peters, S. T. Fredrich, J. Johannsen, M. Mond, G. Huber, M. Bernhagen, and R. Uecker, “Continuous wave laser operation of Yb3+:YVO4,” Appl. Phys. B 79, 543–546 (2004). [CrossRef]

29.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, “Rare-earth-doped sesquioxides,” J. Lumin. 87–89, 973–975 (2000). [CrossRef]

30.

P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3(1), 125–132 (1986). [CrossRef]

31.

D. E. McCumber, “Einstein Relations Connecting Broadband Emission and Absorption Spectra,” Phys. Rev. 136, A954–957 (1964). [CrossRef]

32.

R. A. Buchanan, K. A. Wickersheim, J. J. Pearson, and G. F. Herrmann, “Energy Levels of Yb3+ in Gallium and Aluminum Garnets. I. Spectra,” Phys. Rev. 159(2), 245–251 (1967). [CrossRef]

33.

D. L. Wood, “Energy Levels of Yb3+ in Garnets,” J. Chem. Phys. 39(7), 1671–1673 (1963). [CrossRef]

34.

J. A. Koningstein, “Energy Levels and Crystal-field Calculations of Trivalent Ytterbium in Yttrium Aluminum Garnet and Yttrium Gallium Garnet,” Theor. Chim. Acta 3(3), 271–277 (1965). [CrossRef]

35.

G. A. Bogomolova, L. A. Bumagina, A. A. Kaminskii, and B. Z. Malkin, “Crystal field in laser garnets with TR3+ ions in the exchange charge model,” Sov. Phys. Solid State 19 (1977).

36.

J. Kawanaka, H. Nishioka, N. Inoue, and K. Ueda, “Tunable continuous-wave Yb:YLF laser operation with a diode-pumped chirped-pulse amplification system,” Appl. Opt. 40(21), 3542–3546 (2001). [CrossRef]

37.

J. Morikawa, C. Leong, T. Hashimoto, T. Ogawa, Y. Urata, S. Wada, M. Higuchi, and J. Takahashi, “Thermal conductivity/diffusivity of Nd3+ doped GdVO4, YVO4, LuVO4, and Y3Al5O12 by temperature wave analysis,” J. Appl. Phys. 103, 063522 (2008). [CrossRef]

38.

E. S. R. Gopal, Specific Heats at Low Temperatures (Plenum Press, New York, 1966).

39.

X. Xu, Z. Zhao, P. Song, G. Zhou, J. Xu, and P. Deng, “Structural, thermal, and luminescent properties of Yb-doped Y3Al5O12 crystals,” J. Opt. Soc. Am. B 21(3), 543–547 (2004). [CrossRef]

40.

T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-Doped Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007). [CrossRef]

41.

R. Gaumé, B. Viana, D. Vivien, J.-P. Roger, and D. Fournier, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. 83(7), 1355–1357 (2003). [CrossRef]

42.

W. J. Parker, R. J. Jenkins, C. P. Butler, and G. L. Abbott, “Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity,” J. Appl. Phys. 32(9), 1679–1684 (1961). [CrossRef]

43.

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modelling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29(8), 697–703 (1999). [CrossRef]

44.

K. Contag, Modellierung und numerische Auslegung des Yb:YAG Scheibenlasers (PhD-thesis, IFSW, University of Stuttgart, 2002).

OCIS Codes
(140.3380) Lasers and laser optics : Laser materials
(140.3480) Lasers and laser optics : Lasers, diode-pumped
(140.3580) Lasers and laser optics : Lasers, solid-state
(140.3615) Lasers and laser optics : Lasers, ytterbium

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 14, 2010
Revised Manuscript: August 16, 2010
Manuscript Accepted: August 20, 2010
Published: September 15, 2010

Citation
Kolja Beil, Susanne T. Fredrich-Thornton, Friedjof Tellkamp, Rigo Peters, Christian Kränkel, Klaus Petermann, and Günter Huber, "Thermal and laser properties of Yb:LuAG for kW thin disk lasers," Opt. Express 18, 20712-20722 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-20712


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References

  1. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable Concept for Diode-Pumped High-Power Solid-State Lasers,” Appl. Phys. B 58, 365–372 (1994).
  2. A. Giesen and J. Speiser, “Fifteen Years of Work on Thin-Disk Lasers: Results and Scaling Laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007). [CrossRef]
  3. A. Ellens, H. Andres, M. L. H. ter Heerdt, R. T. Wegh, A. Meijerink, and G. Blasse, “Spectral-line-broadening study of the trivalent lanthanide-ion series. II. The variation of the electron-phonon coupling strength through the series,” Phys. Rev. B 55(1), 180–186 (1997). [CrossRef]
  4. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Broadly tunable high-power Yb:Lu(2)O(3) thin disk laser with 80% slope efficiency,” Opt. Express 15(11), 7075–7082 (2007). [CrossRef] [PubMed]
  5. C. Kränkel, R. Peters, K. Petermann, P. Loiseau, G. Aka, and G. Huber, “Efficient continuous-wave thin disk laser operation of Yb:Ca4YO(BO3)3 in EIIZ and EIIX orientations with 26 W output power,” J. Opt. Soc. Am. B 26(7), 1310–1314 (2009). [CrossRef]
  6. C. Kränkel, J. Johannsen, R. Peters, K. Petermann, and G. Huber, “Continuous-wave high power laser operation and tunability of Yb:LaSc3(BO3)4 in thin disk configuration,” Appl. Phys. B 87(2), 217–220 (2007). [CrossRef]
  7. C. R. E. Baer, C. Kränkel, O. H. Heckl, M. Golling, T. Südmeyer, R. Peters, K. Petermann, G. Huber, and U. Keller, “227-fs pulses from a mode-locked Yb:LuScO3 thin disk laser,” Opt. Express 17(13), 10725–10730 (2009). [CrossRef] [PubMed]
  8. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Crystal growth by the heat exchanger method, spectroscopic characterization and laser operation of high-purity Yb:Lu2O3,” J. Cryst. Growth 310(7-9), 1934–1938 (2008). [CrossRef]
  9. P. G. Klemens, “Thermal Resistance due to Point Defects at High Temperatures,” Phys. Rev. 119(2), 507–509 (1960). [CrossRef]
  10. G. A. Slack and D. W. Oliver, “Thermal Conductivity of Garnets and Phonon Scattering by Rare-Earth Ions,” Phys. Rev. B 4(2), 592–609 (1971). [CrossRef]
  11. Y. Kuwano, K. Suda, N. Ishizawa, and T. Yamada, “Crystal growth and properties of (Lu,Y)3Al5O12,” J. Cryst. Growth 260(1-2), 159–165 (2004). [CrossRef]
  12. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80-300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]
  13. J. Liu, V. Petrov, H. Zhang, J. Wang, and M. Jiang, “High-power laser performance of a-cut and c-cut Yb:LuVO4 crystals,” Opt. Lett. 31(22), 3294–3296 (2006). [CrossRef] [PubMed]
  14. G. Palmer, M. Schultze, M. Siegel, M. Emons, U. Bünting, and U. Morgner, “Passively mode-locked Yb:KLu(WO4)2 thin-disk oscillator operated in the positive and negative dispersion regime,” Opt. Lett. 33(14), 1608–1610 (2008). [CrossRef] [PubMed]
  15. A. Bensalah, Y. Guyot, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Spectroscopic properties of Yb3+:LuLiF4 crystal grown by the Czochralski method for laser applications and evaluation of quenching processes: a comparison with Yb3+:YLiF4,” J. Alloy. Comp. 380(1-2), 15–26 (2004). [CrossRef]
  16. D. Fagundes-Peters, N. Martynyuk, K. Lünstedt, V. Peters, K. Petermann, G. Huber, S. Basun, V. Laguta, and A. Hofstaetter, “High quantum efficiency YbAG-crystals,” J. Lumin. 125(1-2), 238–247 (2007). [CrossRef]
  17. A. Brenier, Y. Guyot, H. Canibano, G. Boulon, A. Ródenas, D. Jaque, A. Eganyan, and A. G. Petrosyan, “Growth, spectroscopic, and laser properties of Yb3+-doped Lu3Al5O12 garnet crystal,” J. Opt. Soc. Am. B 23(4), 676–683 (2006). [CrossRef]
  18. J. L. Caslavsky and D. J. Viechnicki, “Melting behaviour and matastability of yttrium aluminium garnet (YAG) and YAlO3 determined by optical differential thermal analysis,” J. Mater. Sci. 15(7), 1709–1718 (1980). [CrossRef]
  19. H. Okamoto, “The Ir-Re (Iridium-Rhenium) System,” J. Phase Equilibria 13(6), 649–650 (1992). [CrossRef]
  20. F. Euler and J. A. Bruce, “Oxygen coordinates of compounds with garnet structure,” Acta Crystallogr. 19(6), 971–978 (1965). [CrossRef]
  21. A. A. Kaminskii, Laser Crystals: Their Physics and Properties (Springer Verlag, Heidelberg, 1990).
  22. T. B. Coplen, “Atomic Weights of the Elements 1999 Technical Report,” Pure Appl. Chem. 73(4), 667–683 (2001). [CrossRef]
  23. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Heidelberg, Germany, 1999).
  24. D. Klimm, data from FactSage 5.3 (personal communication, 2009).
  25. N. P. Padture and P. G. Klemens, “Low Thermal Conductivity in Garnets,” J. Am. Ceram. Soc. 80(4), 1018–1020 (1997). [CrossRef]
  26. F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser Demonstration of Yb3Al5O12 (YbAG) and Materials Properties of Highly Doped Yb:YAG,” IEEE J. Quantum Electron. 37(1), 135–144 (2001). [CrossRef]
  27. H. Kühn, S. T. Fredrich-Thornton, C. Kränkel, R. Peters, and K. Petermann, “Model for the calculation of radiation trapping and description of the pinhole method,” Opt. Lett. 32(13), 1908–1910 (2007). [CrossRef] [PubMed]
  28. C. Kränkel, D. Fagundes-Peters, S. T. Fredrich, J. Johannsen, M. Mond, G. Huber, M. Bernhagen, and R. Uecker, “Continuous wave laser operation of Yb3+:YVO4,” Appl. Phys. B 79, 543–546 (2004). [CrossRef]
  29. K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, “Rare-earth-doped sesquioxides,” J. Lumin. 87–89, 973–975 (2000). [CrossRef]
  30. P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3(1), 125–132 (1986). [CrossRef]
  31. D. E. McCumber, “Einstein Relations Connecting Broadband Emission and Absorption Spectra,” Phys. Rev. 136, A954–957 (1964). [CrossRef]
  32. R. A. Buchanan, K. A. Wickersheim, J. J. Pearson, and G. F. Herrmann, “Energy Levels of Yb3+ in Gallium and Aluminum Garnets. I. Spectra,” Phys. Rev. 159(2), 245–251 (1967). [CrossRef]
  33. D. L. Wood, “Energy Levels of Yb3+ in Garnets,” J. Chem. Phys. 39(7), 1671–1673 (1963). [CrossRef]
  34. J. A. Koningstein, “Energy Levels and Crystal-field Calculations of Trivalent Ytterbium in Yttrium Aluminum Garnet and Yttrium Gallium Garnet,” Theor. Chim. Acta 3(3), 271–277 (1965). [CrossRef]
  35. G. A. Bogomolova, L. A. Bumagina, A. A. Kaminskii, and B. Z. Malkin, “Crystal field in laser garnets with TR3+ ions in the exchange charge model,” Sov. Phys. Solid State 19 (1977).
  36. J. Kawanaka, H. Nishioka, N. Inoue, and K. Ueda, “Tunable continuous-wave Yb:YLF laser operation with a diode-pumped chirped-pulse amplification system,” Appl. Opt. 40(21), 3542–3546 (2001). [CrossRef]
  37. J. Morikawa, C. Leong, T. Hashimoto, T. Ogawa, Y. Urata, S. Wada, M. Higuchi, and J. Takahashi, “Thermal conductivity/diffusivity of Nd3+ doped GdVO4, YVO4, LuVO4, and Y3Al5O12 by temperature wave analysis,” J. Appl. Phys. 103, 063522 (2008). [CrossRef]
  38. E. S. R. Gopal, Specific Heats at Low Temperatures (Plenum Press, New York, 1966).
  39. X. Xu, Z. Zhao, P. Song, G. Zhou, J. Xu, and P. Deng, “Structural, thermal, and luminescent properties of Yb-doped Y3Al5O12 crystals,” J. Opt. Soc. Am. B 21(3), 543–547 (2004). [CrossRef]
  40. T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-Doped Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007). [CrossRef]
  41. R. Gaumé, B. Viana, D. Vivien, J.-P. Roger, and D. Fournier, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. 83(7), 1355–1357 (2003). [CrossRef]
  42. W. J. Parker, R. J. Jenkins, C. P. Butler, and G. L. Abbott, “Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity,” J. Appl. Phys. 32(9), 1679–1684 (1961). [CrossRef]
  43. K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modelling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29(8), 697–703 (1999). [CrossRef]
  44. K. Contag, Modellierung und numerische Auslegung des Yb:YAG Scheibenlasers (PhD-thesis, IFSW, University of Stuttgart, 2002).

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