OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 28 — Dec. 31, 2012
  • pp: 29531–29539

Optics InfoBase > Optics Express > Volume 20 > Issue 28 > Page 29531

« Show journal navigation

Evaluation of thermo-optic characteristics of cryogenically cooled Yb:YAG ceramics

Ryo Yasuhara, Hiroaki Furuse, Akifumi Iwamoto, Junji Kawanaka, and Takagimi Yanagitani  »View Author Affiliations


Optics Express, Vol. 20, Issue 28, pp. 29531-29539 (2012)
http://dx.doi.org/10.1364/OE.20.029531


View Full Text Article

Acrobat PDF (992 KB)


Advanced Search

Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The temperature dependence of the thermo-optic effect in cryogenically cooled Yb:YAG ceramics was evaluated by measuring the thermo-optic coefficient (the derivative of refractive index with respect to temperature, i.e., dn/dT), thermal expansion coefficient (α), and thermal conductivity (κ) between 70 and 300 K. These parameters significantly improved at low temperature. Observed values indicated that a laser gain medium cooled to 70 K can sustain a thermal load up to 20 times higher than that at 300 K, for comparable thermo-optic effects. To our best knowledge, this is the first quantitative evaluation of the improvement in thermo-optic characteristics of cryogenically cooled Yb:YAG ceramics.

© 2012 OSA

1. Introduction

A high energy pulsed laser with a high repetition rate is strongly desired for a wide range of applications such as laser material processing‎ [1

A. M. Korsunsky, J. Liu, D. Laundy, M. Golshan, and K. Kim, “Residual elastic strain due to laser shock peening,” J. Strain Analysis 41(2), 113–120 (2006). [CrossRef]

], laser-accelerated particle beams [2

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300(5622), 1107–1111 (2003). [CrossRef] [PubMed]

], hard X-ray generation [3

J. D. Kmetec, C. L. Gordon 3rd, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV X-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68(10), 1527–1530 (1992). [CrossRef] [PubMed]

]‎, laser Thomson scattering diagnostics [4

R. Yasuhara, M. Yoshikawa, M. Morimoto, I. Yamada, K. Kawahata, H. Funaba, Y. Shima, J. Kohagura, M. Sakamoto, Y. Nakashima, T. Imai, and T. Minami, “Design of the polarization multi-pass Thomson scattering system,” Rev. Sci. Instrum. 83(10), 10E326 (2012). [CrossRef] [PubMed]

], and nuclear fusion applications [5

E. I. Moses, “Ignition on the national ignition facility: a path towards inertial fusion energy,” Nuc. Fus. 49(10), 104022 (2009). [CrossRef]

,6

T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, G. Hays, and K. B. Wharton, “Nuclear fusion from explosions of femtosecond laser-heated deuterium clusters,” Nature 398(6727), 489–492 (1999). [CrossRef]

]. One of the solutions for realizing a high-energy and high-average-power laser operation is a diode-pumped solid-state laser (DPSSL) with a large laser gain medium. In the last decade, pulsed DPSSLs capable of producing more than 10 J per pulse have been demonstrated, including the Mercury laser system (61 J × 10 Hz) [7

A. Bayramian, J. Armstrong, G. Beer, R. Campbell, B. Chai, R. Cross, A. Erlandson, Y. Fei, B. Freitas, R. Kent, J. Menapace, W. Molander, K. Schaffers, C. Siders, S. Sutton, J. Tassano, S. Telford, C. Ebbers, J. Caird, and C. Barty, “High-average-power femto-petawatt laser pumped by the mercury laser facility,” J. Opt. Soc. Am. B 25(7), B57–B61 (2008). [CrossRef]

], the HALNA laser system (21 J × 10 Hz) [8

R. Yasuhara, T. Kawashima, T. Sekine, T. Kurita, T. Ikegawa, O. Matsumoto, M. Miyamoto, H. Kan, H. Yoshida, J. Kawanaka, M. Nakatsuka, N. Miyanaga, Y. Izawa, and T. Kanabe, “213 W average power of 2.4 GW pulsed thermally controlled Nd:glass zigzag slab laser with a stimulated Brillouin scattering mirror,” Opt. Lett. 33(15), 1711–1713 (2008). [CrossRef] [PubMed]

], the POLARIS system (12 J × 0.05 Hz) [9

M. Hornung, R. Bödefeld, M. Siebold, A. Kessler, M. Schnepp, R. Wachs, A. Sävert, S. Podleska, S. Keppler, J. Hein, and M. C. Kaluza, “Temporal pulse control of a multi-10 TW diode-pumped Yb:glass laser,” Appl. Phys. B 101(1–2), 93–102 (2010). [CrossRef]

], and the Lucia system (10 J × 2 Hz) [10

J.-C. Chanteloup and D. Albach, “Current status on high average power and energy diode pumped solid state lasers,” IEEE Photon. J. 3(2), 245–248 (2011). [CrossRef]

]. The laser gain mediums used in these laser systems are Yb:S-FAP, Nd:glass, Yb:YAG, and Yb:glass, all at room temperature. These materials can be produced with large size in order to form a large aperture, to avoid laser-induced damage, and with a moderate emission cross-section that is ideal for high-energy storage leading to high-energy-per-pulse operation.

In these laser systems, the thermo-optic effect is one of the limiting factors for increasing the repetition rate and output beam quality. This effect strongly depends on the thermal properties of the laser gain medium. Cryogenically cooled Yb:YAG ceramics are the most promising material for high-average-power and high-energy laser systems. They have excellent thermal properties at low temperatures, preferable spectroscopic properties, and can be manufactured in large sizes. Recently, high-average-power operation attained by using cryogenically cooled Yb:YAG has been reported for cw [11

D. J. Ripin, J. R. Ochoa, R. L. Aggarwal, and T. Y. Fan, “165-W cryogenically cooled Yb:YAG laser,” Opt. Lett. 29(18), 2154–2156 (2004). [CrossRef] [PubMed]

–13

N. Vretenar, T. C. Newell, T. Carson, P. Peterson, T. Lucas, W. P. Latham, H. Bostanci, J. J. Lindauer, B. A. Saarloos, and D. P. Rini, “Cryogenic ceramic 277 watt Yb:YAG thin-disk laser,” Opt. Eng. 51(1), 014201 (2012). [CrossRef]

] and pulsed [14

J. Kawanaka, Y. Takeuchi, A. Yoshida, S. J. Pearce, R. Yasuhara, T. Kawashima, and H. Kan, “Highly efficient cryogenically cooled Yb:YAG laser,” Laser Phys. 20(5), 1079–1084 (2010). [CrossRef]

,15

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012). [CrossRef] [PubMed]

] laser systems. As a result, development of laser systems capable of producing more than 1 J per pulse is currently underway at several institutes [14

J. Kawanaka, Y. Takeuchi, A. Yoshida, S. J. Pearce, R. Yasuhara, T. Kawashima, and H. Kan, “Highly efficient cryogenically cooled Yb:YAG laser,” Laser Phys. 20(5), 1079–1084 (2010). [CrossRef]

–17

M. Sawicka, M. Divoky, J. Novak, A. Lucianetti, B. Rus, and T. Mocek, “Modeling of amplified spontaneous emission, heat deposition, and energy extraction in cryogenically cooled multislab Yb3+:YAG laser amplifier for the HiLASE Project,” J. Opt. Soc. Am. B 29(6), 1270–1276 (2012). [CrossRef]

].

The temperature dependence of thermal properties is important in the design of cryogenically cooled Yb:YAG laser systems. It should be considered both in the thermal design and in estimating the laser output performance. In particular, the thermal properties of the temperature dependences of 1) the thermo-optic coefficient, (the derivative of the refractive index with respect to temperature, dn/dT), 2) the linear thermal expansion coefficient (α), and 3) the thermal conductivity (κ) are essential properties. The temperature dependences of dn/dT, α, and κ in a Yb:YAG crystal at low temperature can be found in previous works [18

J. D. Foster and L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7(12), 2428–2429 (1968). [CrossRef] [PubMed]

–21

D. C. Brown, “The promise of cryogenic solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 11(3), 587–599 (2005). [CrossRef]

]. For YAG ceramics, V. Cardinali et al., reported the temperature dependences of α and dn/dT at temperatures of over 100 K by separate measurements using the push-rod dilatometer method for α and the interferometer method for dn/dT [22

V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

]. At temperatures over 100 K, these parameters are useful for the design of the cryogenically cooled Yb:YAG ceramics laser. However, there are no data for the temperature dependence of dn/dT and α in Yb:YAG ceramics at temperatures below 100 K. The temperature dependence of κ of YAG ceramics has been reported by T. Numazawa et al. [23

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

] and H. Yagi, et al. [24

H. Yagi, T. Yanagitani, T. Numazawa, and K. Ueda, “The physical properties of transparent Y3Al5O12: Elastic modulus at high temperature and thermal conductivity at low temperature,” Ceram. Int. 33(5), 711–714 (2007). [CrossRef]

]; however, their reports do not include data on Yb-doped YAG ceramics. The thermal conductivity of the YAG ceramics is dramatically changed at temperatures below 100 K as shown in Ref [23

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

, 24

H. Yagi, T. Yanagitani, T. Numazawa, and K. Ueda, “The physical properties of transparent Y3Al5O12: Elastic modulus at high temperature and thermal conductivity at low temperature,” Ceram. Int. 33(5), 711–714 (2007). [CrossRef]

]. Knowledge of the thermal properties below 100 K is indispensable for designing the cryogenically cooled Yb:YAG ceramics laser system. In addition, the enhancement of the thermo-optical effects in cryogenically cooled Yb:YAG ceramics has never been characterized from the view of material properties by using figure of merits (FOM).

In this paper, we report an evaluation of the improvement of the thermo-optic effects in cryogenically cooled Yb:YAG ceramics by simultaneously measuring the temperature dependences of dn/dT and α in YAG ceramics from 73 K to 296 K and measuring the temperature dependence of κ of 9.8 at% Yb:YAG ceramics from 70 K to 300 K and then fitting these dependences with precise theoretical models. From these data, we characterized the temperature dependence of the thermo-optic effects of Yb:YAG ceramics by using the FOM. As a result, we have quantitatively substantiated the improvement of thermo-optic characteristics in Yb:YAG ceramics at cryogenic temperature. These data will assist in the development of high-energy and high-power laser systems based on cryogenically cooled Yb:YAG ceramics.

2. Experimental methods

2.1 Experimental set-up for the measurement of the temperature dependence of dn/dT and α

The Fizeau interferometer method is used for measuring the temperature dependence of α and dn/dT in YAG ceramics [18

J. D. Foster and L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7(12), 2428–2429 (1968). [CrossRef] [PubMed]

,19

R. Wynne, J. L. Daneu, and T. Y. Fan, “Thermal coefficients of the expansion and refractive index in YAG,” Appl. Opt. 38(15), 3282–3284 (1999). [CrossRef] [PubMed]

]. Figure 1 shows the undoped YAG ceramics (Konoshima Chemical Co., Ltd.,) used for measurement. Undoped YAG ceramic flats were diffusion-bonded to the ends of a 15.7-mm-long piece of undoped YAG ceramic to form a Fizeau interferometer. A part of the outer surface of each of the flats is antireflection- (AR-) coated at the laser wavelength for the vacuum path of the interferometer. A schematic diagram of the experimental set-up is shown in Fig. 2 . The sample was placed in a vacuum chamber and attached to the cold finger of the temperature-controllable cryostat (Iwatani HE05) with thermal conductive paste (Dotite, Fujikura Kasei Co., Ltd.,) to improve the thermal contact. Two Fizeau interferometers, one with a vacuum path and the other with a YAG ceramic path, were illuminated through the half mirror by a He–Ne laser operating at 633 nm. The reflection that formed the Fizeau fringe was observed after the half mirror. After the beam passed through a pin-hole, the intensities of the reflected fringes were recorded by photo-detectors 1 and 2 as the temperature was varied while the cold finger was heated. The temperature was measured by a calibrated Kp-Au thermocouple on the material surface with a nano-voltmeter (34420A, Agilent). The accuracy of the measurements is estimated to be ± 0.2 × 10−6 K−1. The temperature must be varied over a range of about 10 K to obtain one value of α and of dn/dT. Light intensity as a function of temperature was fitted with a sinusoid to extract the physical path-length change. Note that a count of one fringe corresponds to a change in optical path-length of λ/2, where λ is the wavelength of the incident light, L is the length of the interferometer path, and n is the refractive index of the interferometer path. α and dn/dT were determined using Eq. (1) [18

J. D. Foster and L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7(12), 2428–2429 (1968). [CrossRef] [PubMed]

] with data from each of the interferometer paths:
1 Ln d(Ln) dT=α+ 1n dn dT
(1)
where the value of the refractive index of the YAG ceramics is 1.8293 at room temperature.

Fig. 1 A photograph of the diffusion-bonded YAG ceramic sample for the measurement of dn/dT and α.
Fig. 2 A schematic diagram of the experimental set-up for the measurement of dn/dT and α.

2.2. Experimental set-up for the measurement of the temperature dependence of κ

The thermal conductivity of 9.8% doped YAG ceramics was measured by the steady-state longitudinal heat flow method shown in Fig. 3 . The sample size of the Yb:YAG ceramics is 15 mm in length with a 5 mm × 5 mm cross-section. The sample was prepared by Konoshima Chemical Co., Ltd. The Yb:YAG ceramic sample was sandwiched between the oxygen-free copper holders. One face of the Yb:YAG ceramic sample was placed in thermal contact with the oxygen-free copper by using a thermally conductive epoxy (Stycast 2850FT, Emerson & Cuming Microwave Products). One side of the oxygen-free copper was attached to the cooling head of the temperature-controlled cryostat. Then, we attached the heater to the other side of the oxygen-free copper. The temperature between pairs of points was measured using thermometers.

Fig. 3 A schematic diagram of the experimental set-up for the measurement of κ.

3. Experimental results

3.1 Determination of the temperature dependence of dn/dT and α

Figure 4 shows the results for the temperature dependence of the thermal expansion coefficient α and the thermo-optic coefficient dn/dT that we obtained for the undoped YAG ceramics. α and dn/dT decreased when the temperature of the YAG ceramics was decreased. α decreased to 4 × 10−7 K−1 at 73 K, which is 15 times lower than the value of α at 296 K. The dn/dT value of YAG ceramics also decreased, to 8 × 10−7 K−1 at 73 K, which is 10 times lower than that at 296 K. The α and dn/dT values measured in this work are in reasonable agreement with the previous work on the YAG crystal and YAG ceramics. Our data for YAG ceramics, at temperatures generally above 100 K, are consistent with that of V. Cardinali et al. [22

V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

]. The temperature dependence of the coefficient α for undoped YAG ceramics is close to the value of the YAG crystal [20

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, 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]

]. Note that the effect of the Yb concentration is negligible for α and dn/dT, as shown in Ref [22

V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

]. In the commonly used Grüneisen theory, the linear expansion coefficient of an isotropic solid is given by
α(T)= 13K (T) γGρ (T) CV (T)
(2)
where K is the compressibility, γG is the Grüneisen constant (which is of the order of 2), ρ is the value of the material density, and CV(T) is the specific heat at constant volume [25

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]

]. We can express the temperature dependence of CV(T) within the temperature range of our experiment as shown in Eq. (3),
CV (T)∝exp ( − ℏω kBT)
(3)
where ħ is the reduced Planck constant, ω is the angular frequency, and kB is the Boltzmann constant. From Eqs. (2) and (3), the linear thermal expansion can be expressed as a function of temperature by using two constants, A and B. The thermal coefficients of K(T) and ρ(T) are relatively small, so we approximate those components as constants.
α(T)=Aexp ( − BT)
(4)
We fitted the experimental result of α with Eq. (4) and found that A = 1.1434 × 10−5 K−1 and B = 174.59 K. There is no such simple relationship to represent the temperature dependence of the dn/dT data. Therefore, we used a third-order polynomial fit to interpolate the dn/dT values within this temperature range.
dn dT (T)= M0+ M1T+ M2 T2+ M3 T3
(5)
By fitting this polynomial to the dn/dT data, we obtained the parameters M0 = −1.3698 × 10−6 K−1, M1 = 1.5974 × 10−8 K−2, M2 = 1.9468 × 10−10 K−3, and M3 = −4.6369 × 10−13 K−4.

Fig. 4 Temperature dependence of the refractive index (red) and thermal expansion (blue). The solid lines show the fitted curves obtained by using Eqs. (4) and (5). The filled circles show our experimental data. The green triangles show α for the YAG ceramics from Ref [20

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, 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]

]. The green circles represent dn/dT for the YAG ceramics from Ref [20

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, 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]

]. The black triangles show α for the YAG crystal from Ref [19

R. Wynne, J. L. Daneu, and T. Y. Fan, “Thermal coefficients of the expansion and refractive index in YAG,” Appl. Opt. 38(15), 3282–3284 (1999). [CrossRef] [PubMed]

]. The black squares show dn/dT for the YAG crystal from Ref [18

J. D. Foster and L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7(12), 2428–2429 (1968). [CrossRef] [PubMed]

].

3.2 Determination of the temperature dependence of κ

Figure 5 shows the temperature dependence of κ for four materials: 9.8 at% Yb:YAG ceramics, an undoped YAG single crystal from Ref [23

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

], undoped YAG ceramics from Ref [23

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

], and undoped YAG ceramics that had a 3-μm grain size, as obtained in Ref [24

H. Yagi, T. Yanagitani, T. Numazawa, and K. Ueda, “The physical properties of transparent Y3Al5O12: Elastic modulus at high temperature and thermal conductivity at low temperature,” Ceram. Int. 33(5), 711–714 (2007). [CrossRef]

]. The κ of 9.8 at% Yb:YAG ceramics is 15.9 W/mK at 70 K. This value is 1.9 times higher than that at 300 K. The κ of undoped YAG ceramics is 50 W/mK at 70 K. We have confirmed a significant reduction of thermal conductivity in the doped YAG ceramics. To confirm the accuracy of our measurement, we measured another sample that had a different length, 15 mm. There is up to a 5% discrepancy between the 15-mm and 20-mm samples at temperatures below 130 K. We attribute this to the thermal impedance of the glue. We have measured the sample length dependence of κ to evaluate the thermal impedance as well in [26

A. Iwamoto, R. Maekawa, and T. Mito, “Development of evaluation technique on thermal impedance between dissimilar solids,” Advances in Cryogenic Engineering: Transactions of the Cryogenic Engineering Conference 49(204), 643–649 (2004).

]. In the near future, we will also measure κ for different doping concentrations to study the dopant dependence of κ in YAG ceramics.

Fig. 5 Temperature dependence of the thermal conductivity of Yb:YAG ceramics. The filled circles represent the experimental data from this work. The open triangles show the κ of the undoped YAG single crystal from Ref [23

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

]. The open squares show the κ of the undoped YAG ceramics from Ref [23

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

]. The filled squares show the κ of the undoped YAG ceramics from Ref [24

H. Yagi, T. Yanagitani, T. Numazawa, and K. Ueda, “The physical properties of transparent Y3Al5O12: Elastic modulus at high temperature and thermal conductivity at low temperature,” Ceram. Int. 33(5), 711–714 (2007). [CrossRef]

]. The solid lines show the fitted curves obtained by using Eq. (6).

The thermal conductivity of isotropic non-metallic solids can be estimated by using the Callaway model [27

J. Callaway, “Model for lattice thermal conductivity at low temperatures,” Phys. Rev. 113(4), 1046–1051 (1959). [CrossRef]

]. The temperature dependence of thermal conductivity is expressed as
κ (T)= C1+ C2 T 3/2+ C3 T 9/2+ C4 T 1/2
(6)
where C1, C2, C3, and C4 are constants that depend on material properties. We fitted the temperature dependence of κ to Eq. (6). The calculated parameters are C1 = 0.91904, C2 = 9895.6, C3 = 9393.8 × 105, and C4 = 0.32309 for 9.8 at% Yb:YAG ceramics and C1 = 8.7721, C2 = 26949, C3 = −11002 × 105, and C4 = −0.07581 for undoped YAG ceramics.

4. Evaluation of the thermo-optic characteristics and discussion

To estimate the thermo-optic effect in cryogenically cooled Yb:YAG ceramics, we use two parameters. One is the figure of merit for thermal lensing FOMD, and the other is the figure of merit for thermal birefringence FOMB. T. Y. Fan defined FOMD and FOMB as follows,
FOMD= κ χ QL ( dn dT+nα)
(7)
FOMB= κ χ QLα
(8)
where χQL is the ratio of (i) the thermal load from energy being left behind when pump photons are converted to stimulated emission photons to (ii) the energy being carried by the stimulated emission photons, in the ideal case [25

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]

]. We assume that χQL is a constant within the temperature range from 300 K to 70 K. The temperature dependence of the thermo-optic effect is evaluated by using Eq. (7) and Eq. (8) with the experimental results for α, dn/dT, and κ. No difference in α and dn/dT is expected between doped and undoped samples [22

V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

] as mentioned before. In this case, we used the values for the undoped YAG ceramics to calculate the FOMs.

Figure 6 shows the temperature dependence of FOMD and FOMB normalized to the values at 300 K. The normalized FOMD indicates that the amount of wavefront distortion (caused by thermal expansion and the temperature dependence of the refractive index) in a 300-K Yb:YAG ceramic laser is equivalent to that of a 70-K Yb:YAG ceramic laser operating at 24 times the thermal load. The normalized FOMB for Yb:YAG ceramics at 300 K indicates that it experiences the same level of stress-optic effects as a 70-K Yb:YAG ceramics laser system operating at 21 times the thermal load. The FOMD and FOMB at the intermediate temperature of 150 K are about two times larger than the corresponding values at 300 K.

Fig. 6 Temperature dependence of thermo-optic effects. The solid line shows the FOMD, and the dashed line shows the FOMB. The temperature is plotted on a logarithmic scale.

Recently, the temperature of cryogenically cooled Yb:YAG ceramics was measured during high-power laser action [28

H. Furuse, J. Kawanaka, N. Miyanaga, H. Chosrowjan, M. Fujita, K. Takeshita, and Y. Izawa, “Output characteristics of high power cryogenic Yb:YAG TRAM laser oscillator,” Opt. Express 20(19), 21739–21748 (2012). [CrossRef] [PubMed]

]. At the laser output power of 260 W, the spatially averaged temperature of the active medium was about 160 K. For that case, we can infer that the thermo-optic effect was decreased to half of that in the room-temperature medium. From the view of the thermo-optic effect, if we can suppress the temperature of the active medium to around liquid nitrogen temperature, a laser output power that is 10 times higher can be obtained with good output beam quality from the same volume of gain medium. The development of an efficient cooling method such as forced convection cooling will be the next stage for the cryogenically cooled Yb:YAG ceramic laser system. At very low temperatures, amplified spontaneous emission (ASE) losses will increase and limit the laser output power, even if the FOM value improves. An optimum temperature exists for a particular laser system and an output power. Now, we are preparing to evaluate the optimum temperature by taking into account ASE losses and thermal properties.

5. Conclusion

In conclusion, we have evaluated the thermo-optic characteristics in cryogenic cooled Yb:YAG ceramics. We have simultaneously measured the temperature dependence of dn/dT and α in YAG ceramics from 73 K to 296 K. The temperature dependence of κ of 9.8 at% Yb:YAG ceramics was also measured from 70 K to 300 K. Around liquid nitrogen temperature, α and dn/dT of the YAG ceramics were respectively found to decrease to 15 times and 10 times below the corresponding values at room temperature. The κ of 9.8 at% Yb:YAG ceramics at 70 K is also improved to a value 1.9 times higher than the value at room temperature. From these data, we have evaluated the temperature dependence of the thermo-optic characteristics of Yb:YAG ceramics by using FOMs. We found that a cryogenically cooled Yb:YAG ceramic laser at 70 K permits 20 times as much thermal load as a 300-K Yb:YAG ceramic laser. In this paper, we have quantitatively substantiated the improvement of thermo-optic characteristics in Yb:YAG ceramics at cryogenic temperature by the measurement of their thermal properties. Our measurements will contribute to the development of a high-energy and high-power laser system based on cryogenically cooled Yb:YAG ceramics.

Acknowledgments

This work was performed with the support and under the auspices of the National Institute for Fusion Science (Grant No. NIFS11UJHH002, NIFS Collaboration Research program of NIFS11KLEH021 and NIFS11KBAH004) and was performed as a part of a joint research project of the Institute of Laser Engineering, Osaka University (under contract subject “B2-34”).

References and links

1.

A. M. Korsunsky, J. Liu, D. Laundy, M. Golshan, and K. Kim, “Residual elastic strain due to laser shock peening,” J. Strain Analysis 41(2), 113–120 (2006). [CrossRef]

2.

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300(5622), 1107–1111 (2003). [CrossRef] [PubMed]

3.

J. D. Kmetec, C. L. Gordon 3rd, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV X-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68(10), 1527–1530 (1992). [CrossRef] [PubMed]

4.

R. Yasuhara, M. Yoshikawa, M. Morimoto, I. Yamada, K. Kawahata, H. Funaba, Y. Shima, J. Kohagura, M. Sakamoto, Y. Nakashima, T. Imai, and T. Minami, “Design of the polarization multi-pass Thomson scattering system,” Rev. Sci. Instrum. 83(10), 10E326 (2012). [CrossRef] [PubMed]

5.

E. I. Moses, “Ignition on the national ignition facility: a path towards inertial fusion energy,” Nuc. Fus. 49(10), 104022 (2009). [CrossRef]

6.

T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, G. Hays, and K. B. Wharton, “Nuclear fusion from explosions of femtosecond laser-heated deuterium clusters,” Nature 398(6727), 489–492 (1999). [CrossRef]

7.

A. Bayramian, J. Armstrong, G. Beer, R. Campbell, B. Chai, R. Cross, A. Erlandson, Y. Fei, B. Freitas, R. Kent, J. Menapace, W. Molander, K. Schaffers, C. Siders, S. Sutton, J. Tassano, S. Telford, C. Ebbers, J. Caird, and C. Barty, “High-average-power femto-petawatt laser pumped by the mercury laser facility,” J. Opt. Soc. Am. B 25(7), B57–B61 (2008). [CrossRef]

8.

R. Yasuhara, T. Kawashima, T. Sekine, T. Kurita, T. Ikegawa, O. Matsumoto, M. Miyamoto, H. Kan, H. Yoshida, J. Kawanaka, M. Nakatsuka, N. Miyanaga, Y. Izawa, and T. Kanabe, “213 W average power of 2.4 GW pulsed thermally controlled Nd:glass zigzag slab laser with a stimulated Brillouin scattering mirror,” Opt. Lett. 33(15), 1711–1713 (2008). [CrossRef] [PubMed]

9.

M. Hornung, R. Bödefeld, M. Siebold, A. Kessler, M. Schnepp, R. Wachs, A. Sävert, S. Podleska, S. Keppler, J. Hein, and M. C. Kaluza, “Temporal pulse control of a multi-10 TW diode-pumped Yb:glass laser,” Appl. Phys. B 101(1–2), 93–102 (2010). [CrossRef]

10.

J.-C. Chanteloup and D. Albach, “Current status on high average power and energy diode pumped solid state lasers,” IEEE Photon. J. 3(2), 245–248 (2011). [CrossRef]

11.

D. J. Ripin, J. R. Ochoa, R. L. Aggarwal, and T. Y. Fan, “165-W cryogenically cooled Yb:YAG laser,” Opt. Lett. 29(18), 2154–2156 (2004). [CrossRef] [PubMed]

12.

H. Furuse, J. Kawanaka, K. Takeshita, N. Miyanaga, T. Saiki, K. Imasaki, M. Fujita, and S. Ishii, “Total-reflection active-mirror laser with cryogenic Yb:YAG ceramics,” Opt. Lett. 34(21), 3439–3441 (2009). [CrossRef] [PubMed]

13.

N. Vretenar, T. C. Newell, T. Carson, P. Peterson, T. Lucas, W. P. Latham, H. Bostanci, J. J. Lindauer, B. A. Saarloos, and D. P. Rini, “Cryogenic ceramic 277 watt Yb:YAG thin-disk laser,” Opt. Eng. 51(1), 014201 (2012). [CrossRef]

14.

J. Kawanaka, Y. Takeuchi, A. Yoshida, S. J. Pearce, R. Yasuhara, T. Kawashima, and H. Kan, “Highly efficient cryogenically cooled Yb:YAG laser,” Laser Phys. 20(5), 1079–1084 (2010). [CrossRef]

15.

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012). [CrossRef] [PubMed]

16.

J.-C. Chanteloup, D. Albach, A. Lucianetti, K. Ertel, S. Banerjee, P. D. Mason, C. Hernandez-Gomez, J. L. Collier, J. Hein, M. Wolf, J. Körner, and B. J. L. Garrec, “Multi kJ level laser concepts for HiPER facility,” J. Phys.: Conf. Ser. 244(1), 012010 (2010). [CrossRef]

17.

M. Sawicka, M. Divoky, J. Novak, A. Lucianetti, B. Rus, and T. Mocek, “Modeling of amplified spontaneous emission, heat deposition, and energy extraction in cryogenically cooled multislab Yb3+:YAG laser amplifier for the HiLASE Project,” J. Opt. Soc. Am. B 29(6), 1270–1276 (2012). [CrossRef]

18.

J. D. Foster and L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7(12), 2428–2429 (1968). [CrossRef] [PubMed]

19.

R. Wynne, J. L. Daneu, and T. Y. Fan, “Thermal coefficients of the expansion and refractive index in YAG,” Appl. Opt. 38(15), 3282–3284 (1999). [CrossRef] [PubMed]

20.

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, 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]

21.

D. C. Brown, “The promise of cryogenic solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 11(3), 587–599 (2005). [CrossRef]

22.

V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater. 34(6), 990–994 (2012). [CrossRef]

23.

T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol. 12(12), 2089–2094 (2001). [CrossRef]

24.

H. Yagi, T. Yanagitani, T. Numazawa, and K. Ueda, “The physical properties of transparent Y3Al5O12: Elastic modulus at high temperature and thermal conductivity at low temperature,” Ceram. Int. 33(5), 711–714 (2007). [CrossRef]

25.

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]

26.

A. Iwamoto, R. Maekawa, and T. Mito, “Development of evaluation technique on thermal impedance between dissimilar solids,” Advances in Cryogenic Engineering: Transactions of the Cryogenic Engineering Conference 49(204), 643–649 (2004).

27.

J. Callaway, “Model for lattice thermal conductivity at low temperatures,” Phys. Rev. 113(4), 1046–1051 (1959). [CrossRef]

28.

H. Furuse, J. Kawanaka, N. Miyanaga, H. Chosrowjan, M. Fujita, K. Takeshita, and Y. Izawa, “Output characteristics of high power cryogenic Yb:YAG TRAM laser oscillator,” Opt. Express 20(19), 21739–21748 (2012). [CrossRef] [PubMed]

OCIS Codes
(140.3380) Lasers and laser optics : Laser materials
(140.6810) Lasers and laser optics : Thermal effects

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: October 31, 2012
Revised Manuscript: November 26, 2012
Manuscript Accepted: November 26, 2012
Published: December 19, 2012

Citation
Ryo Yasuhara, Hiroaki Furuse, Akifumi Iwamoto, Junji Kawanaka, and Takagimi Yanagitani, "Evaluation of thermo-optic characteristics of cryogenically cooled Yb:YAG ceramics," Opt. Express 20, 29531-29539 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29531


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. M. Korsunsky, J. Liu, D. Laundy, M. Golshan, and K. Kim, “Residual elastic strain due to laser shock peening,” J. Strain Analysis41(2), 113–120 (2006). [CrossRef]
  2. K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science300(5622), 1107–1111 (2003). [CrossRef] [PubMed]
  3. J. D. Kmetec, C. L. Gordon, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV X-ray generation with a femtosecond laser,” Phys. Rev. Lett.68(10), 1527–1530 (1992). [CrossRef] [PubMed]
  4. R. Yasuhara, M. Yoshikawa, M. Morimoto, I. Yamada, K. Kawahata, H. Funaba, Y. Shima, J. Kohagura, M. Sakamoto, Y. Nakashima, T. Imai, and T. Minami, “Design of the polarization multi-pass Thomson scattering system,” Rev. Sci. Instrum.83(10), 10E326 (2012). [CrossRef] [PubMed]
  5. E. I. Moses, “Ignition on the national ignition facility: a path towards inertial fusion energy,” Nuc. Fus.49(10), 104022 (2009). [CrossRef]
  6. T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, G. Hays, and K. B. Wharton, “Nuclear fusion from explosions of femtosecond laser-heated deuterium clusters,” Nature398(6727), 489–492 (1999). [CrossRef]
  7. A. Bayramian, J. Armstrong, G. Beer, R. Campbell, B. Chai, R. Cross, A. Erlandson, Y. Fei, B. Freitas, R. Kent, J. Menapace, W. Molander, K. Schaffers, C. Siders, S. Sutton, J. Tassano, S. Telford, C. Ebbers, J. Caird, and C. Barty, “High-average-power femto-petawatt laser pumped by the mercury laser facility,” J. Opt. Soc. Am. B25(7), B57–B61 (2008). [CrossRef]
  8. R. Yasuhara, T. Kawashima, T. Sekine, T. Kurita, T. Ikegawa, O. Matsumoto, M. Miyamoto, H. Kan, H. Yoshida, J. Kawanaka, M. Nakatsuka, N. Miyanaga, Y. Izawa, and T. Kanabe, “213 W average power of 2.4 GW pulsed thermally controlled Nd:glass zigzag slab laser with a stimulated Brillouin scattering mirror,” Opt. Lett.33(15), 1711–1713 (2008). [CrossRef] [PubMed]
  9. M. Hornung, R. Bödefeld, M. Siebold, A. Kessler, M. Schnepp, R. Wachs, A. Sävert, S. Podleska, S. Keppler, J. Hein, and M. C. Kaluza, “Temporal pulse control of a multi-10 TW diode-pumped Yb:glass laser,” Appl. Phys. B101(1–2), 93–102 (2010). [CrossRef]
  10. J.-C. Chanteloup and D. Albach, “Current status on high average power and energy diode pumped solid state lasers,” IEEE Photon. J.3(2), 245–248 (2011). [CrossRef]
  11. D. J. Ripin, J. R. Ochoa, R. L. Aggarwal, and T. Y. Fan, “165-W cryogenically cooled Yb:YAG laser,” Opt. Lett.29(18), 2154–2156 (2004). [CrossRef] [PubMed]
  12. H. Furuse, J. Kawanaka, K. Takeshita, N. Miyanaga, T. Saiki, K. Imasaki, M. Fujita, and S. Ishii, “Total-reflection active-mirror laser with cryogenic Yb:YAG ceramics,” Opt. Lett.34(21), 3439–3441 (2009). [CrossRef] [PubMed]
  13. N. Vretenar, T. C. Newell, T. Carson, P. Peterson, T. Lucas, W. P. Latham, H. Bostanci, J. J. Lindauer, B. A. Saarloos, and D. P. Rini, “Cryogenic ceramic 277 watt Yb:YAG thin-disk laser,” Opt. Eng.51(1), 014201 (2012). [CrossRef]
  14. J. Kawanaka, Y. Takeuchi, A. Yoshida, S. J. Pearce, R. Yasuhara, T. Kawashima, and H. Kan, “Highly efficient cryogenically cooled Yb:YAG laser,” Laser Phys.20(5), 1079–1084 (2010). [CrossRef]
  15. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett.37(12), 2175–2177 (2012). [CrossRef] [PubMed]
  16. J.-C. Chanteloup, D. Albach, A. Lucianetti, K. Ertel, S. Banerjee, P. D. Mason, C. Hernandez-Gomez, J. L. Collier, J. Hein, M. Wolf, J. Körner, and B. J. L. Garrec, “Multi kJ level laser concepts for HiPER facility,” J. Phys.: Conf. Ser.244(1), 012010 (2010). [CrossRef]
  17. M. Sawicka, M. Divoky, J. Novak, A. Lucianetti, B. Rus, and T. Mocek, “Modeling of amplified spontaneous emission, heat deposition, and energy extraction in cryogenically cooled multislab Yb3+:YAG laser amplifier for the HiLASE Project,” J. Opt. Soc. Am. B29(6), 1270–1276 (2012). [CrossRef]
  18. J. D. Foster and L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt.7(12), 2428–2429 (1968). [CrossRef] [PubMed]
  19. R. Wynne, J. L. Daneu, and T. Y. Fan, “Thermal coefficients of the expansion and refractive index in YAG,” Appl. Opt.38(15), 3282–3284 (1999). [CrossRef] [PubMed]
  20. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, 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]
  21. D. C. Brown, “The promise of cryogenic solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.11(3), 587–599 (2005). [CrossRef]
  22. V. Cardinali, E. Marmois, B. Le Garrec, and G. Bourdet, “Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature,” Opt. Mater.34(6), 990–994 (2012). [CrossRef]
  23. T. Numazawa, O. Arai, Q. Hu, and T. Noda, “Thermal conductivity measurements for evaluation of crystal perfection at low temperatures,” Meas. Sci. Technol.12(12), 2089–2094 (2001). [CrossRef]
  24. H. Yagi, T. Yanagitani, T. Numazawa, and K. Ueda, “The physical properties of transparent Y3Al5O12: Elastic modulus at high temperature and thermal conductivity at low temperature,” Ceram. Int.33(5), 711–714 (2007). [CrossRef]
  25. 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]
  26. A. Iwamoto, R. Maekawa, and T. Mito, “Development of evaluation technique on thermal impedance between dissimilar solids,” Advances in Cryogenic Engineering: Transactions of the Cryogenic Engineering Conference 49(204), 643–649 (2004).
  27. J. Callaway, “Model for lattice thermal conductivity at low temperatures,” Phys. Rev.113(4), 1046–1051 (1959). [CrossRef]
  28. H. Furuse, J. Kawanaka, N. Miyanaga, H. Chosrowjan, M. Fujita, K. Takeshita, and Y. Izawa, “Output characteristics of high power cryogenic Yb:YAG TRAM laser oscillator,” Opt. Express20(19), 21739–21748 (2012). [CrossRef] [PubMed]

Cited By

 Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited