## Thermal conductivity measurements of laser crystals by infrared thermography. Application to Nd:doped crystals

Optics Express, Vol. 16, Issue 12, pp. 8995-9010 (2008)

http://dx.doi.org/10.1364/OE.16.008995

Acrobat PDF (253 KB)

### Abstract

We present a thermal conductivity measurement method for laser crystals based on thermal mapping of the crystal face by an infrared camera. Those measurements are performed under end-pumping of the laser crystal and during laser operation. The calculation of the fraction of pump power converted into heat is therefore simplified, and it is possible to link easily the temperature in the crystal to the thermal conductivity. We demonstrate the efficiency of this measurement method with a Nd:YAG crystal, before using it to compare Nd:YVO_{4} and Nd:GdVO_{4} crystals.

© 2008 Optical Society of America

## 1. Introduction

_{c}=α

_{T}. ρ. C

_{p}(α

_{T}is the thermal diffusivity, ρ is the density and Cp is the specific heat). The most common method to measure this diffusivity is the Flash method presented by Parker,

*et al.*[1

1. J. Parker, R. J. Jenkins, C. P. Butler, and G. L. Abbott, “Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity,” J. of Appl. Phys. **32**, 1679 (1961). [CrossRef]

2. L. Pottier, “Micrometer scale visualization of thermal waves by photoreflectance microscopy,” Appl. Phys. Lett. **64**, 1618 (1994). [CrossRef]

3. A. Salazar, A. Sanchez-Lavega, and J. Fernandez, “Thermal diffusivity measurements in solids by the ‘mirage’ technique: Experimental results,” J. of Appl. Phys. **69**, 1216 (1991). [CrossRef]

4. J. F. Bisson, D. Fournier, M. Poulain, O. Lavigne, and R. Mévre, “Thermal conductivity of Yttria-Zirconia single crystals determined by spatially resolved infrared thermography,” J. Am. Ceram. Soc. **83**, 1993–1998 (2000). [CrossRef]

5. Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express **14**, 10528–10536 (2006). [CrossRef] [PubMed]

^{3+}[7

7. L. J. Qin, X. L. Meng, H. Y. Shen, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, “Thermal conductivity and refractive indices of Nd:GdVO4 crystals,” Cryst. Res. Technol. **38**, 793–797 (2003). [CrossRef]

_{4}[8] and Nd:GdVO

_{4}[9

9. A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbakov, T. Jensen, J. P. Meyen, and G. Huber, “The Nd:GdVO4 crystal, a new material for diode-pumped lasers,” Sov. Quantum Electron. **22**, 1071–1072 (1992). [CrossRef]

5. Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express **14**, 10528–10536 (2006). [CrossRef] [PubMed]

_{4}crystals, and from 6.5 W/(m.K) [11

11. C. Kränkel, *et al.*, “Continuous wave laser operation of Yb3+:GdVO4,” Appl. Phys. B **79**, 543–546 (2004). [CrossRef]

12. P. A. Studenikin, A. I. Zagumennyi, Yu. D. Zavartsev, P. A. Popov, and I. A. Shcherbakov, “GdVO_{4} as a new medium for solid-state lasers: some optical and thermal properties of crystals doped with Cd^{3+}, Tm^{3+}, and Er^{3+} ions,, Quantum Electron. **25**, 1162 (1995). [CrossRef]

_{4}crystals. Many publications, like Qin,

*et al.*[7

7. L. J. Qin, X. L. Meng, H. Y. Shen, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, “Thermal conductivity and refractive indices of Nd:GdVO4 crystals,” Cryst. Res. Technol. **38**, 793–797 (2003). [CrossRef]

_{4}lattice on the YVO

_{4}one, whereas, Sato and Taira [5

5. Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express **14**, 10528–10536 (2006). [CrossRef] [PubMed]

^{3+}, the Nd:YVO

_{4}has a higher conductivity. We think that another method of thermal conductivity measurements could be of great interest to complete those results. In this paper, we present a new method to measure the thermal conductivity, by direct thermal mapping of the crystals under laser operation. In section 2 we will deal with the theoretical principle of the method. Section 3 presents the experimental setup. In section 4 we validate our method by measurement on a Nd:YAG sample. Section 5 presents measurements on Nd:YVO

_{4}and Nd:GdVO

_{4}crystals.

## 2. Principle of thermal conductivity measurement by thermal mapping under laser operation

- The heat load repartition has a radial symmetry. This is justified in fiber-coupled laser diode pumping.
- The thermal conductivity is a scalar: it does not depend on the crystal axis. This is a strong approximation, as many laser crystals are not isotropic, and therefore can have different thermo-mechanical properties along their different axis.
- The heat evacuation is radial. To check this hypothesis, we define the heat transfer coefficient H between two media, thanks to Eq. (1).

_{c}is the thermal conductivity, T is the temperature, and n is the coordinate normal to the interface. For a laser crystal placed in a copper mount, H was estimated around 1 W.cm

^{-2}.K

^{-1}[13]. For the faces of the crystal in contact with air, the heat transfer coefficient was estimated to be approximately 10

^{-3}W.cm

^{-2}.K

^{-1}[14

14. A. Cousins
, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. **28**, 1057 (1992). [CrossRef]

_{0}is given by the expression below [15

15. S. Chenais, F. Druon, S. Forget, and F. Balembois, “On thermal effects in solid-state lasers: The case of ytterbium doped materials,” Prog. Quantum Electron. **30**, 89–153 (2006). [CrossRef]

_{h}is the fractional thermal loading, dP/dz (z) represents evolution of the pump power along the z axis, and f(r,z) is a geometrical function depending on the pump geometry. Assuming a flattop radial profile for the pump beam, this function can be described by Eq. (3):

_{p}(z) represents the waist radius of the pump beam along the z axis. Figure 1 presents the general scheme for an end-pumped crystal with the hypothesis mentionned before.

## 2.1 Determination of dP/dz

_{p}inside the crystal can be described by Eq. (4), assuming there is no reabsorption at the laser wavelength. In our case, this hypothesis is fully justified for the 1-µm transition in Nd

^{3+}as it is a 4-level laser system :

_{NS}is the unsaturated absorption coefficient at the pump wavelength, and the saturation intensity of the pump (I

_{psat}) and the laser (I

_{lsat}) are defined as :

_{abs}(λ) and σ

_{em}(λ) are the absorption and stimulated emission cross sections, respectively. The evolution of the pump intensity I

_{p}(z) can therefore be calculated numerically, by dividing the crystal in small slices of thickness dz. It is then possible to calculate the dP/dz factor with a good accuracy, taking into account bleaching effects. However, one can remark that for a high intracavity laser intensity, the absorption is desaturated by the laser effect and the absorption coefficient α becomes close to α

_{NS}. We calculated [thanks to Eq. (4)] the evolution of the absorption coefficient along the z-axis of a 1% at. doped Nd:YAG crystal under the experimental conditions described in section 4, with and without laser effect, to show that the absorption is clearly desaturated by the intracavity laser intensity. The result is shown on Fig. 2.

_{NS}=constant under laser effect in our experimental conditions. It is then possible to simply write :

_{0}is the incident pump power.

## 2.2 Estimation of the η_{h} parameter

_{p}is the pump quantum efficiency, η

_{l}is the laser extraction efficiency, corresponding to the fraction of ions of the upper laser level extracted by stimulated emission (=0 without laser operation), and η

_{r}is the radiative quantum efficiency of the upper metastable level. λ

_{p}is the pump wavelength, λ

_{f}is the average fluorescence wavelength, and λ

_{l}is the laser wavelength.

_{p}can be considered to be close to unity [15

15. S. Chenais, F. Druon, S. Forget, and F. Balembois, “On thermal effects in solid-state lasers: The case of ytterbium doped materials,” Prog. Quantum Electron. **30**, 89–153 (2006). [CrossRef]

_{p}~1.

_{l}=0. In this case, it is difficult to give an accurate value of the fractionnal thermal load. The lack of an efficient laser extraction leads to accumulation of ions in the excited level, enhancing parasitic heating effects like cross-relaxations, upconversion, etc. Those effects are difficult to evaluate with good precision and depend on the experimental conditions, and consquently η

_{h}is uneasy to determinate.

_{l}can be estimated through Eq. (10) [15

15. S. Chenais, F. Druon, S. Forget, and F. Balembois, “On thermal effects in solid-state lasers: The case of ytterbium doped materials,” Prog. Quantum Electron. **30**, 89–153 (2006). [CrossRef]

_{e}is the emission cross section at the laser wavelength, I is the intracavity laser power, τ is the lifetime of the active ion. One can remark that with high intracavity laser power, η

_{l}tends to become close to unity. This is equivalent to saying that every ion in the excited state will contribute to stimulated emission. In this case, the fractional thermal load η

_{h}is independent of the radiative quantum efficiency η

_{r}, and η

_{h}is simply equal to the quantum defect:

_{l}=1.

_{l}versus intracavity laser power are plotted in Fig. 3 for typical 1% at. doped Nd:YAG, Nd:YVO

_{4}and Nd:GdVO

_{4}crystals, for a laser waist of 400 µm diameter. For intracavity laser power above 200 W, it is a very good approximation to consider the laser extraction efficiency close to unity at the center of the laser mode (r=0), where the intensity is maximum. Nethertheless, as the laser beam is Gaussian, it is important to check if η

_{l}remains close to unity in all the area where the pump is absorbed and in particular in a plane perpendicular to the z axis. For that purpose, we plotted in Fig. 4 the evolution of the η

_{l}function versus the radial coordinate r, assuming a Gaussian laser mode, a supergaussian pump mode corresponding to our experimental setup (cf. section 3) and using formula (10).

_{l}value remains very close to unity in all the pumped region if the intracavity laser power is high enough. In this case, considering pumping at 808 nm and laser effect at 1064 nm, Eq. (11) gives η

_{h}=0.24 in laser operation within all the pumped region of the crystal. Such fractionnal thermal load was measured experimentally by Taira and al. for a 1% at. doped Nd:YAG crystal in laser operation [17

17. I. Shoji, T. Taira, T. Taira, and A. Ikesue, “Thermally-induced-birefringence effects of highly Nd3+-doped Y3Al5O12 ceramic lasers,” Opt. Mater. **29**, 1271–1276 (2007). [CrossRef]

### 2.3 Determination of Kc

_{0},z=0) will be measured by IR thermography. Kc is the only unknown parameter, all the others parameters can be calculated with values corresponding to the experimental setup. Therefore, Kc can be adjusted to fit the experimental results to the calculations.

## 3. Experimental setup

_{2}and a plane mirror M

_{1}(which can be one face of the crystal with a high reflection (HR) coating). To ensure η

_{l}=1 in formula (10), the laser must operate far above threshold, with high intracavity power. For that purpose, we used high reflectivity mirrors instead of output couplers. The laser cavities were designed by ABCD matrix simulations to fit the laser mode with the size of the pumped area. We used different crystal mounts and different laser cavities and we checked that the experimental results were independent from the experimental parameters.

*Flir system Inc.*operating in the 8–12 µm range. The detection matrix is composed of 320×240 microbolometers working at room temperature. The resolution of the image is limited by the size of the microbolometers (62×62µm

^{2}) and the magnification of the total thermal imaging system is close to unity. Therefore, a 3×3 mm

^{2}crystal face will be imaged in approximately 50×50 pixels.

### 3.1 Measurement of the pump beam profile

_{p}(z), can be described by Eq. (13):

_{p0}is the radius of the pump beam measured at the focal point, M

^{2}

_{p}is the M

^{2}factor of the pump beam, and z

_{0}is the longitudinal coordinate of the focal point. We measured w

_{p0}=220 µm for a magnification of 1 of the output of the diode by two doublets, and w

_{p0}=170 µm for a magnification of 0.75. M

^{2}

_{p}was measured to be approximately 150. The pump was focused close to the input face of the crystal (z

_{0}=0) (cf. Fig. 1).

### 3.2 Evaluation of the measurements accuracy

_{0}parameter is 3.5%. The function f(r,z) mainly depends on the measurement of ω

_{p}, which is the radius of the pump spot [see Eq. (3)]. This radius, if measured with a high sensibility camera, can be known with a precision around 2%, resulting in a precision of f(r,z) estimated around 1% by error propagation calculations.

## 4. Thermal conductivity measurements on Nd:YAG

^{2}, length 4 mm. The faces of the crystal received anti-reflection coatings at 808 nm and 1064 nm. The pump power incident on the crystal is P

_{0}=24 W. The 400 µm output fiber of the laser diode is imaged in the crystal with a magnification of 1, by two doublets. The unsaturated absorption coefficient of the crystal is measured to be α=3.1 cm

^{-1}. Laser operation at 1064 nm is achieved in a two mirror cavity. M1 is a flat dichroïc mirror and M2 is a concave mirror with radius of curvature 300 mm. Both are highly reflective at 1064 nm. The laser threshold is very low, around 1W of pump power. This confirms that the cavity has low losses. By measuring the power leak of the ZnSe plate, we estimated the laser power intracavity to 140 W. By using formula (10) in this configuration, we found η

_{l}=0.998 (see Fig. 3).

## 5. Thermal conductivity measurements on Nd:YVO_{4} and Nd:GdVO_{4} crystals

_{4}and Nd:GdVO

_{4}are uniaxial crystals, with different conductivities on their a and c axes. In anisotropic crystals with thermal conductivity strongly depending on the axis, the temperature map doesn’t have radial symmetry, and formula (2) is no more applicable. More precisely, the analytical geometrical function f(r,z) defined by (3) is not representative of the heat repartition in the crystal. If we want to make measurements on such crystals, it is possible to bypass the approximations made to demonstrate formula (2) and fit temperature measurements with numerical simulations, by Finite Element Analysis. Those simulations codes, by calculating the heat transfer between one small element and every neighbor element, can take into account the possible anisotropy of the thermo-mechanical properties of the crystals. FEA simulations are carried out with the LASCAD software.

_{h}, the absorption coefficient α

_{NS}, the pump characteristics, and the geometry of the cooling system. The thermal conductivities values on the crystal axes perpendicular to the pump axis, K

_{cx}and K

_{cy}, are the fit parameters. The result of the simulation is a complete temperature map of the crystal, and the simulated temperature profiles of the pumped face can be compared to the measurements made with the experimental setup, to find the best fit parameters. Figure 10 presents the optimization process.

_{4}and Nd:GdVO

_{4}crystals : 0.1% at. doped, 3×3×10 mm

^{3}crystals, and 1% at. doped, 3×3×5 mm

^{3}crystals. All crystals come from CASIX inc.. They are a-cut and one face received HR coating at 1064 nm and anti-reflection (AR) coating at 808 nm. The experimental setup is similar to the one presented in Fig. 5, but the mirror M1 is directly deposed on the crystal face, and a polarizer was inserted in the collimated pump beam to pump the crystal on the pi polarization, corresponding to the c-axis of the crystal.

_{0}parameters are summarized in table 1. The laser cavity is composed of the HR coated face of the crystal and a concave mirror M2 with a radius of curvature of 150 mm. With a 15% output coupler, under a pump power of 23W, we achieved a power of 12.3W of laser in the Nd:YVO4 crystal and 11 W in the Nd:GdVO4 crystal in order to check their good laser quality. For all thermal measurements, we used a high reflectivity mirror to increase the intracavity laser power and reach the condition η

_{l}=1. (cf. Section 2). The threshold of the laser effect is smaller than 1 W of pump power. The cavity length is adjusted to around L=80 mm in order to achieve single-spatial mode laser emission. The intracavity laser power is evaluated to 250 W with the Nd:GdVO

_{4}crystals and 300 W with the Nd:YVO

_{4}crystals. The corresponding values of η

_{l}are 0.995 and 0.997, respectively.

_{4}crystal are presented in Fig. 11.

_{4}, Kc between 6 and 12 W/mK for a-cut Nd:GdVO

_{4}crystals, along the c-axis), and show a clear advantage for the Nd:GdVO

_{4}crystal compared to Nd:YVO

_{4}, which would result in a 20% lower temperature elevation for the same absorbed pump power.

_{0}coefficients are summarized in table 3.

_{00}emission, and it is closed by a high reflectivity mirror M2 with a radius of curvature of 150 mm.

_{4}. This gives η

_{l}values of 0.996 and 0.994 for the Nd:YVO

_{4}and Nd:GdVO

_{4}, respectively. The temperature profiles for a Nd:GdVO

_{4}crystal are shown on Fig. 12. The numerical fit gives values of Kc summarized in Table 4. Those values are very close to the one obtained with 0.1% at. doped crystals.

18. R. Gaume, B. Viana, and D. Vivien, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. **83**, 1355–1357 (2003). [CrossRef]

_{4}the thermal conductivity should only decrease from 6.6 W/(mK) in a 0.1% doped crystal to 6.4 W/(mK) in 1% at. doped crystal. In Nd:GdVO

_{4}, the drop off is less noticeable, since the Gadolinium ion have a ionic radius closer to Neodymium than the Yttrium ion : the thermal conductivity should stay very close to 8.0 W/(mK) from 0.1% to 1% at. of Neodymium.

_{4}. This is in good agreement with previous measurements made by flash method by Ogawa and al. [19]. This also proves that the measurement method is reliable even for highly doped crystals.

_{4}crystals, and 15% in the Nd:YVO

_{4}crystals. Those observations are coherent with the slightly higher anisotropy of the Nd:GdVO

_{4}. Previous work reported typical values of 20% of variation between the axes in both crystals [5

**14**, 10528–10536 (2006). [CrossRef] [PubMed]

11. C. Kränkel, *et al.*, “Continuous wave laser operation of Yb3+:GdVO4,” Appl. Phys. B **79**, 543–546 (2004). [CrossRef]

## 6. Discussion and conclusion

_{4}and Nd:GdVO

_{4}crystals, we found thermal conductivity values inside the range of previously published values. Conductivity of the Nd:GdVO

_{4}crystal was measured to be higher than the one of Nd:YVO

_{4}. Those results are in agreement with some previous works [20][7

7. L. J. Qin, X. L. Meng, H. Y. Shen, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, “Thermal conductivity and refractive indices of Nd:GdVO4 crystals,” Cryst. Res. Technol. **38**, 793–797 (2003). [CrossRef]

**14**, 10528–10536 (2006). [CrossRef] [PubMed]

_{4}crystals for doping concentrations below 1% at. in Neodymium. The dispersion of the measurements observed with the flash method and its derivatives can be attributed to several factors, including variations of the quality of the different samples, and experimental issues discussed in the introduction. It is also possible that the heat diffusivity measurement method, using uniform heating on the crystal surface, doesn’t really represent the heat conduction properties under pumping and laser conditions, because of the stress induced by the focalization of the pump beam in the crystal. To our knowledge, no study of the variation of the thermal conductivity with the stress conditions has been carried out in laser crystals. If this effect is really important, the new method presented in this work has the advantage to measure the conductivity in operational conditions, under diode-pumping and with laser effect.

## Acknowledgments

## References and links

1. | J. Parker, R. J. Jenkins, C. P. Butler, and G. L. Abbott, “Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity,” J. of Appl. Phys. |

2. | L. Pottier, “Micrometer scale visualization of thermal waves by photoreflectance microscopy,” Appl. Phys. Lett. |

3. | A. Salazar, A. Sanchez-Lavega, and J. Fernandez, “Thermal diffusivity measurements in solids by the ‘mirage’ technique: Experimental results,” J. of Appl. Phys. |

4. | J. F. Bisson, D. Fournier, M. Poulain, O. Lavigne, and R. Mévre, “Thermal conductivity of Yttria-Zirconia single crystals determined by spatially resolved infrared thermography,” J. Am. Ceram. Soc. |

5. | Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express |

6. | A. I. Zagumennyi, G. B. Lutts, P. A. Popov, N. N. Sirota, and I. A. Shcherbakov, “The thermal conductivity of YAG and YSAG laser crystals,” Laser Phys. |

7. | L. J. Qin, X. L. Meng, H. Y. Shen, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, “Thermal conductivity and refractive indices of Nd:GdVO4 crystals,” Cryst. Res. Technol. |

8. | J.R. O’connor, “Unusual crystal field energy levels and efficient laser properties of YVO4:Nd3+,” Appl. Phys. Lett.9, 407. |

9. | A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbakov, T. Jensen, J. P. Meyen, and G. Huber, “The Nd:GdVO4 crystal, a new material for diode-pumped lasers,” Sov. Quantum Electron. |

10. | B. H. T. Chai, G. Loutts, J. Lefaucheur, X. X. Zhang, P. Hong, M. Bass, I. A. Shcherbakov, and A. I. Zagumennyi, “Comparison of laser performance of Nd-doped YVO |

11. | C. Kränkel, |

12. | P. A. Studenikin, A. I. Zagumennyi, Yu. D. Zavartsev, P. A. Popov, and I. A. Shcherbakov, “GdVO |

13. | W. Koechner, “ |

14. | A. Cousins
, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. |

15. | S. Chenais, F. Druon, S. Forget, and F. Balembois, “On thermal effects in solid-state lasers: The case of ytterbium doped materials,” Prog. Quantum Electron. |

16. | T. Y. Fan, “Heat Generation in Nd:YAG and Yb:YAG,” J. of Quantum Electron. |

17. | I. Shoji, T. Taira, T. Taira, and A. Ikesue, “Thermally-induced-birefringence effects of highly Nd3+-doped Y3Al5O12 ceramic lasers,” Opt. Mater. |

18. | R. Gaume, B. Viana, and D. Vivien, “A simple model for the prediction of thermal conductivity in pure and doped insulating crystals,” Appl. Phys. Lett. |

19. | T. Ogawa, Y. Urata, S. Wada, K. Onodera, H. Machida, H. Sagae, M. Higuch, and K. Kodaira, “879nm-LD-pumped Nd:GdVO4 laser and its thermal property,” OSA Trends in Optics and Photonics |

20. | A. I. Zagumennyi, V. A. Mikhailov, V. I. Vlasov, A. A. Sirotkin, V. I. Podreshetnikov, Yu. L. Kalachev, Yu. D. Zavartsev, S. A. Kutovoi, and I. A. Shcherbakov, “Diode-pumped lasers based on GdVO |

**OCIS Codes**

(140.3380) Lasers and laser optics : Laser materials

(140.5680) Lasers and laser optics : Rare earth and transition metal solid-state lasers

(140.6810) Lasers and laser optics : Thermal effects

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: September 14, 2007

Revised Manuscript: January 17, 2008

Manuscript Accepted: January 21, 2008

Published: June 4, 2008

**Citation**

Julien Didierjean, Emilie Herault, François Balembois, and Patrick Georges, "Thermal conductivity measurements of laser crystals by infrared thermography. Application to Nd:doped crystals," Opt. Express **16**, 8995-9010 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8995

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### References

- J. Parker, R. J. Jenkins, C. P. Butler, and G. L. Abbott, "Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity," J. of Appl. Phys. 32, 1679 (1961). [CrossRef]
- L. Pottier, "Micrometer scale visualization of thermal waves by photoreflectance microscopy," Appl. Phys. Lett. 64, 1618 (1994). [CrossRef]
- A. Salazar, A. Sanchez-Lavega, and J. Fernandez, "Thermal diffusivity measurements in solids by the ??mirage?? technique: Experimental results," J. of Appl. Phys. 69, 1216 (1991). [CrossRef]
- J. F. Bisson, D. Fournier, M. Poulain, O. Lavigne, and R. Mévre, "Thermal conductivity of Yttria-Zirconia single crystals determined by spatially resolved infrared thermography," J. Am. Ceram. Soc. 83, 1993-1998 (2000). [CrossRef]
- Y. Sato and T. Taira, "The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method," Opt. Express 14, 10528-10536 (2006). [CrossRef] [PubMed]
- A. I. Zagumennyi, G. B. Lutts, P. A. Popov, N. N. Sirota, and I. A. Shcherbakov, "The thermal conductivity of YAG and YSAG laser crystals," Laser Phys. 3, 1064-1065 (1993).
- L. J. Qin, X. L. Meng, H. Y. Shen, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, "Thermal conductivity and refractive indices of Nd:GdVO4 crystals," Cryst. Res. Technol. 38,793-797 (2003). [CrossRef]
- J. R. O??connor, "Unusual crystal field energy levels and efficient laser properties of YVO4:Nd3+," Appl. Phys. Lett. 9, 407-409 (1966).
- A. I. Zagumennyi, V. G. Ostroumov, I. A. Shcherbakov, T. Jensen, J. P. Meyen, and G. Huber, "The Nd:GdVO4 crystal, a new material for diode-pumped lasers," Sov. Quantum Electron. 22, 1071-1072 (1992). [CrossRef]
- B. H. T. Chai, G. Loutts, J. Lefaucheur, X. X. Zhang, P. Hong, M. Bass, I. A. Shcherbakov, and A. I. Zagumennyi, "Comparison of laser performance of Nd-doped YVO4, GdVO4, Ca5(PO4)3F, Sr5(PO4)3F, and Sr5(VO4)3F," Proceeding OSA ASSL 1994, 20, 41 (1994).
- C. Kränkel, et al., "Continuous wave laser operation of Yb3+:GdVO4," Appl. Phys. B 79, 543-546 (2004). [CrossRef]
- P. A. Studenikin, A. I. Zagumennyi, Yu. D. Zavartsev, P. A. Popov, I. A. Shcherbakov, "GdVO4 as a new medium for solid-state lasers: some optical and thermal properties of crystals doped with Cd3+, Tm3+, and Er3+ ions," Quantum Electron. 25, 1162 (1995). [CrossRef]
- W. Koechner, Solid State Laser Engineering, 5th Edition (Springer, 1999).
- A. Cousins, "Temperature and thermal stress scaling in finite-length end-pumped laser rods," IEEE J. Quantum Electron. 28, 1057 (1992). [CrossRef]
- S. Chenais, F. Druon, S. Forget, and F. Balembois, "On thermal effects in solid-state lasers: The case of ytterbium doped materials," Prog. Quantum Electron. 30, 89-153 (2006). [CrossRef]
- T. Y. Fan, "Heat Generation in Nd:YAG and Yb:YAG," J. of Quantum Electron. 29, 1457-1459 (1993). [CrossRef]
- I. Shoji, T. Taira, T. Taira, and A. Ikesue, "Thermally-induced-birefringence effects of highly Nd3+-doped Y3Al5O12 ceramic lasers," Opt. Mater. 29, 1271-1276 (2007). [CrossRef]
- R. Gaume, B. Viana, and D. Vivien, "A simple model for the prediction of thermal conductivity in pure and doped insulating crystals," Appl. Phys. Lett. 83, 1355-1357 (2003). [CrossRef]
- T. Ogawa, Y. Urata, S. Wada, K. Onodera, H. Machida, H. Sagae, M. Higuch, and K. Kodaira, "879nm-LD-pumped Nd:GdVO4 laser and its thermal property, " OSA Trends in Optics and Photonics 94, 293-297 (2004).
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