## Fracture characteristics of ceramic Nd:YAG |

Optics Express, Vol. 22, Issue 9, pp. 11331-11339 (2014)

http://dx.doi.org/10.1364/OE.22.011331

Acrobat PDF (1088 KB)

### Abstract

The fracture of laser material in a ceramic Nd:YAG laser pumped by a fiber-coupled laser diode was analyzed. The fracture of the laser material was found to occur when the critical temperature difference between the center of the material and the surface exceeded 355°C. To quantitatively analyze the material fracture, the heat-generation length and heat-generation radius of the laser material were calculated and the critical pump power per unit volume was examined. Under lasing and non-lasing conditions, the fracture of laser material occurred at 24.41 kW/cm^{3} and 19.53 kW/cm^{3}, respectively, for 2 at.% ceramic Nd:YAG and 25.57 kW/cm^{3} and 20.47 kW/cm^{3}, respectively, for 4 at.% ceramic Nd:YAG.

© 2014 Optical Society of America

## 1. Introduction

3. M. Ohmi, M. Akatsuka, K. Ishikawa, K. Naito, Y. Yonezawa, Y. Nishida, M. Yamanaka, Y. Izawa, and S. Nakai, “High-sensitivity two-dimensional thermal- and mechanical-stress-induced birefringence measurements in a Nd:YAG rod,” Appl. Opt. **33**(27), 6368–6372 (1994). [CrossRef] [PubMed]

7. R. Kawai, Y. Miyasaka, K. Otsuka, T. Ohtomo, T. Narita, J.-Y. Ko, I. Shoji, and T. Taira, “Oscillation spectra and dynamic effects in a highly-doped microchip Nd:YAG ceramic laser,” Opt. Express **12**(10), 2293–2302 (2004). [CrossRef] [PubMed]

^{1/2}) are up to 3, 1.3, 1.1, and 5 times greater than those of the Nd:YAG crystal, respectively [8

8. I. Shoji, Y. Sato, S. Kurimura, V. Lupei, T. Taira, A. Ikesue, and K. Yoshida, “Thermal-birefringence-induced depolarization in Nd:YAG ceramics,” Opt. Lett. **27**(4), 234–236 (2002). [CrossRef] [PubMed]

9. D. Welford, D. M. Rines, B. J. Dinerman, and R. Martinsen, “Observation of enhanced thermal lensing due to near-Gaussian pump energy deposition in a laser-diode side-pumped Nd:YAG laser,” IEEE J. Quantum Electron. **28**(4), 1075–1080 (1992). [CrossRef]

^{3+}dopant concentration, critical temperature difference, and heat generation volume of the laser material. Based on these findings, the critical temperature difference per unit volume is calculated to assess the cause of material fracture.

## 2. Experiment setup

^{3+}dopant concentrations of 2 at.% and 4 at.%, respectively. The results of the experiment with a dopant concentration of 2 at.% revealed an output power of 2.21 W for a 6.54-W pump power, giving a maximum of approximately 33.3% output efficiency, 39.3% slope efficiency, and a 0.92-W lasing threshold. When the pump power exceeded 6 W, the output decreased due to the thermal lens effect, and at approximately 12 W, the laser did not oscillate [14

14. C.-M. Ok, B.-T. Kim, and D.-L. Kim, “The output characteristics of a fiber-coupled laser-diode pumped ceramic Nd:YAG laser due to thermal lensing effect,” Kor. J. Opt. Photonics **17**(5), 455–460 (2006). [CrossRef]

## 3. Temperature distribution in the laser material

15. A. Lucianetti, T. Graf, R. Weber, and H. P. Weber, “Thermooptical properties of transversely pumped composite YAG rods with a Nd-doped core,” IEEE J. Quantum Electron. **36**(2), 220–227 (2000). [CrossRef]

18. J. M. Eichenholz and M. Richardson, “Measurement of thermal lensing in Cr^{3+}-doped colquiriites,” IEEE J. Quantum Electron. **34**(5), 910–919 (1998). [CrossRef]

^{−1}and 40 cm

^{−1}are used for 2 at.% and 4 at.% Nd

^{3+}, respectively. In the above equation,

19. P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, and D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. **35**(4), 647–655 (1999). [CrossRef]

20. Z. Xiong, Z. G. Li, N. Moore, W. L. Huang, and G. C. Lim, “Detailed investigation of thermal effects in longitudinally diode-pumped Nd:YVO_{4} laser,” IEEE J. Quantum Electron. **39**(8), 979–986 (2003). [CrossRef]

## 4. Thermal shock resistance

## 5. Critical temperature difference

^{2}K was used for the heat transfer coefficient for the material surface covered with indium foil [21

21. R. Weber, B. Neuenschwander, M. MacDonald, M. B. Roos, and H. P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. **34**(6), 1046–1053 (1998). [CrossRef]

22. D. P. H. Hasselman, “Figures-of-merit for the thermal stress resistance of high-temperature brittle materials: a review,” Ceramurgia International **4**(4), 147–150 (1978). [CrossRef]

## 6. Difference heat generation rate in the laser material

## 7. Fracture analysis results

^{3}. Under the non-lasing condition, the critical pump power was 11.9 W, and the corresponding critical pump power per unit volume was 19.5 kW/cm

^{3}. The calculated critical pump power per unit volume is a quantitative value indicating the point at which material facture for 2 at.% ceramic Nd:YAG occurs. The critical pump powers for the material with a dopant concentration of 4 at.% under lasing and non-lasing conditions are 6.87 W and 5.50 W, respectively, and the critical pump powers per unit volume are 25.57 kW/cm

^{3}and 20.47 kW/cm

^{3}, respectively. Although the beam diameter of the pump changes, because the critical pump power per unit volume is constant for a given dopant concentration and lasing condition, the critical pump power can be easily predicted. Thus, for a pump beam diameter of 560 μm and a dopant concentration of 4 at.%, the heat generation radius and length are 652 μm and 2.30 mm, respectively. The critical pump powers are 7.85 W and 6.28 W for lasing and non-lasing conditions, respectively, and the critical pump powers per unit volume are 25.57 kW/cm

^{3}and 20.47 kW/cm

^{3}, respectively. The pump power needed to induce the critical temperature difference increased as the pump beam diameter increased because the increase in the beam diameter increases the heat generation volume, allowing much more heat to accumulate.

## 8. Conclusion

^{3}and 19.53 kW/cm

^{3}under the lasing and non-lasing conditions, respectively, for 2 at.% ceramic Nd:YAG and 25.57 kW/cm

^{3}and 20.47 kW/cm

^{3}under the lasing and non-lasing conditions, respectively, for 4 at.% ceramic Nd:YAG. To reduce the occurrences of fracture in ceramic Nd:YAG, the critical temperature difference was analyzed in terms of material diameter. It was found that when the diameter decreases from 5 mm to 2 mm, 1.4 times more incident pump power is allowed. Lastly, to use ceramic Nd:YAG in a wider range of applications, more studies on the fracture characteristics of various material shapes are needed.

## Acknowledgments

## References and links

1. | W. Koechner, |

2. | N. Hodgson and H. Weber, |

3. | M. Ohmi, M. Akatsuka, K. Ishikawa, K. Naito, Y. Yonezawa, Y. Nishida, M. Yamanaka, Y. Izawa, and S. Nakai, “High-sensitivity two-dimensional thermal- and mechanical-stress-induced birefringence measurements in a Nd:YAG rod,” Appl. Opt. |

4. | I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd |

5. | J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramics,” Appl. Phys. B |

6. | J. Lu, H. Yagi, K. Takaichi, T. Uematsu, J.-F. Bisson, Y. Feng, A. Shirakawa, K.-I. Ueda, T. Yanagitani, and A. A. Kaminskii, “110 W ceramic Nd |

7. | R. Kawai, Y. Miyasaka, K. Otsuka, T. Ohtomo, T. Narita, J.-Y. Ko, I. Shoji, and T. Taira, “Oscillation spectra and dynamic effects in a highly-doped microchip Nd:YAG ceramic laser,” Opt. Express |

8. | I. Shoji, Y. Sato, S. Kurimura, V. Lupei, T. Taira, A. Ikesue, and K. Yoshida, “Thermal-birefringence-induced depolarization in Nd:YAG ceramics,” Opt. Lett. |

9. | D. Welford, D. M. Rines, B. J. Dinerman, and R. Martinsen, “Observation of enhanced thermal lensing due to near-Gaussian pump energy deposition in a laser-diode side-pumped Nd:YAG laser,” IEEE J. Quantum Electron. |

10. | D. J. Green, |

11. | S. P. Timoshenko and J. N. Goodier, |

12. | B. A. Boley and J. H. Weiner, |

13. | Y. A. Cengel, |

14. | C.-M. Ok, B.-T. Kim, and D.-L. Kim, “The output characteristics of a fiber-coupled laser-diode pumped ceramic Nd:YAG laser due to thermal lensing effect,” Kor. J. Opt. Photonics |

15. | A. Lucianetti, T. Graf, R. Weber, and H. P. Weber, “Thermooptical properties of transversely pumped composite YAG rods with a Nd-doped core,” IEEE J. Quantum Electron. |

16. | Y. Chen, B. Chen, M. K. R. Patle, A. Kar, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab Laser-II,” IEEE J. Quantum Electron. |

17. | Y. Aoyagi, T. Taira, and I. Shoji, “Thermal analysis simulation using depolarization loss in solid-state microchip laser,” SICE 2003 Annual Conference in Fukui |

18. | J. M. Eichenholz and M. Richardson, “Measurement of thermal lensing in Cr |

19. | P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, and D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. |

20. | Z. Xiong, Z. G. Li, N. Moore, W. L. Huang, and G. C. Lim, “Detailed investigation of thermal effects in longitudinally diode-pumped Nd:YVO |

21. | R. Weber, B. Neuenschwander, M. MacDonald, M. B. Roos, and H. P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. |

22. | D. P. H. Hasselman, “Figures-of-merit for the thermal stress resistance of high-temperature brittle materials: a review,” Ceramurgia International |

23. | D. Munz and T. Fett, |

**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

(140.6810) Lasers and laser optics : Thermal effects

**ToC Category:**

Materials

**History**

Original Manuscript: March 10, 2014

Revised Manuscript: April 28, 2014

Manuscript Accepted: April 28, 2014

Published: May 2, 2014

**Citation**

Duck-Lae Kim and Byung-Tai Kim, "Fracture characteristics of ceramic Nd:YAG," Opt. Express **22**, 11331-11339 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-11331

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### References

- W. Koechner, Solid-State Laser Engineering (Springer-Verlag, 1999), Chap. 7.
- N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer, 2005), Chap. 13.
- M. Ohmi, M. Akatsuka, K. Ishikawa, K. Naito, Y. Yonezawa, Y. Nishida, M. Yamanaka, Y. Izawa, S. Nakai, “High-sensitivity two-dimensional thermal- and mechanical-stress-induced birefringence measurements in a Nd:YAG rod,” Appl. Opt. 33(27), 6368–6372 (1994). [CrossRef] [PubMed]
- I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941 (2000).
- J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramics,” Appl. Phys. B 71(4), 469–473 (2000). [CrossRef]
- J. Lu, H. Yagi, K. Takaichi, T. Uematsu, J.-F. Bisson, Y. Feng, A. Shirakawa, K.-I. Ueda, T. Yanagitani, A. A. Kaminskii, “110 W ceramic Nd3+: Y3Al5O12 laser,” Appl. Phys. B 79(1), 25–28 (2004). [CrossRef]
- R. Kawai, Y. Miyasaka, K. Otsuka, T. Ohtomo, T. Narita, J.-Y. Ko, I. Shoji, T. Taira, “Oscillation spectra and dynamic effects in a highly-doped microchip Nd:YAG ceramic laser,” Opt. Express 12(10), 2293–2302 (2004). [CrossRef] [PubMed]
- I. Shoji, Y. Sato, S. Kurimura, V. Lupei, T. Taira, A. Ikesue, K. Yoshida, “Thermal-birefringence-induced depolarization in Nd:YAG ceramics,” Opt. Lett. 27(4), 234–236 (2002). [CrossRef] [PubMed]
- D. Welford, D. M. Rines, B. J. Dinerman, R. Martinsen, “Observation of enhanced thermal lensing due to near-Gaussian pump energy deposition in a laser-diode side-pumped Nd:YAG laser,” IEEE J. Quantum Electron. 28(4), 1075–1080 (1992). [CrossRef]
- D. J. Green, An Introduction to the Mechanical Properties of Ceramics (Cambridge University, 1998), Chap. 9.
- S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, 1970), Chap. 13.
- B. A. Boley and J. H. Weiner, Theory of Thermal Stresses (Dover, 2011), Chap. 8.
- Y. A. Cengel, Heat Transfer: A Practical Approach (McGraw-Hill, 2003), Chap. 3.
- C.-M. Ok, B.-T. Kim, D.-L. Kim, “The output characteristics of a fiber-coupled laser-diode pumped ceramic Nd:YAG laser due to thermal lensing effect,” Kor. J. Opt. Photonics 17(5), 455–460 (2006). [CrossRef]
- A. Lucianetti, T. Graf, R. Weber, H. P. Weber, “Thermooptical properties of transversely pumped composite YAG rods with a Nd-doped core,” IEEE J. Quantum Electron. 36(2), 220–227 (2000). [CrossRef]
- Y. Chen, B. Chen, M. K. R. Patle, A. Kar, M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab Laser-II,” IEEE J. Quantum Electron. 40(7), 917–928 (2004). [CrossRef]
- Y. Aoyagi, T. Taira, and I. Shoji, “Thermal analysis simulation using depolarization loss in solid-state microchip laser,” SICE 2003 Annual Conference in Fukui 2, 195–2000 (2003).
- J. M. Eichenholz, M. Richardson, “Measurement of thermal lensing in Cr3+-doped colquiriites,” IEEE J. Quantum Electron. 34(5), 910–919 (1998). [CrossRef]
- P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35(4), 647–655 (1999). [CrossRef]
- Z. Xiong, Z. G. Li, N. Moore, W. L. Huang, G. C. Lim, “Detailed investigation of thermal effects in longitudinally diode-pumped Nd:YVO4 laser,” IEEE J. Quantum Electron. 39(8), 979–986 (2003). [CrossRef]
- R. Weber, B. Neuenschwander, M. MacDonald, M. B. Roos, H. P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34(6), 1046–1053 (1998). [CrossRef]
- D. P. H. Hasselman, “Figures-of-merit for the thermal stress resistance of high-temperature brittle materials: a review,” Ceramurgia International 4(4), 147–150 (1978). [CrossRef]
- D. Munz and T. Fett, Ceramics (Springer, 1998), Chap. 11.

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