## Heat transport in solid and air-clad fibers for high-power fiber lasers

Optics Express, Vol. 15, Issue 25, pp. 16787-16793 (2007)

http://dx.doi.org/10.1364/OE.15.016787

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### Abstract

An analytical approach for the thermal design for high-power fiber lasers and fiber components is presented. The approach is based on defining a thermal resistance for each fiber layer. Thus the importance of each layer for the heat transport is made transparent and the influence of the parameters can be studied for each layer separately. Furthermore the analysis and analytic optimization of interacting effects of groups of layers is possible. The approach is applied to air-clad-fiber with results differing up to 40 % from previous works. Furthermore the heat transport from splices is analyzed and recommendations for the thermal packaging of splices and fiber integrated components are given.

© 2007 Optical Society of America

## 1. Introduction

1. D. C. Brown and H. J. Hoffman, “Thermal Stress and Thermo-Optic Effects in High Average Power Double-Clad Silica Fiber Lasers,” IEEE J. Quantum Electron. **37**, 2, (2001). [CrossRef]

3. Y. Wang, C.-Q. Xu, and H. Po “Analysis of Raman and thermal effects in kilowatt fiber lasers,” Opt.Commun. **242**, 487–502 (2004). [CrossRef]

## 2. Method

_{1})=T

_{s1}and T(r=r

_{2})=T

_{s2}with r

_{1}as the inner and r

_{2}as the outer radius of the layer leads to Eq. (3).

_{tcond}of a hollow cylinder can be expressed as:

5. J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express **11**, 2982 (2003). [CrossRef] [PubMed]

5. J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express **11**, 2982 (2003). [CrossRef] [PubMed]

5. J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express **11**, 2982 (2003). [CrossRef] [PubMed]

_{tconv}is given in Eq. (7) with α as the convective heat transfer coefficient:

## 3. Application to Air-Clad Fibers

_{tbridge}and the air chambers R′

_{tair}separately and combining these with:

**11**, 2982 (2003). [CrossRef] [PubMed]

**11**, 2982 (2003). [CrossRef] [PubMed]

**11**, 2982 (2003). [CrossRef] [PubMed]

## 4. Optimization of the active fiber

^{2}K).

^{4}W/(mK) for a fluid velocity of 1 m/s Eq. (13) leads to an inner coating radius smaller than the pump cladding radius.

_{p}can be identified with Eq (14):

## 5. Packaging of Splices

_{1}is the heat generated in the fiber or at the surface of the fiber, q′

_{2}is the heat generated by absorption of the scattered light at the boundary layer of the recoat.

_{1}is zero the maximum temperature occurs at the boundary layer between recoat and surrounding medium, if q′

_{1}is not zero, the maximum temperature is at the surface of pump cladding. We varied the thickness of the recoat with a varying fraction of q′

_{1}of the total heat-flow. The applied thermal conductivities of the layers are 1.38 W/(mK) for the glass part, 0.3 W/(mK) for the recoat, 2 W/(mK) for the heat conducting paste and 380 W/(mK) for the splice holder with an outer radius of 10 mm. The thermal resistance of the convective water cooling was calculated for a plane of 10 mm width and a convective heat transfer coefficient of 4000 W/(m

^{2}K) which corresponds to a fluid velocity of 1 m/s. The results are given in Fig. 3. The applied heat flow per unit length q′

_{tot}=q′

_{1}+q′

_{2}was 4255 W/m.

## 6. Accuracy of the model

## 7. Conclusion

## Acknowledgements

## References and links

1. | D. C. Brown and H. J. Hoffman, “Thermal Stress and Thermo-Optic Effects in High Average Power Double-Clad Silica Fiber Lasers,” IEEE J. Quantum Electron. |

2. | N. A. Brilliant and K. Lagonik, “Thermal effects in a dual-clad ytterbium fiber laser,” Opt. Lett. |

3. | Y. Wang, C.-Q. Xu, and H. Po “Analysis of Raman and thermal effects in kilowatt fiber lasers,” Opt.Commun. |

4. | F. Incropera and D. DeWitt, |

5. | J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express |

6. | Verein Deutscher Ingenieure, |

7. | F. Seguin, A. Wetter, L. Martineau, M. Faucher, C. Delisle, and S. Caplette “Tapered fused bundle coupler package for reliable high optical power dissipation,” Proc. SPIE |

8. | W. Kuester, “Die Waermeleitfähigkeit thermoplastischer Kunststoffe,” Heat and Mass Transfer |

9. | B. Zintzen, A. Emmerich, J. Geiger, D. Hoffmann, and P. Loosen, “Effective Cooling for High-Power Fiber Lasers,” Proc. Fourth International WLT-Conference on Lasers in Manufacturing, Munich, (2007). |

**OCIS Codes**

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.2400) Fiber optics and optical communications : Fiber properties

(140.3510) Lasers and laser optics : Lasers, fiber

(140.6810) Lasers and laser optics : Thermal effects

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: September 12, 2007

Revised Manuscript: October 23, 2007

Manuscript Accepted: October 23, 2007

Published: December 3, 2007

**Citation**

B. Zintzen, T. Langer, J. Geiger, D. Hoffmann, and P. Loosen, "Heat transport in solid and air-clad fibers for high-power fiber lasers," Opt. Express **15**, 16787-16793 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16787

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### References

- D. C. Brown and H. J. Hoffman, "Thermal Stress and Thermo-Optic Effects in High Average Power Double-Clad Silica Fiber Lasers," IEEE J. Quantum Electron. 37, 2, (2001). [CrossRef]
- N. A. Brilliant and K. Lagonik, "Thermal effects in a dual-clad ytterbium fiber laser," Opt. Lett. 26, 1669 - 1671, (2001). [CrossRef]
- Y. Wang, C.-Q. Xu, and H. Po "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt.Commun. 242, 487-502 (2004). [CrossRef]
- F. Incropera, and D. DeWitt, Fundamentals of Heat and Mass Transfer, (John Wiley & Sons, Hoboken, 2002).
- J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, "Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation," Opt. Express 11, 2982 (2003). [CrossRef] [PubMed]
- Verein Deutscher Ingenieure, VDI-Wärmeatlas, Berechnungsblätter für den Wärmeübergang, 6. Edition, (VDI-Verlag GmbH Düsseldorf, 1991).
- F. Seguin, A. Wetter, L. Martineau, M. Faucher, C. Delisle, and S. Caplette; "Tapered fused bundle coupler package for reliable high optical power dissipation," Proc. SPIE 6102, 61021N, (2006). [CrossRef]
- W. Kuester, "Die Waermeleitfähigkeit thermoplastischer Kunststoffe," Heat and Mass Transfer 1,121- 128 (1968).
- B. Zintzen, A. Emmerich, J. Geiger, D. Hoffmann, and P. Loosen, "Effective Cooling for High-Power Fiber Lasers," Proc. Fourth International WLT-Conference on Lasers in Manufacturing, Munich, (2007).

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