## Study of the distributed thermal lens of LD end pumped rectangular gain |

Optics Express, Vol. 21, Issue 20, pp. 23197-23205 (2013)

http://dx.doi.org/10.1364/OE.21.023197

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### Abstract

In the LD end pumped rectangular laser gain medium, the thermal induced refractive index is not only non-uniformly transversely, but also non-uniformly and distributed along the pumping beam propagation, the effect of thermal lens is a distributed not a lumped lens effect as previously considered. In this paper, the effect of a distributed thermal lens is analyzed.

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## 1. Introduction

2. J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, “The slab geometry laser- Part I: Theory,” IEEE J. Quantum Electron. **20**, 289–301 (1984), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1072386.

3. M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave and end-pumped solid-state lasers,” Appl. Phys. Lett. **56**(19), 1831–1833 (1990), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?reload=true&arnumber=4860571. [CrossRef]

4. Z. Ying, D. Yu, Y. Shuna, L. Jun, C. Jiabin, C. Shufen, and X. Jianguo, “Three-dimensional thermal effects of the diode-pumped Nd:YVO_{4} slab,” Acta Phys. Sin. **62**, 024210 (2013), http://wulixb.iphy.ac.cn/CN/Y2013/V62/I2/024210.

4. Z. Ying, D. Yu, Y. Shuna, L. Jun, C. Jiabin, C. Shufen, and X. Jianguo, “Three-dimensional thermal effects of the diode-pumped Nd:YVO_{4} slab,” Acta Phys. Sin. **62**, 024210 (2013), http://wulixb.iphy.ac.cn/CN/Y2013/V62/I2/024210.

2. J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, “The slab geometry laser- Part I: Theory,” IEEE J. Quantum Electron. **20**, 289–301 (1984), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1072386.

## 2. The equivalent group of the thermal cylindrical lens in LD end pumped rectangular laser medium

9. H. Kogelnik, “On the propagation of gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. **4**(12), 1562–1569 (1965), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-4-12-1562. [CrossRef]

_{m}, each of which is equivalent to one different lens subject to its location in the gain medium, the product of matrices finally provide the value of 1/C

_{m}, which gives the focal length of the total cylindrical thermal lens.

^{2}with the pumping size on the end surface of the rectangular crystal from 0.15mm to 0.65mm high and 10mm wide; the pumping peak power were kept from 375watts to 1625watts to maintain the pumping peak power density of 25kw/cm

^{2}with the pumping size on the end surface of the rectangular crystal from 0.15mm to 0.65mm high and 10mm wide; the pumping peak power were kept from 450watts to 1950watts to maintain the pumping peak power density of 30kw/cm

^{2}with the pumping size on the end surface of the rectangular crystal from 0.15mm to 0.65mm high and 10mm wide. The pumping laser pulse width is kept at 300us; the heat induced refractive index distribution is derived at the highest temperature distribution of the laser mediums.

^{2}with the pumping size on the end surface of the rectangular crystal from 0.15mm to 0.65mm high and 10mm wide; the pumping peak power were kept from 375watts to 1625watts to maintain the pumping power density of 25kw/cm

^{2}with the pumping size on the end surface of the rectangular crystal from 0.15mm to 0.65mm high and 10mm wide; the pumping power were kept from 450watts to 1950watts to maintain the pumping power density of 30kw/cm

^{2}with the pumping size on the end surface of the rectangular crystal from 0.15mm to 0.65mm high and 10mm wide. The heat induced refractive index distribution is derived at the steady state temperature distribution.

^{2}to 35kw/cm

^{2}with the pumping size of 0.10mm high and 10mm wide on the end surface of the rectangular crystal; The pumping peak power were kept from 100watts to 700watts to have the pumping peak power density from 5kw/cm

^{2}to 35kw/cm

^{2}with the pumping size of 0.20mm high and 10mm wide on the end surface of the rectangular crystal; The pumping peak power were kept from 150watts to 1050watts to have the pumping peak power density from 5kw/cm

^{2}to 35kw/cm

^{2}with the pumping size of 0.30mm high and 10mm wide on the end surface of the rectangular crystal. The pumping laser pulse width is kept at 300us; the heat induced refractive index distribution is derived at the highest temperature distribution.

^{2}to 35kw/cm

^{2}with the pumping size of 0.10mm high and 10mm wide on the end surface of the rectangular crystal; The pumping power were kept from 200watts to 700watts to have the pumping power density from 10kw/cm

^{2}to 35kw/cm

^{2}with the pumping size of 0.20mm high and 10mm wide on the end surface of the rectangular crystal; The pumping power were kept from 300watts to 1050watts to have the pumping power density from 10kw/cm

^{2}to 35kw/cm

^{2}with the pumping size of 0.30mm high and 10mm wide on the end surface of the rectangular crystal. The heat induced refractive index distribution is derived at the steady state temperature distribution.

## 3. Conclusion

## References and links

1. | W. Koechner, |

2. | J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, “The slab geometry laser- Part I: Theory,” IEEE J. Quantum Electron. |

3. | M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave and end-pumped solid-state lasers,” Appl. Phys. Lett. |

4. | Z. Ying, D. Yu, Y. Shuna, L. Jun, C. Jiabin, C. Shufen, and X. Jianguo, “Three-dimensional thermal effects of the diode-pumped Nd:YVO |

5. | S. Timoshenko and S. Woinowsky-Krieger, |

6. | G. Yingzheng, |

7. | J. F. Nye, F.R.S, |

8. | H. Kogelnik, “Imaging of Optical Modes-Resonators with Internal Lenses,” Bell Syst. Tech. J. |

9. | H. Kogelnik, “On the propagation of gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. |

10. | L. Baida, |

**OCIS Codes**

(140.3480) Lasers and laser optics : Lasers, diode-pumped

(140.3580) Lasers and laser optics : Lasers, solid-state

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: July 17, 2013

Revised Manuscript: September 5, 2013

Manuscript Accepted: September 5, 2013

Published: September 24, 2013

**Citation**

Yu Zhongsheng, Liu Jiao, Liu Jun, Xin Jianguo, and Chen Jiabin, "Study of the distributed thermal lens of LD end pumped rectangular gain," Opt. Express **21**, 23197-23205 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23197

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### References

- W. Koechner, Solid-state Laser Engineering (Springer Verlag, 1985), Chap 7.
- J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, “The slab geometry laser- Part I: Theory,” IEEE J. Quantum Electron.20, 289–301 (1984), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1072386 .
- M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave and end-pumped solid-state lasers,” Appl. Phys. Lett.56(19), 1831–1833 (1990), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?reload=true&arnumber=4860571 . [CrossRef]
- Z. Ying, D. Yu, Y. Shuna, L. Jun, C. Jiabin, C. Shufen, and X. Jianguo, “Three-dimensional thermal effects of the diode-pumped Nd:YVO4 slab,” Acta Phys. Sin.62, 024210 (2013), http://wulixb.iphy.ac.cn/CN/Y2013/V62/I2/024210 .
- S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGrow-Hill Book Company, Inc, 1959).
- G. Yingzheng, Material Mechanics (China Communications Press, 2009).
- J. F. Nye, F.R.S, Physical Properties of Crystals (Clarendon Press, Oxford, 1985)
- H. Kogelnik, “Imaging of Optical Modes-Resonators with Internal Lenses,” Bell Syst. Tech. J.44(3), 455–494 (1965), http://www3.alcatel-lucent.com/bstj/vol44-1965/articles/bstj44-3-455.pdf . [CrossRef]
- H. Kogelnik, “On the propagation of gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt.4(12), 1562–1569 (1965), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-4-12-1562 . [CrossRef]
- L. Baida, Laser Optics (Higher Education Press, 2003).

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