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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References

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  1. W. Koechner, Solid-state Laser Engineering (Springer Verlag, 1985), Chap 7.
  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:YVO4 slab,” Acta Phys. Sin.62, 024210 (2013), http://wulixb.iphy.ac.cn/CN/Y2013/V62/I2/024210 .
  5. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGrow-Hill Book Company, Inc, 1959).
  6. G. Yingzheng, Material Mechanics (China Communications Press, 2009).
  7. J. F. Nye, F.R.S, Physical Properties of Crystals (Clarendon Press, Oxford, 1985)
  8. 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]
  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]
  10. L. Baida, Laser Optics (Higher Education Press, 2003).

2013 (1)

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 .

1990 (1)

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]

1984 (1)

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 .

1965 (2)

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]

Byer, R. L.

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 .

Eggleston, J. M.

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 .

Fields, R. A.

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]

Fincher, C. L.

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]

Innocenzi, M. E.

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]

Jiabin, C.

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 .

Jianguo, X.

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 .

Jun, L.

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 .

Kane, T. J.

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 .

Kogelnik, H.

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]

Kuhn, K.

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 .

Shufen, C.

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 .

Shuna, Y.

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 .

Unternahrer, J.

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 .

Ying, Z.

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 .

Yu, D.

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 .

Yura, H. T.

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]

Acta Phys. Sin. (1)

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 .

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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]

Bell Syst. Tech. J. (1)

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]

IEEE J. Quantum Electron. (1)

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 .

Other (5)

W. Koechner, Solid-state Laser Engineering (Springer Verlag, 1985), Chap 7.

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)

L. Baida, Laser Optics (Higher Education Press, 2003).

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Figures (7)

Fig. 1
Fig. 1

The single-end-pumped Yb:YAG crystal

Fig. 2
Fig. 2

The double-end-pumped Yb:YAG crystal

Fig. 3
Fig. 3

Single-end-pumped refractive index nx distribution

Fig. 4
Fig. 4

Double-end-pumped refractive index nx distribution

Fig. 5
Fig. 5

the group of equivalent thermal cylindrical lens in the single end pumped rectangular laser medium

Fig. 6
Fig. 6

the group of equivalent thermal cylindrical lens in the double end pumped rectangular laser medium

Fig. 7
Fig. 7

the thermal focal length as a function of the pumping intensity and beam radius

Tables (1)

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Table 1 Physical properties of Yb:YAG crystal

Equations (11)

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σ x ( x,y,z )=0
σ y ( x,y,z )={ 2αE ( 1μ )δ [ t( δ 2 ,y,z )t( 0,y,z ) ]( x δ 4 )αEt( x,y,z ),( 0x δ 2 ) 2αE ( 1μ )δ [ t( δ 2 ,y,z )t( 0,y,z ) ]( x 3δ 4 )αEt( x,y,z ),( δ 2 xδ )
σ z ( x,y,z )={ 2αE ( 1μ )δ [ t( δ 2 ,y,z )t( 0,y,z ) ]( x δ 4 ),( 0x δ 2 ) 2αE ( 1μ )δ [ t( δ 2 ,y,z )t( 0,y,z ) ]( x 3δ 4 ),( δ 2 xδ )  
n ij = n 0 + dn dT ΔT+ kl B ijkl σ kl
{ n x = n 0 + dn dT t+ B ( σ y + σ z ) n y = n 0 + dn dT t+ B σ z + B σ y n z = n 0 + dn dT t+ B σ y + B σ z
n( x,y )= n 0 [ 1 k 2 2 k 0 ( x 2 + y 2 ) ]
n( x,z )= n 0 (z)[1+γ( z ) x 2 ]
[ cosβl 1 β sinβl βsinβl cosβl ]
M 0 =[ A 0 B 0 C 0 D 0 ]= T 2 M m M 2 M 1 T 1
M m =[ A m B m C m D m ]=[ cosβ( z m )l 1 β( z m ) sinβ( z m )l β( z m )sinβ( z m )l cosβ( z m )l ] T 1 =[ 1 0 0 n 0 /n ] T 2 =[ 1 0 0 n/ n 0 ]
f=1/ C m

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