Abstract

Based on the theory of semianalytical thermal analysis, we investigate the heat capacity of Nd:YAG laser rods for pumping and cooling. A general expression for the temperature field within Nd:YAG laser rod crystals is obtained for the pumping stage and the relation of the maximum temperature rise with pumping time. We also achieve an expression for the temperature field for the cooling stage and the relation of the maximum temperature rise with cooling time. These results show that, when using the output power of 300W LD pumped Nd:YAG laser rod crystals for 5 s, the maximum temperature rise in the center of the pump face is 154.79°C. After we stop the pumping for 30 s, the maximum temperature rise drops to 0.8%. These results are in agreement with those reported by others. Our results provide a theoretical basis for the optimized design of a LD end-pumped heat capacity laser.

© 2009 Optical Society of America

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  1. H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.
  2. B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.
  3. H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.
  4. P. Shi, W. Chen, L. Li, and A. S. Gan, “Semianalytical thermal analysis on a Nd:YVO4 crystal,” Appl. Opt. 46, 4046-4061(2007).
    [CrossRef] [PubMed]
  5. P. Shi, W. Chen, L. Li, and A. S. Gan, “Semianalytical thermal analysis of thermal focal length on Nd:YAG rods,” Appl. Opt. 46, 6655-6661 (2007).
    [CrossRef] [PubMed]
  6. J. M. Li, “Development trend and application of high average power diode pumped lasers,” Laser Optoelectron. Prog. 45 (7), 16-29 (2008), in Chinese.
    [CrossRef]
  7. Y. Yang, X. J. Xu, and B. H. Shu, “The effect of the thermal lens in optically pumped laser rods operated in heat capacity mode,” Proc. SPIE 5627, 312-318 (2005).
    [CrossRef]
  8. M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47, 2317-2325 (2008).
    [CrossRef] [PubMed]

2008

J. M. Li, “Development trend and application of high average power diode pumped lasers,” Laser Optoelectron. Prog. 45 (7), 16-29 (2008), in Chinese.
[CrossRef]

M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47, 2317-2325 (2008).
[CrossRef] [PubMed]

2007

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

P. Shi, W. Chen, L. Li, and A. S. Gan, “Semianalytical thermal analysis on a Nd:YVO4 crystal,” Appl. Opt. 46, 4046-4061(2007).
[CrossRef] [PubMed]

P. Shi, W. Chen, L. Li, and A. S. Gan, “Semianalytical thermal analysis of thermal focal length on Nd:YAG rods,” Appl. Opt. 46, 6655-6661 (2007).
[CrossRef] [PubMed]

2005

Y. Yang, X. J. Xu, and B. H. Shu, “The effect of the thermal lens in optically pumped laser rods operated in heat capacity mode,” Proc. SPIE 5627, 312-318 (2005).
[CrossRef]

Cai, Z.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Chen, J.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Chen, W.

Chen, W. D.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Cheng, Y.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Gan, A. S.

Hu, H.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Huang, C. H.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Huang, L. X.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Jiang, H. H.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Jiang, J. F.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Li, J. M.

J. M. Li, “Development trend and application of high average power diode pumped lasers,” Laser Optoelectron. Prog. 45 (7), 16-29 (2008), in Chinese.
[CrossRef]

Li, L.

Lin, L. F.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Mousave, L.

Nadgaran, H.

Pei, Z. P.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Sabaeian, M.

Shi, P.

Shu, B. H.

Y. Yang, X. J. Xu, and B. H. Shu, “The effect of the thermal lens in optically pumped laser rods operated in heat capacity mode,” Proc. SPIE 5627, 312-318 (2005).
[CrossRef]

Sun, D. L.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Tang, C.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Tao, S. H.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Tu, B.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Wang, B. S.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Wei, Y.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Xu, X. J.

Y. Yang, X. J. Xu, and B. H. Shu, “The effect of the thermal lens in optically pumped laser rods operated in heat capacity mode,” Proc. SPIE 5627, 312-318 (2005).
[CrossRef]

Yang, Y.

Y. Yang, X. J. Xu, and B. H. Shu, “The effect of the thermal lens in optically pumped laser rods operated in heat capacity mode,” Proc. SPIE 5627, 312-318 (2005).
[CrossRef]

Yin, S. T.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Zhang, G.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Zhang, Q. L.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Zhou, T. J.

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Zhu, H. Y.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Acta Photon. Sin.

H. Y. Zhu, G. Zhang, C. H. Huang, Y. Wei, L. X. Huang, J. Chen, and W. D. Chen, “Temperature characteristics analysis of double-end-pumped heat-capacity laser,” Acta Photon. Sin. 36 (5), 773-776 (2007), in Chinese.

Appl. Opt.

Chin. J. Lasers

H. Hu, Z. Cai, J. F. Jiang, B. Tu, Z. P. Pei, T. J. Zhou, Y. Cheng, and C. Tang, “Numerical simulation of thermodynamics in cooling for heat capacity laser,” Chin. J. Lasers 34 (11), 1507-1511 (2007), in Chinese.

Chin. J. Quantum Electron.

B. S. Wang, H. H. Jiang, Q. L. Zhang, D. L. Sun, S. T. Yin, L. F. Lin, and S. H. Tao, “Analysis on the temperature field of LD array pumped Nd:GGG disc laser in heat-capacity mode,” Chin. J. Quantum Electron. 24 (6), 688-693 (2007), in Chinese.

Laser Optoelectron. Prog.

J. M. Li, “Development trend and application of high average power diode pumped lasers,” Laser Optoelectron. Prog. 45 (7), 16-29 (2008), in Chinese.
[CrossRef]

Proc. SPIE

Y. Yang, X. J. Xu, and B. H. Shu, “The effect of the thermal lens in optically pumped laser rods operated in heat capacity mode,” Proc. SPIE 5627, 312-318 (2005).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic diagram of the Nd:YAG rods heat capacity laser. The pump light is made up of one group of two-dimensional LD array (LDA) stacks with coupling optics collimation in the z axis. The group of LDA stacks has 36 bars. The radius of the pump light is 9 mm , and the diameter of the YAG rod crystal is 30 mm × 15 mm. (b) Cylindrical coordinates of the calculated thermal effects. (c) Heat sink. Silicone grease of thermal conduction coats both sides of the YAG rod, then the whole is wrapped with indium and placed in the copper thermal sink.

Fig. 2
Fig. 2

Temperature field distribution diagram of a Nd:YAG rod pumped for 5 s.

Fig. 3
Fig. 3

Isotherm diagram of a Nd:YAG rod pumped for 5 s.

Fig. 4
Fig. 4

Maximum temperature rise located at r = 0 and z = 0 as a function of pump time.

Fig. 5
Fig. 5

Temperature field distribution diagram of a Nd:YAG rod cooled for 30 s.

Fig. 6
Fig. 6

Maximum temperature rise as a function of cooling time for different radii.

Tables (2)

Tables Icon

Table 1 Percentage of the Maximum Temperature Rise to Saturation Temperature for Different Pump Times

Tables Icon

Table 2 Dropped Percentage of the Maximum Temperature Rise for the Cooling Stage to the Maximum Temperature Rise when the Pump Stops

Equations (38)

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I ( r , 0 ) = I 0 e 2 r 2 w 2 ,
q V ( r , z ) = η I ( r , z ) β = I 0 η β e 2 r 2 w 2 e β z ,
ρ C u t = K ( 2 u r 2 + 1 r u r + 1 r 2 2 u φ 2 + 2 u z 2 ) + q V ( r , z ) ,
ρ C u t = K ( 2 u r 2 + 1 r u r + 2 u z 2 ) + q V ( r , z ) .
u ( r , z , t ) z | z = 0 = 0 , u ( r , z , t ) z | z = L = 0.
J 0 ( μ n ( 0 ) R r ) ,
u ( r , z , t ) z | z = 0 = 0 , u ( r , z , t ) z | z = L = 0 ,
u ( r , z , t ) = n = 1 m = 0 A n m ( t ) cos ( m π L z ) J 0 ( μ n ( 0 ) R r ) ,
ρ C n = 1 m = 0 d A n m ( t ) d t cos ( m π L z ) J 0 ( μ n ( 0 ) R r ) = K n = 1 m = 0 A n m ( t ) cos ( m π L z ) [ ( μ n ( 0 ) R ) 2 J 0 ( μ n ( 0 ) R r ) + 1 r ( μ n ( 0 ) R ) J 0 ( μ n ( 0 ) R r ) m 2 π 2 L 2 J 0 ( μ n ( 0 ) R r ) ] + q V .
0 c cos m π L z cos k π L z d z = L 2 δ m k .
ρ C n = 1 d A n m d t ( t ) J 0 ( μ n ( 0 ) R r ) = K n = 1 A n m ( t ) [ ( μ n ( 0 ) R ) 2 J 0 ( μ n ( 0 ) R r ) + 1 r ( μ n ( 0 ) R ) J 0 ( μ n ( 0 ) R r ) m 2 π 2 L 2 J 0 ( μ n ( 0 ) R r ) ] + 2 L · 0 L q V ( cos m π L z ) d z .
J 0 ( x ) + 1 x J 0 ( x ) + J 0 ( x ) = 0 ,
x = μ n ( 0 ) R r .
ρ C n = 1 d A n m d t ( t ) J 0 ( μ n ( 0 ) R r ) = K n = 1 A n m ( t ) m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 L 2 R 2 J 0 ( μ n ( 0 ) R r ) + 2 L · 0 L q V ( cos m π L z ) d z .
0 R J 0 ( μ k ( 0 ) R r ) J 0 ( μ n ( 0 ) R r ) r d r = R 2 2 J 1 2 ( μ n ( 0 ) ) δ n k .
J 0 ( μ k ( 0 ) R r ) r ,
ρ C d A n m ( t ) d t = K A n m ( t ) m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 L 2 R 2 + 4 L R 2 J 1 2 ( μ n ( 0 ) ) 0 R 0 L q V ( cos m π L z ) J 0 ( μ n ( 0 ) R r ) r d z d r .
C 1 = 4 ρ C L R 2 J 1 2 ( μ n ( 0 ) ) 0 R 0 L q V ( cos m π L z ) J 0 ( μ n ( 0 ) R r ) r d z d r ,
C 2 = K [ m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 ] ρ C L 2 R 2 .
d A n m ( t ) d t = C 2 A n m ( t ) + C 1 .
A n m ( t ) = C 1 C 2 + C 3 e C 2 t ,
A n m ( t ) = 4 L 3 I 0 β 2 η ( 1 e β L cos m π ) K ( β 2 L 2 + m 2 π 2 ) [ m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 ] J 1 2 ( μ n ( 0 ) ) ( 1 e K [ m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 ] ρ C L 2 R 2 t ) 0 R e 2 r 2 w 2 J 0 ( μ n ( 0 ) R r ) r d r .
ρ C T t = K ( 2 T r 2 + 1 r · T r + 2 T z 2 ) .
T ( r , z , t ) z | z = 0 = 0 , T ( r , z , t ) z | z = L = 0.
ρ C K d τ ( t ) d t R ( r ) Z ( z ) = τ ( t ) Z ( z ) 2 R ( r ) r 2 + τ ( t ) Z ( z ) 1 r R ( r ) r + τ ( t ) R ( r ) 2 Z ( z ) z 2 .
ρ C K 1 τ ( t ) d τ ( t ) d t = 1 R ( r ) 2 R ( r ) r 2 + 1 R ( r ) 1 r R ( r ) r + 1 Z ( z ) 2 Z ( z ) z 2 .
2 Z ( z ) z 2 + C z Z ( z ) = 0.
Z ( z ) = B sin ( C z z ) + A cos ( C z z ) .
Z ( z ) = A cos n π L z ,
1 R ( r ) 2 R ( r ) r 2 + 1 R ( r ) 1 r R ( r ) r = C r ,
R ( r ) = B J 0 ( μ n ( 0 ) R r ) ,
C r = ( μ n ( 0 ) ) 2 R 2 .
C t = C z C r = [ ( m π L ) 2 + ( μ n ( 0 ) R ) 2 ] = m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 L 2 R 2 .
d τ ( t ) τ ( t ) = C r K ρ C d t .
τ ( t ) = C 4 e C r K ρ C ( t t 1 ) ,
T ( r , z , t ) = n = 1 m = 0 B n m e K m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 ρ C L 2 R 2 ( t t 1 ) cos ( m π L z ) J 0 ( μ n ( 0 ) R r ) ,
T ( r , z , t 1 ) = = n = 1 m = 0 B n m cos ( m π L z ) J 0 ( μ n ( 0 ) R r ) = u ( r , z , t 1 ) = n = 1 m = 0 A n m ( t 1 ) cos ( m π L z ) J 0 ( μ n ( 0 ) R r ) .
B n m = A n m ( t 1 ) = 4 L 3 I 0 β 2 η ( 1 e β L cos m π ) λ ( β 2 L 2 + m 2 π 2 ) [ m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 ] J 1 2 ( μ n ( 0 ) ) × ( 1 e K [ m 2 π 2 R 2 + L 2 ( μ n ( 0 ) ) 2 ] ρ C L 2 R 2 t 1 ) × 0 R e 2 r 2 w 2 J 0 ( μ n ( 0 ) R r ) r d r .

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