Abstract

The temperature nonuniformity occurring during the cooling process of a KDP crystal is studied, along with its effects on the second-harmonic generation (SHG) of a high-average-power laser. A comprehensive model is proposed incorporating principles of thermodynamics, mechanics, and optics, and it is applied to investigate the temperature nonuniformity and its effects. The temperature rise caused by linear absorption is calculated, while the temperature nonuniformity occurring during the cooling process is analyzed using the finite-element method (FEM). The stress induced by the nonuniformity is then studied using the FEM, and the trend of its change is determined. Moreover, the changes in refractive index caused by the stress are calculated, the results of which are used to determine the variations in the induced phase mismatch. The SHG efficiency considering the phase mismatch is eventually obtained by solving the coupling wave equations. The results demonstrate that the temperature nonuniformity has negative effects on the SHG efficiency.

© 2014 Optical Society of America

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2013 (3)

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Z. Y. Ren, J. Q. Zhu, H. B. Huang, and Z. G. Liu, “Numerical research and optimization of convective heat transfer for multi-segment amplifiers,” Opt. Laser Technol. 47, 189–193 (2013).
[CrossRef]

J. Rothhardt, S. Demmler, S. Hadrich, T. Peschel, J. Limpert, and A. Tunnermann, “Thermal effects in high average power optical parametric amplifiers,” Opt. Lett. 38, 763–765 (2013).
[CrossRef]

2012 (1)

2010 (2)

2009 (1)

2008 (2)

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]

P. Millar, R. B. Brich, A. J. Kemp, and D. Burns, “Synthetic diamond for intracavity thermal management in compact solid-state lasers,” IEEE J. Quantum Electron. 44, 709–717 (2008).
[CrossRef]

2007 (1)

2006 (1)

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
[CrossRef]

2005 (3)

D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Megajoule (LMJ) project dedicate to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

G. Wagner, M. Shiler, and V. Wulfmeyer, “Simulations of thermal lensing of a Ti: Sapphire crystal end-pumped with high average power,” Opt. Express 13, 8045–8055 (2005).
[CrossRef]

2004 (1)

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

2000 (1)

M. Z. Rossi, F. Lindner, C. L. Blanc, G. Cheriaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

1999 (1)

O. Lubin and C. Gouedard, “Modeling of the effects of KDP crystals gravity sag on third harmonic generation,” Proc. SPIE 3492, 802–808 (1999).
[CrossRef]

1998 (2)

V. G. Dmitriev and Y. V. Yur’ev, “Calculation of thermo-optical distortions of some nonlinear crystals during second-harmonic generation,” IEEE J. Quantum Electron. 28, 1002–1006 (1998).
[CrossRef]

Y. K. Yap, K. Deki, N. Kitatochi, Y. Mori, and T. Sasaki, “Alleviation of thermally induced phase mismatch in CsLiB6O10 crystal by means of temperature-profile compensation,” Opt. Lett. 23, 1016–1018 (1998).
[CrossRef]

1997 (1)

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high average power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
[CrossRef]

1995 (1)

R. A. Hass, “Influence of a constant temperature gradient on the spectral bandwidth of second-harmonic generation in nonlinear crystals,” Opt. Commun. 113, 523–529 (1995).
[CrossRef]

Auerbach, J. M.

Balembois, F.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
[CrossRef]

Blanc, C. L.

M. Z. Rossi, F. Lindner, C. L. Blanc, G. Cheriaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Bourgade, J. L.

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Megajoule (LMJ) project dedicate to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

Bowers, M. W.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008), Chap. 2.

Brich, R. B.

P. Millar, R. B. Brich, A. J. Kemp, and D. Burns, “Synthetic diamond for intracavity thermal management in compact solid-state lasers,” IEEE J. Quantum Electron. 44, 709–717 (2008).
[CrossRef]

Burns, D.

P. Millar, R. B. Brich, A. J. Kemp, and D. Burns, “Synthetic diamond for intracavity thermal management in compact solid-state lasers,” IEEE J. Quantum Electron. 44, 709–717 (2008).
[CrossRef]

Cavailler, C.

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Megajoule (LMJ) project dedicate to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

Chambaret, J. P.

M. Z. Rossi, F. Lindner, C. L. Blanc, G. Cheriaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Chen, G. F.

S. X. Shi, G. F. Chen, W. Zhao, and J. F. Liu, Nonlinear Optics (Xidian University, 2012), Chap. 4 (in Chinese).

Chen, Y. B.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Chenais, S.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
[CrossRef]

Cheriaux, G.

M. Z. Rossi, F. Lindner, C. L. Blanc, G. Cheriaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Dang, Z.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Deki, K.

Demmler, S.

Ding, L.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Ding, X.

D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

Dixit, S. N.

Dmitriev, V. G.

V. G. Dmitriev and Y. V. Yur’ev, “Calculation of thermo-optical distortions of some nonlinear crystals during second-harmonic generation,” IEEE J. Quantum Electron. 28, 1002–1006 (1998).
[CrossRef]

Druon, F.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
[CrossRef]

Erbert, G. V.

Feng, B.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Fleurot, N.

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Megajoule (LMJ) project dedicate to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

Forget, S.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
[CrossRef]

Fujita, M.

Furuse, H.

Georges, P.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
[CrossRef]

Glick, Y.

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

Godard, A.

Goldring, S.

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

Gouedard, C.

O. Lubin and C. Gouedard, “Modeling of the effects of KDP crystals gravity sag on third harmonic generation,” Proc. SPIE 3492, 802–808 (1999).
[CrossRef]

Guo, L. F.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Hadrich, S.

Hass, R. A.

R. A. Hass, “Influence of a constant temperature gradient on the spectral bandwidth of second-harmonic generation in nonlinear crystals,” Opt. Commun. 113, 523–529 (1995).
[CrossRef]

Haynam, C. A.

Heestand, G. M.

Henesian, M. A.

Hermann, M. R.

Hu, D. X.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Hu, J. G.

D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

Huang, H. B.

Z. Y. Ren, J. Q. Zhu, H. B. Huang, and Z. G. Liu, “Numerical research and optimization of convective heat transfer for multi-segment amplifiers,” Opt. Laser Technol. 47, 189–193 (2013).
[CrossRef]

Imasaki, K.

Ishii, S.

Jancaitis, K. S.

Jing, F.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Kaufman, G.

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

Kawanaka, J.

Kemp, A. J.

P. Millar, R. B. Brich, A. J. Kemp, and D. Burns, “Synthetic diamond for intracavity thermal management in compact solid-state lasers,” IEEE J. Quantum Electron. 44, 709–717 (2008).
[CrossRef]

Kitatochi, N.

Lavi, R.

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

Lebiush, E.

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

Lefebvre, M.

Li, E. B.

D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

Limpert, J.

Lin, D. H.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Lindner, F.

M. Z. Rossi, F. Lindner, C. L. Blanc, G. Cheriaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Liu, J. F.

S. X. Shi, G. F. Chen, W. Zhao, and J. F. Liu, Nonlinear Optics (Xidian University, 2012), Chap. 4 (in Chinese).

Liu, L. Q.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Liu, Z. G.

Z. Y. Ren, J. Q. Zhu, H. B. Huang, and Z. G. Liu, “Numerical research and optimization of convective heat transfer for multi-segment amplifiers,” Opt. Laser Technol. 47, 189–193 (2013).
[CrossRef]

Lubin, O.

O. Lubin and C. Gouedard, “Modeling of the effects of KDP crystals gravity sag on third harmonic generation,” Proc. SPIE 3492, 802–808 (1999).
[CrossRef]

Manes, K. R.

Mann, G.

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high average power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
[CrossRef]

Marshall, C. D.

Mehta, N. C.

Menapace, J.

Michel, A. M.

Millar, P.

P. Millar, R. B. Brich, A. J. Kemp, and D. Burns, “Synthetic diamond for intracavity thermal management in compact solid-state lasers,” IEEE J. Quantum Electron. 44, 709–717 (2008).
[CrossRef]

Miyanaga, N.

Mori, Y.

Moses, E.

Mousave, L.

Murray, J.

Nadgaran, H.

Niu, Y. X.

D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

Nostrand, M. C.

Orth, C. D.

Patterson, R.

Pealat, M.

Peng, Z. T.

Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

Peschel, T.

Pitts, D.

D. Pitts and L. Sissom, Schaum’s Outline of Theory and Problems of Heat Transfer (McGraw-Hill, 1998), Chap. 2.

Raybaut, M.

Ren, Z. Y.

Z. Y. Ren, J. Q. Zhu, H. B. Huang, and Z. G. Liu, “Numerical research and optimization of convective heat transfer for multi-segment amplifiers,” Opt. Laser Technol. 47, 189–193 (2013).
[CrossRef]

Rossi, M. Z.

M. Z. Rossi, F. Lindner, C. L. Blanc, G. Cheriaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Rothhardt, J.

Sabaeian, M.

Sacks, R. A.

Saiki, T.

Sasaki, T.

Schmid, T.

Seidel, S.

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high average power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
[CrossRef]

Shaw, M. J.

Shi, S. X.

S. X. Shi, G. F. Chen, W. Zhao, and J. F. Liu, Nonlinear Optics (Xidian University, 2012), Chap. 4 (in Chinese).

Shiler, M.

Sissom, L.

D. Pitts and L. Sissom, Schaum’s Outline of Theory and Problems of Heat Transfer (McGraw-Hill, 1998), Chap. 2.

Spaeth, M.

Sutton, S. B.

Tai, A.

Y. Tzuk, A. Tai, S. Goldring, Y. Glick, E. Lebiush, G. Kaufman, and R. Lavi, “Diamond cooling of high power diode-pumped solid state lasers,” IEEE J. Quantum Electron. 40, 262–269 (2004).
[CrossRef]

Takeshita, K.

Tunnermann, A.

Tzuk, Y.

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[CrossRef]

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[CrossRef]

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Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

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D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

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D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
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[CrossRef]

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D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

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Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
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Q. H. Zhu, W. G. Zheng, X. F. Wei, F. Jing, D. X. Hu, W. Zhou, B. Feng, J. J. Wang, Z. T. Peng, L. Q. Liu, Y. B. Chen, L. Ding, D. H. Lin, L. F. Guo, and Z. Dang, “Research and construction progress of SG-III laser facility,” Proc. SPIE 8786, 87861G (2013).
[CrossRef]

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[CrossRef]

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[CrossRef]

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D. G. Xu, J. Q. Yao, B. G. Zhang, R. Zhou, E. B. Li, S. Y. Zhao, X. Ding, W. Q. Wen, Y. X. Niu, J. G. Hu, and P. Wang, “110  W high stability green laser using type II phase matching KTiOPO4 (KTP) crystal with boundary temperature control,” Opt. Commun. 245, 341–347 (2005).
[CrossRef]

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Opt. Laser Technol. (1)

Z. Y. Ren, J. Q. Zhu, H. B. Huang, and Z. G. Liu, “Numerical research and optimization of convective heat transfer for multi-segment amplifiers,” Opt. Laser Technol. 47, 189–193 (2013).
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R. W. Boyd, Nonlinear Optics (Academic, 2008), Chap. 2.

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Figures (6)

Fig. 1.
Fig. 1.

Optical configuration of the crystal.

Fig. 2.
Fig. 2.

Mechanical mounting configuration and cooling scheme of the crystal.

Fig. 3.
Fig. 3.

Finite-element model of the mounting configuration.

Fig. 4.
Fig. 4.

Temperature distribution and its nonuniformity throughout the cooling process.

Fig. 5.
Fig. 5.

Stress distribution and the trend of its change throughout the cooling process.

Fig. 6.
Fig. 6.

Phase mismatch and SHG efficiency throughout the cooling process.

Tables (1)

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Table 1. Material Properties of the Mounting Components

Equations (11)

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{Q=Q0×α1×lQ0=P0×τP0=I0×A,
{ΔTt=k×(Δ2Tx2+Δ2Ty2+Δ2Tz2)ΔT|t=0=Qch×m,
{σxxx+σxyy+σxzz+fxx=0σxyx+σyyy+σyzz+fyy=0σxzx+σyzy+σzzz+fzz=0.
{εxx=uxεyy=vyεzz=wzεyz=wy+vzεxz=uz+wxεxy=vx+uy.
{εxx=1E[σxxυ(σyy+σzz)]+γxxΔTxxεyy=1E[σyyυ(σxx+σzz)]+γyyΔTyyεzz=1E[σzzυ(σxx+σyy)]+γzzΔTzzεyz=2(1+υ)Eσyzεxz=2(1+υ)Eσxzεxy=2(1+υ)Eσxy.
{σxxσyyσzzσyzσxzσxy}=[D11D12D13000D12D11D13000D13D13D33000000D44000000D44000000D66]{εxxεyyεzz2εyz2εxz2εxy},
[ΔBxxΔByyΔBzzΔByzΔBxzΔBxy]=[Bxx1/no2Byy1/no2Bzz1/ne2ByzBxzBzy]=[π11π12π13000π12π11π13000π31π31π33000000π44000000π44000000π66][σxxσyyσzzσyzσxzσxy],
{Δno=(no3/2)×(ΔBxx×sin2φ+ΔByy×cos2φΔBxy×sin2φ)Δne=(ne3/2)×(ΔBxx×cos2θ×cos2φ+ΔByy×cos2θ×sin2φ+ΔBzz×sin2θ+ΔBxy×cos2θ×sin2φΔBxz×sin2θ×cosφΔByz×sin2θ×sinφ),
{ΔK=(K2+ΔK2)2×(K1+ΔK1)=ΔK22×ΔK1ΔK1=(ω1/c)×Δno(ω1)ΔK2=(ω2/c)×Δne(ω2),
{dE(ω1,z)dz=2iω12K1c2×deff×E(ω2,z)×E*(ω1,z)exp(iΔKz)12×α1×E(ω1,z)dE(ω2,z)dz=iω22K2c2×deff×E2(ω1,z)exp(iΔKz)12×α2×E(ω2,z),
{η=P2P1P1=12×no(ω)×c×ε0×|E1|2P2=12×ne(2ω)×c×ε0×|E2|2,

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