Abstract

A plane wave model with nonuniform temperature distribution in the thin-disk crystal is developed to describe the dynamic behavior of an end-pumped Yb:YAG thin-disk laser. A set of couple-rate equations and 2D stationary heat-conduction equations are derived. The stable temperature distribution in the disk crystal is calculated using a numerical iterative method. The analytic expression is capable of dealing with more practical laser systems than previous works on this subject as it allows for nonuniform temperature distribution in the disk crystal. Based on these results, we examined laser output intensity as a function of pump intensity, dopant concentration, resonator coupler reflectivity, crystal thickness and temperature of cooling liquid.

© 2012 Optical Society of America

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References

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  1. A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
  2. M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).
  3. A. J. Kemp, G. J. Valentine, and D. Burns, “Progress towards high-power, high-brightness, neodymium-based thin-disk lasers,” Progr. in Quant. Electr. 28, 305–344 (2004).
    [CrossRef]
  4. R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
    [CrossRef]
  5. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
  6. D. A. Copeland, “Optical extraction model and optimal outcoupling for a CW quasi-three level thin disk laser” Proc. SPIE 791279120D1 (2011).
  7. D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Elec. 47, 3–12 (2011).
    [CrossRef]
  8. K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
    [CrossRef]
  9. K. Contag, S. Erhard, and A. Giesen, “Calculations of optimum design parameters for Yb:YAG thin disk laser,” in Advanced Solid State Lasers, OSA Technical Digest Series34, 124–130 (2000).
  10. G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. 39, 966–971 (2000).
    [CrossRef]
  11. H. Yu and G. Bourdet, “Thickness optimization of the composite gain medium for the oscillator and amplifier of the Lucia laser,” Appl. Opt. 44, 7161–7169 (2005).
    [CrossRef]
  12. H. Yu, G. Bourdet, and S. Ferre, “Comprehensive modeling of the temperature-related laser performances of the amplifiers of the LUCIA laser,” Appl. Opt. 44, 6413–6418 (2005).
  13. C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. 38, 306–311 (2002).
    [CrossRef]
  14. A. K. Jafari and M. Aas, “Continuous-wave theory of Yb:YAG end-pumped thin-disk lasers,” Appl. Opt. 48, 106–113(2009).
    [CrossRef]
  15. C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
    [CrossRef]
  16. Q. Liu, X. Fu, M. Gong, and L. Huang, “Effects of the temperature dependence of the absorption coefficients in edge-pumped Yb:YAG slab lasers,” J. Opt. Soc. Am. B 24, 2081–2089 (2007).
    [CrossRef]
  17. B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).
  18. K. Liang, Methods of Mathematical Physics, Higher Education (1998), p. 148.
  19. M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
    [CrossRef]

2011 (2)

D. A. Copeland, “Optical extraction model and optimal outcoupling for a CW quasi-three level thin disk laser” Proc. SPIE 791279120D1 (2011).

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Elec. 47, 3–12 (2011).
[CrossRef]

2010 (1)

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

2009 (2)

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

A. K. Jafari and M. Aas, “Continuous-wave theory of Yb:YAG end-pumped thin-disk lasers,” Appl. Opt. 48, 106–113(2009).
[CrossRef]

2007 (1)

2005 (2)

H. Yu and G. Bourdet, “Thickness optimization of the composite gain medium for the oscillator and amplifier of the Lucia laser,” Appl. Opt. 44, 7161–7169 (2005).
[CrossRef]

H. Yu, G. Bourdet, and S. Ferre, “Comprehensive modeling of the temperature-related laser performances of the amplifiers of the LUCIA laser,” Appl. Opt. 44, 6413–6418 (2005).

2004 (2)

A. J. Kemp, G. J. Valentine, and D. Burns, “Progress towards high-power, high-brightness, neodymium-based thin-disk lasers,” Progr. in Quant. Electr. 28, 305–344 (2004).
[CrossRef]

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

2003 (1)

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

2002 (1)

C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. 38, 306–311 (2002).
[CrossRef]

2000 (2)

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. 39, 966–971 (2000).
[CrossRef]

1999 (1)

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

1996 (1)

R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
[CrossRef]

1994 (1)

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Aas, M.

Aghaeifar, F.

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

Barati, E.

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

Bass, M.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

Beach, R. J.

R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
[CrossRef]

Bourdet, G.

H. Yu, G. Bourdet, and S. Ferre, “Comprehensive modeling of the temperature-related laser performances of the amplifiers of the LUCIA laser,” Appl. Opt. 44, 6413–6418 (2005).

H. Yu and G. Bourdet, “Thickness optimization of the composite gain medium for the oscillator and amplifier of the Lucia laser,” Appl. Opt. 44, 7161–7169 (2005).
[CrossRef]

Bourdet, G. L.

Brauch, U.

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Brown, D. C.

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Elec. 47, 3–12 (2011).
[CrossRef]

Burns, D.

A. J. Kemp, G. J. Valentine, and D. Burns, “Progress towards high-power, high-brightness, neodymium-based thin-disk lasers,” Progr. in Quant. Electr. 28, 305–344 (2004).
[CrossRef]

Chen, B.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

Chen, G.

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

Chen, Y.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

Contag, K.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

K. Contag, S. Erhard, and A. Giesen, “Calculations of optimum design parameters for Yb:YAG thin disk laser,” in Advanced Solid State Lasers, OSA Technical Digest Series34, 124–130 (2000).

Copeland, D. A.

D. A. Copeland, “Optical extraction model and optimal outcoupling for a CW quasi-three level thin disk laser” Proc. SPIE 791279120D1 (2011).

Dong, J.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

Erhard, S.

K. Contag, S. Erhard, and A. Giesen, “Calculations of optimum design parameters for Yb:YAG thin disk laser,” in Advanced Solid State Lasers, OSA Technical Digest Series34, 124–130 (2000).

Ferre, S.

H. Yu, G. Bourdet, and S. Ferre, “Comprehensive modeling of the temperature-related laser performances of the amplifiers of the LUCIA laser,” Appl. Opt. 44, 6413–6418 (2005).

Fu, X.

Giesen, A.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

K. Contag, S. Erhard, and A. Giesen, “Calculations of optimum design parameters for Yb:YAG thin disk laser,” in Advanced Solid State Lasers, OSA Technical Digest Series34, 124–130 (2000).

Golpaygani, A. H.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Gong, M.

Q. Liu, X. Fu, M. Gong, and L. Huang, “Effects of the temperature dependence of the absorption coefficients in edge-pumped Yb:YAG slab lasers,” J. Opt. Soc. Am. B 24, 2081–2089 (2007).
[CrossRef]

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

Hajiesmaeilbaigi, F.

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

Huang, L.

Hugel, H.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Izawa, Y.

C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. 38, 306–311 (2002).
[CrossRef]

Jafari, A. K.

Javadi-Dashcasan, M.

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

Kar, A.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

Karszewski, M.

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

Kemp, A. J.

A. J. Kemp, G. J. Valentine, and D. Burns, “Progress towards high-power, high-brightness, neodymium-based thin-disk lasers,” Progr. in Quant. Electr. 28, 305–344 (2004).
[CrossRef]

Larionov, M.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

Li, C.

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

Liang, K.

K. Liang, Methods of Mathematical Physics, Higher Education (1998), p. 148.

Lim, C.

C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. 38, 306–311 (2002).
[CrossRef]

Liu, Q.

Q. Liu, X. Fu, M. Gong, and L. Huang, “Effects of the temperature dependence of the absorption coefficients in edge-pumped Yb:YAG slab lasers,” J. Opt. Soc. Am. B 24, 2081–2089 (2007).
[CrossRef]

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

Najafi, M.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Opower, H.

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Patel, M.

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

Roozbehani, M.

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

Sabbaghzadeh, J.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Sepehr, A.

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

Stewen, C.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

Valentine, G. J.

A. J. Kemp, G. J. Valentine, and D. Burns, “Progress towards high-power, high-brightness, neodymium-based thin-disk lasers,” Progr. in Quant. Electr. 28, 305–344 (2004).
[CrossRef]

Vitali, V. A.

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Elec. 47, 3–12 (2011).
[CrossRef]

Voss, A.

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Witting, K.

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

Yan, P.

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

Yu, H.

H. Yu and G. Bourdet, “Thickness optimization of the composite gain medium for the oscillator and amplifier of the Lucia laser,” Appl. Opt. 44, 7161–7169 (2005).
[CrossRef]

H. Yu, G. Bourdet, and S. Ferre, “Comprehensive modeling of the temperature-related laser performances of the amplifiers of the LUCIA laser,” Appl. Opt. 44, 6413–6418 (2005).

Appl. Opt. (4)

Appl. Phys. B (1)

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).

IEEE J. Quantum Elec. (1)

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Elec. 47, 3–12 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. 38, 306–311 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser.” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. 123, 385–393 (1996).
[CrossRef]

M. Najafi, A. Sepehr, A. H. Golpaygani, and J. Sabbaghzadeh, “Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property,” Opt. Commun. 282, 4103–4108 (2009).
[CrossRef]

C. Li, Q. Liu, M. Gong, G. Chen, and P. Yan, “Q-switched operation of end-pumped Yb:YAG lasers with non-uniform temperature distribution,” Opt. Commun. 231, 331–341 (2004).
[CrossRef]

Proc. SPIE (3)

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, “Modeling of high power solid-state slab lasers,” Proc. SPIE 4968, 1–10 (2003).

D. A. Copeland, “Optical extraction model and optimal outcoupling for a CW quasi-three level thin disk laser” Proc. SPIE 791279120D1 (2011).

M. Javadi-Dashcasan, F. Hajiesmaeilbaigi, E. Barati, F. Aghaeifar, and M. Roozbehani, “Modeling and designing of a side-pumped composite Yb:YAG/YAG hexagonal disk laser,” Proc. SPIE 7721, 77210P1 (2010).

Progr. in Quant. Electr. (1)

A. J. Kemp, G. J. Valentine, and D. Burns, “Progress towards high-power, high-brightness, neodymium-based thin-disk lasers,” Progr. in Quant. Electr. 28, 305–344 (2004).
[CrossRef]

Quantum Elec. (1)

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Elec. 29, 697–703 (1999).
[CrossRef]

Other (2)

K. Contag, S. Erhard, and A. Giesen, “Calculations of optimum design parameters for Yb:YAG thin disk laser,” in Advanced Solid State Lasers, OSA Technical Digest Series34, 124–130 (2000).

K. Liang, Methods of Mathematical Physics, Higher Education (1998), p. 148.

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Figures (13)

Fig. 1.
Fig. 1.

Schematic drawing of the crystal divided along thickness for mathematical modeling.

Fig. 2.
Fig. 2.

Schematic of the laser radiation transmitting in the gain medium for different optical resonators. (a) TrN=1 for I-resonator and (b)TrN=2 for V-resonator.

Fig. 3.
Fig. 3.

Schematic of the pump optical rays as they bounce in the thin-disk crystal.

Fig. 4.
Fig. 4.

Yb:YAG energy level diagram.

Fig. 5.
Fig. 5.

(fojL+f1jL) and (fojP+f1jP) versus temperature.

Fig. 6.
Fig. 6.

The curves of σP, σL, and σPj/σLj versus temperature.

Fig. 7.
Fig. 7.

Corresponding orientation of axes and thermal boundary conditions of disk module.

Fig. 8.
Fig. 8.

A stable temperature distribution inside the disk module. (a) Temperature distribution along radial position and (b) temperature distribution along axial position.

Fig. 9.
Fig. 9.

Output intensity, laser threshold, absorption efficiency, and optical efficiency as a function of pump intensity for different optical resonator shape, shown in (a) and (b).

Fig. 10.
Fig. 10.

The dependence of laser output intensity (left scale) and average temperature of disk crystal (right scale) on crystal thickness for various dopant concentrations at given parameters. (IP,0=5kW/cm2, Rr,P=98%, Rf,P=99%, Rr,L=97%, Rf,L=98%, TrN=1).

Fig. 11.
Fig. 11.

A normalized contour map of the laser output intensity as a function of crystal thickness and dopant concentration for given system parameters. (IP,0=5kW/cm2, Rr,P=98%, Rf,P=99%, Rr,L=97%, Rf,L=98%, TrN=1).

Fig. 12.
Fig. 12.

A normalized contour map of laser output intensity as a function of pump intensity and resonator coupler reflectivity for given parameters. (Rr,P=98%, Rf,P=99%, Rr,L=97%, Rf,L=98%, cYb=6at%, L=200μm, Tf=20°C).

Fig. 13.
Fig. 13.

A normalized contour map of laser output intensity as a function of temperature of cooling liquid and coupler reflectivity for given system parameters. (IP,0=5kW/cm2, Rr,P=98%, Rf,P=99%, Rr,L=97%, Rf,L=98%, cYb=6at%, L=200μm).

Tables (1)

Tables Icon

Table 1. Basic Parameters Used for this Model

Equations (41)

Equations on this page are rendered with MathJax. Learn more.

N1j(t,z)t=N0j(t,z)t=σPj(fojPN0jf1jPN1j)Pj+σLj(fojLN0jf1jLN1j)LjN1jτj,
ILj(z)z=±σLj(fojLN0j(z)f1jLN1j(z))ILj(z),
IPj,i(z)z=±σPj(fojPN0j(z)f1jPN1j(z))IPj,i(z),
Pj=i=1N(IPj,i++IPj,i)hvPLj=TrN·(ILj++ILj)hvL,
{IL+(L)=IL+(0)exp(j=1MgjΔl)IL(0)=IL(L)exp(j=1MgjΔl)and{IL(L)=IL+(L)Rr,LIL+(0)=IL(0)Rf,L(TrN=1),
{IL+(L)=IL+(L)exp(LLgjΔl)=IL+(L)exp(TrN·j=1MgjΔl)IL(L)=IL(L)exp(LLgjΔl)=IL(L)exp(TrN·j=1MgjΔl)and{IL(L)=IL+(L)Rr,LIL+(L)=IL(L)Rf,L(TrN=2),
j=1M(gjΔl)=1TrNln(1Rr,LRf,L).
{IP,i+(0)=Rf,PIP,i(0)IP,i+1(L)=Rr,PIP,i+(L).
{Ip,i(L)=IP,0·Rr,Pi1·Rf,Pi1·exp[2(i1)j=1MδjΔl]Ip,i+(0)=IP,0·Rf,Pexp(j=1MδjΔl){Rr,Pi1·Rf,Pi1·exp[2(i1)j=1MδjΔl]}(IP,1(L)=IP,0),
fAij=exp(EAiKTj)q=13exp(EAqKTj),
fZij=exp(EZiKTj)q=03exp(EZqKTj),
FL=(fojL+f1jL)=(f0L+f1L),
FP=(fojP+f1jP)=(foP+f1P).
σP(941,T)=[0.207+0.637exp(T273288)]×1020cm2,
σL(1030,T)=[0.95334+33.608exp(T92.82465)]×1020cm2,
σPσLσPjσLj.
N0j(z)=σPjf1jPPj+σLjf1jLLj+1τjσPj(f0jP+f1jP)Pj+σLj(f0jL+f1jL)Lj+1τjNt,
N1j(z)=σPjf0jPPj+σLjf0jLLjσPj(f0jP+f1jP)Pj+σLj(f0jL+f1jL)Lj+1τjNt,
σLj(fojL+f1jL)1IPj,i±(z)dIPj,i±(z)dzσPj(fojP+f1jP)1ILj±(z)dILj±(z)dz=±NtσLjσPj(f0jLf1jPf1jLf0jP)
σLj(f0jLN0jf1jL×N1j)dIPj,i±(z)IPj,i±(z)=σPj(f0jPN0jf1jP×N1j)dILj±(z)ILj±(z).
Δj=(f0jLf1jPf1jLf0jP).
j=1M[σLj(fojL+f1jL)δjΔl]j=1M[σPj(fojP+f1jP)gjΔl]=j=1M[NtσLjσPjΔjΔl].
0L(δjΔl)=j=1M(δjΔl)=j=1M[σPj(fojP+f1jP)σLj(fojL+f1jL)gjΔl]+j=1M[σPjΔj(fojL+f1jL)NtΔl]=σPFPσLFLj=1M(gjΔl)+NtFLj=1M(σPjΔjΔl)=σPFPσLFL1TrNln(1Rr,LRf,L)+NtFLj=1M(σPjΔjΔl).
1ΔjfojLσPjτjdIPj,i±(z)IPj,i±(z)+i=1N(IPj,i++IPj,i)hvPdIPj,i±(z)IPj,i±(z)=1ΔjfojPσLjτjdILj±(z)ILj±(z)TrN·(ILj++ILj)hvLdILj±(z)ILj±(z).
Aj+=i=1N(IPj,i++IPj,i)hvPdIPj,i+(z)IPj,i+(z)=i=1N1hvP(1+IPj,iIPj,i+)dIPj,i+(z),
Bj+=TrN·(ILj++ILj)hvLdILj±(z)ILj±(z)=TrNhvL(1+ILjILj,i+)dILj+(z),
Cj+=1Δj(fojLσPjτjdIPj,i+(z)IPj,i+(z)fojPσLjτjdILj+(z)ILj+(z)).
A+=TrN·j=1M(IP+(lj1)IP+(lj)Aj+)=TrNhvPi=1N[IP,i+(L)IP,i+(0)+IP,i(0)IP,i(L)]=TrNhvPIP,0i=1N{Rr,Pi1·Rf,Pi1·exp[2(i1)j=1MδjΔl]}·(exp(j=1MδjΔl)Rf,P+1)·(exp(j=1MδjΔl)1),
B+=L+L(IL+(lj1)IL+(lj)Bj+)=TrNhvL(IL+(L)IL+(L)+IL(L)IL(L))=TrNhvL(1Rr,LRf,L)(1+Rr,LRf,L)IL+(L),
C+=LL(IL+(lj)IL+(lj+1)Cj+)=LL(N1j(z)τjΔl)=Δlτ{1σLAvg·FL[LLσLjf0jLNt+1Δlln(1Rr,LRf,L)]}=Δlτ{1σLAvg·FL[TrN·j=1MσLjf0jLNt+1Δlln(1Rr,LRf,L)]}
IL+(L)=AB(IP,0+CA),
I=(1Rr,L)IL+(L)=ηslope(IP,0Ith),
ηslope=AB(1Rr,L)=vLvP(1Rr,L)(1Rr,LRf,L)(1+Rr,LRf,L)×i=1N{Rr,Pi1·Rf,Pi1·exp[2(i1)j=1MδjΔl]}·(exp(j=1MδjΔl)Rf,P+1)·(exp(j=1MδjΔl)1)
Ith=CA=hvPΔlτ{1σLAvg·FL[TrN·j=1M(σLjf0jL)Nt+1Δlln(1Rr,LRf,L)]}TrN·i=1N{Rr,Pi1·Rf,Pi1·exp[2(i1)j=1MδjΔl]}·(exp(j=1MδjΔl)Rf,P+1)·(exp(j=1MδjΔl)1).
{2TYAGr2+1rTYAGr+2TYAGz2=QkYAGH(rPr)TYAG(r,z)r|r=R=0TYAG(r,z)z|z=z0=0kYAGTYAG(r,z)z|z=0=kCu-WTCu-W(r,z)z|z=0(for disk crystal),
{2TCu-Wr2+1rTCu-Wr+2TCu-Wz2=0TCu-W(r,z)r|r=R=0TCu-W(r,z)z|z=z1=hkCu-W[TCu-W(r,0)Tf](for Cu-W heat sink),
H(rPr)={10<r<rP0rP<r<R.
TYAG(r,0)=TCu-W(r,0).
TYAG(r,z)=A0+B0z+n=1[Anexp(xn(0)Rz)+Bnexp(xn(0)Rz)]·J0(xn(0)Rr)12z2[G0+n=1Gn·J0(xn(0)Rr)],
TCuW(r,z)=Tf+A0+B0z+n=1[Anexp(xn(0)Rz)+Bnexp(xn(0)Rz)]·J0(xn(0)Rr),
A0=Tf+A0=Tf+(1+hz1kCu-W)z0QrP2hR2,B0=z0Qk2R20rPrdr=z0QrP2kYAGR2,A0=kCu-Wh(1+hz1kCu-W)B0=(1+hz1kCu-W)z0QrP2hR2,B0=kYAGkCu-WB0=z0QrP2kCu-WR2,An=2fn(hHnbkCu-WEnb)(kCu-WEnahHna){[(1+kCu-WkYAG)(hHnbkCu-WEnb)(kCu-WEnahHna)+(1kCu-WkYAG)]Ena+[(1kCu-WkYAG)(hHnbkCu-WEnb)(kCu-WEnahHna)+(1+kCu-WkYAG)]Enb}Bn=2fn{[(1+kCu-WkYAG)(hHnbkCu-WEnb)(kCu-WEnahHna)+(1kCu-WkYAG)]Ena+[(1kCu-WkYAG)(hHnbkCu-WEnb)(kCu-WEnahHna)+(1+kCu-WkYAG)]Enb}An=12[(1+kCu-WkYAG)An+(1kCu-WkYAG)Bn]=Bn2[(1+kCu-WkYAG)(hHnbkCu-WEnb)(kCu-WEnahHna)+(1kCu-WkYAG)]Bn=12[(1kCu-WkYAG)An+(1+kCu-WkYAG)Bn]=Bn2[(1kCu-WkYAG)(hHnbkCu-WEnb)(kCu-WEnahHna)+(1+kCu-WkYAG)]G0=QrP2kYAGR2Gn=2QrPkYAG[J0(xn(0))]2[xn(0)]RJ1(xn(0)RrP).

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