Abstract

We employ a Monte Carlo ray-tracing code along with the ANSYS package to predict the optical and structural behavior in end-pumped CW Yb:YAG disk lasers. The presence of inhomogeneous temperature, stress, and strain distributions is responsible for many deleterious effects for laser action through disk fracture, strain-induced birefringence, and thermal lensing. The thermal lensing, in turn, results in the optical phase distortion in solid-state lasers. Furthermore, the dependence of optical phase distortion on variables such as the heat transfer coefficient, the cooling fluid temperature, and crystal thickness is discussed.

© 2010 Optical Society of America

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References

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  1. A. J. Kamp, G. J. Valentine, and D. Burns, “Review: progress toward high-power, high-brightness neodymium-based thin-disk lasers,” Prog. Quantum Electron. 28, 305–344 (2004).
    [CrossRef]
  2. A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
    [CrossRef]
  3. A. K. Jafari and M. Aas, “Continuous-wave theory of Yb:YAG end-pumped thin-disk lasers,” Appl. Opt. 48, 106–113 (2009).
    [CrossRef]
  4. S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “A model of lasing action in a quasi-four-level thin active media,” IEEE J. Quantum Electron. 46, 871–876 (2010).
    [CrossRef]
  5. B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
    [CrossRef]
  6. S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers,” Opt. Laser Technol. 41, 800–803 (2009).
    [CrossRef]
  7. S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “Review: on thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153 (2006).
    [CrossRef]
  8. W. Koechner, Solid State Laser Engineering, 6th ed. (Springer, 2006).
  9. D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
    [CrossRef]
  10. 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).
    [CrossRef]
  11. “ANSYS heat flow analysis guide,” ANSYS Inc., Canonsburg, Penna., ANSYS Release 9, Chap. 6 (2007).
  12. 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 Electron. 29, 697–703 (1999).
    [CrossRef]
  13. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “1 kW CW thin disk laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
    [CrossRef]
  14. X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
    [CrossRef]
  15. J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
    [CrossRef]
  16. J. E. Marion, “Fracture of solid state laser slabs,” J. Appl. Phys. 60, 69–77 (1986).
    [CrossRef]
  17. J. E. Marion, “Appropriate use of the strength parameter in solid-state slab laser design,” J. Appl. Phys. 62, 1595–1604(1987).
    [CrossRef]
  18. J. Speiser and A. Giesen, “Numerical modeling of high power continuous wave Yb:YAG thin disk lasers, scaling to 14 kW,” in Advanced Solid-State Photonics 2007, OSA Technical Digest (Optical Society of America, 2007), paper WB9.
  19. J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 1985).

2010

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “A model of lasing action in a quasi-four-level thin active media,” IEEE J. Quantum Electron. 46, 871–876 (2010).
[CrossRef]

2009

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers,” Opt. Laser Technol. 41, 800–803 (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

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

2006

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

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

2005

D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
[CrossRef]

2004

A. J. Kamp, G. J. Valentine, and D. Burns, “Review: progress toward high-power, high-brightness neodymium-based thin-disk lasers,” Prog. Quantum Electron. 28, 305–344 (2004).
[CrossRef]

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
[CrossRef]

2003

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).
[CrossRef]

2000

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

1999

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 Electron. 29, 697–703 (1999).
[CrossRef]

1987

J. E. Marion, “Appropriate use of the strength parameter in solid-state slab laser design,” J. Appl. Phys. 62, 1595–1604(1987).
[CrossRef]

1986

J. E. Marion, “Fracture of solid state laser slabs,” J. Appl. Phys. 60, 69–77 (1986).
[CrossRef]

1985

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
[CrossRef]

Aas, M.

Balembois, F.

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

Bass, M.

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

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).
[CrossRef]

Brown, D. C.

D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
[CrossRef]

Burns, D.

A. J. Kamp, G. J. Valentine, and D. Burns, “Review: progress toward high-power, high-brightness neodymium-based thin-disk lasers,” Prog. Quantum Electron. 28, 305–344 (2004).
[CrossRef]

Chen, B.

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

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).
[CrossRef]

Chen, Y.

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

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).
[CrossRef]

Chenais, S.

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

Chung, T. Y.

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

Cone, R. L.

D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
[CrossRef]

Contag, K.

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

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 Electron. 29, 697–703 (1999).
[CrossRef]

Deng, P.

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
[CrossRef]

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).
[CrossRef]

Druon, F.

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

Equall, R. W.

D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
[CrossRef]

Forget, S.

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

Georges, P.

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

Giesen, A.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

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

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 Electron. 29, 697–703 (1999).
[CrossRef]

J. Speiser and A. Giesen, “Numerical modeling of high power continuous wave Yb:YAG thin disk lasers, scaling to 14 kW,” in Advanced Solid-State Photonics 2007, OSA Technical Digest (Optical Society of America, 2007), paper WB9.

Golpayegani, A. H.

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “A model of lasing action in a quasi-four-level thin active media,” IEEE J. Quantum Electron. 46, 871–876 (2010).
[CrossRef]

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers,” Opt. Laser Technol. 41, 800–803 (2009).
[CrossRef]

Hugel, H.

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

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 Electron. 29, 697–703 (1999).
[CrossRef]

Jafari, A. K.

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “A model of lasing action in a quasi-four-level thin active media,” IEEE J. Quantum Electron. 46, 871–876 (2010).
[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]

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers,” Opt. Laser Technol. 41, 800–803 (2009).
[CrossRef]

Kamp, A. J.

A. J. Kamp, G. J. Valentine, and D. Burns, “Review: progress toward high-power, high-brightness neodymium-based thin-disk lasers,” Prog. Quantum Electron. 28, 305–344 (2004).
[CrossRef]

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).
[CrossRef]

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 Electron. 29, 697–703 (1999).
[CrossRef]

Koechner, W.

W. Koechner, Solid State Laser Engineering, 6th ed. (Springer, 2006).

Larionov, M.

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

Marion, J.

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
[CrossRef]

Marion, J. E.

J. E. Marion, “Appropriate use of the strength parameter in solid-state slab laser design,” J. Appl. Phys. 62, 1595–1604(1987).
[CrossRef]

J. E. Marion, “Fracture of solid state laser slabs,” J. Appl. Phys. 60, 69–77 (1986).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 1985).

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).
[CrossRef]

Simmons, J.

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

Speiser, J.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

J. Speiser and A. Giesen, “Numerical modeling of high power continuous wave Yb:YAG thin disk lasers, scaling to 14 kW,” in Advanced Solid-State Photonics 2007, OSA Technical Digest (Optical Society of America, 2007), paper WB9.

Stewen, C.

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

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 Electron. 29, 697–703 (1999).
[CrossRef]

Sun, Y.

D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
[CrossRef]

Toroghi, S.

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “A model of lasing action in a quasi-four-level thin active media,” IEEE J. Quantum Electron. 46, 871–876 (2010).
[CrossRef]

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers,” Opt. Laser Technol. 41, 800–803 (2009).
[CrossRef]

Valentine, G. J.

A. J. Kamp, G. J. Valentine, and D. Burns, “Review: progress toward high-power, high-brightness neodymium-based thin-disk lasers,” Prog. Quantum Electron. 28, 305–344 (2004).
[CrossRef]

Xu, J.

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
[CrossRef]

Xu, X.

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
[CrossRef]

Zhao, Z.

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
[CrossRef]

Appl. Opt.

Appl. Phys. B

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, “Thermal lensing of edge-pumped slab lasers-I,” Appl. Phys. B 82, 413–418 (2006).
[CrossRef]

Appl. Phys. Lett.

J. Marion, “Strengthened solid-state laser materials,” Appl. Phys. Lett. 47, 694–696 (1985).
[CrossRef]

IEEE J. Quantum Electron.

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “A model of lasing action in a quasi-four-level thin active media,” IEEE J. Quantum Electron. 46, 871–876 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

D. C. Brown, R. L. Cone, Y. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
[CrossRef]

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

J. Appl. Phys.

J. E. Marion, “Fracture of solid state laser slabs,” J. Appl. Phys. 60, 69–77 (1986).
[CrossRef]

J. E. Marion, “Appropriate use of the strength parameter in solid-state slab laser design,” J. Appl. Phys. 62, 1595–1604(1987).
[CrossRef]

Opt. Laser Technol.

S. Toroghi, A. K. Jafari, and A. H. Golpayegani, “The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers,” Opt. Laser Technol. 41, 800–803 (2009).
[CrossRef]

Proc. SPIE

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).
[CrossRef]

Prog. Quantum Electron.

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

A. J. Kamp, G. J. Valentine, and D. Burns, “Review: progress toward high-power, high-brightness neodymium-based thin-disk lasers,” Prog. Quantum Electron. 28, 305–344 (2004).
[CrossRef]

Quantum Electron.

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 Electron. 29, 697–703 (1999).
[CrossRef]

Solid State Commun.

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12 (x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529–532(2004).
[CrossRef]

Other

“ANSYS heat flow analysis guide,” ANSYS Inc., Canonsburg, Penna., ANSYS Release 9, Chap. 6 (2007).

J. Speiser and A. Giesen, “Numerical modeling of high power continuous wave Yb:YAG thin disk lasers, scaling to 14 kW,” in Advanced Solid-State Photonics 2007, OSA Technical Digest (Optical Society of America, 2007), paper WB9.

J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 1985).

W. Koechner, Solid State Laser Engineering, 6th ed. (Springer, 2006).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the thermal lensing and deformation effects in a typical end-pumped thin-disk laser. The bowing of the disk is exaggerated for clarity [1].

Fig. 2
Fig. 2

Generic sketch of optical setup of a typical end-pumped thin-disk laser [6].

Fig. 3
Fig. 3

Corresponding orientation of axes and thermal boundary conditions of the disk configuration [6].

Fig. 4
Fig. 4

(a) Absorption power profile inside the Yb:YAG crystal. (b) Distribution of temperature throughout the Yb:YAG crystal.

Fig. 5
Fig. 5

(a) Axial displacement (m), (b) Von Mises stress (Pa), (c) hoop strain.

Fig. 6
Fig. 6

OPD and the aspherical part of the OPD in the radial direction of the disk.

Fig. 7
Fig. 7

OPD in the radial direction of the disk for three different values of the heat exchange coefficient.

Fig. 8
Fig. 8

OPD in the radial direction of the disk for three different quantities of the coolant fluid temperature.

Fig. 9
Fig. 9

OPD in the radial direction of the disk for three different thicknesses.

Tables (4)

Tables Icon

Table 1 Design Parameters for Yb:YAG Thin-Disk Gain Medium

Tables Icon

Table 2 Numerical Results for Heat Exchange Coefficient Variation

Tables Icon

Table 3 Numerical Results for Coolant Fluid Temperature Variation

Tables Icon

Table 4 Numerical Results for Crystal Thickness Variation

Equations (14)

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

2 T = P th k ( T ) ,
T n 1 = h 1 k ( T ) ( T coolant T S 1 ) , on   S 1  surface,
T n i = h 2 k ( T ) ( T air T S i ) , on   S i   surface , i = 2 , 3 , 4 ,
k ( T , C Yb ) = k th ( 300 k , C Yb ) · ( 204 T 96 ) 0.48 0.46 × C Yb ,
k th ( 300 k , C Yb ) = ( 7.28 7.3 × C Yb ) W m · K .
OPD ( r ) = 2 [ 0 d Crystal n T ( T ( r , z ) T 0 ) · [ 1 + ε z ( r , z ) ] d z + 0 d Crystal Δ n s ( r , z ) · [ 1 + ε z ( r , z ) ] d z + 0 d Crystal [ n 0 1 ] · ε z ( r , z ) d z z 0 ( r ) ] ,
Φ ( r ) = 2 π λ · OPD ( r ) ,
E normalized ( r ) = exp ( r 2 w 2 + i φ ) ,
E normalized ( r ) = exp ( r 2 w 2 + i φ i Φ ( r ) ) .
Φ ( r ) = 2 π r 2 λ R L + Δ Φ ( r ) .
E normalized ( r ) = exp [ r 2 w 2 + i φ i Φ ( r ) ] .
c 00 = E E * r d r d ψ = 2 π exp ( i Δ Φ ( r ) ) exp ( r 2 w 2 ) r d r .
Δ B i j = p i j k l · ε k l ,
Δ n r , θ = 1 2 n 0 3 Δ B r , θ = n r , θ ε r ε r + n r , θ ε θ ε θ + n r , θ ε z ε z ,

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