Abstract

Thermal lensing in the thin-disk laser influences the output beam quality and optical efficiency significantly. In this paper, an analytical approach is taken to study the production mechanisms, features, and influences of thermal lensing in the end-pumped thin-disk laser. We calculate the distributions of temperature, stress, strain, and expansion in the disk and the curvature of the crystal using an analytic method. The expressions of the thermal lens focal length depending on the radius are presented. The optical path difference, a major cause of thermal lensing, is induced by the thermo-optical effect, the photoelastic effect, and inhomogeneous distribution of thermal expansion and the excited population. Thermal lensing is found to be aspheric with undesired aberrations and birefringence effects. Furthermore, a convex mirror due to the axial temperature gradient occurs in a free disk, and the convex mirror is found to be spherical in the center region of the disk. Based on the results of our analysis, the aspect ratio and size of the laser mode of the gain region may be adjusted to limit the damaging effects of thermal lensing.

© 2011 Optical Society of America

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  3. A. Giesen, “Results and scaling laws of thin disk lasers,” Proc. SPIE 5332, 202–227 (2004).
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    [CrossRef]
  5. A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
    [CrossRef]
  6. 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, OSA Technical DigestSeries (CD) (Optical Society of America, 2007), paper WB9.
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  8. J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
    [CrossRef]
  9. B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
    [CrossRef]
  10. J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.
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    [CrossRef]
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    [CrossRef]
  14. M. Karszewski, S. Erhard, A. Giesen, and T. Rupp, “Efficient high power TEM00 mode operation of diode-pumped Yb:YAG thin disk lasers,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper WE4.
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    [CrossRef]
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  22. A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
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  23. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (Intext Educational, 1973).
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    [CrossRef]

2010 (3)

2009 (3)

2008 (3)

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

2007 (1)

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

2006 (3)

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]

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (2006).
[CrossRef]

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31, 763–765 (2006).
[CrossRef] [PubMed]

2004 (3)

X. Xu, Z. Zhao, P. Song, G. Zhou, J. Xu, and P. Deng, “Structural, thermal, and luminescent properties of Yb-doped Y3Al5O12 crystals,” J. Opt. Soc. Am. B 21, 543–547 (2004).
[CrossRef]

A. Giesen, “Results and scaling laws of thin disk lasers,” Proc. SPIE 5332, 202–227 (2004).
[CrossRef]

A. Giesen, “Thin-disk solid-state lasers,” Proc. SPIE 5620, 112–127 (2004).
[CrossRef]

2003 (1)

C. Tang, C. L. Yang, and J. Chen, “Design of diode-pumped 10 kW high-power Nd: YAG disc laser,” Proc. SPIE 5120, 509–512 (2003).
[CrossRef]

2000 (1)

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

1997 (1)

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

1992 (1)

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

1970 (1)

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[CrossRef]

Aas, M.

Anashkina, E.

Antipov, O.

Antipov, O. L.

Austerschulte, A.

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

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]

Blazquez-Sanchez, D.

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

Bohn, W. L.

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

Boly, B. A.

B. A. Boly and J. H. Weiner, Theory of Thermal Stresses(Wiley, 1960).

Bredikhin, D. V.

Brockmann, R.

J. Deile, R. Brockmann, and D. Havrilla, “Current status and most recent developments of industrial high power disk lasers,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA4.

Bruesselbach, H. W.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Byren, R. W.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Chen, J.

C. Tang, C. L. Yang, and J. Chen, “Design of diode-pumped 10 kW high-power Nd: YAG disc laser,” Proc. SPIE 5120, 509–512 (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]

Contag, K.

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

Cousins, A. K.

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

Dashcasan, M. J.

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

Deile, J.

J. Deile, R. Brockmann, and D. Havrilla, “Current status and most recent developments of industrial high power disk lasers,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA4.

Deng, P.

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]

Eremeykin, O. N.

Erhard, S.

M. Karszewski, S. Erhard, A. Giesen, and T. Rupp, “Efficient high power TEM00 mode operation of diode-pumped Yb:YAG thin disk lasers,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper WE4.

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]

Francois, B.

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (2006).
[CrossRef]

Frederic, D.

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (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.

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

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

A. Giesen, “Thin-disk solid-state lasers,” Proc. SPIE 5620, 112–127 (2004).
[CrossRef]

A. Giesen, “Results and scaling laws of thin disk lasers,” Proc. SPIE 5332, 202–227 (2004).
[CrossRef]

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

M. Karszewski, S. Erhard, A. Giesen, and T. Rupp, “Efficient high power TEM00 mode operation of diode-pumped Yb:YAG thin disk lasers,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper WE4.

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, OSA Technical DigestSeries (CD) (Optical Society of America, 2007), paper WB9.

J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.

Goodier, J. N.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (Intext Educational, 1973).

Graf, T.

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

Hajiesmaeilbaigi, F.

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

Havrilla, D.

J. Deile, R. Brockmann, and D. Havrilla, “Current status and most recent developments of industrial high power disk lasers,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA4.

Hügel, H.

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

Ito, A.

Ivakin, E. V.

Jafari, A. K.

Karszewski, M.

M. Karszewski, S. Erhard, A. Giesen, and T. Rupp, “Efficient high power TEM00 mode operation of diode-pumped Yb:YAG thin disk lasers,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper WE4.

Killi, A.

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Kleinbauer, J.

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Koechner, W.

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[CrossRef]

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

Kozawa, Y.

Larionov, M.

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

Mahdizadeh, M.

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

Mende, J.

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.

Milani, M. R. J.

Moghadam, M.

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

Neuhaus, J.

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Patrick, G.

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (2006).
[CrossRef]

Razzaghi, H.

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

Reeder, R. A.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Rice, D. K.

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[CrossRef]

Rupp, T.

M. Karszewski, S. Erhard, A. Giesen, and T. Rupp, “Efficient high power TEM00 mode operation of diode-pumped Yb:YAG thin disk lasers,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper WE4.

Sato, S.

Savikin, A. P.

Sazegari, V.

Schad, S.

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Schmid, E.

J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.

Schmitz, C.

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Sebastien, C.

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (2006).
[CrossRef]

Sebastien, F.

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (2006).
[CrossRef]

Song, P.

Speiser, J.

J. Speiser, “Scaling of thin-disk lasers—influence of amplified spontaneous emission,” J. Opt. Soc. Am. B 26, 26–35 (2009).
[CrossRef]

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

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

J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.

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, OSA Technical DigestSeries (CD) (Optical Society of America, 2007), paper WB9.

Spindler, G.

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.

Stewen, C.

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

Sukhadolau, A. V.

Sumida, D. S.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Sutter, D.

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Tang, C.

C. Tang, C. L. Yang, and J. Chen, “Design of diode-pumped 10 kW high-power Nd: YAG disc laser,” Proc. SPIE 5120, 509–512 (2003).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (Intext Educational, 1973).

Voss, A.

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

Weichelt, B.

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

Weiner, J. H.

B. A. Boly and J. H. Weiner, Theory of Thermal Stresses(Wiley, 1960).

Xu, J.

Xu, X.

Yang, C. L.

C. Tang, C. L. Yang, and J. Chen, “Design of diode-pumped 10 kW high-power Nd: YAG disc laser,” Proc. SPIE 5120, 509–512 (2003).
[CrossRef]

Zawischa, I.

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Zhao, Z.

Zhou, G.

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

W. Koechner and D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

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

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

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

M. J. Dashcasan, F. Hajiesmaeilbaigi, H. Razzaghi, M. Mahdizadeh, and M. Moghadam, “Optimizing the Yb:YAG thin disc laser design parameters,” Opt. Commun. 281, 4753–4757 (2008).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (6)

C. Tang, C. L. Yang, and J. Chen, “Design of diode-pumped 10 kW high-power Nd: YAG disc laser,” Proc. SPIE 5120, 509–512 (2003).
[CrossRef]

J. Mende, J. Speiser, G. Spindler, W. L. Bohn, and A. Giesen, “Mode dynamics and thermal lens effects of thin-disk lasers,” Proc. SPIE 6871, 68710M (2008).
[CrossRef]

B. Weichelt, D. Blazquez-Sanchez, A. Austerschulte, A. Voss, T. Graf, and A. Killi, “Improving the brightness of a multi-kW thin disk laser with a single disk by an aspherical phase-front correction,” Proc. SPIE 7721, 77210M (2010).
[CrossRef]

A. Giesen, “Results and scaling laws of thin disk lasers,” Proc. SPIE 5332, 202–227 (2004).
[CrossRef]

A. Giesen, “Thin-disk solid-state lasers,” Proc. SPIE 5620, 112–127 (2004).
[CrossRef]

A. Killi, I. Zawischa, D. Sutter, J. Kleinbauer, S. Schad, J. Neuhaus, and C. Schmitz, “Current status and development trends of disk laser technology,” Proc. SPIE 6871, 68710L(2008).
[CrossRef]

Prog. Quantum Electron. (2)

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]

C. Sebastien, D. Frederic, F. Sebastien, B. Francois, and G. Patrick, “On thermal effects in solid state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 3, 89–126 (2006).
[CrossRef]

Other (7)

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

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (Intext Educational, 1973).

B. A. Boly and J. H. Weiner, Theory of Thermal Stresses(Wiley, 1960).

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, OSA Technical DigestSeries (CD) (Optical Society of America, 2007), paper WB9.

J. Deile, R. Brockmann, and D. Havrilla, “Current status and most recent developments of industrial high power disk lasers,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA4.

J. Mende, G. Spindler, E. Schmid, J. Speiser, and A. Giesen, “Thin-disk lasers with dynamically stable resonators,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper WB19.

M. Karszewski, S. Erhard, A. Giesen, and T. Rupp, “Efficient high power TEM00 mode operation of diode-pumped Yb:YAG thin disk lasers,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper WE4.

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Figures (22)

Fig. 1
Fig. 1

Energy level diagram of the Yb:YAG system.

Fig. 2
Fig. 2

Obvious saturated absorption effect in the nonlasing condition.

Fig. 3
Fig. 3

Absorbed efficiency with transmission of the output mirror in the CW laser condition.

Fig. 4
Fig. 4

Schematic diagram of the heat exchange model.

Fig. 5
Fig. 5

Distribution of temperature in the disk crystal.

Fig. 6
Fig. 6

Radial profile of temperature for pumping spots of different sizes.

Fig. 7
Fig. 7

Radial profile of temperature for crystals of different thickness.

Fig. 8
Fig. 8

Distributions of normal stress inside the disk crystal in the plane stress approximation with different pumping spots: (a) radial stress and (b) tangential stress.

Fig. 9
Fig. 9

Distributions of normal strain inside the disk crystal with different pumping spots: (a) radial strain, (b) tangential strain, and (c) axial strain.

Fig. 10
Fig. 10

Values of deformation of the bent surface. The solid curve with symbols is from FEA software, and the dashed curve is from analytic calculation.

Fig. 11
Fig. 11

Temperature-induced OPD with different absorbed power.

Fig. 12
Fig. 12

Thermal-expansion-induced OPD with different absorbed power.

Fig. 13
Fig. 13

Orientation of the indicatrix of the RIC caused by the photoelastic effect in a plane perpendicular to the z axis.

Fig. 14
Fig. 14

Strain-induced OPD with different absorbed power: solid symbol, tangential; hollow symbol, radial.

Fig. 15
Fig. 15

Electronic lens effects under the conditions of nonlasing and CW laser.

Fig. 16
Fig. 16

Production mechanism of thermal lens in thin-disk laser.

Fig. 17
Fig. 17

Total OPD with the increment of pumping power: (a) CW laser condition and (b) nonlasing condition.

Fig. 18
Fig. 18

Distribution of OPD-induced dioptric power: solid curve, radial; dashed curve, tangential.

Fig. 19
Fig. 19

Distribution of OPD-induced dioptric power with different disk thickness: (a) profile of dioptric power and (b) change of dioptric power with thickness in different aperture.

Fig. 20
Fig. 20

Distribution of OPD-induced dioptric power with pumping spots of different sizes.

Fig. 21
Fig. 21

Focal length of crystal curvature induced thermal lens with different thickness of disk (free disk).

Fig. 22
Fig. 22

Results of the experiment and the previous researches. (a) Temperature distribution of crystal measured by thermal infrared imager. (b) 3D temperature distribution using the FEA [15]. (c) OPD distribution (aspherical part) of a heavy doping disk crystal measured with a Shack–Hartmann sensor [10].

Tables (1)

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Table 1 Parameters Used for Calculations

Equations (58)

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f Z i = j 1 4 exp ( E Z j E Z i k T ) ,
f A i = j 1 3 exp ( E A j E A i k T ) ,
n 0 = ( n Y b n 2 f b ) f a ,
n 1 = ( n Y b n 2 f b ) f a ,
n 3 = n 2 f b f b .
n 2 t = f b I pump h ν p σ ( a ) ( λ p ) ( n 0 n 3 ) n 2 τ I laser h ν l σ ( e ) ( λ l ) ( n 2 n 1 ) = 0 ,
I pump = i = 0 N 1 I in exp [ σ ( a ) ( λ p ) ( n 0 n 3 ) i l ] = I in { 1 exp [ σ ( a ) ( λ p ) ( n 0 n 3 ) l ] } N { 1 exp [ σ ( a ) ( λ p ) ( n 0 n 3 ) l ] } ,
n 2 = f b I in { 1 exp [ σ ( a ) ( λ p ) ( n 0 n 3 ) l ] } N h ν p { 1 exp [ σ ( a ) ( λ p ) ( n 0 n 3 ) l ] } σ ( a ) ( λ p ) ( n 0 n 3 ) τ .
α = σ ( a ) ( λ p ) ( n 0 n 3 ) = σ ( a ) ( λ p ) ( f a n Y b f a + f b f b n 2 )
P abs = P pump [ 1 exp ( α N l ) ] .
e 2 g l R ( 1 L ) = 1 ,
g = σ ( e ) ( λ l ) ( n 2 n 1 ) = ln [ R ( 1 L ) ] 2 l .
n 2 = f b f a + f b { f a n Y b ln [ R ( 1 L ) ] 2 l σ ( e ) ( λ l ) } .
1 r r ( r T ( r , z ) r ) + 2 T ( r , z ) r 2 = ϕ k circ ( r 0 ) ,
T ( r 1 , z ) r = 0 ,
T ( r , l ) z = 0 ,
T ( r , 0 ) z = h k [ T ( r , 0 ) T C ] ,
ϕ = P abs π r 0 2 l η ,
T ( r , z ) = T C + A 0 + B 0 z + n = 1 [ A n exp ( x n ( 0 ) r 1 z ) + B n exp ( x n ( 0 ) r 1 z ) ] · J 0 ( x n ( 0 ) r 1 r ) 1 2 z 2 [ C 0 + n = 1 C n · J 0 ( x n ( 0 ) r 1 r ) ] ,
A 0 = l ϕ r 0 2 h r 1 2 , B 0 = l ϕ r 0 2 h r 1 2 , C 0 = ϕ r 0 2 k r 1 2 ,
A n = ( h + k x n ( 0 ) r 1 ) · l ϕ r 0 k ( x n ( 0 ) ) 2 [ J 0 ( x n ( 0 ) ) ] 2 J 1 ( x n ( 0 ) r 1 r 0 ) h cosh ( x n ( 0 ) l r 1 ) + k x n ( 0 ) r 1 sinh ( x n ( 0 ) l r 1 ) ,
B n = ( h k x n ( 0 ) r 1 ) · l ϕ r 0 k ( x n ( 0 ) ) 2 [ J 0 ( x n ( 0 ) ) ] 2 J 1 ( x n ( 0 ) r 1 r 0 ) h cosh ( x n ( 0 ) l r 1 ) + k x n ( 0 ) r 1 sinh ( x n ( 0 ) l r 1 ) ,
C n = 2 ϕ r 0 k r 1 x n ( 0 ) [ J 0 ( x n ( 0 ) ) ] 2 J 1 ( x n ( 0 ) r 1 r 0 ) .
T ( r ) = 1 l 0 l T ( r , z ) d z .
σ r ( r ) = E α ( 1 r 1 2 0 r 1 T ( r ) r d r 1 r 2 0 r T ( r ) r d r ) ,
σ θ ( r ) = E α ( 1 r 1 2 0 r 1 T ( r ) r d r + 1 r 2 0 r T ( r ) r d r T ( r ) ) ,
τ r θ ( r ) = 0.
T ( r ) = 1 l { ( T C + A 0 ) l + 1 2 B 0 l 2 1 6 C 0 l 3 + n = 1 J 0 ( x n ( 0 ) r 1 r ) [ A n r 1 x n ( 0 ) ( e x n ( 0 ) r 1 l 1 ) B n r 1 x n ( 0 ) exp ( e x n ( 0 ) r 1 l 1 ) 1 6 l 3 C n ] } ,
0 a T ( r ) r d r = 1 l { 1 2 ( T C + A 0 ) l a 2 + 1 4 B 0 l 2 a 2 1 12 C 0 l 3 a 2 + n = 1 a r 1 x n ( 0 ) J 1 ( x n ( 0 ) r 1 r ) [ A n r 1 x n ( 0 ) ( e x n ( 0 ) r 1 l 1 ) B n r 1 x n ( 0 ) exp ( e x n ( 0 ) r 1 l 1 ) 1 6 l 3 C n ] } .
[ ε r γ r θ γ r z γ θ r ε θ γ θ z γ z r γ z θ ε z ] = S i j k l ( 4 ) [ σ r τ r θ τ r z τ θ r σ θ τ θ z τ z r τ z θ σ z ] + α i j Δ T ,
S i j k l = { 1 E ( i = j = k = l ) ν E ( i = j ; k = l ; i , j k , j ) 2 ( 1 + ν ) E ( i = k ; j = l ; i , k j , l ) 0 ( other ) ,
ε r = 1 E [ σ r ν σ θ ] + α Δ T ,
ε θ = 1 E [ σ θ ν σ r ] + α Δ T ,
ε z = ν E ( σ r + σ θ ) + α Δ T ,
γ i j = 0.
Δ l ( r ) = 0 l ε z ( r ) d z = l ε z ( r ) .
ε z ( r ) = ν α ( 2 0 r 1 T ( r ) r d r r 1 2 T ( r ) ) + α Δ T ( r ) .
Δ l ( r ) Δ l ( 0 ) = ( ν + 1 ) α l ( T ( r ) T ( 0 ) ) .
κ mirror = 6 α ( 1 + ν ) l 3 0 l T ( 0 , z ) ( z l 2 ) d z ,
Δ t ( r ) = 2 0 l [ T ( r , z ) T c ] n T d z ,
Δ expan ( r ) = 2 ( n 1 ) Δ l ( r ) .
Δ B i j = p i j k l ε k l ,
Δ B i = j = 1 3 p 12 ε j + ( p 11 p 12 ) ε i ( i = 1 , 2 , 3 ) ,
Δ B i = p 44 ε i ( i = 4 , 5 , 6 ) ,
B x x x 2 + B y y y 2 + B z z z 2 + B z x z x + B y z y z + B x y x y = 1.
( B x * x * 0 + Δ B x * x * ) x * 2 + ( B y * y * 0 + Δ B y * y * ) y * 2 = 1 ,
Δ n r , θ ( S ) ( r ) = j = r , θ , z n r , θ ε j ε j ( r ) ,
n i ε j = n 0 3 12 ( a i j p 11 + b i j p 12 + c i j p 44 ) ,
a i j = [ 3 1 2 1 3 2 ] ,
b i j = [ 3 5 4 5 3 4 ] ,
c i j = [ 6 2 4 2 6 4 ] .
f mirror = ( 2 κ mirror ) 1 .
Δ n e = 2 π F L 2 n Δ p n 2 f b ,
Δ e = 2 Δ n e l circ ( r 0 ) ,
OPD Σ = Δ t + Δ s + Δ expan + Δ e .
[ ( r + d r ) 2 + f 2 ( r ) ] 1 2 + Δ ( r + d r ) = [ r 2 + f 2 ( r ) ] 1 2 + Δ ( r ) .
Δ ( r + d r ) = Δ ( r ) + d Δ .
D OPD ( r ) = 1 f ( r ) = 1 r d r d Δ ( r ) + r 2 1 r d Δ ( r ) d r .

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