Abstract

By using the well-known Green’s function methods, we study the three-dimensional temperature distributions and thermal deformations of the output windows of unstable optical resonators induced by an incident annular laser beam. Some expressions and theoretical profiles of the temperature distributions and thermal deformations as functions of the radius and of the thickness of optical windows are obtained. Moreover, the influence of the thermal deformations of sapphire, silica, and silicon windows within unstable optical resonators on the Strehl ratio and on the far-field laser intensity distribution is also discussed. Under conditions of 50-kW intense laser irradiation during 5 s, the maximum thermal deformation in sapphire, silica, and silicon substrates is 1.993, 0.393, and 6.251 μm, respectively. Under the same conditions the Strehl ratio of sapphire is higher than that of silica.

© 2004 Optical Society of America

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References

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  1. D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
    [CrossRef]
  2. M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
    [CrossRef]
  3. D. Furman, B. D. Barmashenko, S. Rosenwaks, “Parametric study of an efficient supersonic chemical oxygen-iodine laser/jet generator system operating without buffer gas,” IEEE J. Quantum Electron. 34, 1068–1074 (1998).
    [CrossRef]
  4. G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
    [CrossRef]
  5. M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).
  6. M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
    [CrossRef]
  7. M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Laser-induced local heating of multilayers,” Appl. Opt. 21, 1106–1114 (1982).
    [CrossRef] [PubMed]
  8. A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
    [CrossRef]
  9. O. W. Shih, “A multilayer heat conduction solution for magneto-optical disk recording,” J. Appl. Phys. 75, 4382–4395 (1994).
    [CrossRef]
  10. A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
    [CrossRef]
  11. W. A. McGahan, K. D. Cole, “Solutions of the heat conduction equation in multilayers for photothermal deflection experiments,” J. Appl. Phys. 72, 1362–1373 (1992).
    [CrossRef]
  12. P. Loza, D. Kouznetsov, R. Ortega, “Temperature distribution in a uniform medium heated by absorption of a Gaussian light beam,” Appl. Opt. 33, 3831–3836 (1994).
    [CrossRef] [PubMed]
  13. M. K. Loze, C. D. Wright, “Temperature distributions in laser-heated semi-infinite and finite-thickness media with convective surface losses,” Appl. Opt. 37, 6822–6832 (1998).
    [CrossRef]
  14. M. N. Özişik, Heat Conduction (Wiley, New York, 1980).
  15. Y. Peng, Z. Cheng, Y. Zhang, J. Qiu, “Temperature distributions and thermal deformations of mirror substrates in laser resonators,” Appl. Opt. 40, 4824–4830 (2001).
    [CrossRef]
  16. Y. Takeuti, S. Zaima, N. Noda, “Thermal stresses problems in industry. 1. On thermoelastic distortion in machine metals,” J. Therm. Stress 1, 199–210 (1978).
    [CrossRef]
  17. J. L. Nowinski, Theory of Thermoelasticity with Applications (Sijthoff & Noordhoff Alphen aan den Rijn, The Netherlands, 1978).
    [CrossRef]
  18. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).
  19. H. F. Wolf, Silicon Semiconduction Data (Signetics Corporation, Sunnyvale, Calif., 1969).
  20. H. E. Bennett, A. J. Glass, A. H. Guenther, B. E. Newnam, Laser Induced Damage in Optical Materials: 1980 (National Bureau of Standards, Boulder, Colo., 1981).
  21. W. M. Rohsenow, J. P. Hartnett, Handbook of Heat Transfer (McGraw-Hill, New York, 1973).

2001 (1)

2000 (1)

M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).

1998 (3)

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

D. Furman, B. D. Barmashenko, S. Rosenwaks, “Parametric study of an efficient supersonic chemical oxygen-iodine laser/jet generator system operating without buffer gas,” IEEE J. Quantum Electron. 34, 1068–1074 (1998).
[CrossRef]

M. K. Loze, C. D. Wright, “Temperature distributions in laser-heated semi-infinite and finite-thickness media with convective surface losses,” Appl. Opt. 37, 6822–6832 (1998).
[CrossRef]

1996 (1)

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

1994 (2)

O. W. Shih, “A multilayer heat conduction solution for magneto-optical disk recording,” J. Appl. Phys. 75, 4382–4395 (1994).
[CrossRef]

P. Loza, D. Kouznetsov, R. Ortega, “Temperature distribution in a uniform medium heated by absorption of a Gaussian light beam,” Appl. Opt. 33, 3831–3836 (1994).
[CrossRef] [PubMed]

1993 (1)

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

1992 (1)

W. A. McGahan, K. D. Cole, “Solutions of the heat conduction equation in multilayers for photothermal deflection experiments,” J. Appl. Phys. 72, 1362–1373 (1992).
[CrossRef]

1987 (1)

A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
[CrossRef]

1985 (1)

A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
[CrossRef]

1982 (1)

1978 (1)

Y. Takeuti, S. Zaima, N. Noda, “Thermal stresses problems in industry. 1. On thermoelastic distortion in machine metals,” J. Therm. Stress 1, 199–210 (1978).
[CrossRef]

1971 (1)

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

Abbott, S. J.

A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
[CrossRef]

Abtahi, A.

A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
[CrossRef]

Barmashenko, B. D.

D. Furman, B. D. Barmashenko, S. Rosenwaks, “Parametric study of an efficient supersonic chemical oxygen-iodine laser/jet generator system operating without buffer gas,” IEEE J. Quantum Electron. 34, 1068–1074 (1998).
[CrossRef]

Bauer, A. H.

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

Bennett, H. E.

H. E. Bennett, A. J. Glass, A. H. Guenther, B. E. Newnam, Laser Induced Damage in Optical Materials: 1980 (National Bureau of Standards, Boulder, Colo., 1981).

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).

Bräunlich, P. F.

A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
[CrossRef]

Burgess, A. N.

A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
[CrossRef]

Cheng, Z.

Cole, K. D.

W. A. McGahan, K. D. Cole, “Solutions of the heat conduction equation in multilayers for photothermal deflection experiments,” J. Appl. Phys. 72, 1362–1373 (1992).
[CrossRef]

Connell, G. A. N.

Copeland, D. A.

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

Crowell, P.

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

Endo, M.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Erkkila, J.

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

Evans, K. E.

A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
[CrossRef]

Fuijii, H.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Fujioka, T.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Furman, D.

D. Furman, B. D. Barmashenko, S. Rosenwaks, “Parametric study of an efficient supersonic chemical oxygen-iodine laser/jet generator system operating without buffer gas,” IEEE J. Quantum Electron. 34, 1068–1074 (1998).
[CrossRef]

Gasiot, J.

A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
[CrossRef]

Glass, A. J.

H. E. Bennett, A. J. Glass, A. H. Guenther, B. E. Newnam, Laser Induced Damage in Optical Materials: 1980 (National Bureau of Standards, Boulder, Colo., 1981).

Goodman, J. W.

Guenther, A. H.

H. E. Bennett, A. J. Glass, A. H. Guenther, B. E. Newnam, Laser Induced Damage in Optical Materials: 1980 (National Bureau of Standards, Boulder, Colo., 1981).

Hager, G. D.

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

Hallada, M. R.

M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).

Hartnett, J. P.

W. M. Rohsenow, J. P. Hartnett, Handbook of Heat Transfer (McGraw-Hill, New York, 1973).

Helms, C. A.

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

Kelly, P.

A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
[CrossRef]

Kouznetsov, D.

Loza, P.

Loze, M. K.

Mackay, M.

A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
[CrossRef]

Mansuripur, M.

McGahan, W. A.

W. A. McGahan, K. D. Cole, “Solutions of the heat conduction equation in multilayers for photothermal deflection experiments,” J. Appl. Phys. 72, 1362–1373 (1992).
[CrossRef]

Nagatomo, S.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Nanri, K.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Newnam, B. E.

H. E. Bennett, A. J. Glass, A. H. Guenther, B. E. Newnam, Laser Induced Damage in Optical Materials: 1980 (National Bureau of Standards, Boulder, Colo., 1981).

Nikolaev, V. D.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Noda, N.

Y. Takeuti, S. Zaima, N. Noda, “Thermal stresses problems in industry. 1. On thermoelastic distortion in machine metals,” J. Therm. Stress 1, 199–210 (1978).
[CrossRef]

Nowinski, J. L.

J. L. Nowinski, Theory of Thermoelasticity with Applications (Sijthoff & Noordhoff Alphen aan den Rijn, The Netherlands, 1978).
[CrossRef]

Ortega, R.

Özisik, M. N.

M. N. Özişik, Heat Conduction (Wiley, New York, 1980).

Peng, Y.

Plummer, D.

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

Qiu, J.

Rohsenow, W. M.

W. M. Rohsenow, J. P. Hartnett, Handbook of Heat Transfer (McGraw-Hill, New York, 1973).

Rosenwaks, S.

D. Furman, B. D. Barmashenko, S. Rosenwaks, “Parametric study of an efficient supersonic chemical oxygen-iodine laser/jet generator system operating without buffer gas,” IEEE J. Quantum Electron. 34, 1068–1074 (1998).
[CrossRef]

Seiffert, S. L.

M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).

Shih, O. W.

O. W. Shih, “A multilayer heat conduction solution for magneto-optical disk recording,” J. Appl. Phys. 75, 4382–4395 (1994).
[CrossRef]

Sparks, M.

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

Sugimoto, D.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Sunako, K.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Takeda, S.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Takeuti, Y.

Y. Takeuti, S. Zaima, N. Noda, “Thermal stresses problems in industry. 1. On thermoelastic distortion in machine metals,” J. Therm. Stress 1, 199–210 (1978).
[CrossRef]

Truesdell, K. A.

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

Vetrovec, J.

M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).

Walker, R. F.

M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).

Wani, F.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).

Wolf, H. F.

H. F. Wolf, Silicon Semiconduction Data (Signetics Corporation, Sunnyvale, Calif., 1969).

Wright, C. D.

Zagidullin, M. V.

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

Zaima, S.

Y. Takeuti, S. Zaima, N. Noda, “Thermal stresses problems in industry. 1. On thermoelastic distortion in machine metals,” J. Therm. Stress 1, 199–210 (1978).
[CrossRef]

Zhang, Y.

Appl. Opt. (4)

IEEE J. Quantum Electron. (4)

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

M. Endo, S. Nagatomo, S. Takeda, M. V. Zagidullin, V. D. Nikolaev, H. Fuijii, F. Wani, D. Sugimoto, K. Sunako, K. Nanri, T. Fujioka, “High-efficiency operation of a chemical oxygen-iodine laser using nitrogen as a buffer gas,” IEEE J. Quantum Electron. 34, 393–398 (1998).
[CrossRef]

D. Furman, B. D. Barmashenko, S. Rosenwaks, “Parametric study of an efficient supersonic chemical oxygen-iodine laser/jet generator system operating without buffer gas,” IEEE J. Quantum Electron. 34, 1068–1074 (1998).
[CrossRef]

G. D. Hager, C. A. Helms, K. A. Truesdell, D. Plummer, J. Erkkila, P. Crowell, “A simplified analytic model for gain saturation and power extraction in the flowing chemical oxygen-iodine laser,” IEEE J. Quantum Electron. 32, 1525–1536 (1996).
[CrossRef]

J. Appl. Phys. (5)

A. N. Burgess, K. E. Evans, M. Mackay, S. J. Abbott, “Comparison of transient thermal conduction in tellurium and organic dye based digital optical storage media,” J. Appl. Phys. 61, 74–80 (1987).
[CrossRef]

O. W. Shih, “A multilayer heat conduction solution for magneto-optical disk recording,” J. Appl. Phys. 75, 4382–4395 (1994).
[CrossRef]

A. Abtahi, P. F. Bräunlich, P. Kelly, J. Gasiot, “Laser stimulated thermoluminescence,” J. Appl. Phys. 58, 1626–1639 (1985).
[CrossRef]

W. A. McGahan, K. D. Cole, “Solutions of the heat conduction equation in multilayers for photothermal deflection experiments,” J. Appl. Phys. 72, 1362–1373 (1992).
[CrossRef]

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

J. Therm. Stress (1)

Y. Takeuti, S. Zaima, N. Noda, “Thermal stresses problems in industry. 1. On thermoelastic distortion in machine metals,” J. Therm. Stress 1, 199–210 (1978).
[CrossRef]

Laser Focus World (1)

M. R. Hallada, S. L. Seiffert, R. F. Walker, J. Vetrovec, “Exotic lasers: iodine laser deliver high laser via fiber,” Laser Focus World 36(5), 205–212 (2000).

Other (6)

J. L. Nowinski, Theory of Thermoelasticity with Applications (Sijthoff & Noordhoff Alphen aan den Rijn, The Netherlands, 1978).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).

H. F. Wolf, Silicon Semiconduction Data (Signetics Corporation, Sunnyvale, Calif., 1969).

H. E. Bennett, A. J. Glass, A. H. Guenther, B. E. Newnam, Laser Induced Damage in Optical Materials: 1980 (National Bureau of Standards, Boulder, Colo., 1981).

W. M. Rohsenow, J. P. Hartnett, Handbook of Heat Transfer (McGraw-Hill, New York, 1973).

M. N. Özişik, Heat Conduction (Wiley, New York, 1980).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the unstable optical resonator of a high-power laser system.

Fig. 2
Fig. 2

Schematic of the analysis of a heat-conduction problem.

Fig. 3
Fig. 3

(a) Three-dimensional temperature rise distribution in the Al2O3 substrate for 50-kW irradiation during 5 s. (b) Maximum temperature rises in the irradiated region (at z = 0, r = 2 cm) as functions of laser irradiation time.

Fig. 4
Fig. 4

(a) Thermal deformation profiles of the Al2O3 substrate versus radial coordinate r for an irradiation time of 5 s. (b) Maximum thermal deformation at the irradiated region (r = 2, z = 0) versus laser irradiation time t.

Fig. 5
Fig. 5

(a) Thermal deformation profiles of the SiO2 substrate versus radial coordinate r for an irradiation time of 5 s. (b) Maximum thermal deformation at the irradiated region (r = 2.1, z = 0) versus laser irradiation time t.

Fig. 6
Fig. 6

(a) Thermal deformation profiles of the Si substrate versus radial coordinate r for an irradiation time of 5 s. (b) Maximum thermal deformation at the irradiated region (r = 2, z = 0) versus laser irradiation time t.

Fig. 7
Fig. 7

Strehl ratios of Al2O3 and SiO2 for the temperature effect of the refractive index versus laser irradiating power.

Fig. 8
Fig. 8

Strehl ratio of the Al2O3 substrate versus laser irradiation time t.

Fig. 9
Fig. 9

Far-field normalized intensity distribution of the Al2O3 and SiO2 substrates versus coordinate kα for laser power 50 kW and irradiation time 5 s.

Tables (1)

Tables Icon

Table 1 Properties of Sapphire, Silica, and Silicona

Equations (21)

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

2Tr, z, tr2+1rTr, z, tr+2Tr, z, tz2+1κ gz=1αTr, z, tt, 0r<b, 0<z<d, t>0.
Tr+HT=0, r=b, t>0,
Tz=0, z=0, t>0,
Tz+HT=0, z=d, t>0,
T=0, t=0, 0r<b, 0<z<d,
Tr, z, t=ακVτ=0t×Gr, z, t|r, z, τgz2πrdrdzdτ,
Gr, z, t|r, z, τ=m=1p=1×exp-αβm2+ηp2t-τNβmNηp×R0βm, rZηp, zR0βm, r×Zηp, z,
R0βm, r=J0βmr, 1Nβm=2J02βmbβm2b2H2+βm2
βmJ1βmb=HJ0βmb,
Zηp, z=cos ηpz, 1Nηp=2 ηp2+H2dηp2+H2+H,
ηp tan ηpd=H.
Tr, z, t=ακr=εaaz=0dτ=0tm=1p=1×exp-αβm2+ηp2t-τNβmNηp×R0βm, rZηp, zR0βm, r×Zηp, zgz2πrdrdzdτ,
gz=Pπa2-εa2 μ exp-μz,
Δd=Δdf+Δda+Δdt,
ΔdΔdf.
S=11-ε22a4π202πεaaexp2πiΔΦr, θrdrdθ2,
S=11-ε22a4π202πεaaexp2πiΔΦr, θ+wλ0d Tr, z, tdzrdrdθ2,
Uβ, ϕ=C 0a02πexp-ikρβ cosθ-ϕρdρdθ,
Uβ, ϕ=C 0a02πexp-ikρβ cosθ-ϕexp2πiΔΦr, θ+wλ0d Tr, z, tdzρdρdθ.
Uβ, ϕ=C εaa02πexp-ikrβ cosθ-ϕexp2πiΔΦr, θ+wλ0d Tr, z, tdzrdrdθ.
In=εaa J0rkβexp2πiΔΦr, θ+wλ0d Tr, z, tdzrdr2,

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