Abstract

An analysis is given of how nonuniformities in the laser beam intensity translate into variations on the induced temperature distribution on an irradiated sample. The study involves materials with different thermal conductivities. By use of a reshaped irradiating beam obtained with a multifaceted integrating mirror, a three-dimensional numerical calculation allows us to establish both surface and in-depth temperature distributions. The results show that in the case of materials such as glass (i.e., with low thermal conductivity) large thermal gradients occur both on the surface and in depth during irradiation. However, the lateral heat flow is high enough to strongly reduce the surface gradients as soon as the laser irradiation ends. Conversely, in good thermal conductors such as nickel, the laser intensity nonuniformities induce a thermal peaking of the surface with lateral thermal gradients that are by no means negligible. Experimental evidence during laser glass polishing that confirms the numerical assessments are also provided.

© 1999 Optical Society of America

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References

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  1. P. W. Rodhes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
    [CrossRef]
  2. W. B. Weldkamp, “Technique for generating focal-plane flattop laser beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
    [CrossRef]
  3. J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2542 (1993).
    [CrossRef] [PubMed]
  4. M. Duparré, M. A. Golub, B. Lüdge, V. S. Pavelyev, V. A. Soifer, G. V. Uspleniev, S. G. Volotovskii, “Investigation of computer-generated diffractive beam shapers for flattening ofsingle-modal CO2 laser beams,” Appl. Opt. 34, 2489–2497 (1995).
    [CrossRef]
  5. S. K. Dew, R. R. Parsons, “Absorbing filter to flatten Gaussian beams,” Appl. Opt. 31, 3416–3419 (1992).
    [CrossRef] [PubMed]
  6. S. P. Chang, J. Kuo, Y. Lee, C. Lu, K. Ling, “Transformation of Gaussian to coherent uniform beams by inverse-Gaussian transmittive filters,” Appl. Opt. 37, 747–752 (1998).
    [CrossRef]
  7. J. Armengol, F. Vega, N. Lupón, F. Laguarta, “Two-faceted mirror for active integration of coherent high-power laser beams,” Appl. Opt. 36, 658–661 (1997).
    [CrossRef] [PubMed]
  8. T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
    [CrossRef]
  9. D. M. Dagenais, J. A. Woodroffe, I. Itzkan, “Optical beam shaping of a high power laser for uniform target illumination,” Appl. Opt. 24, 671–675 (1985).
    [CrossRef] [PubMed]
  10. F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE818, 94–104 (1987).
  11. R. E. Grojean, D. Feldman, J. F. Roach, “Production of flat top beam profiles for high energy lasers,” Rev. Sci. Instrum. 51, 375–376 (1980).
    [CrossRef] [PubMed]
  12. M. R. Latta, K. Jain, “Beam intensity uniformization by mirror folding,” Opt. Commun. 49, 435–439 (1984).
    [CrossRef]
  13. F. Laguarta, N. Lupón, J. Armengol, “Optical glass polishing by controlled laser surface-heat treatment,” Appl. Opt. 33, 6508–6513 (1994).
    [CrossRef] [PubMed]
  14. A. Kar, J. E. Scott, W. P. Lattann, “Effects of the mode estructure on three-dimensional laser heating due to single or multiple rectangular beams,” J. Appl. Phys. 80, 667–674 (1996) and references therein.
  15. M. Von Allmen, A. Blatter, Laser-Beam Interactions with Materials: Physical Principles and Applications (Springer-Verlag, Berlin, 1995), Chap. 3.
    [CrossRef]
  16. P. Strömbek, A. Kar, “Self-focusing and beam attenaution in laser material processing,” J. Phys. D 31, 1438–1448 (1998).
    [CrossRef]
  17. A. García-Beltrán, “Desarrollo y validación de un modelo computacional para la predicción y caracterización de procesos de tratamiento térmico superficial de materiales con laser,” Ph.D. dissertation (Universidad Politécnica de Madrid, Madrid, Spain, 1996).
  18. Y. M. Xiao, M. Bass, “Thermal stress limitations to laser fire polishing of glasses,” Appl. Opt. 22, 2933–2936 (1983).
    [CrossRef] [PubMed]
  19. F. Vega, N. Lupón, J. Armengol, F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
    [CrossRef]
  20. D. A. MacGraw, “The transfer of heat in glass during forming,” J. Am. Ceram. Soc. 44, 353–363 (1961).
    [CrossRef]
  21. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).
  22. E. M. Breinan, B. H. Kear, “Rapid solidification laser processing at high power density,” in Laser Materials Processing, M. Bass, ed., Vol. 3 of Materials Processing Theory and Practices (North-Holland, Amsterdam, 1983), pp. 235–295.
    [CrossRef]
  23. M. Bass, ed., Handbook of Optics II (McGraw-Hill, New York, 1995).
  24. V. P. Veiko, Y. Yakovlev, “Physical fundamentals of laser forming of micro-optical components,” Opt. Eng. 33, 3567–3571 (1994).
    [CrossRef]
  25. M. Wakai, Y. Komagachi, G. Kanai, “Microlenses and microlens arrays formed on a glass plate by use of a CO2 laser,” Appl. Opt. 37, 627–631 (1998).
    [CrossRef]
  26. G. Da Costa, “Competition between capillary and gravity forces in a viscous liquid film heated by a Gaussian laser beam,” J. Phys. (Paris) 43, 1503–1508 (1982).
    [CrossRef]
  27. J. Calatroni, G. Da Costa, “Interferometric determination of the surface profile of a liquid heated by a laser beam,” Opt. Commun. 42, 5–9 (1982).
    [CrossRef]

1998 (4)

S. P. Chang, J. Kuo, Y. Lee, C. Lu, K. Ling, “Transformation of Gaussian to coherent uniform beams by inverse-Gaussian transmittive filters,” Appl. Opt. 37, 747–752 (1998).
[CrossRef]

P. Strömbek, A. Kar, “Self-focusing and beam attenaution in laser material processing,” J. Phys. D 31, 1438–1448 (1998).
[CrossRef]

F. Vega, N. Lupón, J. Armengol, F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[CrossRef]

M. Wakai, Y. Komagachi, G. Kanai, “Microlenses and microlens arrays formed on a glass plate by use of a CO2 laser,” Appl. Opt. 37, 627–631 (1998).
[CrossRef]

1997 (1)

1996 (1)

A. Kar, J. E. Scott, W. P. Lattann, “Effects of the mode estructure on three-dimensional laser heating due to single or multiple rectangular beams,” J. Appl. Phys. 80, 667–674 (1996) and references therein.

1995 (1)

1994 (2)

F. Laguarta, N. Lupón, J. Armengol, “Optical glass polishing by controlled laser surface-heat treatment,” Appl. Opt. 33, 6508–6513 (1994).
[CrossRef] [PubMed]

V. P. Veiko, Y. Yakovlev, “Physical fundamentals of laser forming of micro-optical components,” Opt. Eng. 33, 3567–3571 (1994).
[CrossRef]

1993 (1)

1992 (1)

1985 (1)

1984 (1)

M. R. Latta, K. Jain, “Beam intensity uniformization by mirror folding,” Opt. Commun. 49, 435–439 (1984).
[CrossRef]

1983 (1)

1982 (3)

W. B. Weldkamp, “Technique for generating focal-plane flattop laser beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

G. Da Costa, “Competition between capillary and gravity forces in a viscous liquid film heated by a Gaussian laser beam,” J. Phys. (Paris) 43, 1503–1508 (1982).
[CrossRef]

J. Calatroni, G. Da Costa, “Interferometric determination of the surface profile of a liquid heated by a laser beam,” Opt. Commun. 42, 5–9 (1982).
[CrossRef]

1980 (2)

P. W. Rodhes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
[CrossRef]

R. E. Grojean, D. Feldman, J. F. Roach, “Production of flat top beam profiles for high energy lasers,” Rev. Sci. Instrum. 51, 375–376 (1980).
[CrossRef] [PubMed]

1961 (1)

D. A. MacGraw, “The transfer of heat in glass during forming,” J. Am. Ceram. Soc. 44, 353–363 (1961).
[CrossRef]

Armengol, J.

Bass, M.

Blatter, A.

M. Von Allmen, A. Blatter, Laser-Beam Interactions with Materials: Physical Principles and Applications (Springer-Verlag, Berlin, 1995), Chap. 3.
[CrossRef]

Breinan, E. M.

E. M. Breinan, B. H. Kear, “Rapid solidification laser processing at high power density,” in Laser Materials Processing, M. Bass, ed., Vol. 3 of Materials Processing Theory and Practices (North-Holland, Amsterdam, 1983), pp. 235–295.
[CrossRef]

Calatroni, J.

J. Calatroni, G. Da Costa, “Interferometric determination of the surface profile of a liquid heated by a laser beam,” Opt. Commun. 42, 5–9 (1982).
[CrossRef]

Chang, S. P.

Cordingley, J.

Da Costa, G.

J. Calatroni, G. Da Costa, “Interferometric determination of the surface profile of a liquid heated by a laser beam,” Opt. Commun. 42, 5–9 (1982).
[CrossRef]

G. Da Costa, “Competition between capillary and gravity forces in a viscous liquid film heated by a Gaussian laser beam,” J. Phys. (Paris) 43, 1503–1508 (1982).
[CrossRef]

Dagenais, D. M.

Dew, S. K.

Dickey, F. M.

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE818, 94–104 (1987).

Duparré, M.

Feldman, D.

R. E. Grojean, D. Feldman, J. F. Roach, “Production of flat top beam profiles for high energy lasers,” Rev. Sci. Instrum. 51, 375–376 (1980).
[CrossRef] [PubMed]

García-Beltrán, A.

A. García-Beltrán, “Desarrollo y validación de un modelo computacional para la predicción y caracterización de procesos de tratamiento térmico superficial de materiales con laser,” Ph.D. dissertation (Universidad Politécnica de Madrid, Madrid, Spain, 1996).

Golub, M. A.

Grojean, R. E.

R. E. Grojean, D. Feldman, J. F. Roach, “Production of flat top beam profiles for high energy lasers,” Rev. Sci. Instrum. 51, 375–376 (1980).
[CrossRef] [PubMed]

Habich, U.

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

Henning, T.

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

Herziger, G.

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

Itzkan, I.

Jain, K.

M. R. Latta, K. Jain, “Beam intensity uniformization by mirror folding,” Opt. Commun. 49, 435–439 (1984).
[CrossRef]

Kanai, G.

Kar, A.

P. Strömbek, A. Kar, “Self-focusing and beam attenaution in laser material processing,” J. Phys. D 31, 1438–1448 (1998).
[CrossRef]

A. Kar, J. E. Scott, W. P. Lattann, “Effects of the mode estructure on three-dimensional laser heating due to single or multiple rectangular beams,” J. Appl. Phys. 80, 667–674 (1996) and references therein.

Kear, B. H.

E. M. Breinan, B. H. Kear, “Rapid solidification laser processing at high power density,” in Laser Materials Processing, M. Bass, ed., Vol. 3 of Materials Processing Theory and Practices (North-Holland, Amsterdam, 1983), pp. 235–295.
[CrossRef]

Komagachi, Y.

Kuo, J.

Laguarta, F.

Latta, M. R.

M. R. Latta, K. Jain, “Beam intensity uniformization by mirror folding,” Opt. Commun. 49, 435–439 (1984).
[CrossRef]

Lattann, W. P.

A. Kar, J. E. Scott, W. P. Lattann, “Effects of the mode estructure on three-dimensional laser heating due to single or multiple rectangular beams,” J. Appl. Phys. 80, 667–674 (1996) and references therein.

Lebert, R.

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

Lee, Y.

Ling, K.

Lu, C.

Lüdge, B.

Lupón, N.

MacGraw, D. A.

D. A. MacGraw, “The transfer of heat in glass during forming,” J. Am. Ceram. Soc. 44, 353–363 (1961).
[CrossRef]

O’Neil, B. D.

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE818, 94–104 (1987).

Parsons, R. R.

Pavelyev, V. S.

Roach, J. F.

R. E. Grojean, D. Feldman, J. F. Roach, “Production of flat top beam profiles for high energy lasers,” Rev. Sci. Instrum. 51, 375–376 (1980).
[CrossRef] [PubMed]

Rodhes, P. W.

Scholl, M.

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

Scott, J. E.

A. Kar, J. E. Scott, W. P. Lattann, “Effects of the mode estructure on three-dimensional laser heating due to single or multiple rectangular beams,” J. Appl. Phys. 80, 667–674 (1996) and references therein.

Shealy, D. L.

Soifer, V. A.

Strömbek, P.

P. Strömbek, A. Kar, “Self-focusing and beam attenaution in laser material processing,” J. Phys. D 31, 1438–1448 (1998).
[CrossRef]

Unnebrink, L.

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

Uspleniev, G. V.

Vega, F.

F. Vega, N. Lupón, J. Armengol, F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[CrossRef]

J. Armengol, F. Vega, N. Lupón, F. Laguarta, “Two-faceted mirror for active integration of coherent high-power laser beams,” Appl. Opt. 36, 658–661 (1997).
[CrossRef] [PubMed]

Veiko, V. P.

V. P. Veiko, Y. Yakovlev, “Physical fundamentals of laser forming of micro-optical components,” Opt. Eng. 33, 3567–3571 (1994).
[CrossRef]

Volotovskii, S. G.

Von Allmen, M.

M. Von Allmen, A. Blatter, Laser-Beam Interactions with Materials: Physical Principles and Applications (Springer-Verlag, Berlin, 1995), Chap. 3.
[CrossRef]

Wakai, M.

Weldkamp, W. B.

W. B. Weldkamp, “Technique for generating focal-plane flattop laser beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

Woodroffe, J. A.

Xiao, Y. M.

Yakovlev, Y.

V. P. Veiko, Y. Yakovlev, “Physical fundamentals of laser forming of micro-optical components,” Opt. Eng. 33, 3567–3571 (1994).
[CrossRef]

Appl. Opt. (10)

J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2542 (1993).
[CrossRef] [PubMed]

M. Duparré, M. A. Golub, B. Lüdge, V. S. Pavelyev, V. A. Soifer, G. V. Uspleniev, S. G. Volotovskii, “Investigation of computer-generated diffractive beam shapers for flattening ofsingle-modal CO2 laser beams,” Appl. Opt. 34, 2489–2497 (1995).
[CrossRef]

S. K. Dew, R. R. Parsons, “Absorbing filter to flatten Gaussian beams,” Appl. Opt. 31, 3416–3419 (1992).
[CrossRef] [PubMed]

S. P. Chang, J. Kuo, Y. Lee, C. Lu, K. Ling, “Transformation of Gaussian to coherent uniform beams by inverse-Gaussian transmittive filters,” Appl. Opt. 37, 747–752 (1998).
[CrossRef]

J. Armengol, F. Vega, N. Lupón, F. Laguarta, “Two-faceted mirror for active integration of coherent high-power laser beams,” Appl. Opt. 36, 658–661 (1997).
[CrossRef] [PubMed]

P. W. Rodhes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
[CrossRef]

D. M. Dagenais, J. A. Woodroffe, I. Itzkan, “Optical beam shaping of a high power laser for uniform target illumination,” Appl. Opt. 24, 671–675 (1985).
[CrossRef] [PubMed]

F. Laguarta, N. Lupón, J. Armengol, “Optical glass polishing by controlled laser surface-heat treatment,” Appl. Opt. 33, 6508–6513 (1994).
[CrossRef] [PubMed]

Y. M. Xiao, M. Bass, “Thermal stress limitations to laser fire polishing of glasses,” Appl. Opt. 22, 2933–2936 (1983).
[CrossRef] [PubMed]

M. Wakai, Y. Komagachi, G. Kanai, “Microlenses and microlens arrays formed on a glass plate by use of a CO2 laser,” Appl. Opt. 37, 627–631 (1998).
[CrossRef]

J. Am. Ceram. Soc. (1)

D. A. MacGraw, “The transfer of heat in glass during forming,” J. Am. Ceram. Soc. 44, 353–363 (1961).
[CrossRef]

J. Appl. Phys. (1)

A. Kar, J. E. Scott, W. P. Lattann, “Effects of the mode estructure on three-dimensional laser heating due to single or multiple rectangular beams,” J. Appl. Phys. 80, 667–674 (1996) and references therein.

J. Phys. (Paris) (1)

G. Da Costa, “Competition between capillary and gravity forces in a viscous liquid film heated by a Gaussian laser beam,” J. Phys. (Paris) 43, 1503–1508 (1982).
[CrossRef]

J. Phys. D (1)

P. Strömbek, A. Kar, “Self-focusing and beam attenaution in laser material processing,” J. Phys. D 31, 1438–1448 (1998).
[CrossRef]

Opt. Commun. (2)

M. R. Latta, K. Jain, “Beam intensity uniformization by mirror folding,” Opt. Commun. 49, 435–439 (1984).
[CrossRef]

J. Calatroni, G. Da Costa, “Interferometric determination of the surface profile of a liquid heated by a laser beam,” Opt. Commun. 42, 5–9 (1982).
[CrossRef]

Opt. Eng. (2)

V. P. Veiko, Y. Yakovlev, “Physical fundamentals of laser forming of micro-optical components,” Opt. Eng. 33, 3567–3571 (1994).
[CrossRef]

F. Vega, N. Lupón, J. Armengol, F. Laguarta, “Laser application for optical glass polishing,” Opt. Eng. 37, 272–279 (1998).
[CrossRef]

Rev. Sci. Instrum. (2)

R. E. Grojean, D. Feldman, J. F. Roach, “Production of flat top beam profiles for high energy lasers,” Rev. Sci. Instrum. 51, 375–376 (1980).
[CrossRef] [PubMed]

W. B. Weldkamp, “Technique for generating focal-plane flattop laser beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

Other (7)

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE818, 94–104 (1987).

T. Henning, M. Scholl, L. Unnebrink, U. Habich, R. Lebert, G. Herziger, “Beam shaping for laser materials processing with non-rotationally symmetric optical elements,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 126–129 (1997).
[CrossRef]

M. Von Allmen, A. Blatter, Laser-Beam Interactions with Materials: Physical Principles and Applications (Springer-Verlag, Berlin, 1995), Chap. 3.
[CrossRef]

A. García-Beltrán, “Desarrollo y validación de un modelo computacional para la predicción y caracterización de procesos de tratamiento térmico superficial de materiales con laser,” Ph.D. dissertation (Universidad Politécnica de Madrid, Madrid, Spain, 1996).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).

E. M. Breinan, B. H. Kear, “Rapid solidification laser processing at high power density,” in Laser Materials Processing, M. Bass, ed., Vol. 3 of Materials Processing Theory and Practices (North-Holland, Amsterdam, 1983), pp. 235–295.
[CrossRef]

M. Bass, ed., Handbook of Optics II (McGraw-Hill, New York, 1995).

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Figures (11)

Fig. 1
Fig. 1

Experimental laser intensity profile obtained at the sample plane with a 6 × 6 multifaceted integrating mirror. To have a good spatial resolution, we recorded the profile by scanning the laser intensity distribution along a line with a pinhole positioned in front of a pyroelectric detector.

Fig. 2
Fig. 2

(a) Calculated laser intensity distribution and (b) intensity profile along a line passing through the intensity maxima at the sample plane. Results are obtained with application of Eq. (1) and correspond to a 6 × 6 multifaceted integrating mirror. For the sake of clarity only half of the intensity distribution is shown.

Fig. 3
Fig. 3

Simulated surface temperature distribution on a 5-mm-thick, surface-infinite slab of B-270 optical glass preheated to T o = 550 °C. Calculations are performed with the uniform intensity distribution. Results are obtained with P o = 72.5 W and l = 8.4 mm. The irradiation time was 1.5 s.

Fig. 4
Fig. 4

Simulated surface temperature distribution on a 5-mm-thick, surface-infinite slab of B-270 optical glass preheated to T o = 550 °C. Calculations are performed with the peak patterned intensity distribution. Results are obtained with P o = 72.5 W and l = 8.4 mm. The irradiation time was 1.5 s.

Fig. 5
Fig. 5

Calculated in-depth temperatures as a function of time obtained on a 5-mm-thick, surface-infinite slab of B-270 optical glass preheated to T o = 550 °C. Results correspond to the uniform laser intensity distribution with P o = 72.5 W, spot size l = 8.4 mm, and irradiation time t = 1.5 s.

Fig. 6
Fig. 6

Calculated in-depth temperatures as a function of time obtained on a 5-mm-thick, surface-infinite slab of B-270 optical glass preheated to T o = 550 °C. Results correspond to the peak patterned laser intensity distribution with P o = 72.5 W, spot size l = 8.4 mm, and irradiation time t = 1.5 s. Calculations are carried out under a surface point that receives a maximum of intensity.

Fig. 7
Fig. 7

Calculated surface temperature curves (scale on left-hand side) as a function of time in a 5-mm-thick, surface-infinite slab of B-270 optical glass preheated to T o = 550 °C and irradiated with the peak patterned laser intensity distribution. Temperature curves labeled T MAX and T MIN correspond to adjacent surface points that receive either a maximum or a minimum of intensity. The temperature difference between these points as a function of time (curve labeled T MAX - T MIN, right-hand axis) is also included. The irradiation parameters were P o = 72.5 W, spot size l = 8.4 mm, and irradiation time t = 1.5 s.

Fig. 8
Fig. 8

Simulated surface temperature distribution on a 5-mm-thick, surface-infinite slab of nickel preheated to T o = 550 °C. Calculations are performed with the peak patterned intensity distribution. Results are obtained with P o = 800 W and spot size l = 8.4 mm. The irradiation time was t = 1.5 s.

Fig. 9
Fig. 9

Calculated surface temperature curves (scale on left-hand side) as a function of time in nickel preheated to 550 °C and irradiated with the peak patterned laser intensity distribution. Temperature curves labeled T MAX and T MIN correspond to adjacent surface points that receive either a maximum or a minimum of intensity. The temperature difference between these points as a function of time (curve labeled T MAX - T MIN, right-hand axis) is also included. The irradiation parameters were P o = 800 W, spot size l = 8.4 mm, and irradiation time t = 1.5 s.

Fig. 10
Fig. 10

Optical image of the surface of the B-270 optical glass after irradiation with a laser intensity distribution obtained by means of a 6 × 6 faceted integrating mirror. To avoid thermal cracking, the sample was preheated prior to the laser treatment to T o = 550 °C. The irradiation was carried out with P o = 72.5 W, spot size l = 8.4 mm, and irradiation time t = 1.5 s.

Fig. 11
Fig. 11

Glass surface profile after irradiation with a laser intensity distribution obtained by means of a 6 × 6 faceted integrating mirror. To avoid thermal cracking, the sample was preheated prior to the laser treatment to T o = 550 °C. The irradiation was carried out with P o = 50 W, spot size l = 8.4 mm, and irradiation time t = 3 s. The surface profile was obtained with a commercial phase-shifting optical profiler with a 2.5× objective featuring a Michelson interferometer.

Tables (2)

Tables Icon

Table 1 Thermal and Optical Parameters of B-270 Optical Glass and Nickela

Tables Icon

Table 2 Laser Intensity Distributions Used in Thermal Calculationsa

Equations (4)

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

Ix, y=n=136 Anx, yexpik±x sinαn±y sinβn2,
ρcpTt=xκ Tx+yκ Ty+zκ Tz+Px, y, z, t,
Px, y, z, t=1-RIlaserx, y, tα exp-αz,
Tz=0 for z=0,  z=L at all times.

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