Abstract

The damage conversion behavior of high-reflection coatings under multiple shot of 1064nm nanosecond pulse laser has been investigated. The mechanism of initiation and evolution law of multi-shot damage has been revealed by use of surface profiler and focus ion beam with SEM. The scald damage tends to become delaminate damage under some certain condition. Huge experiments supports that this morphology change condition has a close connection with scald initial fluence, scald size, subsequent fluence and shot number. The relationship among these factors is for the first time achieved to offer the “safety lines” for components. The thermal accumulation effect on the decline of damage threshold under multi-shot has been studied in theory and verified experimentally. In addition, a theory-based formula is used to fit the experiment data for further prediction of thin film life-time.

© 2014 Optical Society of America

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  1. D. Milam, R. A. Bradbury, M. Bass, “Laser damage threshold for dielectric coatings as determined by inclusions,” Appl. Phys. Lett. 23(12), 654–657 (1973).
    [CrossRef]
  2. E. S. Bliss, D. Milam, R. A. Bradbury, “Dielectric mirror damage by laser radiation over a range of pulse durations and beam radii,” Appl. Opt. 12(4), 677–689 (1973).
    [CrossRef] [PubMed]
  3. L. J. Shaw-Klein, S. J. Burns, S. D. Jacobs, “Model for laser damage dependence on thin-film morphology,” Appl. Opt. 32(21), 3925–3929 (1993).
    [CrossRef] [PubMed]
  4. F. Y. Génin, C. J. Stolz, “Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,” Proc. SPIE 2870, 439–448 (1996).
    [CrossRef]
  5. D. Reicher, P. Black, K. Jungling, “Defect formation in hafnium dioxide thin films,” Appl. Opt. 39(10), 1589–1599 (2000).
    [CrossRef] [PubMed]
  6. J.-Y. Natoli, L. Gallais, H. Akhouayri, C. Amra, “Laser-induced damage of materials in bulk, thin-film, and liquid forms,” Appl. Opt. 41(16), 3156–3166 (2002).
    [CrossRef] [PubMed]
  7. L. Gallais, J. Capoulade, J.-Y. Natoli, M. Commandré, M. Cathelinaud, C. Koc, M. Lequime, “Laser damage resistance of hafnia thin films deposited by electron beam deposition, reactive low voltage ion plating, and dual ion beam sputtering,” Appl. Opt. 47(13), C107–C113 (2008).
    [CrossRef] [PubMed]
  8. D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
    [CrossRef]
  9. X. Liu, Y. Zhao, D. Li, G. Hu, Y. Gao, Z. Fan, J. Shao, “Characteristics of plasma scalds in multilayer dielectric films,” Appl. Opt. 50(21), 4226–4231 (2011).
    [CrossRef] [PubMed]
  10. A. Melninkaitis, T. Tolenis, L. Mažulė, J. Mirauskas, V. Sirutkaitis, B. Mangote, X. Fu, M. Zerrad, L. Gallais, M. Commandré, S. Kičas, R. Drazdys, “Characterization of zirconia- and niobia-silica mixture coatings produced by ion-beam sputtering,” Appl. Opt. 50(9), C188–C196 (2011).
    [CrossRef] [PubMed]
  11. L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50(9), C178–C187 (2011).
    [CrossRef] [PubMed]
  12. X. Liu, Y. Zhao, Y. Gao, D. Li, G. Hu, M. Zhu, Z. Fan, J. Shao, “Investigations on the catastrophic damage in multilayer dielectric films,” Appl. Opt. 52(10), 2194–2199 (2013).
    [CrossRef] [PubMed]
  13. M. F. Koldunov, A. A. Manenkov, I. L. Pocotilo, “Multishot laser damage in transparent solids: theory of accumulation effect,” Proc. SPIE 2428, 653–667 (1995).
    [CrossRef]
  14. F. Y. Génin, C. J. Stolz, M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997).
    [CrossRef]
  15. A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
    [CrossRef]
  16. P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
    [CrossRef]
  17. M. Mero, L. A. Emmert, W. Rudolph, “The role of native and photoinduced defects in the multi-pulse subpicosecond damage behavior of oxide films,” Proc. SPIE 7132, 713209 (2008).
    [CrossRef]
  18. A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
    [CrossRef]
  19. Z. Y. Li, C. F. Li, J. P. Guo, “Multiple pulse laser damage to thin-film optical coating,” Proc. SPIE 1519, 374–379 (1991).
    [CrossRef]
  20. K. Mann, B. Granitza, E. Eva, “Multiple-pulse damage thresholds of optical components for excimer lasers,” Proc. SPIE 2966, 496–504 (1997).
    [CrossRef]
  21. X. Fu, A. Melnikaitis, L. Gallais, S. Kiáčas, R. Drazdys, V. Sirutkaitis, M. Commandré, “Investigation of the distribution of laser damage precursors at 1064 nm, 12 ns on Niobia-Silica and Zirconia-Silica mixtures,” Opt. Express 20(23), 26089–26098 (2012).
    [CrossRef] [PubMed]
  22. H. Jiao, T. Ding, Q. Zhang, “Comparative study of laser induced damage of HfO2/SiO2 and TiO2/SiO2 mirrors at 1064 nm,” Opt. Express 19(5), 4059–4066 (2011).
    [CrossRef] [PubMed]
  23. L. Gallais, J. Y. Natoli, C. Amra, “Statistical study of single and multiple pulse laser-induced damage in glass,” Opt. Express 10(25), 1465–1477 (2002).
    [CrossRef]
  24. J. W. Arenberg, “Life testing for laser optics: a first look,” Proc. SPIE 7504, 75041I (2009).
    [CrossRef]
  25. J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
    [CrossRef]
  26. L. Sheehan, M. Kozlowski, B. Tench, “Full aperture laser conditioning of multilayer mirrors and polarizers,” Proc. SPIE 2633, 457–463 (1997).
    [CrossRef]
  27. H. Bercegol, “What is laser conditioning: a review focused on dielectric multilayers,” Proc. SPIE 3578, 421–426 (1998).
  28. C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
    [CrossRef]
  29. L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
    [CrossRef]
  30. H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
    [CrossRef]
  31. Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
    [CrossRef]
  32. M. Commandré, G. Demésy, X. Fu, L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010).
    [CrossRef]
  33. B. Wang, H. Zhang, Y. Qin, X. Wang, X. Ni, Z. Shen, J. Lu, “Temperature field analysis of single layer TiO2 film components induced by long-pulse and short-pulse lasers,” Appl. Opt. 50(20), 3435–3441 (2011).
    [CrossRef] [PubMed]

2013 (1)

2012 (1)

2011 (5)

2010 (3)

M. Commandré, G. Demésy, X. Fu, L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010).
[CrossRef]

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

2009 (1)

J. W. Arenberg, “Life testing for laser optics: a first look,” Proc. SPIE 7504, 75041I (2009).
[CrossRef]

2008 (3)

M. Mero, L. A. Emmert, W. Rudolph, “The role of native and photoinduced defects in the multi-pulse subpicosecond damage behavior of oxide films,” Proc. SPIE 7132, 713209 (2008).
[CrossRef]

L. Gallais, J. Capoulade, J.-Y. Natoli, M. Commandré, M. Cathelinaud, C. Koc, M. Lequime, “Laser damage resistance of hafnia thin films deposited by electron beam deposition, reactive low voltage ion plating, and dual ion beam sputtering,” Appl. Opt. 47(13), C107–C113 (2008).
[CrossRef] [PubMed]

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

2007 (1)

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

2005 (2)

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

2002 (3)

2000 (1)

1999 (1)

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

1998 (2)

H. Bercegol, “What is laser conditioning: a review focused on dielectric multilayers,” Proc. SPIE 3578, 421–426 (1998).

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

1997 (3)

K. Mann, B. Granitza, E. Eva, “Multiple-pulse damage thresholds of optical components for excimer lasers,” Proc. SPIE 2966, 496–504 (1997).
[CrossRef]

L. Sheehan, M. Kozlowski, B. Tench, “Full aperture laser conditioning of multilayer mirrors and polarizers,” Proc. SPIE 2633, 457–463 (1997).
[CrossRef]

F. Y. Génin, C. J. Stolz, M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997).
[CrossRef]

1996 (1)

F. Y. Génin, C. J. Stolz, “Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,” Proc. SPIE 2870, 439–448 (1996).
[CrossRef]

1995 (1)

M. F. Koldunov, A. A. Manenkov, I. L. Pocotilo, “Multishot laser damage in transparent solids: theory of accumulation effect,” Proc. SPIE 2428, 653–667 (1995).
[CrossRef]

1993 (1)

1991 (1)

Z. Y. Li, C. F. Li, J. P. Guo, “Multiple pulse laser damage to thin-film optical coating,” Proc. SPIE 1519, 374–379 (1991).
[CrossRef]

1973 (2)

D. Milam, R. A. Bradbury, M. Bass, “Laser damage threshold for dielectric coatings as determined by inclusions,” Appl. Phys. Lett. 23(12), 654–657 (1973).
[CrossRef]

E. S. Bliss, D. Milam, R. A. Bradbury, “Dielectric mirror damage by laser radiation over a range of pulse durations and beam radii,” Appl. Opt. 12(4), 677–689 (1973).
[CrossRef] [PubMed]

Akhouayri, H.

Allais, C.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

Allenspacher, P.

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

Amra, C.

Arenberg, J.

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

Arenberg, J. W.

J. W. Arenberg, “Life testing for laser optics: a first look,” Proc. SPIE 7504, 75041I (2009).
[CrossRef]

Bass, M.

D. Milam, R. A. Bradbury, M. Bass, “Laser damage threshold for dielectric coatings as determined by inclusions,” Appl. Phys. Lett. 23(12), 654–657 (1973).
[CrossRef]

Bercegol, H.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

H. Bercegol, “What is laser conditioning: a review focused on dielectric multilayers,” Proc. SPIE 3578, 421–426 (1998).

Bernardino, D.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

Black, P.

Bliss, E. S.

Bradbury, R. A.

E. S. Bliss, D. Milam, R. A. Bradbury, “Dielectric mirror damage by laser radiation over a range of pulse durations and beam radii,” Appl. Opt. 12(4), 677–689 (1973).
[CrossRef] [PubMed]

D. Milam, R. A. Bradbury, M. Bass, “Laser damage threshold for dielectric coatings as determined by inclusions,” Appl. Phys. Lett. 23(12), 654–657 (1973).
[CrossRef]

Burns, S. J.

Capanni, A.

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

Capoulade, J.

Cathelinaud, M.

Cavarro, V.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

Ciapponi, A.

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

Commandré, M.

Cui, Y.

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Demésy, G.

M. Commandré, G. Demésy, X. Fu, L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010).
[CrossRef]

Ding, T.

Drazdys, R.

Emmert, L. A.

M. Mero, L. A. Emmert, W. Rudolph, “The role of native and photoinduced defects in the multi-pulse subpicosecond damage behavior of oxide films,” Proc. SPIE 7132, 713209 (2008).
[CrossRef]

Era, F.

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

Eva, E.

K. Mann, B. Granitza, E. Eva, “Multiple-pulse damage thresholds of optical components for excimer lasers,” Proc. SPIE 2966, 496–504 (1997).
[CrossRef]

Fan, Z.

X. Liu, Y. Zhao, Y. Gao, D. Li, G. Hu, M. Zhu, Z. Fan, J. Shao, “Investigations on the catastrophic damage in multilayer dielectric films,” Appl. Opt. 52(10), 2194–2199 (2013).
[CrossRef] [PubMed]

X. Liu, Y. Zhao, D. Li, G. Hu, Y. Gao, Z. Fan, J. Shao, “Characteristics of plasma scalds in multilayer dielectric films,” Appl. Opt. 50(21), 4226–4231 (2011).
[CrossRef] [PubMed]

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

Fejer, M. M.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Fu, X.

Furch, F.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Gallais, L.

X. Fu, A. Melnikaitis, L. Gallais, S. Kiáčas, R. Drazdys, V. Sirutkaitis, M. Commandré, “Investigation of the distribution of laser damage precursors at 1064 nm, 12 ns on Niobia-Silica and Zirconia-Silica mixtures,” Opt. Express 20(23), 26089–26098 (2012).
[CrossRef] [PubMed]

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50(9), C178–C187 (2011).
[CrossRef] [PubMed]

A. Melninkaitis, T. Tolenis, L. Mažulė, J. Mirauskas, V. Sirutkaitis, B. Mangote, X. Fu, M. Zerrad, L. Gallais, M. Commandré, S. Kičas, R. Drazdys, “Characterization of zirconia- and niobia-silica mixture coatings produced by ion-beam sputtering,” Appl. Opt. 50(9), C188–C196 (2011).
[CrossRef] [PubMed]

M. Commandré, G. Demésy, X. Fu, L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010).
[CrossRef]

L. Gallais, J. Capoulade, J.-Y. Natoli, M. Commandré, M. Cathelinaud, C. Koc, M. Lequime, “Laser damage resistance of hafnia thin films deposited by electron beam deposition, reactive low voltage ion plating, and dual ion beam sputtering,” Appl. Opt. 47(13), C107–C113 (2008).
[CrossRef] [PubMed]

L. Gallais, J. Y. Natoli, C. Amra, “Statistical study of single and multiple pulse laser-induced damage in glass,” Opt. Express 10(25), 1465–1477 (2002).
[CrossRef]

J.-Y. Natoli, L. Gallais, H. Akhouayri, C. Amra, “Laser-induced damage of materials in bulk, thin-film, and liquid forms,” Appl. Opt. 41(16), 3156–3166 (2002).
[CrossRef] [PubMed]

Gao, Y.

Gao, Z.

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Génin, F. Y.

F. Y. Génin, C. J. Stolz, M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997).
[CrossRef]

F. Y. Génin, C. J. Stolz, “Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,” Proc. SPIE 2870, 439–448 (1996).
[CrossRef]

Granitza, B.

K. Mann, B. Granitza, E. Eva, “Multiple-pulse damage thresholds of optical components for excimer lasers,” Proc. SPIE 2966, 496–504 (1997).
[CrossRef]

Grigonis, R.

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

Guo, J. P.

Z. Y. Li, C. F. Li, J. P. Guo, “Multiple pulse laser damage to thin-film optical coating,” Proc. SPIE 1519, 374–379 (1991).
[CrossRef]

Han, Y.

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

Herringer, J.

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

Hu, G.

Hue, J.

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

Jacobs, S. D.

Jeskevic, M.

Jiao, H.

Josse, M.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

Jungling, K.

Kiácas, S.

Kicas, S.

Koc, C.

Koldunov, M. F.

M. F. Koldunov, A. A. Manenkov, I. L. Pocotilo, “Multishot laser damage in transparent solids: theory of accumulation effect,” Proc. SPIE 2428, 653–667 (1995).
[CrossRef]

Kozlowski, M.

L. Sheehan, M. Kozlowski, B. Tench, “Full aperture laser conditioning of multilayer mirrors and polarizers,” Proc. SPIE 2633, 457–463 (1997).
[CrossRef]

Kozlowski, M. R.

F. Y. Génin, C. J. Stolz, M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997).
[CrossRef]

Krous, E. M.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Kuzma, D.

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

Lamaignère, L.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

Langdon, B.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Langston, P.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Lequime, M.

Li, C. F.

Z. Y. Li, C. F. Li, J. P. Guo, “Multiple pulse laser damage to thin-film optical coating,” Proc. SPIE 1519, 374–379 (1991).
[CrossRef]

Li, D.

Li, Z. Y.

Z. Y. Li, C. F. Li, J. P. Guo, “Multiple pulse laser damage to thin-film optical coating,” Proc. SPIE 1519, 374–379 (1991).
[CrossRef]

Liu, X.

Lu, J.

Manenkov, A. A.

M. F. Koldunov, A. A. Manenkov, I. L. Pocotilo, “Multishot laser damage in transparent solids: theory of accumulation effect,” Proc. SPIE 2428, 653–667 (1995).
[CrossRef]

Mangote, B.

Mann, K.

K. Mann, B. Granitza, E. Eva, “Multiple-pulse damage thresholds of optical components for excimer lasers,” Proc. SPIE 2966, 496–504 (1997).
[CrossRef]

Maricle, S. M.

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

Markosyan, A.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Mažule, L.

Melnikaitis, A.

Melninkaitis, A.

Menoni, C. S.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Mero, M.

M. Mero, L. A. Emmert, W. Rudolph, “The role of native and photoinduced defects in the multi-pulse subpicosecond damage behavior of oxide films,” Proc. SPIE 7132, 713209 (2008).
[CrossRef]

Miksys, D.

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

Milam, D.

D. Milam, R. A. Bradbury, M. Bass, “Laser damage threshold for dielectric coatings as determined by inclusions,” Appl. Phys. Lett. 23(12), 654–657 (1973).
[CrossRef]

E. S. Bliss, D. Milam, R. A. Bradbury, “Dielectric mirror damage by laser radiation over a range of pulse durations and beam radii,” Appl. Opt. 12(4), 677–689 (1973).
[CrossRef] [PubMed]

Mirauskas, J.

Natoli, J. Y.

Natoli, J.-Y.

Ni, X.

Patel, D.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Pocotilo, I. L.

M. F. Koldunov, A. A. Manenkov, I. L. Pocotilo, “Multishot laser damage in transparent solids: theory of accumulation effect,” Proc. SPIE 2428, 653–667 (1995).
[CrossRef]

Qi, H.

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Qin, Y.

Reagan, B.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Reicher, D.

Riede, W.

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

Rocca, J. J.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Route, R.

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

Rudolph, W.

M. Mero, L. A. Emmert, W. Rudolph, “The role of native and photoinduced defects in the multi-pulse subpicosecond damage behavior of oxide films,” Proc. SPIE 7132, 713209 (2008).
[CrossRef]

Schwartz, S.

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

Shao, J.

Shaw-Klein, L. J.

Sheehan, L.

L. Sheehan, M. Kozlowski, B. Tench, “Full aperture laser conditioning of multilayer mirrors and polarizers,” Proc. SPIE 2633, 457–463 (1997).
[CrossRef]

Sheehan, L. M.

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

Shen, Z.

Sirutkaitis, V.

Skokov, G.

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

Stolz, C. J.

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

F. Y. Génin, C. J. Stolz, M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997).
[CrossRef]

F. Y. Génin, C. J. Stolz, “Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,” Proc. SPIE 2870, 439–448 (1996).
[CrossRef]

Tench, B.

L. Sheehan, M. Kozlowski, B. Tench, “Full aperture laser conditioning of multilayer mirrors and polarizers,” Proc. SPIE 2633, 457–463 (1997).
[CrossRef]

Thomsen, M.

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

Tolenis, T.

Tumosa, D.

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

Wang, B.

Wang, X.

Wernham, D.

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

Wu, Z. L.

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

Yi, K.

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Yu, H.

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Zerrad, M.

Zhang, H.

Zhang, Q.

Zhao, Q.

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

Zhao, Y.

Zhu, M.

Appl. Opt. (10)

X. Liu, Y. Zhao, D. Li, G. Hu, Y. Gao, Z. Fan, J. Shao, “Characteristics of plasma scalds in multilayer dielectric films,” Appl. Opt. 50(21), 4226–4231 (2011).
[CrossRef] [PubMed]

A. Melninkaitis, T. Tolenis, L. Mažulė, J. Mirauskas, V. Sirutkaitis, B. Mangote, X. Fu, M. Zerrad, L. Gallais, M. Commandré, S. Kičas, R. Drazdys, “Characterization of zirconia- and niobia-silica mixture coatings produced by ion-beam sputtering,” Appl. Opt. 50(9), C188–C196 (2011).
[CrossRef] [PubMed]

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50(9), C178–C187 (2011).
[CrossRef] [PubMed]

X. Liu, Y. Zhao, Y. Gao, D. Li, G. Hu, M. Zhu, Z. Fan, J. Shao, “Investigations on the catastrophic damage in multilayer dielectric films,” Appl. Opt. 52(10), 2194–2199 (2013).
[CrossRef] [PubMed]

D. Reicher, P. Black, K. Jungling, “Defect formation in hafnium dioxide thin films,” Appl. Opt. 39(10), 1589–1599 (2000).
[CrossRef] [PubMed]

J.-Y. Natoli, L. Gallais, H. Akhouayri, C. Amra, “Laser-induced damage of materials in bulk, thin-film, and liquid forms,” Appl. Opt. 41(16), 3156–3166 (2002).
[CrossRef] [PubMed]

L. Gallais, J. Capoulade, J.-Y. Natoli, M. Commandré, M. Cathelinaud, C. Koc, M. Lequime, “Laser damage resistance of hafnia thin films deposited by electron beam deposition, reactive low voltage ion plating, and dual ion beam sputtering,” Appl. Opt. 47(13), C107–C113 (2008).
[CrossRef] [PubMed]

E. S. Bliss, D. Milam, R. A. Bradbury, “Dielectric mirror damage by laser radiation over a range of pulse durations and beam radii,” Appl. Opt. 12(4), 677–689 (1973).
[CrossRef] [PubMed]

L. J. Shaw-Klein, S. J. Burns, S. D. Jacobs, “Model for laser damage dependence on thin-film morphology,” Appl. Opt. 32(21), 3925–3929 (1993).
[CrossRef] [PubMed]

B. Wang, H. Zhang, Y. Qin, X. Wang, X. Ni, Z. Shen, J. Lu, “Temperature field analysis of single layer TiO2 film components induced by long-pulse and short-pulse lasers,” Appl. Opt. 50(20), 3435–3441 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. Milam, R. A. Bradbury, M. Bass, “Laser damage threshold for dielectric coatings as determined by inclusions,” Appl. Phys. Lett. 23(12), 654–657 (1973).
[CrossRef]

Opt. Express (3)

Proc. SPIE (19)

J. W. Arenberg, “Life testing for laser optics: a first look,” Proc. SPIE 7504, 75041I (2009).
[CrossRef]

J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010).
[CrossRef]

L. Sheehan, M. Kozlowski, B. Tench, “Full aperture laser conditioning of multilayer mirrors and polarizers,” Proc. SPIE 2633, 457–463 (1997).
[CrossRef]

H. Bercegol, “What is laser conditioning: a review focused on dielectric multilayers,” Proc. SPIE 3578, 421–426 (1998).

C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999).
[CrossRef]

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002).
[CrossRef]

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007).
[CrossRef]

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998).
[CrossRef]

M. Commandré, G. Demésy, X. Fu, L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010).
[CrossRef]

M. F. Koldunov, A. A. Manenkov, I. L. Pocotilo, “Multishot laser damage in transparent solids: theory of accumulation effect,” Proc. SPIE 2428, 653–667 (1995).
[CrossRef]

F. Y. Génin, C. J. Stolz, M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997).
[CrossRef]

A. Melninkaitis, D. Miksys, R. Grigonis, V. Sirutkaitis, D. Tumosa, G. Skokov, D. Kuzma, “Multiple pulse laser-induced damage of antireflection coated lithium triborate,” Proc. SPIE 5963, 59631I (2005).
[CrossRef]

P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, “Vacuum laser damage test bench,” Proc. SPIE 5991, 599128 (2005).
[CrossRef]

M. Mero, L. A. Emmert, W. Rudolph, “The role of native and photoinduced defects in the multi-pulse subpicosecond damage behavior of oxide films,” Proc. SPIE 7132, 713209 (2008).
[CrossRef]

A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010).
[CrossRef]

Z. Y. Li, C. F. Li, J. P. Guo, “Multiple pulse laser damage to thin-film optical coating,” Proc. SPIE 1519, 374–379 (1991).
[CrossRef]

K. Mann, B. Granitza, E. Eva, “Multiple-pulse damage thresholds of optical components for excimer lasers,” Proc. SPIE 2966, 496–504 (1997).
[CrossRef]

F. Y. Génin, C. J. Stolz, “Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,” Proc. SPIE 2870, 439–448 (1996).
[CrossRef]

D. Patel, P. Langston, A. Markosyan, E. M. Krous, B. Langdon, F. Furch, B. Reagan, R. Route, M. M. Fejer, J. J. Rocca, C. S. Menoni, “SiO2/HfO2 multilayers: impact of process parameters and stack geometry on the optical and structural properties,” Proc. SPIE 7132, 71320L (2008).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

The layout of the small beam damage test bench.

Fig. 2
Fig. 2

Typical images of scald damage, a) under 100 × Nomarski microscope; b) multi-hole structure and sphere clusters under high magnification SEM (up to 150000 × ); c) 3-D image of scald taken by surface profiler; and d) the profile of damaged region.

Fig. 3
Fig. 3

Typical images of there different phase of delaminate under surface profiler, Nomarski microscope and SEM (from left to right), a) single ring structure at the beginning of delaminate; b) three rings appears after several pulse irradiation; and c) multi-rings structure after dozens of pulse irradiation.

Fig. 4
Fig. 4

The diameter of delaminate increase with pulse number under two different beam spot size of 495μm and 1470μm (1/e2 diameter), respectively. The laser fluence is 72.5J/cm2 and 55J/cm2.

Fig. 5
Fig. 5

Growth behavior of final size of delaminate (after 1000 shots) vs. laser fluence.

Fig. 6
Fig. 6

The schematic diagram of several phases in damage growth process.

Fig. 7
Fig. 7

The contours of morphology change threshold vs. scald initial fluence under varying shot number.

Fig. 8
Fig. 8

The contours of morphology change threshold vs. scald size under varying shot number.

Fig. 9
Fig. 9

The SEM images of thin film cross section which were measured with duel beam system, a) is the unirradiated regions as reference b1) scald damage region with clusters under 35000 × ; b2) scald damage region with micro-crack under 70000 × .

Fig. 10
Fig. 10

Contours of threshold vs. shot number under varying damage probabilities (from 0% to 100%).

Fig. 11
Fig. 11

The distribution of standing wave field (above) and calculated temperature in a couple of layers under several different numbers of shot, from1 to 1000 (below). The repetition rate is 30Hz, the pulse duration is 10ns and the fluence is 50J/cm2. The thin film stack is (HL) ^15H0.5L2.36H0.7L1.41H0.7L1.29H0.12L /Air, and the substrate is fused silica.

Fig. 12
Fig. 12

The time-variation of temperature in the 2nd layer (HfO2). The dash line shows the tendency of maximum temperature along with pulses.

Fig. 13
Fig. 13

The 0% probability LIDT vs. shot number in theory, the red dash line represent fitting result.

Fig. 14
Fig. 14

Fitting results of 0% probability LIDT vs. shot number for delaminate initiation (upper) and scald (bottom), the correlation coefficients R2 are 0.985 and 0.945, respectively.

Tables (1)

Tables Icon

Table 1 The material parameters used in simulation

Equations (5)

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

ρ i c i T i t k i ( 2 T i r 2 + 1 r T i r + 2 T i Z 2 )=η I 0 α i n i | E | 2
k T r | r= r 0 =0
k T Z | Z=0 =h( T E T)
T(r,Z,0)= T 0 , T 0 =293K
F(N)= P 1 + P 2 exp( P 3 N)+ P 4 exp( P 5 N)

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