Abstract

By coupling statistics and heat transfer, we investigate numerically laser-induced crystal damage by multi-gigawatt nanosecond pulses. Our model is based on the heating of nanometric absorbing defects that may cooperate when sufficiently aggregated. In that configuration, they induce locally a strong increase of temperature that may lead to a subsequent damage. This approach allows to predict cluster size distribution and damage probabilities as a function of the laser fluence. By studying the influence of the pulse duration onto the laser-induced damage threshold, we have established scaling laws that link the critical laser fluence to its pulse duration τ. In particular, this approach provides an explanation to the deviation from the standard τ 1/2 scaling law that has been recently observed in laser-induced damage experiments with KH2PO4 (KDP) crystals [J.J. Adams et al, Proc. of SPIE 5991, 5991R-1 (2005)]. In the present paper, despite the 3D problem is tackled, we focus our attention on a 1D modeling of thermal diffusion that is shown to provide more reliable predictions than the 3D one. These results indicate that absorbers involved in KDP damage may be associated with a collection of planar defects. First general comparisons with some experimental facts have been performed.

© 2007 Optical Society of America

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  2. C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
    [CrossRef] [PubMed]
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  4. C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
    [CrossRef]
  5. C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
    [CrossRef]
  6. C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
    [CrossRef] [PubMed]
  7. S. G. Demos, M. Staggs, J. J. De Yoreo and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001)
    [CrossRef]
  8. S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
    [CrossRef]
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  14. A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications
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2006

C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
[CrossRef]

Z. L. Xia, Z. X. Fan and J. D. Shao, "A new theory for evaluating the number density of inclusions in films," Appl. Surf. Sci. 252 (23), 8235-8238 (2006)
[CrossRef]

2005

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

J. J. Adams et al, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," in Laser-induced damage in optical materials, Proc. SPIE 5991,59911R-1 (2005)

2004

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

M. D. Feit and A. M. Rubenchik, "Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning," in Laser-induced damage in optical materials, Proc. SPIE 5273, 74-82, (2004)

2003

C. W. Carr, H. B. Radousky and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003)
[CrossRef] [PubMed]

C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
[CrossRef] [PubMed]

2002

S. Papernov and A.W. Schmid, "Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulsed-laser radiation," J. Appl. Phys. 92, 5720-5728 (2002)
[CrossRef]

J. J. De Yoreo, A. K. Burnham and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002)
[CrossRef]

F. Bonneauel al, "Study of UV laser interaction with gold nanoparticles embedded in silica," Appl. Phy. B 75, 803-815 (2002)
[CrossRef]

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

L. Gallais, J. Y. Natoli and C. Amra, "Statistical study of single and multiple pulse laser-induced damage in glasses," Opt. Express 10, 1465-1474 (2002)
[PubMed]

2001

1999

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

1998

M. D. Feit, A. M. Rubenchik, M. R. Kozlowski, F. Y. G’enin, S. Schwartz and L. M. Sheehan, "Extrapolation of damage test data to predict performance of large area NIF optics at 355nm," in Laser-induced damage in optical materials, Proc. SPIE 3578, 226-234 (1998)

M. Runkel, J. DeYoreo, W. Sell and D. Milam, "Laser conditioning study of KDP on the optical sciences laser using large area beams," in Laser-induced damage in optical materials, Proc. SPIE 3244, 51 (1998)

1997

J. Dijon, T. Poiroux and C. Desrumaux, "Nano absorbing centers: a key point in the laser damage of thin film," in Laser-induced damage in optical materials, Proc. SPIE 2966315 (1997)

1996

B. C. Stuart,M. D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore andM. D. Perry, "Nanosecond-to-femtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996)
[CrossRef]

1994

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

1992

1990

K. E. Montgomery and F. P. Milanovich, "High-laser-damage-threshold potassium dihydrogen phosphate crystals," J. Appl. Phys. 683979-82 (1990)
[CrossRef]

1988

P. K. Bandyopadhyay and L. D. Merkle, "Laser-induced damage in quartz: a study of the influence of impurities and defects," J. Appl. Phys. 631392-1398 (1988)
[CrossRef]

1984

1977

1976

M. Sparks, "Theory of laser heating of solids: metals," J. Appl. Phys. 47, 837-849 (1976)
[CrossRef]

1971

E. S. Bliss, "Pulse duration dependence of laser damage mechanism" Opto-electronics 3, 99 (1971)
[CrossRef]

1970

R.W. Hopper and D. R. Uhlmann, "Mechanism of inclusion damage in laser glass," J. Appl. Phys. 41, 4023-4037 (1970)
[CrossRef]

1952

H. Goldenberg and C.J. Tranter, "Heat flow in an infinite medium heated by a sphere," Br. J. Appl. Phys. 3, 296-298 (1952)
[CrossRef]

Adams, J. J.

J. J. Adams et al, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," in Laser-induced damage in optical materials, Proc. SPIE 5991,59911R-1 (2005)

Akhouayri, H.

Amra, C.

Bandyopadhyay, P. K.

P. K. Bandyopadhyay and L. D. Merkle, "Laser-induced damage in quartz: a study of the influence of impurities and defects," J. Appl. Phys. 631392-1398 (1988)
[CrossRef]

Blinc, R.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Bliss, E. S.

E. S. Bliss, "Pulse duration dependence of laser damage mechanism" Opto-electronics 3, 99 (1971)
[CrossRef]

Bonneau, F.

F. Bonneauel al, "Study of UV laser interaction with gold nanoparticles embedded in silica," Appl. Phy. B 75, 803-815 (2002)
[CrossRef]

Bradbury, R. A.

Burnham, A. K.

J. J. De Yoreo, A. K. Burnham and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002)
[CrossRef]

Carr, C. W.

C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003)
[CrossRef] [PubMed]

Chase, L. L.

Copic, M.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

De Yoreo, J. J.

J. J. De Yoreo, A. K. Burnham and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002)
[CrossRef]

S. G. Demos, M. Staggs, J. J. De Yoreo and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001)
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

Demos, S. G.

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003)
[CrossRef] [PubMed]

S. G. Demos, M. Staggs, J. J. De Yoreo and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001)
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

Desrumaux, C.

J. Dijon, T. Poiroux and C. Desrumaux, "Nano absorbing centers: a key point in the laser damage of thin film," in Laser-induced damage in optical materials, Proc. SPIE 2966315 (1997)

DeYoreo, J.

M. Runkel, J. DeYoreo, W. Sell and D. Milam, "Laser conditioning study of KDP on the optical sciences laser using large area beams," in Laser-induced damage in optical materials, Proc. SPIE 3244, 51 (1998)

Dijon, J.

J. Dijon, T. Poiroux and C. Desrumaux, "Nano absorbing centers: a key point in the laser damage of thin film," in Laser-induced damage in optical materials, Proc. SPIE 2966315 (1997)

Drevensek, I.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Duchateau, G.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Dyan, A.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Enguehard, F.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Fally, M.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Fan, Z. X.

Z. L. Xia, Z. X. Fan and J. D. Shao, "A new theory for evaluating the number density of inclusions in films," Appl. Surf. Sci. 252 (23), 8235-8238 (2006)
[CrossRef]

Feit, M. D.

C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
[CrossRef]

M. D. Feit and A. M. Rubenchik, "Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning," in Laser-induced damage in optical materials, Proc. SPIE 5273, 74-82, (2004)

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

M. D. Feit, A. M. Rubenchik, M. R. Kozlowski, F. Y. G’enin, S. Schwartz and L. M. Sheehan, "Extrapolation of damage test data to predict performance of large area NIF optics at 355nm," in Laser-induced damage in optical materials, Proc. SPIE 3578, 226-234 (1998)

B. C. Stuart,M. D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore andM. D. Perry, "Nanosecond-to-femtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996)
[CrossRef]

Fuith, A.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Gallais, L.

Génin, F. Y.

Goldenberg, H.

H. Goldenberg and C.J. Tranter, "Heat flow in an infinite medium heated by a sphere," Br. J. Appl. Phys. 3, 296-298 (1952)
[CrossRef]

Herman, S.

B. C. Stuart,M. D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore andM. D. Perry, "Nanosecond-to-femtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996)
[CrossRef]

Hopper, R.W.

R.W. Hopper and D. R. Uhlmann, "Mechanism of inclusion damage in laser glass," J. Appl. Phys. 41, 4023-4037 (1970)
[CrossRef]

Hou, C. J.

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

Johnson, M. A.

C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
[CrossRef]

Kiousis, N.

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

Kioussis, N.

C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
[CrossRef] [PubMed]

Kozlowski, M. R.

M. D. Feit, A. M. Rubenchik, M. R. Kozlowski, F. Y. G’enin, S. Schwartz and L. M. Sheehan, "Extrapolation of damage test data to predict performance of large area NIF optics at 355nm," in Laser-induced damage in optical materials, Proc. SPIE 3578, 226-234 (1998)

Lallich, S.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Liu, C. S.

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
[CrossRef] [PubMed]

Mathis, H.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Merkle, L. D.

P. K. Bandyopadhyay and L. D. Merkle, "Laser-induced damage in quartz: a study of the influence of impurities and defects," J. Appl. Phys. 631392-1398 (1988)
[CrossRef]

Milam, D.

M. Runkel, J. DeYoreo, W. Sell and D. Milam, "Laser conditioning study of KDP on the optical sciences laser using large area beams," in Laser-induced damage in optical materials, Proc. SPIE 3244, 51 (1998)

R. H. Picard, D. Milam and R. A. Bradbury, "Statistical analysis of defect-caused laser damage in thin films" Appl. Opt. 16, 1563-1571 (1977)
[CrossRef] [PubMed]

Milanovich, F. P.

K. E. Montgomery and F. P. Milanovich, "High-laser-damage-threshold potassium dihydrogen phosphate crystals," J. Appl. Phys. 683979-82 (1990)
[CrossRef]

Montgomery, K. E.

K. E. Montgomery and F. P. Milanovich, "High-laser-damage-threshold potassium dihydrogen phosphate crystals," J. Appl. Phys. 683979-82 (1990)
[CrossRef]

Natoli, J. Y.

O’Connell, R. M.

Papernov, S.

S. Papernov and A.W. Schmid, "Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulsed-laser radiation," J. Appl. Phys. 92, 5720-5728 (2002)
[CrossRef]

Picard, R. H.

Piombini, H.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Pistor, T. V.

Poiroux, T.

J. Dijon, T. Poiroux and C. Desrumaux, "Nano absorbing centers: a key point in the laser damage of thin film," in Laser-induced damage in optical materials, Proc. SPIE 2966315 (1997)

Porteus, J. O.

Radousky, H. B.

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003)
[CrossRef] [PubMed]

S. G. Demos, M. Staggs, J. J. De Yoreo and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001)
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

Rubenchik, A. M.

C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
[CrossRef]

M. D. Feit and A. M. Rubenchik, "Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning," in Laser-induced damage in optical materials, Proc. SPIE 5273, 74-82, (2004)

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

M. D. Feit, A. M. Rubenchik, M. R. Kozlowski, F. Y. G’enin, S. Schwartz and L. M. Sheehan, "Extrapolation of damage test data to predict performance of large area NIF optics at 355nm," in Laser-induced damage in optical materials, Proc. SPIE 3578, 226-234 (1998)

Rubenchik, A.M.

B. C. Stuart,M. D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore andM. D. Perry, "Nanosecond-to-femtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996)
[CrossRef]

Runkel, M.

M. Runkel, J. DeYoreo, W. Sell and D. Milam, "Laser conditioning study of KDP on the optical sciences laser using large area beams," in Laser-induced damage in optical materials, Proc. SPIE 3244, 51 (1998)

Salleo, A.

Schmid, A.W.

S. Papernov and A.W. Schmid, "Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulsed-laser radiation," J. Appl. Phys. 92, 5720-5728 (2002)
[CrossRef]

Schranz, W.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Seitel, S. C.

Sell, W.

M. Runkel, J. DeYoreo, W. Sell and D. Milam, "Laser conditioning study of KDP on the optical sciences laser using large area beams," in Laser-induced damage in optical materials, Proc. SPIE 3244, 51 (1998)

Shao, J. D.

Z. L. Xia, Z. X. Fan and J. D. Shao, "A new theory for evaluating the number density of inclusions in films," Appl. Surf. Sci. 252 (23), 8235-8238 (2006)
[CrossRef]

Sparks, M.

M. Sparks, "Theory of laser heating of solids: metals," J. Appl. Phys. 47, 837-849 (1976)
[CrossRef]

Staggs, M.

S. G. Demos, M. Staggs, J. J. De Yoreo and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001)
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

Stuart, B. C.

B. C. Stuart,M. D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore andM. D. Perry, "Nanosecond-to-femtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996)
[CrossRef]

Tranter, C.J.

H. Goldenberg and C.J. Tranter, "Heat flow in an infinite medium heated by a sphere," Br. J. Appl. Phys. 3, 296-298 (1952)
[CrossRef]

Uhlmann, D. R.

R.W. Hopper and D. R. Uhlmann, "Mechanism of inclusion damage in laser glass," J. Appl. Phys. 41, 4023-4037 (1970)
[CrossRef]

Warhanek, H.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Whitman, P. K.

J. J. De Yoreo, A. K. Burnham and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002)
[CrossRef]

Xia, Z. L.

Z. L. Xia, Z. X. Fan and J. D. Shao, "A new theory for evaluating the number density of inclusions in films," Appl. Surf. Sci. 252 (23), 8235-8238 (2006)
[CrossRef]

Yan, M.

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

Zgonik, M.

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

Appl. Opt.

Appl. Phy. B

F. Bonneauel al, "Study of UV laser interaction with gold nanoparticles embedded in silica," Appl. Phy. B 75, 803-815 (2002)
[CrossRef]

Appl. Phys. Lett.

C. W. Carr, M. D. Feit, M. A. Johnson and A. M. Rubenchik, "Complex morphology of laser-induced bulk damage in KH2.xD2xPO4 crystals," Appl. Phys. Lett. 89, 131901 (2006)
[CrossRef]

Appl. Surf. Sci.

Z. L. Xia, Z. X. Fan and J. D. Shao, "A new theory for evaluating the number density of inclusions in films," Appl. Surf. Sci. 252 (23), 8235-8238 (2006)
[CrossRef]

Br. J. Appl. Phys.

H. Goldenberg and C.J. Tranter, "Heat flow in an infinite medium heated by a sphere," Br. J. Appl. Phys. 3, 296-298 (1952)
[CrossRef]

Int. Mater. Rev.

J. J. De Yoreo, A. K. Burnham and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002)
[CrossRef]

J. Appl. Phys

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys 85, 3988-3992 (1999)
[CrossRef]

J. Appl. Phys.

R.W. Hopper and D. R. Uhlmann, "Mechanism of inclusion damage in laser glass," J. Appl. Phys. 41, 4023-4037 (1970)
[CrossRef]

K. E. Montgomery and F. P. Milanovich, "High-laser-damage-threshold potassium dihydrogen phosphate crystals," J. Appl. Phys. 683979-82 (1990)
[CrossRef]

P. K. Bandyopadhyay and L. D. Merkle, "Laser-induced damage in quartz: a study of the influence of impurities and defects," J. Appl. Phys. 631392-1398 (1988)
[CrossRef]

M. Sparks, "Theory of laser heating of solids: metals," J. Appl. Phys. 47, 837-849 (1976)
[CrossRef]

S. Papernov and A.W. Schmid, "Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulsed-laser radiation," J. Appl. Phys. 92, 5720-5728 (2002)
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Optics Communications

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, H. Mathis and G. Duchateau, "Laser-induced damage in KH2PO4 and D2xKH2(1.x)PO4: influence of the laser probed volume and optimization of the conditioning through a revisited thermal approach," submitted toOptics Communications

Opto-electronics

E. S. Bliss, "Pulse duration dependence of laser damage mechanism" Opto-electronics 3, 99 (1971)
[CrossRef]

Phys. Rev. B

B. C. Stuart,M. D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore andM. D. Perry, "Nanosecond-to-femtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996)
[CrossRef]

I. Drevensek, M. Zgonik, M. Copic, R. Blinc, A. Fuith, W. Schranz, M. Fally, and H. Warhanek, Phys. Rev. B 49, 3082-3088 (1994)
[CrossRef]

C. S. Liu, C. J. Hou, N. Kiousis, S. G. Demos and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005)
[CrossRef]

Phys. Rev. Lett.

C. S. Liu, N. Kioussis, S. G. Demos and H. B. Radousky, "Electron-or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2003)
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004)
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003)
[CrossRef] [PubMed]

Proc. SPIE

M. D. Feit, A. M. Rubenchik, M. R. Kozlowski, F. Y. G’enin, S. Schwartz and L. M. Sheehan, "Extrapolation of damage test data to predict performance of large area NIF optics at 355nm," in Laser-induced damage in optical materials, Proc. SPIE 3578, 226-234 (1998)

J. Dijon, T. Poiroux and C. Desrumaux, "Nano absorbing centers: a key point in the laser damage of thin film," in Laser-induced damage in optical materials, Proc. SPIE 2966315 (1997)

J. J. Adams et al, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," in Laser-induced damage in optical materials, Proc. SPIE 5991,59911R-1 (2005)

M. D. Feit and A. M. Rubenchik, "Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning," in Laser-induced damage in optical materials, Proc. SPIE 5273, 74-82, (2004)

M. Runkel, J. DeYoreo, W. Sell and D. Milam, "Laser conditioning study of KDP on the optical sciences laser using large area beams," in Laser-induced damage in optical materials, Proc. SPIE 3244, 51 (1998)

Other

A. Dyan and G. Duchateau, CEA, Centre d’Etudes du Ripault, BP 16, 37260 Monts, France, are preparing a manuscript to be called "Laser-induced damage by a nanosecond pulse: a method coupling heat transfer, Mie’s theory and microscopic processes"

R. M. Wood, Laser-induced damage of optical materials, Institute Of Physics publishing series in optics ans optoelectronics, Bristol and Philadelphia (2003)

I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Alan Jeffrey Editor, Fifth Edition (1994)

H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Oxford Science Publications, Second Edition (1959)

N. W. Ashcroft and N. D. Mermin, Solid state physics, Brooks Cole, first edition, 1976

C. Kittel, Introduction to solid state physics, Wiley, seventh edition, 1995

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Figures (9)

Fig. 1.
Fig. 1.

Temperature rise as a function of the cluster size. Full line and dashed lines correspond to 1D and 3D calculations respectively.

Fig. 2.
Fig. 2.

Temperature evolution as a function of the time for different cluster geometries: 1D sphere (solid line), 3D sphere (dashed line) and flat cylinder or enveloppe of a cone (dotted line).

Fig. 3.
Fig. 3.

Spatial temperature evolution resulting from a particular random throwing. 15 ADNS are present, A/ρC = 1013 K.s -1 and τ = 1 ns are used. The temperature rise is enhanced when several ADNS aggregate. Defects positions are shown by vertical arrows.

Fig. 4.
Fig. 4.

Size distribution of clusters derived from a random throwing. Four defects density are considered : nADNS = 50,100,200 and 400 in a domain of size N = 10000. The criterion of clustering d is set to 10nm (value allowing the ADNS to cooperate for τ = 1ns). 10000 drawings have been performed. Sub-figure shows a typical local cluster density as a function of the cluster size.

Fig. 5.
Fig. 5.

Size distribution of clusters derived from distorted throwing in same conditions of Fig. 4 but with d = 0 and nADNS = 100. Biased parameter b values are : 1,10,100,1000,10000,100000 and 1000000.

Fig. 6.
Fig. 6.

Evolution of the damage probability as a function of fluence within the 1D model. Four pulse durations are considered : τ = 250ps,1ns,4ns and 16ns. Parameters are nADNS = 100 and N = 10000. 200 drawings have been performed for each fluence. Sub-figure displays the scaling law exponent as a function of the pulse duration (see text).

Fig. 7.
Fig. 7.

Evolution of the number of ADNS involved in damage as a function of fluence. Four pulse durations are considered : τ = 250ps, 1ns,4ns and 16ns. Parameters are the same of Fig. 6 but with 10000 drawings.

Fig. 8.
Fig. 8.

Damage probability as a function of fluence. (a) Four defects density are considered : n ADNS = 50,100,200 and 400. (b) Three biased parameters are considered : b = 1,10,100. In both cases, calculations have been performed within the 1D model framework using τ = 1ns.

Fig. 9.
Fig. 9.

Evolution of the damage probability as a function of fluence within the 3D model. Five pulse durations are considered : τ = 125ps(a),250ps(b),500ps(c),1ns(d) and 4ns(e). In all cases, nADNS = 1250 and the domain size is 50×50×50. Sub-figure (f) displays the scaling law exponent as a function of the pulse duration (see text).

Tables (1)

Tables Icon

Table 1. Critical fluence and x-exponent as a function of the pulse duration

Equations (41)

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

Δ T 1 D ( x = 0 , t ) = A ρC { t ( t + l 2 2 D ) erfc ( l 2 Dt ) + l ( t πD ) 1 2 exp ( l 2 4 Dt ) }
Δ T 3 D ( r = 0 , t ) = a 2 A DρC { 1 2 2 π [ πDt 2 l exp ( l 2 4 Dt ) π 2 ( Dt l 2 1 2 ) erf ( 1 Dt 2 ) ] }
F c = T c τ ζ f ( τ )
T t = D 2 T x 2 + A ρC i = 1 n ADNS ( x x i )
{ ( x ) = 1 if x [ x a 2 ; x + a 2 ] ( x ) = 0 elsewhere
T ( x , t ) = T 0 + i = 1 n ADNS Δ T ( i ) ( x , t )
Δ T ( i ) t = D 2 Δ T ( i ) x 2 + A ρC ( x x i )
θ 1 D ( x , t ) = 2 λ { 2 ( Dt π ) 1 2 exp ( x 2 4 Dt ) x erfc ( x Dt 2 ) }
θ 3 D ( r , t ) = Aa 3 3 λr erfc ( r 2 Dt )
{ P d = bn d ( bn d + n dl ) ) P dl = n dl ( bn d + n dl ) )
x = α In τ + β
{ Δ T t = D 2 Δ T x 2 + A ρ C if a x a Δ T t = D 2 Δ T x 2 elsewhere
{ Δ T ¯ ʺ q 2 Δ T ¯ = A sDρC if a x a Δ T ¯ ʺ q 2 Δ T ¯ = 0 elsewhere
{ Δ T ¯ ( x , s ) = αe qx if x a Δ T ¯ ( x , s ) = βe qx + γe qx + A s 2 ρ C Δ T ¯ ( x , s ) = δe qx if x a if a x a
Δ T ˉ ( x , s ) = A 2 ρ Cs 2 ( e q ( x a ) e q ( x + a ) )
1 ( e qx s 2 ) = ( t + x 2 2 D ) erfc ( x Dt 2 ) x ( t πD ) 1 2 exp ( x 2 4 Dt )
Δ T ( x , t ) = A 2 ρC { ( t + ( x a ) 2 2 D ) erfc ( x a 2 Dt ) ( x a ) ( t πD ) 1 2 exp ( ( x a ) 2 4 Dt ) ( t + ( x + a ) 2 2 D ) erfc ( x + a 2 Dt ) + ( x + a ) ( t πD ) 1 2 exp ( ( x + a ) 2 4 Dt ) }
Δ T ( x , t ) = A ρC { t 1 2 ( t + ( a x ) 2 2 D ) erfc ( a x 2 Dt ) a x 2 ( t πD ) 1 2 exp ( ( a x ) 2 4 Dt ) 1 2 ( t + ( x + a ) 2 2 D ) erfc ( x + a 2 Dt ) + x + a 2 ( t πD ) 1 2 exp ( ( x + a ) 2 4 Dt ) }
Δ T = ( r = 0 , t ) = a 2 A λ 2 { λ 1 3 λ 2 + 1 6 2 b π 0 + dy exp ( t γ 1 y 2 ) sin y y cos y y ( ( c sin y y cos y ) 2 + b 2 y 2 sin 2 y ) }
0 dy exp ( αy 2 ) y 3 ( sin y y cos y ) = πα 2 exp ( 1 4 α ) π 2 ( α 1 2 ) erf ( 1 2 α )
Δ T ( r = 0 , t ) = a 2 A DρC { 1 2 2 π [ πDt 2 a exp ( a 2 4 Dt ) π 2 ( Dt a 2 1 2 ) erf ( a 2 Dt ) ] }
Δ T ( r , t ) = a 3 A r λ 1 { 1 3 2 π 0 + exp ( D 1 t a 2 y 2 ) y 4 ( sin y y cos y ) sin ( r a y ) dy }
T ( r , t ) ~ a 3 A 3 { 1 r πDt }
θ 1 D t = D 2 θ 1 D x 2 + ( x ) F ( t ) ρC
θ 1 D ( x , s ) = E 2 λ D s exp { x s D }
{ F ( t ) = 1 τ if 0 t τ F ( t ) = 0 elsewhere
θ 1 D ( x , s ) = E 2 λτ D s exp { x s D } 1 e τs s
θ 1 D ( x , s ) = ζ ( x , s ) e τs ζ ( x , s )
ζ ( x , s ) = E 2 λτ D s 3 exp { x s D }
θ 1 D ( x , t ) = E 2 λτ { 2 ( Dt π ) 1 2 exp ( x 2 4 Dt ) x erfc ( x 2 Dt ) }
θ 3 D ( r , t ) = E 4 πλrτ erfc ( r 2 Dt )
Δ T ( r = 0 , t ) = 1 4 3 π a 3 0 a θ 3 D ( r , t ) d r
Δ T ( r = 0 , t ) = A λ 0 a dr r erfc ( r 2 Dt )
erf ( αx ) dx = x erf ( αx ) + e α 2 x 2 α π
Δ T ( r = 0 , t ) = A 2 λ { a 2 ( 1 erf ( αa ) ) ae α 2 a 2 α π + erf ( αa ) 2 α 2 }
Δ T ( r = 0 , t ) = a 2 A λ { 1 2 2 π ( πDt 2 a e a 2 4 Dt π 2 ( Dt a 2 1 2 ) erf ( a 2 Dt ) ) }
Δ T ( r = 0 , z = 0 , t ) A 4 πλ 0 a dr 2 π r Δ z 1 r erfc ( r 2 Dt ) = A Δ z 2 λ 0 a erfc ( r 2 Dt ) dr
Δ T ( r = 0 , z = 0 , t ) = A Δ z 2 λ { a erfc ( a 2 Dt ) 2 Dt π ( e a 2 4 Dt 1 ) }
Δ T ( r = 0 , z = 0 , t ) = 1 4 3 π a 3 0 h dz Δ R 2 πR ( z ) θ 3 D ( r ( z ) , t )
Δ T ( r = 0 , z = 0 , t ) = A 2 λ a Δ R h 2 + a 2 0 h dz erfc z 1 + a 2 h 2 2 Dt
Δ T ( r = 0 , z = 0 , t ) = A 2 λ a Δ R h 2 + a 2 { h erfc ( αh ) 2 Dt π ( e α 2 h 2 1 ) }

Metrics