Abstract

A model for describing laser-induced damage in optical materials by nanosecond laser pulses is investigated. The laser-damage critical fluence is obtained based on calculating the light absorption of nanoabsorbers by using Mie theory and solving the heat equation. Considering a power law distribution of nano-absorbers, we calculated the damage probability at the surface of fused silica including Pt particles. The theoretical results calculated with appropriate parameters are applied to fit the experimental data in order to identify the properties of nanodefects.

© 2012 Optical Society of America

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  1. P. Miller, J. Bude, T. Suratwala, N. Shen, T. Laurence, W. Steele, J. Menapace, M. Feit, and L. Wong, “Fracture induced sub-band absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35, 2702–2704 (2010).
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  3. T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
    [CrossRef]
  4. C. Carr, J. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B 82, 1843041–1843047 (2010).
    [CrossRef]
  5. R. Hopper and D. Uhlmann, “Mechanism of inclusion damage in laser glass,” J. Appl. Phys. 41, 4023–4037 (1970).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express 13, 10163–10171 (2005).
    [CrossRef]
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    [CrossRef]
  28. A. During, C. Fossati, and M. Commandré, “Multiwavelength imaging of defects in ultraviolet optical materials,” Appl. Opt. 41, 3118–3126 (2002).
    [CrossRef]

2011

2010

P. Miller, J. Bude, T. Suratwala, N. Shen, T. Laurence, W. Steele, J. Menapace, M. Feit, and L. Wong, “Fracture induced sub-band absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35, 2702–2704 (2010).
[CrossRef]

C. Carr, J. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B 82, 1843041–1843047 (2010).
[CrossRef]

Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. 35, 1238–1240 (2010).

R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18, 19966–19976 (2010).
[CrossRef]

2009

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

M. Zhou, J. Shao, Z. Fan, Y. A. Zhao, and D. Li, “Effect of multiple wavelengths combination on laser-induced damage in multilayer mirrors,” Opt. Express 17, 20313–20320(2009).
[CrossRef]

2008

2007

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

2005

2004

2003

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE 5273, 74–82 (2003).
[CrossRef]

2002

2001

1981

T. Walker, A. Guenther, and P. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part II: Theory,” IEEE J. Quantum Electronics. 17, 2053–2065 (1981).
[CrossRef]

1970

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

Adams, J. J.

Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. 35, 1238–1240 (2010).

Akhouayri, H.

Amra, C.

Bercegol, H.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express 13, 10163–10171 (2005).
[CrossRef]

Bertussi, B.

Birolleau, J. C.

Bonneau, F.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Bouillet, S.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

Bude, J.

Bude, J. D.

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Capoulade, J.

L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. 104, 53120–53129 (2008).
[CrossRef]

Carr, C.

C. Carr, J. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B 82, 1843041–1843047 (2010).
[CrossRef]

Carr, C. W.

D. A. Cross and C. W. Carr, “Analysis of 1ω bulk laser damage in KDP,” Appl. Opt. 50, D7–D11 (2011).
[CrossRef]

R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18, 19966–19976 (2010).
[CrossRef]

Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. 35, 1238–1240 (2010).

Combis, P.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Commandre, M.

H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt Commun. 256, 184–189 (2005).
[CrossRef]

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Commandré, M.

L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. 104, 53120–53129 (2008).
[CrossRef]

J. Y. Natoli, B. Bertussi, and M. Commandré, “Effect of multiple laser irradiations on silica at 1064 and 355 nm,” Opt. Lett. 30, 1315–1317 (2005).
[CrossRef]

A. During, C. Fossati, and M. Commandré, “Multiwavelength imaging of defects in ultraviolet optical materials,” Appl. Opt. 41, 3118–3126 (2002).
[CrossRef]

Cottancin, E.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Courchinoux, R.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

Cross, D. A.

DeMange, P.

C. Carr, J. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B 82, 1843041–1843047 (2010).
[CrossRef]

Donval, T.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

Duchateau, G.

During, A.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

A. During, C. Fossati, and M. Commandré, “Multiwavelength imaging of defects in ultraviolet optical materials,” Appl. Opt. 41, 3118–3126 (2002).
[CrossRef]

Dyan, A.

Enguehard, F.

Fan, Z.

Feit, M.

Feit, M. D.

M. D. Feit, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264–272 (2004).
[CrossRef]

M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE 5273, 74–82 (2003).
[CrossRef]

Feldman, T.

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Fossati, C.

Gallais, L.

L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. 104, 53120–53129 (2008).
[CrossRef]

H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt Commun. 256, 184–189 (2005).
[CrossRef]

L. Gallais, P. Voarino, and C. Amra, “Optical measurement of size and complex index of laser-damage precursors: the inverse problem,” J. Opt. Soc. Am. B 21, 1073–1080 (2004).
[CrossRef]

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).

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]

Grezes-Besset, C.

H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt Commun. 256, 184–189 (2005).
[CrossRef]

Guenther, A.

T. Walker, A. Guenther, and P. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part II: Theory,” IEEE J. Quantum Electronics. 17, 2053–2065 (1981).
[CrossRef]

He, H.

Hopper, R.

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

Hughes, J. D.

Hulst, H. C.

H. C. Hulst, Light Scattering by Small Particles (Wiley, 1957).

Josse, M.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, New York, 1995).

Krol, H.

H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt Commun. 256, 184–189 (2005).
[CrossRef]

Lallich, S.

Lamaignere, L.

Lamaignère, L.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

Laurence, T.

Laurence, T. A.

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Li, D.

Liao, Z. M.

Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. 35, 1238–1240 (2010).

Manes, K.

Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. 35, 1238–1240 (2010).

Menapace, J.

Miller, P.

Miller, P. E.

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Natoli, J. Y.

L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. 104, 53120–53129 (2008).
[CrossRef]

H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt Commun. 256, 184–189 (2005).
[CrossRef]

J. Y. Natoli, B. Bertussi, and M. Commandré, “Effect of multiple laser irradiations on silica at 1064 and 355 nm,” Opt. Lett. 30, 1315–1317 (2005).
[CrossRef]

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[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]

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).

Neauport, J.

Negres, R. A.

Nielsen, P.

T. Walker, A. Guenther, and P. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part II: Theory,” IEEE J. Quantum Electronics. 17, 2053–2065 (1981).
[CrossRef]

Norton, M. A.

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]

Pellarin, M.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Pellin, M.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Pilon, F.

Piombini, H.

Poncetta, J. C.

L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J. C. Poncetta, and H. Bercegol, “An accurate, repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum 78, 1031051–1031059 (2007).
[CrossRef]

Rubenchik, A. M.

M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE 5273, 74–82 (2003).
[CrossRef]

Rullier, J. L.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

Savina, M.

F. Bonneau, P. Combis, J. L. Rullier, M. Commandre, A. During, J. Y. Natoli, M. Pellin, M. Savina, E. Cottancin, and M. Pellarin, “Observation by photothermal microscopy of increased silica absorption in laser damage induced by gold nanoparticles,” Appl. Phys. Lett. 83, 3855–3857 (2003).
[CrossRef]

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]

Shao, J.

Shen, N.

P. Miller, J. Bude, T. Suratwala, N. Shen, T. Laurence, W. Steele, J. Menapace, M. Feit, and L. Wong, “Fracture induced sub-band absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35, 2702–2704 (2010).
[CrossRef]

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Spaeth, M. L.

Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. 35, 1238–1240 (2010).

Steele, W.

Steele, W. A.

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Stolz, C. J.

Suratwala, T.

P. Miller, J. Bude, T. Suratwala, N. Shen, T. Laurence, W. Steele, J. Menapace, M. Feit, and L. Wong, “Fracture induced sub-band absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35, 2702–2704 (2010).
[CrossRef]

T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. 94, 1511141–1511143 (2009).
[CrossRef]

Uhlmann, D.

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

Voarino, P.

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, New York, 1995).

Walker, T.

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Figures (8)

Fig. 1.
Fig. 1.

Calculated absorptivity as a function of particle radius for Pt inclusion in fused silica.

Fig. 2.
Fig. 2.

Evolution of temperature at particle-silica interface with particle radius of 100 nm. (Irradiation is at 355 nm or 1064 nm with pulse duration of 10 ns).

Fig. 3.
Fig. 3.

Maximum temperature as a function of particle radius. (Irradiation is at 355 nm or 1064 nm with pulse duration of 10 ns).

Fig. 4.
Fig. 4.

Critical fluence calculated as a function of particle radius for Pt inclusion in fused silica. (Irradiation is at 355 nm or 1064 nm with pulse duration of 10 ns).

Fig. 5.
Fig. 5.

Defect density as a function of critical fluence. (Irradiation is at 355 nm or 1064 nm with pulse duration of 10 ns).

Fig. 6.
Fig. 6.

Calculated laser-damage probability curves as a function of fluence in the case of the surface of fused silica including Pt particles. (Parameter γ is set to 8 and n0 is set to 5×106cm2.) (a) Irradiation is at 355 nm, with different spot-radius parameters (150 μm, 200 μm, and 250 μm); (b) Irradiation is at 1064 nm, with different spot-radius parameters (12, 20, and 30 μm).

Fig. 7.
Fig. 7.

Experimental setup for laser-damage test.

Fig. 8.
Fig. 8.

Experimental laser-damage probability curves measured at the front surface of fused silica and theoretical curves calculated with the parameters γ=8 and n0=5×106cm2: (a) Irradiation is at 355 nm, with a spot radius of 150 μm; (b) Irradiation is at 1064 nm, with a spot radius of 12 μm.

Tables (1)

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Table 1. Material Thermal and Optical Parameters [23]

Equations (16)

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kext=2x2n=1(2n+1)Re(an+bn)
ksca=2x2n=1(2n+1)(|an|2+|bn|2)
α=kextksca,
1r2r(r2Tit)1DiTit=1Ci3Q4πa30r<a,t>0
1r2r(r2Tst)1DsTst=0r>a,t>0,
T˜(r,ω)=+T(r,t)exp(iωt)dt.
1r2r(r2T˜it)βi2T˜i=3αI08aCiπτexp(τ2ω216),
1r2r(r2T˜st)βs2T˜s=0,
T˜i(r,ω)=Airexp(iβir)Airexp(iβir)+3αI08aβi2Ciπτexp(τ2ω216),
T˜s(r,ω)=Asrexp(iβsr).
(T˜i=T˜s,CiT˜ir=CsT˜sr,r=a).
Ti,s(r,t)=12πω=NNT˜i,s(r,ω)exp(iωt)Δω.
ρ(a)=(γ1)n0amin1γamax1γaγ,
0g(Fc)dFc=n0,
P(F)=1exp(N(F)),
N(F)=0Fg(Fc)SFc(F)dFc,

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