Abstract

The nano-precursors in the subsurface of Nd:YLF crystal were limiting factor that decreased the laser-induced damage threshold (LIDT) of HfO2/SiO2 high reflection (HR) coatings irradiated from crystal-film interface. To investigate the contribution of electric-field (E-field) to laser damage originating from nano-precursors and then to probe the distribution of vulnerable nano-precursors in the direction of subsurface depth, two 1064 nm HfO2/SiO2 HR coatings having different standing-wave (SW) E-field distributions in subsurface of Nd:YLF c5424181043036123rystal were designed and prepared. Artificial gold nano-particles were implanted into the crystal-film interface prior to deposition of HR coatings to study the damage behaviors in a more reliable way. The damage test results revealed that the SW E-field rather than the travelling-wave (TW) E-field contributed to laser damage. By comparing the SW E-field distributions and LIDTs of two HR coating designs, the most vulnerable nano-precursors were determined to be concentrated in a thin redeposition layer that is within 100 nm from the crystal-film interface.

© 2013 OSA

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    [Crossref]
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    [Crossref]
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    [Crossref]

2013 (2)

C. Y. Cho, Y. P. Huang, Y. J. Huang, Y. C. Chen, K. W. Su, and Y. F. Chen, “Compact high-pulse-energy passively Q-switched Nd:YLF laser with an ultra-low-magnification unstable resonator: application for efficient optical parametric oscillator,” Opt. Express 21(2), 1489–1495 (2013).
[Crossref] [PubMed]

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

2012 (1)

2011 (3)

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

Z. X. Shen, T. Ding, X. W. Ye, X. D. Wang, B. Ma, X. B. Cheng, H. S. Liu, Y. Q. Ji, and Z. S. Wang, “Influence of cleaning process on the laser-induced damage threshold of substrates,” Appl. Opt. 50(9), C433–C440 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (2)

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

2008 (1)

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(5), 053120 (2008).
[Crossref]

2005 (4)

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[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(25), 10163–10171 (2005).
[Crossref] [PubMed]

2004 (2)

P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. 85(4), 591–593 (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 (2004).
[Crossref]

2003 (2)

2002 (1)

S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulse-laser radiation,” J. Appl. Phys. 92(10), 5720–5728 (2002).
[Crossref]

1998 (2)

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

1989 (1)

R. C. Estler, N. S. Nogar, and R. A. Schmell, “The Detection, Removal and Effect on Damage Thresholds of Cerium Impurities on Fused Silica,” Natl. Bur. Stand (U.S.), Spec. Publ. 775, 183–188 (1989).

1976 (1)

B. E. Newnam, D. H. Gill, and G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Natl. Bur. Stand (U.S.), Spec. Publ. 435, 254–271 (1976).

Bercegol, H.

Bertussi, B.

Besotosnii, V.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Bibeau, C.

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[Crossref]

Birolleau, J.-C.

Bittle, W.

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

Bonneau, F.

Borden, M. R.

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Bude, J.

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

Bude, J. D.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Camp, D.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[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(5), 053120 (2008).
[Crossref]

Carr, C. W.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

Carr, J.

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

Chatterjee, S.

S. Chatterjee, “Simple technique for polishing laser rods,” Opt. Eng. 42(4), 1076–1083 (2003).
[Crossref]

Chen, Y. C.

Chen, Y. F.

Cheng, X. B.

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Z. X. Shen, T. Ding, X. W. Ye, X. D. Wang, B. Ma, X. B. Cheng, H. S. Liu, Y. Q. Ji, and Z. S. Wang, “Influence of cleaning process on the laser-induced damage threshold of substrates,” Appl. Opt. 50(9), C433–C440 (2011).
[Crossref] [PubMed]

Cheshev, E.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Cho, C. Y.

Combis, P.

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(5), 053120 (2008).
[Crossref]

J. Y. Natoli, L. Gallais, B. Bertussi, A. During, M. Commandré, J. L. Rullier, F. Bonneau, and P. Combis, “Localized pulsed laser interaction with submicronic gold particles embedded in silica: a method for investigating laser damage initiation,” Opt. Express 11(7), 824–829 (2003).
[Crossref] [PubMed]

Ding, T.

Donohue, J.

P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. 85(4), 591–593 (2004).
[Crossref]

Dufour, G.

P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. 85(4), 591–593 (2004).
[Crossref]

During, A.

Estler, R. C.

R. C. Estler, N. S. Nogar, and R. A. Schmell, “The Detection, Removal and Effect on Damage Thresholds of Cerium Impurities on Fused Silica,” Natl. Bur. Stand (U.S.), Spec. Publ. 775, 183–188 (1989).

Fargin, E.

Faulkner, G.

B. E. Newnam, D. H. Gill, and G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Natl. Bur. Stand (U.S.), Spec. Publ. 435, 254–271 (1976).

Feit, M. D.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[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 (2004).
[Crossref]

Feldman, T.

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

Folta, J. A.

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Fournier, J.

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(5), 053120 (2008).
[Crossref]

J. Y. Natoli, L. Gallais, B. Bertussi, A. During, M. Commandré, J. L. Rullier, F. Bonneau, and P. Combis, “Localized pulsed laser interaction with submicronic gold particles embedded in silica: a method for investigating laser damage initiation,” Opt. Express 11(7), 824–829 (2003).
[Crossref] [PubMed]

Genin, F.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

Gill, D. H.

B. E. Newnam, D. H. Gill, and G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Natl. Bur. Stand (U.S.), Spec. Publ. 435, 254–271 (1976).

Gorbunkov, M.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Griffin, A. J.

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[Crossref]

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Grua, P.

Huang, Y. J.

Huang, Y. P.

Hutcheon, I.

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

Jakovlev, D.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Ji, Y. Q.

Jonnard, P.

P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. 85(4), 591–593 (2004).
[Crossref]

Jouannigot, S.

Jubera, V.

Kostryukov, P.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Kozlowski, M.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

Kozlowski, M. R.

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

Krivonos, M.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Kupinski, P.

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

Lamaignere, L.

Laurence, T.

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

Laurence, T. A.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Li, H. Q.

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Liu, H. S.

Ma, B.

Menapace, J.

Menapace, J. A.

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[Crossref]

Miller, P.

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

Miller, P. E.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Monticelli, M. V.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

Morreeuw, J. P.

P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. 85(4), 591–593 (2004).
[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(5), 053120 (2008).
[Crossref]

J. Y. Natoli, L. Gallais, B. Bertussi, A. During, M. Commandré, J. L. Rullier, F. Bonneau, and P. Combis, “Localized pulsed laser interaction with submicronic gold particles embedded in silica: a method for investigating laser damage initiation,” Opt. Express 11(7), 824–829 (2003).
[Crossref] [PubMed]

Neauport, J.

Néauport, J.

Newnam, B. E.

B. E. Newnam, D. H. Gill, and G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Natl. Bur. Stand (U.S.), Spec. Publ. 435, 254–271 (1976).

Nogar, N. S.

R. C. Estler, N. S. Nogar, and R. A. Schmell, “The Detection, Removal and Effect on Damage Thresholds of Cerium Impurities on Fused Silica,” Natl. Bur. Stand (U.S.), Spec. Publ. 775, 183–188 (1989).

Norton, M. A.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

Oliver, J. B.

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

Papernov, S.

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulse-laser radiation,” J. Appl. Phys. 92(10), 5720–5728 (2002).
[Crossref]

Pilon, F.

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 (2004).
[Crossref]

Rullier, J. L.

Salleo, A.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

Schaffers, K. I.

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[Crossref]

Schmell, R. A.

R. C. Estler, N. S. Nogar, and R. A. Schmell, “The Detection, Removal and Effect on Damage Thresholds of Cerium Impurities on Fused Silica,” Natl. Bur. Stand (U.S.), Spec. Publ. 775, 183–188 (1989).

Schmid, A. W.

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulse-laser radiation,” J. Appl. Phys. 92(10), 5720–5728 (2002).
[Crossref]

Sheehan, L.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

Shen, N.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Shen, Z. X.

Steele, W.

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

Steele, W. A.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Stolz, C. J.

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[Crossref]

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Su, K. W.

Suratwala, T.

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

Suratwala, T. I.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Tait, A.

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

Talaga, D.

Tang, C. Y.

Tao, D.

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Taylor, J. R.

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Thomas, I.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

Thomas, M. D.

C. J. Stolz, J. A. Menapace, K. I. Schaffers, C. Bibeau, M. D. Thomas, and A. J. Griffin, “Laser damage initiation and growth of antireflection coated S-FAP crystal surfaces prepared by pitch lap and magnetorheological finishing,” Proc. SPIE 5991, 59911I, 59911I-7 (2005).
[Crossref]

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Torres, R.

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

Tunkin, V.

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Tzeng, Y. S.

Wang, X. D.

Wang, Z. S.

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Z. X. Shen, T. Ding, X. W. Ye, X. D. Wang, B. Ma, X. B. Cheng, H. S. Liu, Y. Q. Ji, and Z. S. Wang, “Influence of cleaning process on the laser-induced damage threshold of substrates,” Appl. Opt. 50(9), C433–C440 (2011).
[Crossref] [PubMed]

Wei, Z. Y.

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Wolfe, J. E.

M. R. Borden, J. A. Folta, C. J. Stolz, J. R. Taylor, J. E. Wolfe, A. J. Griffin, and M. D. Thomas, “Improved method for laser damage testing coated optics,” Proc. SPIE 5991, 59912A, 59912A-10 (2005).
[Crossref]

Wong, L. L.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35(16), 2702–2704 (2010).
[Crossref] [PubMed]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X, 75040X-14 (2009).
[Crossref]

Yan, M.

M. R. Kozlowski, J. Carr, I. Hutcheon, R. Torres, L. Sheehan, D. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE 3244, 365–375 (1998).
[Crossref]

Ye, X. W.

Yoshiyama, J.

J. Yoshiyama, F. Genin, A. Salleo, I. Thomas, M. Kozlowski, L. Sheehan, I. Hutcheon, and D. Camp, “Effects of Polishing, Etching, Cleaving, and Water Leaching on the UV Laser Damage of Fused Silica,” Proc. SPIE 3244, 331–340 (1998).
[Crossref]

Zhang, J. L.

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

V. Besotosnii, E. Cheshev, M. Gorbunkov, P. Kostryukov, M. Krivonos, V. Tunkin, and D. Jakovlev, “Diode end-pumped acousto-optically Q-switched compact Nd:YLF laser,” Appl. Phys. B 101(1–2), 71–74 (2010).
[Crossref]

Appl. Phys. Lett. (2)

T. Laurence, J. Bude, N. Shen, T. Feldman, P. Miller, W. Steele, and T. Suratwala, “Metallic-Like Photoluminescence and Absorption in Fused SilicaSurface Flaws,” Appl. Phys. Lett. 94(15), 151114 (2009).
[Crossref]

P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. 85(4), 591–593 (2004).
[Crossref]

J. Am. Ceram. Soc. (1)

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011).
[Crossref]

J. Appl. Phys. (4)

S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulse-laser radiation,” J. Appl. Phys. 92(10), 5720–5728 (2002).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Near-ultraviolet absorption and nanosecond-pulse-laser damage in HfO2 monolayers studied by submicrometer-resolution photothermal heterodyne imaging and atomic force microscopy,” J. Appl. Phys. 109(11), 113106 (2011).
[Crossref]

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(5), 053120 (2008).
[Crossref]

S. Papernov, A. Tait, W. Bittle, A. W. Schmid, J. B. Oliver, and P. Kupinski, “Two mechanisms of crater formation in ultraviolet-pulsed-laser irradiated SiO2 thin films with artificial defects,” J. Appl. Phys. 97(11), 114906 (2005).
[Crossref]

Light: Sci. Appl. (1)

X. B. Cheng, J. L. Zhang, D. Tao, Z. Y. Wei, H. Q. Li, and Z. S. Wang, “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2, e80 (2013), doi:.
[Crossref]

Natl. Bur. Stand (U.S.), Spec. Publ. (2)

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Opt. Eng. (1)

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[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (6)

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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]

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[Crossref]

Other (2)

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Figures (5)

Fig. 1
Fig. 1

SW EFI distributions in HR coatings and subsurface of Nd:YLF crystals. (a) SW EFI distribution of [Air:(HL)^13:Sub] design. (b) SW EFI distribution of [Air:(HL)^13L:Sub] design. (c) Detailed comparison of SW EFI distributions in the shallow subsurface region between two HR coating designs. Shaded areas denote substrate medium.

Fig. 2
Fig. 2

Schematic of [Air:(HL)^13L:Sub] HR coatings on (a) blank Nd:YLF substrate, (b) Nd:YLF substrate with 5 nm gold particles pre-deposited on surface, (c) Nd:YLF substrate having 50 nm gold particles pre-deposited on surface.

Fig. 3
Fig. 3

Representative damage morphologies of two kinds of HR coatings on Nd:YLF substrate with 5 nm gold particles pre-deposited on surface. (a) Low magnification SEM micrograph of [Air:(HL)^13:Sub] HR coatings reflects the high density of damage sites. (b) High magnification SEM micrograph shows the detailed morphologies of damage sites. (c) Optical photograph of a damage site of [Air:(HL)^13L:Sub] HR coatings obtained using Nomarski microscope. (d) Surface topography of a damage site obtained using Veeco DEKTAK Profilometer.

Fig. 4
Fig. 4

Representative damage morphologies of two kinds of HR coatings on Nd:YLF substrates with 50 nm gold particles pre-deposited on surface. (a) Low magnification SEM micrograph of [Air:(HL)^13:Sub] HR coatings reflects the high density of damage sites. (b) High magnification SEM micrograph shows the detailed morphologies of damage sites. (c) Low magnification SEM micrograph of [Air:(HL)^13L:Sub] HR coatings reflects the high density of damage sites. (d) High magnification SEM micrograph shows the detailed morphologies of damage site.

Fig. 5
Fig. 5

Representative damage morphologies of two kinds of HR coatings on Nd:YLF substrate. (a) SEM micrograph of a damage site of [Air:(HL)^13:Sub] HR coating. (b) The optical photograph of a damage site of [Air:(HL)^13L:Sub] HR coating.

Tables (1)

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Table 1 LIDTs of two kinds of HR coatings

Equations (2)

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P( z )α | E( z ) E i | 2 I 0 π a 2
t= 2 n i n i + n sub

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