Abstract

Although the finite-difference time-domain (FDTD) technique has been prevailingly used to calculate the electric field intensity (EFI) enhancement at nodular defects in high-reflection (HR) coatings, the physical insight as to how the nodular features contribute to the intensified EFI is not explicitly revealed yet, which in turn limits the solutions that improve the laser-induced damage threshold (LIDT) of nodules by decreasing the EFI enhancement. Here, a simplified model is proposed to describe the intensified EFI in nodules: 1) the nodule works as a microlens and its focal length can be predicted using a simple formula, 2) the portion of incident light that penetrates through the HR coating can be estimated by knowing the angular dependent transmittance (ADT) of the nodule, 3) strong EFI enhancement is created when the focal point is within the nodule and simultaneously a certain portion of light penetrates to the focal position. In the light of the proposed model, a broadband HR coating was used to reduce the EFI enhancement at the seed by a factor about 10, which leads to a 20 times increment of the LIDT. This work therefore not only deepens the physical understanding of EFI enhancement at nodules but also provides a new way to increase the LIDT of multilayer reflective optics.

© 2015 Optical Society of America

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References

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2014 (8)

A. A. Manenkov, “Fundamental mechanisms of laser-induced damage in optical materials: today’s state of understanding and problems,” Opt. Eng. 53(1), 010901 (2014).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica. 1(4), 192–197 (2014).
[Crossref]

X. B. Cheng and Z. S. Wang, “Defect-related properties of optical coatings,” Adv. Opt. Technol. 3, 65–90 (2014).

X. F. Fan, W. T. Zheng, and D. J. Singh, “Light scattering and surface plasmons on small spherical particles,” Light Sci. Appl. 3(6), e179 (2014).
[Crossref]

X. Cheng, A. Tuniyazi, J. Zhang, T. Ding, H. Jiao, B. Ma, Z. Wei, H. Li, and Z. Wang, “Nanosecond laser-induced damage of nodular defects in dielectric multilayer mirrors,” Appl. Opt. 53(4), A62–A69 (2014).
[Crossref] [PubMed]

C. J. Stolz, J. E. Wolfe, J. J. Adams, M. G. Menor, N. E. Teslich, P. B. Mirkarimi, J. A. Folta, R. Soufli, C. S. Menoni, and D. Patel, “High laser-resistant multilayer mirrors by nodular defect planarization,” Appl. Opt. 53(4), A291–A296 (2014).
[Crossref] [PubMed]

L. Gallais, X. Cheng, and Z. Wang, “Influence of nodular defects on the laser damage resistance of optical coatings in the femtosecond regime,” Opt. Lett. 39(6), 1545–1548 (2014).
[Crossref] [PubMed]

J. Cheng, M. Chen, W. Liao, H. Wang, J. Wang, Y. Xiao, and M. Li, “Influence of surface cracks on laser-induced damage resistance of brittle KH₂PO₄ crystal,” Opt. Express 22(23), 28740–28755 (2014).
[PubMed]

2013 (4)

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(6), e80 (2013).
[Crossref]

C. J. Stolz and J. Runkel, “Brewster angle thin film polarizing beam splitter laser damage competition: “S” polarization,” Proc. SPIE 8885, 888509 (2013).
[Crossref]

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

X. Cheng, H. Jiao, J. Lu, B. Ma, and Z. Wang, “Nanosecond pulsed laser damage characteristics of HfO2/SiO2 high reflection coatings irradiated from crystal-film interface,” Opt. Express 21(12), 14867–14875 (2013).
[Crossref] [PubMed]

2012 (2)

L. Jensen, M. Mende, S. Schrameyer, M. Jupé, and D. Ristau, “Role of two-photon absorption in Ta2O5 thin films in nanosecond laser-induced damage,” Opt. Lett. 37(20), 4329–4331 (2012).
[Crossref] [PubMed]

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

2011 (1)

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]

2010 (5)

2008 (1)

2007 (1)

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

2006 (2)

C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45(7), 1594–1601 (2006).
[Crossref] [PubMed]

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (2)

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

C. J. Stolz, F. Y. Génina, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,” Proc. SPIE 5273, 41–49 (2004).
[Crossref]

2003 (1)

1999 (1)

J. Dijon, M. Poulingue, and J. Hue, “New approach for the critical size of the nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
[Crossref]

1998 (1)

V. E. Gruzdev and A. S. Gruzdeva, “Resonant increasing of high-power laser field in nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–175 (1998).
[Crossref]

1997 (1)

J. Dijon, T. Poiroux, and C. Desrumaux, “Nano absorbing centers: a key point in laser damage thin films,” Proc. SPIE 2966, 315–325 (1997).
[Crossref]

1995 (1)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

1994 (1)

J. R. Milward, K. L. Lewis, K. Sheach, and R. Heinecke, “1.064 μm laser damage studies of silicon oxy-nitride narrow band reflectors,” Proc. SPIE 2114, 309–316 (1994).
[Crossref]

1993 (2)

J. F. DeFord and M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[Crossref]

R. Chow, S. Falabella, G. E. Loomis, F. Rainer, C. J. Stolz, and M. R. Kozlowski, “Reactive evaporation of low-defect density hafnia,” Appl. Opt. 32(28), 5567–5574 (1993).
[Crossref] [PubMed]

1980 (1)

J. K. Murphy, “Effects of surface and thin-film anomalies on miniature infrared filters,” Proc. SPIE 246, 64–82 (1980).
[Crossref]

Adams, J. J.

Bennet, M.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Bercegol, H.

Bertussi, B.

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]

Bonneau, F.

Bude, J. D.

Carr, C. W.

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

Chen, M.

Chen, W.

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

Cheng, J.

Cheng, X.

Cheng, X. B.

X. B. Cheng and Z. S. Wang, “Defect-related properties of optical coatings,” Adv. Opt. Technol. 3, 65–90 (2014).

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(6), e80 (2013).
[Crossref]

Chow, R.

Chris, C. J.

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

Cölfen, H.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Combis, P.

Commandré, M.

DeFord, J. F.

J. F. DeFord and M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[Crossref]

Demos, S. G.

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

Desrumaux, C.

J. Dijon, T. Poiroux, and C. Desrumaux, “Nano absorbing centers: a key point in laser damage thin films,” Proc. SPIE 2966, 315–325 (1997).
[Crossref]

Dijon, J.

J. Dijon, M. Poulingue, and J. Hue, “New approach for the critical size of the nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
[Crossref]

J. Dijon, T. Poiroux, and C. Desrumaux, “Nano absorbing centers: a key point in laser damage thin films,” Proc. SPIE 2966, 315–325 (1997).
[Crossref]

Ding, T.

During, A.

Falabella, S.

Fan, X. F.

X. F. Fan, W. T. Zheng, and D. J. Singh, “Light scattering and surface plasmons on small spherical particles,” Light Sci. Appl. 3(6), e179 (2014).
[Crossref]

Feit, M. D.

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[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]

C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45(7), 1594–1601 (2006).
[Crossref] [PubMed]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Folta, J. A.

Fratzl, P.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Gallais, L.

Gamaly, E. G.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

Génina, F. Y.

C. J. Stolz, F. Y. Génina, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,” Proc. SPIE 5273, 41–49 (2004).
[Crossref]

Gruzdev, V. E.

V. E. Gruzdev and A. S. Gruzdeva, “Resonant increasing of high-power laser field in nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–175 (1998).
[Crossref]

Gruzdeva, A. S.

V. E. Gruzdev and A. S. Gruzdeva, “Resonant increasing of high-power laser field in nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–175 (1998).
[Crossref]

Gu, P.

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

Hader, J.

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica. 1(4), 192–197 (2014).
[Crossref]

Hafeman, S.

Hallo, L.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

He, H.

Heinecke, R.

J. R. Milward, K. L. Lewis, K. Sheach, and R. Heinecke, “1.064 μm laser damage studies of silicon oxy-nitride narrow band reflectors,” Proc. SPIE 2114, 309–316 (1994).
[Crossref]

Hue, J.

J. Dijon, M. Poulingue, and J. Hue, “New approach for the critical size of the nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
[Crossref]

Jensen, L.

Jiao, H.

Juodkazis, S.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

Jupé, M.

Kilen, I.

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica. 1(4), 192–197 (2014).
[Crossref]

Koch, S. W.

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica. 1(4), 192–197 (2014).
[Crossref]

Kofler, H.

J. Tauer, H. Kofler, and E. Wintner, “Laser-initiated ignition,” Laser Photon. Rev. 4(1), 99–122 (2010).
[Crossref]

Kommareddy, K. P.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Kozlowski, M. R.

R. Chow, S. Falabella, G. E. Loomis, F. Rainer, C. J. Stolz, and M. R. Kozlowski, “Reactive evaporation of low-defect density hafnia,” Appl. Opt. 32(28), 5567–5574 (1993).
[Crossref] [PubMed]

J. F. DeFord and M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[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]

Lamaignere, L.

Laurence, T. A.

Lee, K.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Lee, S.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Lewis, K. L.

J. R. Milward, K. L. Lewis, K. Sheach, and R. Heinecke, “1.064 μm laser damage studies of silicon oxy-nitride narrow band reflectors,” Proc. SPIE 2114, 309–316 (1994).
[Crossref]

Li, D.

Li, H.

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(6), e80 (2013).
[Crossref]

Li, M.

Li, S.

Li, X.

Liao, W.

Liu, X.

X. Liu, D. Li, Y. Zhao, and X. Li, “Further investigation of the characteristics of nodular defects,” Appl. Opt. 49(10), 1774–1779 (2010).
[Crossref] [PubMed]

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

Loomis, G. E.

Lu, J.

Luther-Davies, B.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

Ma, B.

Manenkov, A. A.

A. A. Manenkov, “Fundamental mechanisms of laser-induced damage in optical materials: today’s state of understanding and problems,” Opt. Eng. 53(1), 010901 (2014).
[Crossref]

Manjubala, I.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Masic, A.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Menapace, J.

Mende, M.

Menoni, C. S.

Menor, M. G.

Miller, P. E.

Milward, J. R.

J. R. Milward, K. L. Lewis, K. Sheach, and R. Heinecke, “1.064 μm laser damage studies of silicon oxy-nitride narrow band reflectors,” Proc. SPIE 2114, 309–316 (1994).
[Crossref]

Mirkarimi, P. B.

Misawa, H.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

Moloney, J. V.

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica. 1(4), 192–197 (2014).
[Crossref]

Monterrosa, A. M.

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

Murphy, J. K.

J. K. Murphy, “Effects of surface and thin-film anomalies on miniature infrared filters,” Proc. SPIE 246, 64–82 (1980).
[Crossref]

Natoli, J. Y.

Neauport, J.

Negres, R. A.

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

Nicolai, P.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

Nishimura, K.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

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]

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]

Park, S. B.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Patel, D.

Perry, M. D.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Pilon, F.

Pistor, T. V.

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

C. J. Stolz, S. Hafeman, and T. V. Pistor, “Light intensification modeling of coating inclusions irradiated at 351 and 1053 nm,” Appl. Opt. 47(13), C162–C166 (2008).
[Crossref] [PubMed]

C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45(7), 1594–1601 (2006).
[Crossref] [PubMed]

C. J. Stolz, F. Y. Génina, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,” Proc. SPIE 5273, 41–49 (2004).
[Crossref]

Poiroux, T.

J. Dijon, T. Poiroux, and C. Desrumaux, “Nano absorbing centers: a key point in laser damage thin films,” Proc. SPIE 2966, 315–325 (1997).
[Crossref]

Poulingue, M.

J. Dijon, M. Poulingue, and J. Hue, “New approach for the critical size of the nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
[Crossref]

Qiu, S. R.

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

Radousky, H. B.

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

Rainer, F.

Raman, R. N.

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

Rigatti, A. L.

A. L. Rigatti, “Cleaning process versus laser-damage threshold of coated optical components,” Proc. SPIE 5647, 136–140 (2005).
[Crossref]

Ristau, D.

Rubenchik, A. M.

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Rullier, J. L.

Runkel, J.

C. J. Stolz and J. Runkel, “Brewster angle thin film polarizing beam splitter laser damage competition: “S” polarization,” Proc. SPIE 8885, 888509 (2013).
[Crossref]

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]

Schrameyer, S.

Shan, Y.

Sheach, K.

J. R. Milward, K. L. Lewis, K. Sheach, and R. Heinecke, “1.064 μm laser damage studies of silicon oxy-nitride narrow band reflectors,” Proc. SPIE 2114, 309–316 (1994).
[Crossref]

Shen, N.

Shore, B. W.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Singh, D. J.

X. F. Fan, W. T. Zheng, and D. J. Singh, “Light scattering and surface plasmons on small spherical particles,” Light Sci. Appl. 3(6), e179 (2014).
[Crossref]

Soufli, R.

Steele, W. A.

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]

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

Stolz, C. J.

Stuart, B. C.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Suratwala, T. I.

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]

Tanaka, S.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

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(6), e80 (2013).
[Crossref]

Tauer, J.

J. Tauer, H. Kofler, and E. Wintner, “Laser-initiated ignition,” Laser Photon. Rev. 4(1), 99–122 (2010).
[Crossref]

Teslich, N. E.

C. J. Stolz, J. E. Wolfe, J. J. Adams, M. G. Menor, N. E. Teslich, P. B. Mirkarimi, J. A. Folta, R. Soufli, C. S. Menoni, and D. Patel, “High laser-resistant multilayer mirrors by nodular defect planarization,” Appl. Opt. 53(4), A291–A296 (2014).
[Crossref] [PubMed]

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

Tikhonchuk, V. T.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

Tuniyazi, A.

Wagermaier, W.

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Wang, H.

Wang, J.

Wang, Y.

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

Wang, Z.

Wang, Z. S.

X. B. Cheng and Z. S. Wang, “Defect-related properties of optical coatings,” Adv. Opt. Technol. 3, 65–90 (2014).

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(6), e80 (2013).
[Crossref]

Wei, C.

Wei, Z.

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(6), e80 (2013).
[Crossref]

Wintner, E.

J. Tauer, H. Kofler, and E. Wintner, “Laser-initiated ignition,” Laser Photon. Rev. 4(1), 99–122 (2010).
[Crossref]

Wolfe, J. E.

C. J. Stolz, J. E. Wolfe, J. J. Adams, M. G. Menor, N. E. Teslich, P. B. Mirkarimi, J. A. Folta, R. Soufli, C. S. Menoni, and D. Patel, “High laser-resistant multilayer mirrors by nodular defect planarization,” Appl. Opt. 53(4), A291–A296 (2014).
[Crossref] [PubMed]

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

Wong, L. L.

Xiao, Y.

Zhang, J.

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(6), e80 (2013).
[Crossref]

Zhang, Y.

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

Zhao, Y.

Zheng, W. T.

X. F. Fan, W. T. Zheng, and D. J. Singh, “Light scattering and surface plasmons on small spherical particles,” Light Sci. Appl. 3(6), e179 (2014).
[Crossref]

Zhou, M.

Adv. Opt. Technol. (1)

X. B. Cheng and Z. S. Wang, “Defect-related properties of optical coatings,” Adv. Opt. Technol. 3, 65–90 (2014).

Appl. Opt. (7)

J. Appl. Phys. (1)

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]

Laser Photon. Rev. (2)

J. Tauer, H. Kofler, and E. Wintner, “Laser-initiated ignition,” Laser Photon. Rev. 4(1), 99–122 (2010).
[Crossref]

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 1–9 (2013).

Light Sci. Appl. (1)

X. F. Fan, W. T. Zheng, and D. J. Singh, “Light scattering and surface plasmons on small spherical particles,” Light Sci. Appl. 3(6), e179 (2014).
[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(6), e80 (2013).
[Crossref]

Nat. Commun. (1)

K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

Opt. Commun. (1)

Y. Wang, Y. Zhang, X. Liu, W. Chen, and P. Gu, “Gaussian profile laser intensification by nodular defects in mid-infrared high reflectance coatings,” Opt. Commun. 278(2), 317–320 (2007).
[Crossref]

Opt. Eng. (1)

A. A. Manenkov, “Fundamental mechanisms of laser-induced damage in optical materials: today’s state of understanding and problems,” Opt. Eng. 53(1), 010901 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Optica. (1)

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica. 1(4), 192–197 (2014).
[Crossref]

Phys. Rev. Lett. (3)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[Crossref] [PubMed]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004).
[Crossref] [PubMed]

Proc. SPIE (10)

V. E. Gruzdev and A. S. Gruzdeva, “Resonant increasing of high-power laser field in nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–175 (1998).
[Crossref]

C. J. Stolz and J. Runkel, “Brewster angle thin film polarizing beam splitter laser damage competition: “S” polarization,” Proc. SPIE 8885, 888509 (2013).
[Crossref]

A. L. Rigatti, “Cleaning process versus laser-damage threshold of coated optical components,” Proc. SPIE 5647, 136–140 (2005).
[Crossref]

J. Dijon, T. Poiroux, and C. Desrumaux, “Nano absorbing centers: a key point in laser damage thin films,” Proc. SPIE 2966, 315–325 (1997).
[Crossref]

S. R. Qiu, J. E. Wolfe, A. M. Monterrosa, W. A. Steele, N. E. Teslich, M. D. Feit, T. V. Pistor, and C. J. Chris, “Impact of substrate surface scratches on the laser damage resistance of multilayer coatings,” Proc. SPIE 7842, 78421X (2010).
[Crossref]

J. K. Murphy, “Effects of surface and thin-film anomalies on miniature infrared filters,” Proc. SPIE 246, 64–82 (1980).
[Crossref]

J. R. Milward, K. L. Lewis, K. Sheach, and R. Heinecke, “1.064 μm laser damage studies of silicon oxy-nitride narrow band reflectors,” Proc. SPIE 2114, 309–316 (1994).
[Crossref]

J. Dijon, M. Poulingue, and J. Hue, “New approach for the critical size of the nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
[Crossref]

J. F. DeFord and M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[Crossref]

C. J. Stolz, F. Y. Génina, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,” Proc. SPIE 5273, 41–49 (2004).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 The D = sqrt(8dt) and D = sqrt(4dt) nodules in the quarter-wave HfO2/SiO2 HR coating. (a) P-polarized and S-polarized angular dependent transmission curves of the quarter-wave HfO2/SiO2 HR coating. (b and c) Geometrical modeling of the D = sqrt(8dt) nodule (b) and the D = sqrt(4dt) nodule (c). (d and e) FDTD-simulated P-polarized EFI distributions in vicinity of the D = sqrt(8dt) nodule (d) and the D = sqrt(4dt) nodule (e). Two nodular geometries show quite different EFI distributions.
Fig. 2
Fig. 2 The D = sqrt(8dt) and D = sqrt(4dt) nodules in SiO2 single-layer coating. (a) P-polarized and S-polarized angular dependent transmission curves of the SiO2 single-layer coating. (b and c) FDTD-simulated P-polarized EFI distributions in vicinity of the D = sqrt(8dt) nodule (b) and the D = sqrt(4dt) nodule (c). Compared to the D = sqrt(8dt) nodule, D = sqrt(4dt) nodule exhibits a shorter focal length.
Fig. 3
Fig. 3 The D = sqrt(4dt) nodules in two single-layer coatings. (a and b) P-polarized and S-polarized angular dependent transmission curves of the HfO2 single-layer coating (a) and the artificial material single-layer coating (b). (c and d) FDTD-simulated P-polarized EFI distributions in vicinity of the nodules in the HfO2 single-layer coating (c) and the artificial material single-layer coating (d). The focal length of the nodule decreases with the increasing refractive index of the medium and the EFI enhancement gets stronger in the medium having higher refractive index.
Fig. 4
Fig. 4 The D = sqrt(4dt) nodule in the omnidirectional HR coating. (a) P-polarized and S-polarized angular dependent transmission curves of the omnidirectional HR coating. (b) FDTD-simulated P-polarized EFI distribution in vicinity of a nodule. The scale bar is set the same with the one in Fig. 1(e) to show that the omnidirectional HR coating significantly reduces the EFI enhancement at the nodule.
Fig. 5
Fig. 5 The D = sqrt(4dt) nodule in the broadband HfO2/SiO2 HR coating. (a) P-polarized and S-polarized angular dependent transmission curves of the broadband HfO2/SiO2 HR coating. (b) Cross-section pattern of a D = sqrt(4dt) nodule. (c) FDTD-simulated P-polarized EFI distribution in vicinity of a nodule. The scale bar was set the same with the one in Figs. 1(e) and 4(b) to show that the broadband HfO2/SiO2 HR also significantly reduces the EFI enhancement at the nodule. (d) The damage morphologies of a nodule that was created from a SiO2 microsphere. The damage occurred at the central location where the EFI is the strongest. (e) The damage morphologies of a nodule that was created from a hafnium-coated SiO2 microsphere. The damage initiated at the seed where the absorption is the highest.

Tables (3)

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Table 1 A comparison among IARs of nodules and ARBs of HfO2/SiO2 HR coating

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Table 2 A summary of the focal lengths calculated using the microlens formula and the FDTD algorithm

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Table 3 A summary of LIDTs of two kinds of HfO2/SiO2 HR coating (1064 nm, 10 ns)

Equations (2)

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f= 1 11/n r
f=k( r,n ) 1 11/n r

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