Abstract

Electric field enhancement due to nodular defects within quarter-wave optical thickness multilayer mirrors is impacted by the inclusion diameter, inclusion depth, inclusion composition, nodular shape, multilayer angular bandwidth, multilayer coating materials, number of layers, angle of incidence, and polarization. In this modeling study, the electric field enhancement for surface inclusions with diameters up to 2 µm irradiated at 1064 nm at either normal or 45 deg incidence is calculated for high refractive index materials over a refractive index range of 1.7–2.3 for oxide materials commonly used in the near infrared. The thicknesses of the multilayer mirror thin films are determined for each high refractive index material by a requirement to meet a 99.5% reflection. The refractive index was found to have a significant impact on the electric field enhancement, which may offer some insight into the optimal material choice to produce high laser damage threshold mirrors.

© 2019 Optical Society of America

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2019 (1)

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
[Crossref]

2018 (2)

C. J. Stolz and R. A. Negres, “Ten-year summary of the boulder damage symposium annual thin film laser damage competition,” Opt. Eng. 57, 121910 (2018).
[Crossref]

J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
[Crossref]

2017 (1)

2016 (2)

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

2015 (1)

2014 (2)

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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
[Crossref]

M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
[Crossref]

2013 (1)

X. Cheng, J. Zhang, T. Ding, Z. Wei, H. Li, and Z. 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).
[Crossref]

2012 (2)

2011 (5)

Y. Shan, H. He, C. Wei, Y. Wang, and Y. Zhao, “Thermomechanical analysis of nodule damage in HfO2/SiO2 multilayer coatings,” Chin. Opt. Lett. 9, 103101 (2011).
[Crossref]

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
[Crossref]

M. Zhu, K. Yi, Z. Fan, and J. Shao, “Theoretical and experimental research on spectral performance and laser induced damage of Brewster’s thin film polarizers,” Appl. Surf. Sci. 257, 6884–6888 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

2010 (3)

2009 (2)

X. L. Ling, J. D. Shao, and Z. X. Fan, “Thermal-mechanical modeling of nodular defect embedded within multilayer coatings,” J. Vac. Sci. Technol. A 27, 183–186 (2009).
[Crossref]

D. Ristau, M. Jupé, and K. Starke, “Laser damage thresholds of optical coatings,” Thin Solid Films 518, 1607–1613 (2009).
[Crossref]

2008 (2)

I. R. Çapoglu and G. S. Smith, “A total-field/scattered-field plane-wave source for the FDTD analysis of layered media,” IEEE Trans. Antennas Propag. 56, 158–169 (2008).
[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, C162–C165 (2008).
[Crossref]

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, 317–320 (2007).
[Crossref]

2006 (1)

2004 (1)

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

2001 (1)

A. B. Papandrew, C. J. Stolz, S. L. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001).
[Crossref]

1999 (5)

M. Poulingue, J. Dijon, P. Garrec, and P. Lyan, “1:06 µm laser irradiation on high-reflection coatings inside a scanning electron microscope,” Proc. SPIE 3578, 188–195 (1999).
[Crossref]

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

J. Dijon, M. Poulingue, and J. Hue, “Thermomechanical model of mirror laser damage at 1.06  µm: I. Nodule ejection,” Proc. SPIE 3578, 387–397 (1999).
[Crossref]

M. Poulingue, M. Ignat, and J. Dijon, “The effects of particle pollution on the mechanical behaviour of multilayered systems,” Thin Solid Films 348, 215–221 (1999).
[Crossref]

P. Marc, D. Jean, B. Rafin, L. Herve, and I. Michel, “Generation of defects with diamond and silica particles inside high reflection coatings: influence on the laser damage threshold,” Proc. SPIE 3738, 325–336 (1999).
[Crossref]

1998 (1)

V. E. Gruzdev and A. S. Gruzdeva, “Resonance increase of high-power laser field with nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–176 (1998).
[Crossref]

1996 (3)

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, “A comparison of nodular defect seed geometries from different deposition techniques,” Proc. SPIE 2714, 374–382 (1996).
[Crossref]

C. C. Walton, F. Y. Génin, M. R. Kozlowski, G. E. Loomis, and E. Pierce, “Effect of silica overlayers on laser damage of HfO2-SiO2 56° incidence high reflectors,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

1995 (1)

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, “Failure characterization of nodular defects in multi-layer dielectric coatings,” Proc. SPIE. 2428, 333–342 (1995).
[Crossref]

1994 (5)

R. J. Tench, R. Chow, and M. R. Kozlowski, “Characterization of defect geometries in multilayer optical coatings,” Proc. SPIE 2114, 415–425 (1994).
[Crossref]

M. R. Kozlowski and R. Chow, “Role of defects in laser damage of multilayer coatings,” Proc. SPIE 2114, 640–649 (1994).
[Crossref]

R. J. Tench, M. R. Kozlowski, and R. Chow, “Investigation of the microstructure of coatings for high power lasers by non-optical techniques,” Proc. SPIE 2253, 596–602 (1994).
[Crossref]

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, “Influence of defect shape on laser-induced damage in multiplayer coatings,” Proc. SPIE 2253, 743–750 (1994).
[Crossref]

T. Izawa, N. Yamamura, R. Uchimura, and T. Yakuoh, “Damage thresholds and optical stabilities of fluoride HR coatings for 193 nm,” Proc. SPIE 2114, 297–308 (1994).
[Crossref]

1993 (3)

F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
[Crossref]

M. C. Staggs, M. R. Kozlowski, W. J. Siekhaus, and M. Balooch, “Correlation of damage threshold and surface geometry of nodular defects in HR coatings as determined by in-situ atomic force microscopy,” Proc. SPIE 1848, 234–242 (1993).
[Crossref]

F. DeFord and M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE. 1848, 455–470 (1993).
[Crossref]

1992 (3)

M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
[Crossref]

M. R. Kozlowski, M. C. Staggs, M. Balooch, R. J. Tench, and W. J. Siekhaus, “Surface morphology of As-deposited and laser-damaged dielectric mirror coatings studied in-situ by atomic force microscopy,” Proc. SPIE 1556, 68–78 (1992).
[Crossref]

M. C. Staggs, M. Balooch, M. R. Kozlowski, and W. J. Siekhaus, “In-situ atomic-force microscopy of laser-conditioned and laser-damaged HfO2/SiO2 dielectric mirror coatings,” Proc. SPIE 1624, 375–385 (1992).
[Crossref]

1991 (2)

Z. L. Wu, M. Reichling, Z. X. Fan, and Z. J. Wang, “An understanding of the abnormal wavelength effect of overcoats,” Proc. SPIE 1441, 200–213 (1991).
[Crossref]

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
[Crossref]

1989 (1)

Z. L. Wu, Z. Fan, and Z. J. Wang, “Damage threshold dependence on film thickness,” NIST Spec. Publ. 775, 321–327 (1989).

1988 (1)

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

1987 (2)

B. J. Liao, D. J. Smith, and B. Mcintyre, “The formation and development of nodular defects in optical coatings,” NIST Spec. Publ. 746, 305–318 (1987).
[Crossref]

D. J. Smith, “Modeling of nodular defects in thin films for various deposition techniques,” Proc. SPIE 821, 120–128 (1987).
[Crossref]

1985 (1)

C. K. Carniglia, T. T. Hart, and M. C. Staggs, “Effect of overcoats on 355  nm reflectors,” NIST Spec. Publ. 727, 285–290 (1985).

1982 (1)

1981 (2)

C. K. Carniglia, “Oxide coatings for one micrometer laser fusion systems,” Thin Solid Films 77, 225–238 (1981).
[Crossref]

K. H. Guenther, “Nodular defects in dielectric multilayers and thick single layers,” Appl. Opt. 20, 1034–1038 (1981).
[Crossref]

1980 (3)

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

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

W. H. Lowdermilk, D. Milam, and F. Rainer, “Damage to coatings and surfaces by 1.06  µm pulses,” NIST Spec. Publ. 568, 391–403 (1980).

1978 (1)

D. H. Gill, B. E. Newnam, and J. McLeod, “Use of non-quarter-wave designs to increase the damage resistance of reflectors at 532 and 1064 nanometers,” NIST Spec. Publ. 509, 260–270 (1978).

1977 (1)

1976 (1)

Z. X. Fan, “Overcoat effect on laser-induced damage in optical coatings,” Annu. Res. Rep. Shanghai Inst. Opt. Fine Mech. 3, 120–140 (1976).

1974 (1)

T. Spalvins and W. A. Brainard, “Nodular growth in thick-sputtered metallic coatings,” J. Vac. Sci. Technol. 11, 1186–1192 (1974).
[Crossref]

1969 (1)

B. A. Movchan and A. V. Dechisnin, “Study of structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminum oxide, and zirconium dioxide,” Phys. Met. Metallogr. 28, 83–90 (1969).

Allen, J. H.

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

Anzellotti, J. F.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

Apfel, J. H.

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

J. H. Apfel, “Optical coating design with reduced electric field intensity,” Appl. Opt. 16, 1880–1885 (1977).
[Crossref]

Atherton, L. J.

F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
[Crossref]

Balooch, M.

M. C. Staggs, M. R. Kozlowski, W. J. Siekhaus, and M. Balooch, “Correlation of damage threshold and surface geometry of nodular defects in HR coatings as determined by in-situ atomic force microscopy,” Proc. SPIE 1848, 234–242 (1993).
[Crossref]

M. C. Staggs, M. Balooch, M. R. Kozlowski, and W. J. Siekhaus, “In-situ atomic-force microscopy of laser-conditioned and laser-damaged HfO2/SiO2 dielectric mirror coatings,” Proc. SPIE 1624, 375–385 (1992).
[Crossref]

M. R. Kozlowski, M. C. Staggs, M. Balooch, R. J. Tench, and W. J. Siekhaus, “Surface morphology of As-deposited and laser-damaged dielectric mirror coatings studied in-situ by atomic force microscopy,” Proc. SPIE 1556, 68–78 (1992).
[Crossref]

Bevis, R. P.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

Brainard, W. A.

T. Spalvins and W. A. Brainard, “Nodular growth in thick-sputtered metallic coatings,” J. Vac. Sci. Technol. 11, 1186–1192 (1974).
[Crossref]

Brett, M. J.

M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
[Crossref]

Çapoglu, I. R.

I. R. Çapoglu and G. S. Smith, “A total-field/scattered-field plane-wave source for the FDTD analysis of layered media,” IEEE Trans. Antennas Propag. 56, 158–169 (2008).
[Crossref]

Carniglia, C. K.

C. K. Carniglia, T. T. Hart, and M. C. Staggs, “Effect of overcoats on 355  nm reflectors,” NIST Spec. Publ. 727, 285–290 (1985).

F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, and C. K. Carniglia, “Scandium oxide coatings for high-power UV laser applications,” Appl. Opt. 21, 3685–3688 (1982).
[Crossref]

C. K. Carniglia, “Oxide coatings for one micrometer laser fusion systems,” Thin Solid Films 77, 225–238 (1981).
[Crossref]

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

Chen, J.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
[Crossref]

Chen, N.

N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
[Crossref]

Chen, P.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
[Crossref]

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, 317–320 (2007).
[Crossref]

Cheng, X.

J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
[Crossref]

X. Cheng, T. He, J. Zhang, H. Jiao, B. Ma, and Z. Wang, “Contribution of angle-dependent light penetration to electric-field enhancement at nodules in optical coatings,” Opt. Lett. 42, 2086–2089 (2017).
[Crossref]

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
[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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
[Crossref]

X. Cheng, J. Zhang, T. Ding, Z. Wei, H. Li, and Z. 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).
[Crossref]

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Chow, R.

R. J. Tench, M. R. Kozlowski, and R. Chow, “Investigation of the microstructure of coatings for high power lasers by non-optical techniques,” Proc. SPIE 2253, 596–602 (1994).
[Crossref]

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, “Influence of defect shape on laser-induced damage in multiplayer coatings,” Proc. SPIE 2253, 743–750 (1994).
[Crossref]

M. R. Kozlowski and R. Chow, “Role of defects in laser damage of multilayer coatings,” Proc. SPIE 2114, 640–649 (1994).
[Crossref]

R. J. Tench, R. Chow, and M. R. Kozlowski, “Characterization of defect geometries in multilayer optical coatings,” Proc. SPIE 2114, 415–425 (1994).
[Crossref]

Commandré, M.

DeBell, G.

G. DeBell, “The design and measurement of low absorptance optical interference coatings,” Ph.D. thesis (University of Rochester, Institute of Optics, 1972).

Dechisnin, A. V.

B. A. Movchan and A. V. Dechisnin, “Study of structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminum oxide, and zirconium dioxide,” Phys. Met. Metallogr. 28, 83–90 (1969).

DeFord, F.

F. DeFord and M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE. 1848, 455–470 (1993).
[Crossref]

DeMarco, F. P.

F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
[Crossref]

Dew, S. K.

M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
[Crossref]

Dijon, J.

M. Poulingue, J. Dijon, P. Garrec, and P. Lyan, “1:06 µm laser irradiation on high-reflection coatings inside a scanning electron microscope,” Proc. SPIE 3578, 188–195 (1999).
[Crossref]

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

J. Dijon, M. Poulingue, and J. Hue, “Thermomechanical model of mirror laser damage at 1.06  µm: I. Nodule ejection,” Proc. SPIE 3578, 387–397 (1999).
[Crossref]

M. Poulingue, M. Ignat, and J. Dijon, “The effects of particle pollution on the mechanical behaviour of multilayered systems,” Thin Solid Films 348, 215–221 (1999).
[Crossref]

Ding, T.

X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
[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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
[Crossref]

X. Cheng, J. Zhang, T. Ding, Z. Wei, H. Li, and Z. 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).
[Crossref]

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Drazdys, R.

Ehlers, H.

Falabella, S.

A. B. Papandrew, C. J. Stolz, S. L. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001).
[Crossref]

Fan, Z.

C. Wei, K. Yi, Z. Fan, and J. Shao, “Influence of composition and seed dimension on the structure and laser damage of nodular defects in HfO2/SiO2 high reflectors,” Appl. Opt. 51, 6781–6788 (2012).
[Crossref]

M. Zhu, K. Yi, Z. Fan, and J. Shao, “Theoretical and experimental research on spectral performance and laser induced damage of Brewster’s thin film polarizers,” Appl. Surf. Sci. 257, 6884–6888 (2011).
[Crossref]

Z. L. Wu, Z. Fan, and Z. J. Wang, “Damage threshold dependence on film thickness,” NIST Spec. Publ. 775, 321–327 (1989).

Fan, Z. X.

X. L. Ling, J. D. Shao, and Z. X. Fan, “Thermal-mechanical modeling of nodular defect embedded within multilayer coatings,” J. Vac. Sci. Technol. A 27, 183–186 (2009).
[Crossref]

Z. L. Wu, M. Reichling, Z. X. Fan, and Z. J. Wang, “An understanding of the abnormal wavelength effect of overcoats,” Proc. SPIE 1441, 200–213 (1991).
[Crossref]

Z. X. Fan, “Overcoat effect on laser-induced damage in optical coatings,” Annu. Res. Rep. Shanghai Inst. Opt. Fine Mech. 3, 120–140 (1976).

Feit, M. D.

Fornier, A.

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, “A comparison of nodular defect seed geometries from different deposition techniques,” Proc. SPIE 2714, 374–382 (1996).
[Crossref]

Gallais, L.

Garrec, P.

M. Poulingue, J. Dijon, P. Garrec, and P. Lyan, “1:06 µm laser irradiation on high-reflection coatings inside a scanning electron microscope,” Proc. SPIE 3578, 188–195 (1999).
[Crossref]

Génin, F. Y.

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

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

C. C. Walton, F. Y. Génin, M. R. Kozlowski, G. E. Loomis, and E. Pierce, “Effect of silica overlayers on laser damage of HfO2-SiO2 56° incidence high reflectors,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

Gill, D. H.

D. H. Gill, B. E. Newnam, and J. McLeod, “Use of non-quarter-wave designs to increase the damage resistance of reflectors at 532 and 1064 nanometers,” NIST Spec. Publ. 509, 260–270 (1978).

Gruzdev, V. E.

V. E. Gruzdev and A. S. Gruzdeva, “Resonance increase of high-power laser field with nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–176 (1998).
[Crossref]

Gruzdeva, A. S.

V. E. Gruzdev and A. S. Gruzdeva, “Resonance increase of high-power laser field with nodule defects in multilayer optical coatings: theory and simulation,” Proc. SPIE 3263, 169–176 (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, 317–320 (2007).
[Crossref]

Guenther, K. H.

Hafeman, S.

Hart, T. T.

C. K. Carniglia, T. T. Hart, and M. C. Staggs, “Effect of overcoats on 355  nm reflectors,” NIST Spec. Publ. 727, 285–290 (1985).

Hashimoto, I.

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

He, H.

He, P.

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

He, T.

He, W.

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

Herve, L.

P. Marc, D. Jean, B. Rafin, L. Herve, and I. Michel, “Generation of defects with diamond and silica particles inside high reflection coatings: influence on the laser damage threshold,” Proc. SPIE 3738, 325–336 (1999).
[Crossref]

Hofmann, T.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
[Crossref]

Hongfei, J.

Z. Jinlong, M. Hongping, D. Tao, C. Xinbin, J. Hongfei, and W. Zhanshan, “A revisit to the effect of overcoat thickness on laser induced damage threshold of HfO2/SiO2 polarizers at 1064  nm,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds.,OSA Technical Digest (online) (Optical Society of America, 2013), paper FB.4.

Hongping, M.

Z. Jinlong, M. Hongping, D. Tao, C. Xinbin, J. Hongfei, and W. Zhanshan, “A revisit to the effect of overcoat thickness on laser induced damage threshold of HfO2/SiO2 polarizers at 1064  nm,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds.,OSA Technical Digest (online) (Optical Society of America, 2013), paper FB.4.

Hue, J.

J. Dijon, M. Poulingue, and J. Hue, “Thermomechanical model of mirror laser damage at 1.06  µm: I. Nodule ejection,” Proc. SPIE 3578, 387–397 (1999).
[Crossref]

Ignat, M.

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

M. Poulingue, M. Ignat, and J. Dijon, “The effects of particle pollution on the mechanical behaviour of multilayered systems,” Thin Solid Films 348, 215–221 (1999).
[Crossref]

Ishiwata, Y.

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

Izawa, T.

T. Izawa, N. Yamamura, R. Uchimura, and T. Yakuoh, “Damage thresholds and optical stabilities of fluoride HR coatings for 193 nm,” Proc. SPIE 2114, 297–308 (1994).
[Crossref]

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

Jean, D.

P. Marc, D. Jean, B. Rafin, L. Herve, and I. Michel, “Generation of defects with diamond and silica particles inside high reflection coatings: influence on the laser damage threshold,” Proc. SPIE 3738, 325–336 (1999).
[Crossref]

Jensen, L.

Ji, Y.

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Jiao, H.

J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
[Crossref]

X. Cheng, T. He, J. Zhang, H. Jiao, B. Ma, and Z. Wang, “Contribution of angle-dependent light penetration to electric-field enhancement at nodules in optical coatings,” Opt. Lett. 42, 2086–2089 (2017).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
[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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
[Crossref]

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
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Jin, Y.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
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Kamasz, S.

M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
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H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
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J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
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Kolbe, J.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
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Kong, F.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
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C. C. Walton, F. Y. Génin, M. R. Kozlowski, G. E. Loomis, and E. Pierce, “Effect of silica overlayers on laser damage of HfO2-SiO2 56° incidence high reflectors,” Proc. SPIE 2714, 550–558 (1996).
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M. R. Kozlowski and R. Chow, “Role of defects in laser damage of multilayer coatings,” Proc. SPIE 2114, 640–649 (1994).
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R. J. Tench, R. Chow, and M. R. Kozlowski, “Characterization of defect geometries in multilayer optical coatings,” Proc. SPIE 2114, 415–425 (1994).
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[Crossref]

F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
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M. C. Staggs, M. Balooch, M. R. Kozlowski, and W. J. Siekhaus, “In-situ atomic-force microscopy of laser-conditioned and laser-damaged HfO2/SiO2 dielectric mirror coatings,” Proc. SPIE 1624, 375–385 (1992).
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M. R. Kozlowski, M. C. Staggs, M. Balooch, R. J. Tench, and W. J. Siekhaus, “Surface morphology of As-deposited and laser-damaged dielectric mirror coatings studied in-situ by atomic force microscopy,” Proc. SPIE 1556, 68–78 (1992).
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M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
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M. Poulingue, J. Dijon, M. Ignat, H. Leplan, and B. Pinot, “New approach for the critical size of nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
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Li, H.

Li, S.

Li, T.

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
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X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
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Liao, B. J.

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Ling, L.

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Ling, X. L.

X. L. Ling, J. D. Shao, and Z. X. Fan, “Thermal-mechanical modeling of nodular defect embedded within multilayer coatings,” J. Vac. Sci. Technol. A 27, 183–186 (2009).
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B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
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M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
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A. B. Papandrew, C. J. Stolz, S. L. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001).
[Crossref]

C. C. Walton, F. Y. Génin, M. R. Kozlowski, G. E. Loomis, and E. Pierce, “Effect of silica overlayers on laser damage of HfO2-SiO2 56° incidence high reflectors,” Proc. SPIE 2714, 550–558 (1996).
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F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, and C. K. Carniglia, “Scandium oxide coatings for high-power UV laser applications,” Appl. Opt. 21, 3685–3688 (1982).
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Lu, J.

Lv, G.

N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
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M. Poulingue, J. Dijon, P. Garrec, and P. Lyan, “1:06 µm laser irradiation on high-reflection coatings inside a scanning electron microscope,” Proc. SPIE 3578, 188–195 (1999).
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J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
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X. Cheng, T. He, J. Zhang, H. Jiao, B. Ma, and Z. Wang, “Contribution of angle-dependent light penetration to electric-field enhancement at nodules in optical coatings,” Opt. Lett. 42, 2086–2089 (2017).
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Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
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H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
[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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
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X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Ma, H.

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
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Marc, P.

P. Marc, D. Jean, B. Rafin, L. Herve, and I. Michel, “Generation of defects with diamond and silica particles inside high reflection coatings: influence on the laser damage threshold,” Proc. SPIE 3738, 325–336 (1999).
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T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

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Mende, M.

Meyer, F.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
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P. Marc, D. Jean, B. Rafin, L. Herve, and I. Michel, “Generation of defects with diamond and silica particles inside high reflection coatings: influence on the laser damage threshold,” Proc. SPIE 3738, 325–336 (1999).
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F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, and C. K. Carniglia, “Scandium oxide coatings for high-power UV laser applications,” Appl. Opt. 21, 3685–3688 (1982).
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W. H. Lowdermilk, D. Milam, and F. Rainer, “Damage to coatings and surfaces by 1.06  µm pulses,” NIST Spec. Publ. 568, 391–403 (1980).

Milan, W. H. D.

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

Mirauskas, J.

Molau, N. E.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
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C. J. Stolz and R. A. Negres, “Ten-year summary of the boulder damage symposium annual thin film laser damage competition,” Opt. Eng. 57, 121910 (2018).
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D. H. Gill, B. E. Newnam, and J. McLeod, “Use of non-quarter-wave designs to increase the damage resistance of reflectors at 532 and 1064 nanometers,” NIST Spec. Publ. 509, 260–270 (1978).

Owadano, Y.

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

Papandrew, A. B.

A. B. Papandrew, C. J. Stolz, S. L. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001).
[Crossref]

Pierce, E.

C. C. Walton, F. Y. Génin, M. R. Kozlowski, G. E. Loomis, and E. Pierce, “Effect of silica overlayers on laser damage of HfO2-SiO2 56° incidence high reflectors,” Proc. SPIE 2714, 550–558 (1996).
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M. Poulingue, J. Dijon, M. Ignat, H. Leplan, and B. Pinot, “New approach for the critical size of nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
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Pistor, T. V.

Poulingue, M.

M. Poulingue, J. Dijon, P. Garrec, and P. Lyan, “1:06 µm laser irradiation on high-reflection coatings inside a scanning electron microscope,” Proc. SPIE 3578, 188–195 (1999).
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M. Poulingue, J. Dijon, M. Ignat, H. Leplan, and B. Pinot, “New approach for the critical size of nodular defects: the mechanical connection,” Proc. SPIE 3578, 370–381 (1999).
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J. Dijon, M. Poulingue, and J. Hue, “Thermomechanical model of mirror laser damage at 1.06  µm: I. Nodule ejection,” Proc. SPIE 3578, 387–397 (1999).
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M. Poulingue, M. Ignat, and J. Dijon, “The effects of particle pollution on the mechanical behaviour of multilayered systems,” Thin Solid Films 348, 215–221 (1999).
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M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
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Rafin, B.

P. Marc, D. Jean, B. Rafin, L. Herve, and I. Michel, “Generation of defects with diamond and silica particles inside high reflection coatings: influence on the laser damage threshold,” Proc. SPIE 3738, 325–336 (1999).
[Crossref]

Rainer, F.

F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
[Crossref]

F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, and C. K. Carniglia, “Scandium oxide coatings for high-power UV laser applications,” Appl. Opt. 21, 3685–3688 (1982).
[Crossref]

W. H. Lowdermilk, D. Milam, and F. Rainer, “Damage to coatings and surfaces by 1.06  µm pulses,” NIST Spec. Publ. 568, 391–403 (1980).

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

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Z. L. Wu, M. Reichling, Z. X. Fan, and Z. J. Wang, “An understanding of the abnormal wavelength effect of overcoats,” Proc. SPIE 1441, 200–213 (1991).
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C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
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B. Mangote, L. Gallais, M. Commandré, M. Mende, L. Jensen, H. Ehlers, M. Jupé, D. Ristau, A. Melninkaitis, J. Mirauskas, V. Sirutkaitis, S. Kičas, T. Tolenis, and R. Drazdys, “Femtosecond laser damage resistance of oxide and mixture oxide optical coatings,” Opt. Lett. 37, 1478–1480 (2012).
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D. Ristau, M. Jupé, and K. Starke, “Laser damage thresholds of optical coatings,” Thin Solid Films 518, 1607–1613 (2009).
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J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
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R. H. Sawicki, C. C. Shang, and T. L. Swatloski, “Failure characterization of nodular defects in multi-layer dielectric coatings,” Proc. SPIE. 2428, 333–342 (1995).
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Schink, H.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage threshold of dielectric UV/VUV-coatings deposited by conventional evaporation, lAD and IBS,” Proc. SPIE 1624, 221–235 (1991).
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Shan, Y.

Shang, C. C.

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, “Failure characterization of nodular defects in multi-layer dielectric coatings,” Proc. SPIE. 2428, 333–342 (1995).
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Shao, J.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
[Crossref]

M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
[Crossref]

C. Wei, K. Yi, Z. Fan, and J. Shao, “Influence of composition and seed dimension on the structure and laser damage of nodular defects in HfO2/SiO2 high reflectors,” Appl. Opt. 51, 6781–6788 (2012).
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M. Zhu, K. Yi, Z. Fan, and J. Shao, “Theoretical and experimental research on spectral performance and laser induced damage of Brewster’s thin film polarizers,” Appl. Surf. Sci. 257, 6884–6888 (2011).
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Shao, J. D.

X. L. Ling, J. D. Shao, and Z. X. Fan, “Thermal-mechanical modeling of nodular defect embedded within multilayer coatings,” J. Vac. Sci. Technol. A 27, 183–186 (2009).
[Crossref]

Sheehan, L.

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, “Influence of defect shape on laser-induced damage in multiplayer coatings,” Proc. SPIE 2253, 743–750 (1994).
[Crossref]

Sheehan, L. M.

F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
[Crossref]

Shen, Z.

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Shikakura, H.

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

Siekhaus, W. J.

M. C. Staggs, M. R. Kozlowski, W. J. Siekhaus, and M. Balooch, “Correlation of damage threshold and surface geometry of nodular defects in HR coatings as determined by in-situ atomic force microscopy,” Proc. SPIE 1848, 234–242 (1993).
[Crossref]

M. C. Staggs, M. Balooch, M. R. Kozlowski, and W. J. Siekhaus, “In-situ atomic-force microscopy of laser-conditioned and laser-damaged HfO2/SiO2 dielectric mirror coatings,” Proc. SPIE 1624, 375–385 (1992).
[Crossref]

M. R. Kozlowski, M. C. Staggs, M. Balooch, R. J. Tench, and W. J. Siekhaus, “Surface morphology of As-deposited and laser-damaged dielectric mirror coatings studied in-situ by atomic force microscopy,” Proc. SPIE 1556, 68–78 (1992).
[Crossref]

Sirutkaitis, V.

Smith, D. J.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
[Crossref]

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B. J. Liao, D. J. Smith, and B. Mcintyre, “The formation and development of nodular defects in optical coatings,” NIST Spec. Publ. 746, 305–318 (1987).
[Crossref]

Smith, G. S.

I. R. Çapoglu and G. S. Smith, “A total-field/scattered-field plane-wave source for the FDTD analysis of layered media,” IEEE Trans. Antennas Propag. 56, 158–169 (2008).
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Spalvins, T.

T. Spalvins and W. A. Brainard, “Nodular growth in thick-sputtered metallic coatings,” J. Vac. Sci. Technol. 11, 1186–1192 (1974).
[Crossref]

Staggs, M. C.

M. C. Staggs, M. R. Kozlowski, W. J. Siekhaus, and M. Balooch, “Correlation of damage threshold and surface geometry of nodular defects in HR coatings as determined by in-situ atomic force microscopy,” Proc. SPIE 1848, 234–242 (1993).
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F. Rainer, F. P. DeMarco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “Historic perspective of fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–22 (1993).
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M. C. Staggs, M. Balooch, M. R. Kozlowski, and W. J. Siekhaus, “In-situ atomic-force microscopy of laser-conditioned and laser-damaged HfO2/SiO2 dielectric mirror coatings,” Proc. SPIE 1624, 375–385 (1992).
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M. R. Kozlowski, M. C. Staggs, M. Balooch, R. J. Tench, and W. J. Siekhaus, “Surface morphology of As-deposited and laser-damaged dielectric mirror coatings studied in-situ by atomic force microscopy,” Proc. SPIE 1556, 68–78 (1992).
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C. K. Carniglia, T. T. Hart, and M. C. Staggs, “Effect of overcoats on 355  nm reflectors,” NIST Spec. Publ. 727, 285–290 (1985).

Starke, K.

D. Ristau, M. Jupé, and K. Starke, “Laser damage thresholds of optical coatings,” Thin Solid Films 518, 1607–1613 (2009).
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C. J. Stolz and R. A. Negres, “Ten-year summary of the boulder damage symposium annual thin film laser damage competition,” Opt. Eng. 57, 121910 (2018).
[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, C162–C165 (2008).
[Crossref]

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

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

A. B. Papandrew, C. J. Stolz, S. L. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001).
[Crossref]

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
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C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, “A comparison of nodular defect seed geometries from different deposition techniques,” Proc. SPIE 2714, 374–382 (1996).
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Swatloski, T. L.

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, “Failure characterization of nodular defects in multi-layer dielectric coatings,” Proc. SPIE. 2428, 333–342 (1995).
[Crossref]

Tait, R. N.

M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
[Crossref]

Tang, Y.

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
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Tao, D.

Z. Jinlong, M. Hongping, D. Tao, C. Xinbin, J. Hongfei, and W. Zhanshan, “A revisit to the effect of overcoat thickness on laser induced damage threshold of HfO2/SiO2 polarizers at 1064  nm,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds.,OSA Technical Digest (online) (Optical Society of America, 2013), paper FB.4.

Tench, R. J.

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, “A comparison of nodular defect seed geometries from different deposition techniques,” Proc. SPIE 2714, 374–382 (1996).
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M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, “Influence of defect shape on laser-induced damage in multiplayer coatings,” Proc. SPIE 2253, 743–750 (1994).
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R. J. Tench, M. R. Kozlowski, and R. Chow, “Investigation of the microstructure of coatings for high power lasers by non-optical techniques,” Proc. SPIE 2253, 596–602 (1994).
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R. J. Tench, R. Chow, and M. R. Kozlowski, “Characterization of defect geometries in multilayer optical coatings,” Proc. SPIE 2114, 415–425 (1994).
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M. R. Kozlowski, M. C. Staggs, M. Balooch, R. J. Tench, and W. J. Siekhaus, “Surface morphology of As-deposited and laser-damaged dielectric mirror coatings studied in-situ by atomic force microscopy,” Proc. SPIE 1556, 68–78 (1992).
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Tolenis, T.

Tuniyazi, A.

Tuttle, T. H.

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

Tuttle Hart, T.

Uchimura, R.

T. Izawa, N. Yamamura, R. Uchimura, and T. Yakuoh, “Damage thresholds and optical stabilities of fluoride HR coatings for 193 nm,” Proc. SPIE 2114, 297–308 (1994).
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C. J. Stolz, F. Y. Génin, T. A. Reitter, N. E. Molau, R. P. Bevis, M. K. von Gunten, D. J. Smith, and J. F. Anzellotti, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064  nm,” Proc. SPIE 2714, 550–558 (1996).
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C. C. Walton, F. Y. Génin, M. R. Kozlowski, G. E. Loomis, and E. Pierce, “Effect of silica overlayers on laser damage of HfO2-SiO2 56° incidence high reflectors,” Proc. SPIE 2714, 550–558 (1996).
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Wang, Y.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
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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, 317–320 (2007).
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Wang, Z.

J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
[Crossref]

X. Cheng, T. He, J. Zhang, H. Jiao, B. Ma, and Z. Wang, “Contribution of angle-dependent light penetration to electric-field enhancement at nodules in optical coatings,” Opt. Lett. 42, 2086–2089 (2017).
[Crossref]

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
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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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
[Crossref]

X. Cheng, J. Zhang, T. Ding, Z. Wei, H. Li, and Z. 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).
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X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
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N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
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X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
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B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
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Z. L. Wu, Z. Fan, and Z. J. Wang, “Damage threshold dependence on film thickness,” NIST Spec. Publ. 775, 321–327 (1989).

Wei, C.

Wei, Z.

Wu, H.

N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
[Crossref]

Wu, S. L.

A. B. Papandrew, C. J. Stolz, S. L. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001).
[Crossref]

Wu, Y.

N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
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Wu, Z. L.

Z. L. Wu, M. Reichling, Z. X. Fan, and Z. J. Wang, “An understanding of the abnormal wavelength effect of overcoats,” Proc. SPIE 1441, 200–213 (1991).
[Crossref]

Z. L. Wu, Z. Fan, and Z. J. Wang, “Damage threshold dependence on film thickness,” NIST Spec. Publ. 775, 321–327 (1989).

Xia, Z.

N. Chen, Y. Wu, Z. Wang, L. Ling, Z. Xia, H. Wu, and G. Lv, “The influence of micron-sized nodules on the electric-field distribution in thin-film polarizers,” Proc. SPIE 7995, 79950Q (2011).
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Xinbin, C.

Z. Jinlong, M. Hongping, D. Tao, C. Xinbin, J. Hongfei, and W. Zhanshan, “A revisit to the effect of overcoat thickness on laser induced damage threshold of HfO2/SiO2 polarizers at 1064  nm,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds.,OSA Technical Digest (online) (Optical Society of America, 2013), paper FB.4.

Xu, J.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
[Crossref]

Yakuoh, T.

T. Izawa, N. Yamamura, R. Uchimura, and T. Yakuoh, “Damage thresholds and optical stabilities of fluoride HR coatings for 193 nm,” Proc. SPIE 2114, 297–308 (1994).
[Crossref]

Yamamura, N.

T. Izawa, N. Yamamura, R. Uchimura, and T. Yakuoh, “Damage thresholds and optical stabilities of fluoride HR coatings for 193 nm,” Proc. SPIE 2114, 297–308 (1994).
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Yano, M.

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

Yi, K.

M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
[Crossref]

C. Wei, K. Yi, Z. Fan, and J. Shao, “Influence of composition and seed dimension on the structure and laser damage of nodular defects in HfO2/SiO2 high reflectors,” Appl. Opt. 51, 6781–6788 (2012).
[Crossref]

M. Zhu, K. Yi, Z. Fan, and J. Shao, “Theoretical and experimental research on spectral performance and laser induced damage of Brewster’s thin film polarizers,” Appl. Surf. Sci. 257, 6884–6888 (2011).
[Crossref]

Yu, J.

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

Zhang, J.

J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
[Crossref]

X. Cheng, T. He, J. Zhang, H. Jiao, B. Ma, and Z. Wang, “Contribution of angle-dependent light penetration to electric-field enhancement at nodules in optical coatings,” Opt. Lett. 42, 2086–2089 (2017).
[Crossref]

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

Z. Wang, H. Ma, X. Cheng, J. Zhang, P. He, B. Ma, H. Jiao, and Y. Tang, “Nanosecond laser-induced damage of high-reflection coatings: NUV through NIR,” Proc. SPIE 10014, 1001409 (2016).
[Crossref]

X. Cheng, A. Tuniyazi, Z. Wei, J. Zhang, T. Ding, H. Jiao, B. Ma, H. Li, T. Li, and Z. Wang, “Physical insight toward electric field enhancement at nodular defects in optical coatings,” Opt. Express 23, 8609–8619 (2015).
[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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
[Crossref]

X. Cheng, J. Zhang, T. Ding, Z. Wei, H. Li, and Z. 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).
[Crossref]

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

X. Cheng, T. Ding, W. He, J. Zhang, H. Jiao, B. Ma, Z. Shen, and Z. Wang, “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011).
[Crossref]

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Zhang, Y.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
[Crossref]

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, 317–320 (2007).
[Crossref]

Zhanshan, W.

Z. Jinlong, M. Hongping, D. Tao, C. Xinbin, J. Hongfei, and W. Zhanshan, “A revisit to the effect of overcoat thickness on laser induced damage threshold of HfO2/SiO2 polarizers at 1064  nm,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds.,OSA Technical Digest (online) (Optical Society of America, 2013), paper FB.4.

Zhao, Y.

Zhou, G.

B. Ma, T. Ding, H. Jiao, G. Zhou, Z. Shen, X. Cheng, J. Zhang, H. Liu, Y. Ji, P. He, and Z. Wang, “LIDT of HfO2/SiO2 HR films by different test modes at 1064  nm and 532  nm,” Proc. SPIE 7842, 78420E (2010).
[Crossref]

Zhou, M.

Zhu, M.

M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
[Crossref]

M. Zhu, K. Yi, Z. Fan, and J. Shao, “Theoretical and experimental research on spectral performance and laser induced damage of Brewster’s thin film polarizers,” Appl. Surf. Sci. 257, 6884–6888 (2011).
[Crossref]

Zou, X.

X. Zou, F. Kong, Y. Jin, P. Chen, J. Chen, J. Xu, Y. Wang, Y. Zhang, and J. Shao, “Influence of nodular defect size on metal dielectric mixed gratings for ultrashort ultra-high intensity laser system,” Opt. Mater. 91, 177–182 (2019).
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Appl. Opt. (10)

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 [Invited],” Appl. Opt. 53, A62–A69 (2014).
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F. Rainer, W. H. Lowdermilk, D. Milam, T. Tuttle Hart, T. L. Lichtenstein, and C. K. Carniglia, “Scandium oxide coatings for high-power UV laser applications,” Appl. Opt. 21, 3685–3688 (1982).
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C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45, 1594–1601 (2006).
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Y. Shan, H. He, C. Wei, S. Li, M. Zhou, D. Li, and Y. Zhao, “Geometrical characteristics and damage morphology of nodules grown from artificial seeds in multilayer coating,” Appl. Opt. 49, 4290–4295 (2010).
[Crossref]

C. Wei, K. Yi, Z. Fan, and J. Shao, “Influence of composition and seed dimension on the structure and laser damage of nodular defects in HfO2/SiO2 high reflectors,” Appl. Opt. 51, 6781–6788 (2012).
[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, C162–C165 (2008).
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X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, and Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[Crossref]

Appl. Surf. Sci. (1)

M. Zhu, K. Yi, Z. Fan, and J. Shao, “Theoretical and experimental research on spectral performance and laser induced damage of Brewster’s thin film polarizers,” Appl. Surf. Sci. 257, 6884–6888 (2011).
[Crossref]

Chin. Opt. Lett. (1)

IEEE Trans. Antennas Propag. (1)

I. R. Çapoglu and G. S. Smith, “A total-field/scattered-field plane-wave source for the FDTD analysis of layered media,” IEEE Trans. Antennas Propag. 56, 158–169 (2008).
[Crossref]

J. Mater. Sci. Mater. Electron. (1)

M. J. Brett, R. N. Tait, S. K. Dew, S. Kamasz, and A. H. Labun, “Nodular defect growth in thin films,” J. Mater. Sci. Mater. Electron. 3, 64–70 (1992).
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J. Vac. Sci. Technol. (1)

T. Spalvins and W. A. Brainard, “Nodular growth in thick-sputtered metallic coatings,” J. Vac. Sci. Technol. 11, 1186–1192 (1974).
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J. Vac. Sci. Technol. A (1)

X. L. Ling, J. D. Shao, and Z. X. Fan, “Thermal-mechanical modeling of nodular defect embedded within multilayer coatings,” J. Vac. Sci. Technol. A 27, 183–186 (2009).
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Light Sci. Appl. (1)

X. Cheng, J. Zhang, T. Ding, Z. Wei, H. Li, and Z. 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).
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NIST Spec. Publ. (7)

T. Izawa, Y. Ishiwata, I. Hashimoto, H. Shikakura, Y. Owadano, Y. Matsumoto, and M. Yano, “Absorption and damage threshold of dielectric reflectors at 193  nm,” NIST Spec. Publ. 775, 232 (1988) (Abstract).

B. J. Liao, D. J. Smith, and B. Mcintyre, “The formation and development of nodular defects in optical coatings,” NIST Spec. Publ. 746, 305–318 (1987).
[Crossref]

D. H. Gill, B. E. Newnam, and J. McLeod, “Use of non-quarter-wave designs to increase the damage resistance of reflectors at 532 and 1064 nanometers,” NIST Spec. Publ. 509, 260–270 (1978).

C. K. Carniglia, J. H. Apfel, J. H. Allen, T. H. Tuttle, T. A. Lowdermilk, W. H. D. Milan, and F. Rainer, “Recent damage results on silica/titania reflectors at 1 micron,” NIST Spec. Publ. 568, 377–390 (1980).

W. H. Lowdermilk, D. Milam, and F. Rainer, “Damage to coatings and surfaces by 1.06  µm pulses,” NIST Spec. Publ. 568, 391–403 (1980).

C. K. Carniglia, T. T. Hart, and M. C. Staggs, “Effect of overcoats on 355  nm reflectors,” NIST Spec. Publ. 727, 285–290 (1985).

Z. L. Wu, Z. Fan, and Z. J. Wang, “Damage threshold dependence on film thickness,” NIST Spec. Publ. 775, 321–327 (1989).

Opt. Commun. (2)

M. Zhu, K. Yi, D. Li, X. Liu, H. Qi, and J. Shao, “Influence of SiO2 overcoat layer and electric field distribution on laser damage threshold and damage morphology of transport mirror coating,” Opt. Commun. 319, 75–79 (2014).
[Crossref]

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, 317–320 (2007).
[Crossref]

Opt. Eng. (3)

H. Ma, X. Cheng, J. Zhang, B. Ma, H. Jiao, Z. Wang, T. Li, J. Yu, Z. Kang, and Y. Tang, “Electric-field intensity enhancement of a series of artificial nodules in a broadband high-reflection coating,” Opt. Eng. 56, 011027 (2016).
[Crossref]

J. Zhang, H. Jiao, B. Ma, Z. Wang, and X. Cheng, “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57, 121909 (2018).
[Crossref]

C. J. Stolz and R. A. Negres, “Ten-year summary of the boulder damage symposium annual thin film laser damage competition,” Opt. Eng. 57, 121910 (2018).
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Figures (7)

Fig. 1.
Fig. 1. Refractive index ($\lambda = {1064}\,\,{\rm nm}$) range for common oxide coating materials deposited by either electron beam deposition or sputtering.
Fig. 2.
Fig. 2. Typical nodule geometry used for the electric field calculations.
Fig. 3.
Fig. 3. High refractive indices and layer count for the modeled cases (normal incidence; 45 deg incidence at S&P polarization).
Fig. 4.
Fig. 4. Typical light intensification (square of the electric field) for one of the multilayer mirrors with ${{n}_L} = {1.45}$ and ${{n}_H} = {2.0}$ (45 deg incidence angle; $ S $ polarization)
Fig. 5.
Fig. 5. (a), (b) Light intensification magnitude at normal incidence in (a) high and (b) low refractive index material. (c), (d) Depth (in layers from the top of the coating) of the light intensification peak in (c) high and (d) low refractive index material.
Fig. 6.
Fig. 6. (a), (b) Light intensification magnitude at 45 deg angle of incidence ${S}$ polarization in (a) high and (b) low refractive index material. (c), (d) Depth (in layers from the top of the coating) of the light intensification peak in (c) high and (d) low refractive index material.
Fig. 7.
Fig. 7. (a), (b) Light intensification magnitude at 45 deg angle of incidence ${P}$ polarization in (a) high and (b) low refractive index material. (c), (d) Depth (in layers from the top of the coating) of the light intensification peak in (c) high and (d) low refractive index material.

Equations (1)

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