Abstract

The initiation of laser damage within optical coatings can be better understood by electric-field modeling of coating defects. The result of this modeling shows that light intensification as large as 24× can occur owing to these coating defects. Light intensification tends to increase with inclusion diameter. Defects irradiated over a range of incident angles from 0 to 60 deg tend to have a higher light intensification at a 45 deg incidence. Irradiation wavelength has a significant effect on light intensification within the defect and the multilayer. Finally, shallow, or in the case of 45 deg irradiation, deeply embedded inclusions tend to have the highest light intensification.

© 2006 Optical Society of America

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  1. P. W. Baumeister, Optical Coating Technology (SPIE, 2004), Chaps. 5-51.
  2. M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, 'Influence of defect shape on laser-induced damage in multiplayer coatings,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
    [CrossRef]
  3. J. Dijon, G. Ravel, and B. André, 'Thermomechanical model of mirror laser damage at 1.06 µm. Part 2: Flat bottom pits formation,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 398-407 (1999).
    [CrossRef]
  4. F. Y. Génin and C. J. Stolz, 'Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,' in Third International Workshop on Laser Beam and Optics Characterization, M. Morin and A. Giesen, eds., Proc. SPIE 2870, 439-448 (1996).
  5. T. Spalvins and W. A. Brainard, 'Nodular growth in thick-sputtered metallic coatings,' J. Vac. Sci. Technol. 11, 1186-1192 (1974).
    [CrossRef]
  6. J. F. DeFord and M. R. Kozlowski, 'Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,' in Laser-Induced Damage in Optical Materials: 1992, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 1848, 455-470 (1993).
    [CrossRef]
  7. R. H. Sawicki, C. C. Shang, and T. L. Swatloski, 'Failure characterization of nodular defects in multi-layer dielectric coatings,' in Laser-Induced Damage in Optical Materials: 1994, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2428, 333-342 (1995).
    [CrossRef]
  8. 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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
    [CrossRef]
  9. C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
    [CrossRef]
  10. A. Wong, 'Rigorous three-dimensional time-domain finite-difference electromagnetic simulation,' Ph.D. dissertation (University of California at Berkeley, Berkeley, California, 1994).
  11. T. Pistor, 'Electromagnetic simulation and modeling with applications in lithography,' Ph.D. dissertation (University of California at Berkeley, Berkeley, California, 2001).
  12. K. S. Yee, 'Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,' IEEE Trans. Antennas Propag. 14, 302-307 (1966).
    [CrossRef]
  13. J. Berenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Comp. Phys. 114, 185-200 (1994).
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  17. J. Dijon, M. Poulingue, and J. Hue, 'Thermomechanical model of mirror laser damage at 1.06 mm. Part 1: Nodule ejection,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 387-396 (1999).
    [CrossRef]
  18. R. J. Tench, R. Chow, and M. R. Kozlowski, 'Characterization of defect geometries in multilayer optical coatings,' J. Vac. Sci. Technol. A 12, 2808-2813 (1994).
    [CrossRef]
  19. M. Poulingue, M. Ignat, and J. Dijon, 'The effects of particle pollution on the mechanical behaviour of multilayer systems,' Thin Solid Films 348, 215-221 (1999).
    [CrossRef]
  20. A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 53-61 (2001).
    [CrossRef]
  21. C. J. Stolz, F. Y. Génin, and T. V. Pistor, 'Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,' in Laser-Induced Damage in Optical Materials: 2003, Proc. SPIE 5273, 41-49 (2004).
    [CrossRef]
  22. C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, 'A comparison of nodular defect seed geometries from different deposition techniques,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
    [CrossRef]

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° incidence,' in Laser-Induced Damage in Optical Materials: 2003, Proc. SPIE 5273, 41-49 (2004).
[CrossRef]

2001 (1)

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 53-61 (2001).
[CrossRef]

1999 (3)

J. Dijon, M. Poulingue, and J. Hue, 'Thermomechanical model of mirror laser damage at 1.06 mm. Part 1: Nodule ejection,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 387-396 (1999).
[CrossRef]

M. Poulingue, M. Ignat, and J. Dijon, 'The effects of particle pollution on the mechanical behaviour of multilayer systems,' Thin Solid Films 348, 215-221 (1999).
[CrossRef]

J. Dijon, G. Ravel, and B. André, 'Thermomechanical model of mirror laser damage at 1.06 µm. Part 2: Flat bottom pits formation,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 398-407 (1999).
[CrossRef]

1996 (4)

F. Y. Génin and C. J. Stolz, 'Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,' in Third International Workshop on Laser Beam and Optics Characterization, M. Morin and A. Giesen, eds., Proc. SPIE 2870, 439-448 (1996).

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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, 'A comparison of nodular defect seed geometries from different deposition techniques,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
[CrossRef]

1995 (1)

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, 'Failure characterization of nodular defects in multi-layer dielectric coatings,' in Laser-Induced Damage in Optical Materials: 1994, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2428, 333-342 (1995).
[CrossRef]

1994 (3)

R. J. Tench, R. Chow, and M. R. Kozlowski, 'Characterization of defect geometries in multilayer optical coatings,' J. Vac. Sci. Technol. A 12, 2808-2813 (1994).
[CrossRef]

J. Berenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Comp. Phys. 114, 185-200 (1994).
[CrossRef]

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, 'Influence of defect shape on laser-induced damage in multiplayer coatings,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
[CrossRef]

1993 (1)

J. F. DeFord and M. R. Kozlowski, 'Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,' in Laser-Induced Damage in Optical Materials: 1992, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 1848, 455-470 (1993).
[CrossRef]

1974 (1)

T. Spalvins and W. A. Brainard, 'Nodular growth in thick-sputtered metallic coatings,' J. Vac. Sci. Technol. 11, 1186-1192 (1974).
[CrossRef]

1966 (1)

K. S. Yee, 'Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,' IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

1908 (1)

G. Mie, 'Beitraege zur Optik Trueber Medien, Speziell-Kolloidaler Metalosungen,' Ann. Physik 25, 377-445 (1908).

André, B.

J. Dijon, G. Ravel, and B. André, 'Thermomechanical model of mirror laser damage at 1.06 µm. Part 2: Flat bottom pits formation,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 398-407 (1999).
[CrossRef]

Anzellotti, J. F.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004), Chaps. 5-51.

Berenger, J.

J. Berenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Comp. Phys. 114, 185-200 (1994).
[CrossRef]

Bevis, R. P.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (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]

Chow, R.

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, 'Influence of defect shape on laser-induced damage in multiplayer coatings,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
[CrossRef]

R. J. Tench, R. Chow, and M. R. Kozlowski, 'Characterization of defect geometries in multilayer optical coatings,' J. Vac. Sci. Technol. A 12, 2808-2813 (1994).
[CrossRef]

DeFord, J. F.

J. F. DeFord and M. R. Kozlowski, 'Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,' in Laser-Induced Damage in Optical Materials: 1992, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 1848, 455-470 (1993).
[CrossRef]

Dijon, J.

M. Poulingue, M. Ignat, and J. Dijon, 'The effects of particle pollution on the mechanical behaviour of multilayer systems,' Thin Solid Films 348, 215-221 (1999).
[CrossRef]

J. Dijon, G. Ravel, and B. André, 'Thermomechanical model of mirror laser damage at 1.06 µm. Part 2: Flat bottom pits formation,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 398-407 (1999).
[CrossRef]

J. Dijon, M. Poulingue, and J. Hue, 'Thermomechanical model of mirror laser damage at 1.06 mm. Part 1: Nodule ejection,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 387-396 (1999).
[CrossRef]

Falabella, S.

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 53-61 (2001).
[CrossRef]

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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
[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° incidence,' in Laser-Induced Damage in Optical Materials: 2003, Proc. SPIE 5273, 41-49 (2004).
[CrossRef]

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

F. Y. Génin and C. J. Stolz, 'Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,' in Third International Workshop on Laser Beam and Optics Characterization, M. Morin and A. Giesen, eds., Proc. SPIE 2870, 439-448 (1996).

Hue, J.

J. Dijon, M. Poulingue, and J. Hue, 'Thermomechanical model of mirror laser damage at 1.06 mm. Part 1: Nodule ejection,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 387-396 (1999).
[CrossRef]

Ignat, M.

M. Poulingue, M. Ignat, and J. Dijon, 'The effects of particle pollution on the mechanical behaviour of multilayer systems,' Thin Solid Films 348, 215-221 (1999).
[CrossRef]

Kozlowski, M. R.

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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, 'A comparison of nodular defect seed geometries from different deposition techniques,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
[CrossRef]

R. J. Tench, R. Chow, and M. R. Kozlowski, 'Characterization of defect geometries in multilayer optical coatings,' J. Vac. Sci. Technol. A 12, 2808-2813 (1994).
[CrossRef]

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, 'Influence of defect shape on laser-induced damage in multiplayer coatings,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
[CrossRef]

J. F. DeFord and M. R. Kozlowski, 'Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,' in Laser-Induced Damage in Optical Materials: 1992, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 1848, 455-470 (1993).
[CrossRef]

Loomis, G. E.

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

Mie, G.

G. Mie, 'Beitraege zur Optik Trueber Medien, Speziell-Kolloidaler Metalosungen,' Ann. Physik 25, 377-445 (1908).

Molau, N.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

Papendrew, A. B.

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

Pistor, T.

T. Pistor, 'Electromagnetic simulation and modeling with applications in lithography,' Ph.D. dissertation (University of California at Berkeley, Berkeley, California, 2001).

Pistor, T. V.

C. J. Stolz, F. Y. Génin, and T. V. Pistor, 'Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,' in Laser-Induced Damage in Optical Materials: 2003, Proc. SPIE 5273, 41-49 (2004).
[CrossRef]

Poulingue, M.

J. Dijon, M. Poulingue, and J. Hue, 'Thermomechanical model of mirror laser damage at 1.06 mm. Part 1: Nodule ejection,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 387-396 (1999).
[CrossRef]

M. Poulingue, M. Ignat, and J. Dijon, 'The effects of particle pollution on the mechanical behaviour of multilayer systems,' Thin Solid Films 348, 215-221 (1999).
[CrossRef]

Ravel, G.

J. Dijon, G. Ravel, and B. André, 'Thermomechanical model of mirror laser damage at 1.06 µm. Part 2: Flat bottom pits formation,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 398-407 (1999).
[CrossRef]

Reitter, T. A.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

Sawicki, R. H.

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, 'Failure characterization of nodular defects in multi-layer dielectric coatings,' in Laser-Induced Damage in Optical Materials: 1994, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2428, 333-342 (1995).
[CrossRef]

Shang, C. C.

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, 'Failure characterization of nodular defects in multi-layer dielectric coatings,' in Laser-Induced Damage in Optical Materials: 1994, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2428, 333-342 (1995).
[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,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
[CrossRef]

Smith, D. J.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

Spalvins, T.

T. Spalvins and W. A. Brainard, 'Nodular growth in thick-sputtered metallic coatings,' J. Vac. Sci. Technol. 11, 1186-1192 (1974).
[CrossRef]

Stolz, C. J.

C. J. Stolz, F. Y. Génin, and T. V. Pistor, 'Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence,' in Laser-Induced Damage in Optical Materials: 2003, Proc. SPIE 5273, 41-49 (2004).
[CrossRef]

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 53-61 (2001).
[CrossRef]

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, 'A comparison of nodular defect seed geometries from different deposition techniques,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
[CrossRef]

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

F. Y. Génin and C. J. Stolz, 'Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,' in Third International Workshop on Laser Beam and Optics Characterization, M. Morin and A. Giesen, eds., Proc. SPIE 2870, 439-448 (1996).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Sect. 9.25.

Swatloski, T. L.

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, 'Failure characterization of nodular defects in multi-layer dielectric coatings,' in Laser-Induced Damage in Optical Materials: 1994, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2428, 333-342 (1995).
[CrossRef]

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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
[CrossRef]

R. J. Tench, R. Chow, and M. R. Kozlowski, 'Characterization of defect geometries in multilayer optical coatings,' J. Vac. Sci. Technol. A 12, 2808-2813 (1994).
[CrossRef]

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, 'Influence of defect shape on laser-induced damage in multiplayer coatings,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), Sect. 9.2.

Von Gunten, M. K.

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

Walton, C. C.

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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

Wong, A.

A. Wong, 'Rigorous three-dimensional time-domain finite-difference electromagnetic simulation,' Ph.D. dissertation (University of California at Berkeley, Berkeley, California, 1994).

Wu, Z. L.

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 53-61 (2001).
[CrossRef]

Yee, K. S.

K. S. Yee, 'Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,' IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Ann. Physik (1)

G. Mie, 'Beitraege zur Optik Trueber Medien, Speziell-Kolloidaler Metalosungen,' Ann. Physik 25, 377-445 (1908).

IEEE Trans. Antennas Propag. (1)

K. S. Yee, 'Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,' IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

J. Comp. Phys. (1)

J. Berenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Comp. Phys. 114, 185-200 (1994).
[CrossRef]

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).
[CrossRef]

J. Vac. Sci. Technol. A (1)

R. J. Tench, R. Chow, and M. R. Kozlowski, 'Characterization of defect geometries in multilayer optical coatings,' J. Vac. Sci. Technol. A 12, 2808-2813 (1994).
[CrossRef]

Proc. SPIE (11)

A. B. Papendrew, C. J. Stolz, Z. L. Wu, G. E. Loomis, and S. Falabella, 'Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,' in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 4377, 53-61 (2001).
[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° incidence,' in Laser-Induced Damage in Optical Materials: 2003, Proc. SPIE 5273, 41-49 (2004).
[CrossRef]

C. J. Stolz, R. J. Tench, M. R. Kozlowski, and A. Fornier, 'A comparison of nodular defect seed geometries from different deposition techniques,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 374-382 (1996).
[CrossRef]

J. Dijon, M. Poulingue, and J. Hue, 'Thermomechanical model of mirror laser damage at 1.06 mm. Part 1: Nodule ejection,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 387-396 (1999).
[CrossRef]

J. F. DeFord and M. R. Kozlowski, 'Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,' in Laser-Induced Damage in Optical Materials: 1992, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 1848, 455-470 (1993).
[CrossRef]

R. H. Sawicki, C. C. Shang, and T. L. Swatloski, 'Failure characterization of nodular defects in multi-layer dielectric coatings,' in Laser-Induced Damage in Optical Materials: 1994, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2428, 333-342 (1995).
[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,' in Laser-Induced Damage in Optical Materials: 1995, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2714, 550-558 (1996).
[CrossRef]

C. J. Stolz, F. Y. Génin, T. A. Reitter, N. Molau, R. P. Bevis, M. K. Von Gunten, D. J. Smith, and J. F. Anzellotti, 'Effects of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster's angle polarizers at 1064 nm,' in Laser-Induced Damage in Optical Materials: 1996, H. E. Bennett, A. H. Guenther, M. R. Kozlowski, B. E. Newnam, and M. J. Soileau, eds., Proc. SPIE 2966, 265-272 (1996).
[CrossRef]

M. R. Kozlowski, R. J. Tench, R. Chow, and L. Sheehan, 'Influence of defect shape on laser-induced damage in multiplayer coatings,' in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 743-750 (1994).
[CrossRef]

J. Dijon, G. Ravel, and B. André, 'Thermomechanical model of mirror laser damage at 1.06 µm. Part 2: Flat bottom pits formation,' in Laser-Induced Damage in Optical Materials: 1998, G. J. Exarhos, A. H. Guenther, M. R. Kozlowski, K. L. Lewis, and M. J. Soileau, eds., Proc. SPIE 3578, 398-407 (1999).
[CrossRef]

F. Y. Génin and C. J. Stolz, 'Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings,' in Third International Workshop on Laser Beam and Optics Characterization, M. Morin and A. Giesen, eds., Proc. SPIE 2870, 439-448 (1996).

Thin Solid Films (1)

M. Poulingue, M. Ignat, and J. Dijon, 'The effects of particle pollution on the mechanical behaviour of multilayer systems,' Thin Solid Films 348, 215-221 (1999).
[CrossRef]

Other (5)

P. W. Baumeister, Optical Coating Technology (SPIE, 2004), Chaps. 5-51.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Sect. 9.25.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), Sect. 9.2.

A. Wong, 'Rigorous three-dimensional time-domain finite-difference electromagnetic simulation,' Ph.D. dissertation (University of California at Berkeley, Berkeley, California, 1994).

T. Pistor, 'Electromagnetic simulation and modeling with applications in lithography,' Ph.D. dissertation (University of California at Berkeley, Berkeley, California, 2001).

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Figures (12)

Fig. 1
Fig. 1

Line out of the electric field in a perfect coating stack (solid curve) and in a 1 µm deeply embedded inclusion (dashed curve) at normal incidence centered along the z direction.

Fig. 2
Fig. 2

Typical defect geometry used for electric-field calculations.

Fig. 3
Fig. 3

Computed values of | E | 2 in the x–z plane. The field is polarized in the x direction and propagates in the z direction. Colors are selected so that values less than 0.5 are colored black.

Fig. 4
Fig. 4

Overlay of axial values of | E | 2 calculated with tempest (black curve) with those found from the Mie solution (gray curve). The sphere is located between the dashed lines ( 0.5 z + 0.5 ) .

Fig. 5
Fig. 5

Light intensification caused by a 1 µm diameter inclusion as a function of nodule depth, incidence angle, and polarization (pol.).

Fig. 6
Fig. 6

Light intensification of a deeply embedded inclusion (24 layers) as a function of inclusion diameter, incidence angle, and polarization (pol.).

Fig. 7
Fig. 7

Light intensification for a deeply embedded inclusion (24 layers) as a function of incident angle and polarization.

Fig. 8
Fig. 8

Light-intensification simulations of a coating nodule with a 1 µm diameter inclusion as a function of incident angle.

Fig. 9
Fig. 9

Transmission characteristics of a 1 mm diameter inclusion, 24 layers deep, as a function of incident angle. Left panel, s polarization; right panel, p polarization.

Fig. 10
Fig. 10

Light-intensification simulations of a coating nodule with a 1 µm diameter inclusion as a function of incident angle, polarization, low transmission (a, c, e), and high transmission (b, d, f).

Fig. 11
Fig. 11

Light intensification for a deeply embedded inclusion (24 layers) as a function of incident angle (0° and 45°), polarization, and irradiating wavelength.

Fig. 12
Fig. 12

Light-intensification simulations of deeply embedded (24 layers) coating defects with a 1 µm diameter inclusion with vertical boundaries.

Tables (1)

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Table 1 Light Intensification of Nodular Defects for Different Geometries and Incident Angles

Equations (3)

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ϕ = 2 cos - 1 [ 2 t d 2 t + d ] .
0 θ ϕ 2 .
θ i ϕ 2 θ θ i + ϕ 2 ,

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