Abstract

An efficient method based on the modified needle optimization technique is proposed to design high-power laser thin-film polarizers. In order to minimize the influence of the standing-wave electric field on the laser-induced damage threshold of the polarizers, a crucial optimization parameter, the maximum electric field intensity in the high-refractive-index layers, is included in the proposed merit function. The electric field distribution and optical performance obtained by the proposed method are studied. Improved electric field and identical optical characteristics are observed in comparison with those of the designs obtained by optimizing the traditional merit function without a standing-wave electric field term and by the analytical synthesis method.

© 2010 Optical Society of America

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  1. J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
    [CrossRef]
  2. L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
    [CrossRef]
  3. B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
    [CrossRef]
  4. E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.
  5. F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
    [CrossRef]
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    [CrossRef]
  10. F. Y. Genin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2–SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  16. C. J. Stolz, “Brewster’s angle thin film plate polarizer design study from an electric field perspective,” Proc. SPIE 3738, 347–353 (1999).
    [CrossRef]
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  18. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
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  19. A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
    [CrossRef]
  20. A. V. Tikhonravov and M. K. Trubetskov, “Design of coatings for wide angular range applications,” Proc. SPIE 3133, 16–20 (1997).
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    [CrossRef]
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  25. G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
    [CrossRef]
  26. A. V. Tikhonravov and M. K. Trubetskov, “Estimation for the maximum of electric field in multilayer high-reflectors,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuB9.

2007

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46, 704–710 (2007).
[CrossRef] [PubMed]

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

2005

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

R. Chow, M. Runkel, and J. R. Taylor, “Laser damage testing of small optics for the National Ignition Facility,” Appl. Opt. 44, 3527–3531 (2005).
[CrossRef] [PubMed]

2004

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321 (2004).
[CrossRef]

2002

K. Y. Yang and X. W. Long, “Design of high-precision, large-angle incident, nonpolarization anti-reflection coatings,” Chin. J. Lasers A29, 703–706 (2002).

1999

A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
[CrossRef]

C. J. Stolz, “Brewster’s angle thin film plate polarizer design study from an electric field perspective,” Proc. SPIE 3738, 347–353 (1999).
[CrossRef]

C. J. Stolz, F. Y. Genin, T. A. Reitter, and N. Molau, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064 nm,” Proc. SPIE 2966, 265–272 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2–SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, T. Reitter, and M. R. Kozlowski, “Effect of electric field distribution on the morphologies of laser-induced damage in hafnia-silica multilayer polarizers,” Proc. SPIE 2966, 342–352 (1999).
[CrossRef]

1997

A. V. Tikhonravov and M. K. Trubetskov, “Design of coatings for wide angular range applications,” Proc. SPIE 3133, 16–20 (1997).
[CrossRef]

1996

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

1994

P. Gu and J. Tang, “Laser-induced damage resistance of thin-film polarizers prepared by ion-assisted deposition,” Opt. Lett. 19, 81–83 (1994).
[CrossRef] [PubMed]

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

1989

J. C. Monga, “Multilayer thin-film polarizers with reduced electric-field intensity,” J. Mod. Opt. 36, 769–784 (1989).
[CrossRef]

P. F. Gu and J. F. Tang, “Design and preparation of polarizers used in high power laser systems,” Proc. SPIE 1158, 351–356 (1989).

1984

1977

1975

Abromavicius, G.

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

Alexandre, W.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

Amotchkina, T. V.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321 (2004).
[CrossRef]

Apfel, J. H.

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

J. H. Apfel, J. S. Matteucci, B. E. Newnam, and D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, Vol. 462 of NBS Special Publication (U.S. Government Printing Office, 1976), p. 301.

Atherton, L. J.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Buchman, W. W.

Buzelis, R.

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

Chow, R.

De Marco, F. P.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

DeBell, G. W.

Drazdys, R.

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

Duchesne, J.

E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.

Furman, S. A.

S. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, 1992), pp. 123–140.

Geenen, B.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

Genin, F. Y.

C. J. Stolz, F. Y. Genin, T. A. Reitter, and N. Molau, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064 nm,” Proc. SPIE 2966, 265–272 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2–SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, T. Reitter, and M. R. Kozlowski, “Effect of electric field distribution on the morphologies of laser-induced damage in hafnia-silica multilayer polarizers,” Proc. SPIE 2966, 342–352 (1999).
[CrossRef]

Gill, D. H.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, and D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, Vol. 462 of NBS Special Publication (U.S. Government Printing Office, 1976), p. 301.

Gu, P.

Gu, P. F.

P. F. Gu and J. F. Tang, “Design and preparation of polarizers used in high power laser systems,” Proc. SPIE 1158, 351–356 (1989).

Guenther, A. H.

Houbre, F.

E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.

Howe, J. D.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Keck, J.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Kelly, J. H.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Kessler, T. J.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Kokarev, M. A.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321 (2004).
[CrossRef]

Kosc, T. Z.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Kozlov, A.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Kozlowski, M. R.

F. Y. Genin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2–SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, T. Reitter, and M. R. Kozlowski, “Effect of electric field distribution on the morphologies of laser-induced damage in hafnia-silica multilayer polarizers,” Proc. SPIE 2966, 342–352 (1999).
[CrossRef]

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Kruschwitz, B. E.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Lam, O.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

Lavastre, E.

E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.

Leplan, H.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.

Long, X. W.

K. Y. Yang and X. W. Long, “Design of high-precision, large-angle incident, nonpolarization anti-reflection coatings,” Chin. J. Lasers A29, 703–706 (2002).

Loucks, S. J.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Matteucci, J. S.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, and D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, Vol. 462 of NBS Special Publication (U.S. Government Printing Office, 1976), p. 301.

Maywar, D. N.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

McCrory, R. L.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Melninkaitis, A.

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

Meyerhofer, D. D.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Molau, N.

C. J. Stolz, F. Y. Genin, T. A. Reitter, and N. Molau, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064 nm,” Proc. SPIE 2966, 265–272 (1999).
[CrossRef]

Monga, J. C.

J. C. Monga, “Multilayer thin-film polarizers with reduced electric-field intensity,” J. Mod. Opt. 36, 769–784 (1989).
[CrossRef]

Morse, S. F. B.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Ne`auport, J.

E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.

Newnam, B. E.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, and D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, Vol. 462 of NBS Special Publication (U.S. Government Printing Office, 1976), p. 301.

Oliver, J. B.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Pally, P.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

Papernov, S.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Pinot, B.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

Protopopov, V. V.

A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
[CrossRef]

Rainer, F.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Reitter, T.

F. Y. Genin, C. J. Stolz, T. Reitter, and M. R. Kozlowski, “Effect of electric field distribution on the morphologies of laser-induced damage in hafnia-silica multilayer polarizers,” Proc. SPIE 2966, 342–352 (1999).
[CrossRef]

Reitter, T. A.

C. J. Stolz, F. Y. Genin, T. A. Reitter, and N. Molau, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064 nm,” Proc. SPIE 2966, 265–272 (1999).
[CrossRef]

Rigatti, A. L.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Roussel, L. A.

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

Runkel, M.

Schmid, A. W.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Sheehan, L. M.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Sirutkaitis, V.

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

Staggs, M. C.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Stewart, A. F.

Stoeckl, C.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Stolz, C. J.

C. J. Stolz, F. Y. Genin, T. A. Reitter, and N. Molau, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064 nm,” Proc. SPIE 2966, 265–272 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2–SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, T. Reitter, and M. R. Kozlowski, “Effect of electric field distribution on the morphologies of laser-induced damage in hafnia-silica multilayer polarizers,” Proc. SPIE 2966, 342–352 (1999).
[CrossRef]

C. J. Stolz, “Brewster’s angle thin film plate polarizer design study from an electric field perspective,” Proc. SPIE 3738, 347–353 (1999).
[CrossRef]

Szczepanski, J.

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

Tang, J.

Tang, J. F.

P. F. Gu and J. F. Tang, “Design and preparation of polarizers used in high power laser systems,” Proc. SPIE 1158, 351–356 (1989).

Taylor, J. R.

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46, 704–710 (2007).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321 (2004).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, “Design of coatings for wide angular range applications,” Proc. SPIE 3133, 16–20 (1997).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

S. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, 1992), pp. 123–140.

A. V. Tikhonravov and M. K. Trubetskov, “Estimation for the maximum of electric field in multilayer high-reflectors,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuB9.

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46, 704–710 (2007).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321 (2004).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, “Design of coatings for wide angular range applications,” Proc. SPIE 3133, 16–20 (1997).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Estimation for the maximum of electric field in multilayer high-reflectors,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuB9.

Voronov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
[CrossRef]

Waxer, L. J.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Yang, K. Y.

K. Y. Yang and X. W. Long, “Design of high-precision, large-angle incident, nonpolarization anti-reflection coatings,” Chin. J. Lasers A29, 703–706 (2002).

Zuegel, J. D.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Appl. Opt.

Chin. J. Lasers

K. Y. Yang and X. W. Long, “Design of high-precision, large-angle incident, nonpolarization anti-reflection coatings,” Chin. J. Lasers A29, 703–706 (2002).

J. Mod. Opt.

J. C. Monga, “Multilayer thin-film polarizers with reduced electric-field intensity,” J. Mod. Opt. 36, 769–784 (1989).
[CrossRef]

Opt. Lett.

Opt. Photonics News

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16, 30–36 (2005).
[CrossRef]

Proc. SPIE

B. Geenen, H. Leplan, B. Pinot, W. Alexandre, P. Pally, L. A. Roussel, and O. Lam, “Polarizers at 1.053 μm deposited on silica substrate for high laser fluences applications under vacuum,” Proc. SPIE 2776, 270–278 (1996).
[CrossRef]

J. B. Oliver, A. L. Rigatti, J. D. Howe, J. Keck, J. Szczepanski, A. W. Schmid, S. Papernov, A. Kozlov, and T. Z. Kosc, “Thin-film polarizers for the OMEGA EP Laser System,” Proc. SPIE 5991, 599119 (2005).
[CrossRef]

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, and L. M. Sheehan, “A historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

C. J. Stolz, F. Y. Genin, T. A. Reitter, and N. Molau, “Effect of SiO2 overcoat thickness on laser damage morphology of HfO2/SiO2 Brewster’s angle polarizers at 1064 nm,” Proc. SPIE 2966, 265–272 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2–SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1999).
[CrossRef]

F. Y. Genin, C. J. Stolz, T. Reitter, and M. R. Kozlowski, “Effect of electric field distribution on the morphologies of laser-induced damage in hafnia-silica multilayer polarizers,” Proc. SPIE 2966, 342–352 (1999).
[CrossRef]

P. F. Gu and J. F. Tang, “Design and preparation of polarizers used in high power laser systems,” Proc. SPIE 1158, 351–356 (1989).

C. J. Stolz, “Brewster’s angle thin film plate polarizer design study from an electric field perspective,” Proc. SPIE 3738, 347–353 (1999).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321 (2004).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, V. V. Protopopov, and A. V. Voronov, “Application of the needle optimization technique to the design of X-ray mirrors,” Proc. SPIE 3738, 248–254 (1999).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, “Design of coatings for wide angular range applications,” Proc. SPIE 3133, 16–20 (1997).
[CrossRef]

G. Abromavicius, R. Buzelis, R. Drazdys, A. Melninkaitis, and V. Sirutkaitis, “Influence of electric field distribution on laser induced damage threshold and morphology of high reflectance optical coatings,” Proc. SPIE 6720, 67200Y (2007).
[CrossRef]

Other

A. V. Tikhonravov and M. K. Trubetskov, “Estimation for the maximum of electric field in multilayer high-reflectors,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuB9.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, and D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, Vol. 462 of NBS Special Publication (U.S. Government Printing Office, 1976), p. 301.

S. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, 1992), pp. 123–140.

E. Lavastre, J. Ne`auport, J. Duchesne, H. Leplan, and F. Houbre, “Polarizers coatings for the Laser MegaJoule prototype,” in Optical Interference Coatings on CD-ROM, OSA Technical Digest Series (Optical Society of America, 2004), paper TuF3.

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Figures (11)

Fig. 1
Fig. 1

Flow chart of the modified needle optimization program.

Fig. 2
Fig. 2

SWEF profiles of the intermediate structures derived from the (a) low- and (b) high-refractive-index layers after optimization steps (I)–(IV).

Fig. 3
Fig. 3

Schematic structures (a) and (b) of designs 1 and 2, respectively.

Fig. 4
Fig. 4

SWEF profiles corresponding to the structures shown in Figs. 3a, 3b, respectively.

Fig. 5
Fig. 5

Reflectance spectra at 56.0°corresponding to the structures shown in Figs. 3a, 3b, respectively.

Fig. 6
Fig. 6

Transmittance versus incident angle at 1053 nm corresponding to the structures shown in Figs. 3a, 3b, respectively.

Fig. 7
Fig. 7

SWEF profiles at 1053 nm for designs (a) 1 and (b) 2 for the backward propagation. In this figure, odd-numbered layers are high-index layers, even-numbered layers are low-index layers, and the first layer is at the side of the substrate.

Fig. 8
Fig. 8

SWEF profiles of design 3 for both s- and p-polarizations in the (a) forward and (b) backward propagating directions. The odd- and even-numbered layers are high- and low-index layers, respectively, and the first layer is at the side of the substrate.

Fig. 9
Fig. 9

Schematic structure and electric characteristic of design 4. (a) Diagrammatic representation, (b) SWEF profile in the forward propagating direction with the substrate on the left, and (c) SWEF profile in the backward propagating direction with the substrate on the right.

Fig. 10
Fig. 10

Schematic structures of the two HR coatings: (a) design 5 and (b) design 6. In this figure, odd-numbered layers are high-index layers, even-numbered layers are low-index layers, and the first layer is at the side of the substrate.

Fig. 11
Fig. 11

SWEF profiles in the two HR coatings. (a) Design 5 and (b) design 6.

Tables (5)

Tables Icon

Table 1 Electric and Optical Characteristics of the Final Designs

Tables Icon

Table 2 Maximum Electric Field Intensities in the High-Index Layer of the Final Designs

Tables Icon

Table 3 Comparison of the Electric and Optical Characteristics between Designs 3 and 1

Tables Icon

Table 4 Comparison of the Electric and Optical Characteristics between Designs 4 and 1

Tables Icon

Table 5 Manufacturing Yields Obtained by Setting σ to 1% and Coating Thickness

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

f = { 1 ( w s + w p ) L l = 1 L { w s [ R s ( λ l ) R ̃ s ( λ l ) Δ R ̃ s ( λ l ) ] 2 + w p [ R p ( λ l ) R ̃ p ( λ l ) Δ R ̃ p ( λ l ) ] 2 } } 1 / 2 ,
f = { 1 L l = 1 L { [ R ( λ l ) R ̃ ( λ l ) Δ R ̃ ( λ l ) ] 2 } } 1 / 2 .
F = { 1 ( w s R + w p R + w s E + w p E ) L l = 1 L { w s R [ R s ( λ l ) R ̃ s ( λ l ) Δ R ̃ s ( λ l ) ] 2 + w p R [ R p ( λ l ) R ̃ p ( λ l ) Δ R ̃ p ( λ l ) ] 2 + w s E [ E s   max ( λ l ) E ̃ s   max ( λ l ) Δ E ̃ s   max ( λ l ) ] 2 + w p E [ E p   max ( λ l ) E ̃ p   max ( λ l ) Δ E ̃ p   max ( λ l ) ] 2 } } 1 / 2 .

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