Abstract

Several superhydrophobic antireflective silica films have been prepared by a solgel method that uses hexamethyl-disilizane (HMDS) as a modifier. In a high-power laser, laser-induced damage thresholds (LIDTs) of 23–30 J/cm2 were obtained at 1064-nm wavelength with 1-ns pulse duration. By atomic-force microscopy and optical microscopy, the fractal surfaces of films were studied, and multifractal spectra (MFSs) were calculated both before and after laser damage. The two-sided effect of HMDS on particle growth determined the surface fractal of a particle and the multifractal structure of a film’s surface. The bigger Δα was, both before and after laser damage, the lower the LIDT was. The effect of methyl groups should be included in the determination of the MFS of the LIDT.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers: II,” Am. Ceram. Soc. Bull. 74(11), 84–89 (1995).
  2. H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers. III,” Am. Ceram. Soc. Bull. 74(12), 48–52 (1995).
  3. S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).
  4. A. L. Rigatti, D. J. Smith, G. L. Mitchell, J. Dimyer, “Moisture barrier coatings to prevent environmental degradation of KDP crystals,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 139 (2001).
  5. W. Q. Zhang, Y. X. Tang, X. L. Liu, M. H. Jiang, “Protective coatings for large size KDP crystals,” in Third International Conference on Thin Film Physics and Applications, S. X. Zhou, Y. L. Wang, Y. X. Chen, S. Z. Mao, eds., Proc. SPIE3175, 94–97 (1998).
    [CrossRef]
  6. H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).
  7. A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
    [CrossRef]
  8. D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
    [CrossRef]
  9. O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
    [CrossRef]
  10. Z. F. Sun, Y. G. Li, “Surface structural morphology of TiO2 nano-films,” Acta Phys. Chem. Sin. 18, 896–900 (2002).
  11. X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).
  12. H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).
  13. Y. Xu, W. H. Fan, Z. H. Li, D. Wu, Y. H. Sun, “Antireflective silica thin films with super water repellence via solgel process,” Appl. Opt. 42, 108–112 (2003).
    [CrossRef] [PubMed]
  14. A. Chhabra, R. V. Jensen, “Direct determination of the f(alpha) singularity spectrum,” Phys. Rev. Lett. 62, 1327–1330 (1989).
    [CrossRef] [PubMed]
  15. B. Wang, Y. Wang, Z. Q. Wu, “Multifractal behavior of solid-on-solid growth,” Solid State Commun. 96, 69–72 (1995).
    [CrossRef]
  16. H. Li, Z. J. Ding, Z. Q. Wu, “Multifractal analysis of the spatial distribution of secondary-electron emission sites,” Phys. Rev. B 53, 16,631–16,636 (1996).
    [CrossRef]
  17. K. D. Keefer, D. W. Schaefer, “Growth of fractally rough colloids,” Phys. Rev. Lett. 56, 2376–2379 (1986).
    [CrossRef] [PubMed]
  18. N. J. Bazin, J. E. Andrew, H. A. Mcinnes, A. J. Morris, “Temperature effects on the LIDT of single and multilayer sol-gel derived thin film coatings,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 127–138 (2001).

2003 (1)

2002 (2)

Z. F. Sun, Y. G. Li, “Surface structural morphology of TiO2 nano-films,” Acta Phys. Chem. Sin. 18, 896–900 (2002).

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

2000 (1)

X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).

1999 (1)

A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
[CrossRef]

1998 (1)

D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
[CrossRef]

1997 (1)

O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
[CrossRef]

1996 (1)

H. Li, Z. J. Ding, Z. Q. Wu, “Multifractal analysis of the spatial distribution of secondary-electron emission sites,” Phys. Rev. B 53, 16,631–16,636 (1996).
[CrossRef]

1995 (3)

B. Wang, Y. Wang, Z. Q. Wu, “Multifractal behavior of solid-on-solid growth,” Solid State Commun. 96, 69–72 (1995).
[CrossRef]

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers: II,” Am. Ceram. Soc. Bull. 74(11), 84–89 (1995).

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers. III,” Am. Ceram. Soc. Bull. 74(12), 48–52 (1995).

1989 (1)

A. Chhabra, R. V. Jensen, “Direct determination of the f(alpha) singularity spectrum,” Phys. Rev. Lett. 62, 1327–1330 (1989).
[CrossRef] [PubMed]

1986 (1)

K. D. Keefer, D. W. Schaefer, “Growth of fractally rough colloids,” Phys. Rev. Lett. 56, 2376–2379 (1986).
[CrossRef] [PubMed]

Andrew, J. E.

H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).

N. J. Bazin, J. E. Andrew, H. A. Mcinnes, A. J. Morris, “Temperature effects on the LIDT of single and multilayer sol-gel derived thin film coatings,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 127–138 (2001).

Androulaki, E.

A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
[CrossRef]

Avnir, D.

D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
[CrossRef]

O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
[CrossRef]

Bazin, N. J.

H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).

N. J. Bazin, J. E. Andrew, H. A. Mcinnes, A. J. Morris, “Temperature effects on the LIDT of single and multilayer sol-gel derived thin film coatings,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 127–138 (2001).

Belleville, P. F.

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers: II,” Am. Ceram. Soc. Bull. 74(11), 84–89 (1995).

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers. III,” Am. Ceram. Soc. Bull. 74(12), 48–52 (1995).

Bernitzki, H.

S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).

Biham, O.

D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
[CrossRef]

O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
[CrossRef]

Chhabra, A.

A. Chhabra, R. V. Jensen, “Direct determination of the f(alpha) singularity spectrum,” Phys. Rev. Lett. 62, 1327–1330 (1989).
[CrossRef] [PubMed]

Dimyer, J.

A. L. Rigatti, D. J. Smith, G. L. Mitchell, J. Dimyer, “Moisture barrier coatings to prevent environmental degradation of KDP crystals,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 139 (2001).

Ding, Z. J.

H. Li, Z. J. Ding, Z. Q. Wu, “Multifractal analysis of the spatial distribution of secondary-electron emission sites,” Phys. Rev. B 53, 16,631–16,636 (1996).
[CrossRef]

Fan, W. H.

Floch, H. G.

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers: II,” Am. Ceram. Soc. Bull. 74(11), 84–89 (1995).

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers. III,” Am. Ceram. Soc. Bull. 74(12), 48–52 (1995).

Fraras, P.

A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
[CrossRef]

Fu, Z. X.

X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).

Hiskia, A.

A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
[CrossRef]

Jensen, R. V.

A. Chhabra, R. V. Jensen, “Direct determination of the f(alpha) singularity spectrum,” Phys. Rev. Lett. 62, 1327–1330 (1989).
[CrossRef] [PubMed]

Jiang, M. H.

W. Q. Zhang, Y. X. Tang, X. L. Liu, M. H. Jiang, “Protective coatings for large size KDP crystals,” in Third International Conference on Thin Film Physics and Applications, S. X. Zhou, Y. L. Wang, Y. X. Chen, S. Z. Mao, eds., Proc. SPIE3175, 94–97 (1998).
[CrossRef]

Kaiser, N.

S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).

Keefer, K. D.

K. D. Keefer, D. W. Schaefer, “Growth of fractally rough colloids,” Phys. Rev. Lett. 56, 2376–2379 (1986).
[CrossRef] [PubMed]

Klaus, M.

S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).

Lauth, H.

S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).

Laux, S.

S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).

Li, H.

H. Li, Z. J. Ding, Z. Q. Wu, “Multifractal analysis of the spatial distribution of secondary-electron emission sites,” Phys. Rev. B 53, 16,631–16,636 (1996).
[CrossRef]

Li, Y. G.

Z. F. Sun, Y. G. Li, “Surface structural morphology of TiO2 nano-films,” Acta Phys. Chem. Sin. 18, 896–900 (2002).

Li, Z. H.

Lidar, D.

D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
[CrossRef]

O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
[CrossRef]

Liu, X. L.

W. Q. Zhang, Y. X. Tang, X. L. Liu, M. H. Jiang, “Protective coatings for large size KDP crystals,” in Third International Conference on Thin Film Physics and Applications, S. X. Zhou, Y. L. Wang, Y. X. Chen, S. Z. Mao, eds., Proc. SPIE3175, 94–97 (1998).
[CrossRef]

Luo, S. F.

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

Malcai, O.

D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
[CrossRef]

O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
[CrossRef]

Mcinnes, H. A.

H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).

N. J. Bazin, J. E. Andrew, H. A. Mcinnes, A. J. Morris, “Temperature effects on the LIDT of single and multilayer sol-gel derived thin film coatings,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 127–138 (2001).

Mitchell, G. L.

A. L. Rigatti, D. J. Smith, G. L. Mitchell, J. Dimyer, “Moisture barrier coatings to prevent environmental degradation of KDP crystals,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 139 (2001).

Morris, A. J.

H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).

N. J. Bazin, J. E. Andrew, H. A. Mcinnes, A. J. Morris, “Temperature effects on the LIDT of single and multilayer sol-gel derived thin film coatings,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 127–138 (2001).

Peg on, P. M.

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers. III,” Am. Ceram. Soc. Bull. 74(12), 48–52 (1995).

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers: II,” Am. Ceram. Soc. Bull. 74(11), 84–89 (1995).

Porter, K. J.

H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).

Rigatti, A. L.

A. L. Rigatti, D. J. Smith, G. L. Mitchell, J. Dimyer, “Moisture barrier coatings to prevent environmental degradation of KDP crystals,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 139 (2001).

Schaefer, D. W.

K. D. Keefer, D. W. Schaefer, “Growth of fractally rough colloids,” Phys. Rev. Lett. 56, 2376–2379 (1986).
[CrossRef] [PubMed]

Smith, D. J.

A. L. Rigatti, D. J. Smith, G. L. Mitchell, J. Dimyer, “Moisture barrier coatings to prevent environmental degradation of KDP crystals,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 139 (2001).

Sun, X.

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).

Sun, Y. H.

Sun, Z. F.

Z. F. Sun, Y. G. Li, “Surface structural morphology of TiO2 nano-films,” Acta Phys. Chem. Sin. 18, 896–900 (2002).

Tang, Y. X.

W. Q. Zhang, Y. X. Tang, X. L. Liu, M. H. Jiang, “Protective coatings for large size KDP crystals,” in Third International Conference on Thin Film Physics and Applications, S. X. Zhou, Y. L. Wang, Y. X. Chen, S. Z. Mao, eds., Proc. SPIE3175, 94–97 (1998).
[CrossRef]

Wang, B.

B. Wang, Y. Wang, Z. Q. Wu, “Multifractal behavior of solid-on-solid growth,” Solid State Commun. 96, 69–72 (1995).
[CrossRef]

Wang, Y.

B. Wang, Y. Wang, Z. Q. Wu, “Multifractal behavior of solid-on-solid growth,” Solid State Commun. 96, 69–72 (1995).
[CrossRef]

Wang, Y. R.

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

Wu, D.

Wu, Z. Q.

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).

H. Li, Z. J. Ding, Z. Q. Wu, “Multifractal analysis of the spatial distribution of secondary-electron emission sites,” Phys. Rev. B 53, 16,631–16,636 (1996).
[CrossRef]

B. Wang, Y. Wang, Z. Q. Wu, “Multifractal behavior of solid-on-solid growth,” Solid State Commun. 96, 69–72 (1995).
[CrossRef]

Xagas, A. P.

A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
[CrossRef]

Xiong, G.

X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).

Xu, Y.

Yu, H. S.

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

Zhang, W. Q.

W. Q. Zhang, Y. X. Tang, X. L. Liu, M. H. Jiang, “Protective coatings for large size KDP crystals,” in Third International Conference on Thin Film Physics and Applications, S. X. Zhou, Y. L. Wang, Y. X. Chen, S. Z. Mao, eds., Proc. SPIE3175, 94–97 (1998).
[CrossRef]

Acta Phys. Chem. Sin. (1)

Z. F. Sun, Y. G. Li, “Surface structural morphology of TiO2 nano-films,” Acta Phys. Chem. Sin. 18, 896–900 (2002).

Acta Phys. Sin. (2)

X. Sun, G. Xiong, Z. X. Fu, Z. Q. Wu, “Multifractal spectra of atomic force microscope images of ZnO film,” Acta Phys. Sin. 49, 854–862 (2000).

H. S. Yu, X. Sun, S. F. Luo, Y. R. Wang, Z. Q. Wu, “Multifractal of the deposition process of amorphous electroless Ni–Cu–P alloy,” Acta Phys. Sin. 51, 999–1002 (2002).

Am. Ceram. Soc. Bull. (2)

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers: II,” Am. Ceram. Soc. Bull. 74(11), 84–89 (1995).

H. G. Floch, P. F. Belleville, P. M. Peg on, “Sol-gel optical coatings for lasers. III,” Am. Ceram. Soc. Bull. 74(12), 48–52 (1995).

Appl. Opt. (1)

Phys. Rev. B (1)

H. Li, Z. J. Ding, Z. Q. Wu, “Multifractal analysis of the spatial distribution of secondary-electron emission sites,” Phys. Rev. B 53, 16,631–16,636 (1996).
[CrossRef]

Phys. Rev. E (1)

O. Malcai, D. Lidar, O. Biham, D. Avnir, “Scaling range and cutoffs in empirical fractals,” Phys. Rev. E 56, 2817–2828 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

K. D. Keefer, D. W. Schaefer, “Growth of fractally rough colloids,” Phys. Rev. Lett. 56, 2376–2379 (1986).
[CrossRef] [PubMed]

A. Chhabra, R. V. Jensen, “Direct determination of the f(alpha) singularity spectrum,” Phys. Rev. Lett. 62, 1327–1330 (1989).
[CrossRef] [PubMed]

Science (1)

D. Avnir, O. Biham, D. Lidar, O. Malcai, “Applied mathematics: Is the geometry of nature fractal,” Science 279, 39–40 (1998).
[CrossRef]

Solid State Commun. (1)

B. Wang, Y. Wang, Z. Q. Wu, “Multifractal behavior of solid-on-solid growth,” Solid State Commun. 96, 69–72 (1995).
[CrossRef]

Thin Solid Films (1)

A. P. Xagas, E. Androulaki, A. Hiskia, P. Fraras, “Preparation, fractal surface morphology and photocatalytic properties of TiO2 films,” Thin Solid Films 357, 173–178 (1999).
[CrossRef]

Other (5)

N. J. Bazin, J. E. Andrew, H. A. Mcinnes, A. J. Morris, “Temperature effects on the LIDT of single and multilayer sol-gel derived thin film coatings,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 127–138 (2001).

S. Laux, H. Bernitzki, M. Klaus, H. Lauth, N. Kaiser, “Long-time radiation resistant optical coatings for UV excimers laser applications,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 13–16 (2001).

A. L. Rigatti, D. J. Smith, G. L. Mitchell, J. Dimyer, “Moisture barrier coatings to prevent environmental degradation of KDP crystals,” in Laser-Induced Damage in Optical Materials: 2000, G. J. Exarhos, A. H. Guenther, eds., Proc. SPIE4347, 139 (2001).

W. Q. Zhang, Y. X. Tang, X. L. Liu, M. H. Jiang, “Protective coatings for large size KDP crystals,” in Third International Conference on Thin Film Physics and Applications, S. X. Zhou, Y. L. Wang, Y. X. Chen, S. Z. Mao, eds., Proc. SPIE3175, 94–97 (1998).
[CrossRef]

H. A. Mcinnes, J. E. Andrew, N. J. Bazin, A. J. Morris, K. J. Porter, “Ultra violet laser damage and optical properties of high refractive index single layers, multiple layers and high/low index multilayer stacks,” in Laser-Induced Damage in Optical Materials: 1997, G. J. Exarhos, A. H. Guenther, M. K. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 500–508 (1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic of the testing optics of the LIDT: B, calorimeter; C, photodiode; M1, M2, mirrors.

Fig. 2
Fig. 2

MFSs of hydrophobic antireflective films before laser irradiation.

Fig. 3
Fig. 3

Morphologies of the laser damage region obtained with an OM. The magnification is 40×.

Fig. 4
Fig. 4

MFS of hydrophobic antireflective films after laser damage.

Fig. 5
Fig. 5

Growth of particles in methyl-modified SiO2 sols.

Fig. 6
Fig. 6

PSDs of methyl-modified SiO2 sols.

Tables (2)

Tables Icon

Table 1 Data on MFS and LIDTa

Tables Icon

Table 2 Results of XPS of Hydrophobic Films

Equations (9)

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

ɛ = 1 / N ( l ) = l / L .
h i , j ( ɛ ) = 1 ( ɛ + 1 ) 2 ( i - 1 ) ɛ + 1 i ɛ + 1 ( j - 1 ) ɛ + 1 i ɛ + 1 h ( m , n ) .
P i , j ( ɛ ) = h i , j ( ɛ ) i = 1 N ( l ) j = 1 N ( l ) h j , j ( ɛ ) .
P i , j ( ɛ ) ɛ α ,
χ q = i i P i , j ( ɛ ) q = ɛ τ ( q ) ,
f ( α ) = α q - τ ( q ) .
N α ( ɛ ) ɛ f ( α ) .
Si ( OC 2 H 5 ) 4 + 2 H 2 O SiO 2 + 4 C 2 H 5 OH .
2 Si OH + ( CH 3 ) 3 SiNHSi ( CH 3 ) 3 2 Si O - Si ( CH 3 ) 3 + NH 3 .

Metrics