Abstract

Laser-induced damage of the “standard” (λ/4 stack structure) and “modified” (reduced standing-wave field) HfO2/SiO2 mirrors were investigated by a commercial 800 nm Ti:sapphire laser system. Three kinds of pulse duration of 50 fs, 105 fs, and 135 fs were chosen. The results show that the single-shot damage threshold of the “modified” mirror was about 14%–23% higher compared to that of the “standard” mirror. A model based on the rate equation for free electron generation was adopted to explain the threshold results. It took in account the transient changes in the dielectric function of material during the laser pulse. The simulated threshold agreed with the experimental very well. Besides, for two kinds of mirror, typical breakdown craters for both the single-shots and multi-shots damage tests reveal striking distinct characteristics. Interestingly, the multi-shots damage crater with zigzag-like edge was observed only on the “standard” mirror. These phenomena were illustrated reasonably by the distribution features of the electric field intensity within the mirrors.

© 2012 Optical Society of America

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References

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  1. T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part1: experimental,” IEEE J. Quantum Electron. 17, 2041–2052 (1981).
    [CrossRef]
  2. J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
    [CrossRef]
  3. X. Liu, D. Li, Y. Zhao, X. Li, X. Ling, and J. Shao, “Damage characteristics of HfO2/SiO2 high reflector at 45° incidence in 1-on-1 and N-on-1 tests,” Chin. Opt. Lett. 8, 41–44 (2010).
    [CrossRef]
  4. L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
    [CrossRef]
  5. J. H. Apfel, “Optical coating design with reduced electric field intensity,” Appl. Opt. 16, 1880–1885 (1977).
    [CrossRef]
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    [CrossRef]
  7. 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]
  8. S. Chen, Y. Zhao, H. He, and J. Shao, “Effect of standing-wave field distribution on the femtosecond laser-induced damage of HfO2/SiO2 mirror coating,” Chin. Opt. Lett. 9, 083101 (2011).
    [CrossRef]
  9. T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
    [CrossRef]
  10. L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
    [CrossRef]
  11. J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
    [CrossRef]
  12. N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. 10, 375–386 (1974).
    [CrossRef]
  13. S. Chen, Y. Zhao, D. Li, H. He, and J. Shao, “Effect of nanosecond laser pre-irradiation on the femtosecond laser-induced damage of Ta2O5/SiO2 high reflector,” Appl. Opt. 51, 1495–1502 (2012).
    [CrossRef]
  14. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).
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    [CrossRef]
  16. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks Cole, 1976).

2012

2011

2010

X. Liu, D. Li, Y. Zhao, X. Li, X. Ling, and J. Shao, “Damage characteristics of HfO2/SiO2 high reflector at 45° incidence in 1-on-1 and N-on-1 tests,” Chin. Opt. Lett. 8, 41–44 (2010).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

2007

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]

2006

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

2005

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

2002

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

2001

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

1984

1981

T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part1: experimental,” IEEE J. Quantum Electron. 17, 2041–2052 (1981).
[CrossRef]

1977

1974

N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. 10, 375–386 (1974).
[CrossRef]

1965

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

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]

Apfel, J. H.

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks Cole, 1976).

Baudach, S.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

Bloembergen, N.

N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. 10, 375–386 (1974).
[CrossRef]

Bonse, J.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

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]

Chen, S.

Commandré, M.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

Demichelis, F.

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]

Feng, D. H.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Gallais, L.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

Guenther, A. H.

T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part1: experimental,” IEEE J. Quantum Electron. 17, 2041–2052 (1981).
[CrossRef]

He, H.

Jasapara, J.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

Jeskevic, M.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

Jia, T. Q.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Kautek, W.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Krüger, J.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

Kuroda, H.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Lenzner, M.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

Li, C. B.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Li, D.

Li, R. X.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Li, X.

Li, X. X.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Ling, X.

Liu, J.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Liu, X.

Mangote, B.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

Melninkaitis, A.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[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]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks Cole, 1976).

Mero, M.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Mezzetti-Minetti, E.

Mirauskas, J.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

Nampoothiri, A. V. V.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

Nielsen, P. E.

T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part1: experimental,” IEEE J. Quantum Electron. 17, 2041–2052 (1981).
[CrossRef]

Ristau, D.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

Rudolph, W.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

Shao, J.

Sirutkaitis, V.

L. Gallais, B. Mangote, M. Zerrad, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Laser-induced damage of hafnia coatings as a function of pulse duration in the femtosecond to nanosecond range,” Appl. Opt. 50, C178–C187 (2011).
[CrossRef]

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[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]

Starke, K.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

Sun, H. Y.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Tallone, L.

Tresso, E.

Walker, T. W.

T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part1: experimental,” IEEE J. Quantum Electron. 17, 2041–2052 (1981).
[CrossRef]

Xu, S. Z.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Xu, Z. Z.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Zerrad, M.

Zhao, Y.

Appl. Opt.

Appl. Phys. A

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon—modification thresholds and morphology,” Appl. Phys. A 74, 19–25 (2002).
[CrossRef]

Appl. Phys. Lett.

L. Gallais, B. Mangote, M. Commandré, A. Melninkaitis, J. Mirauskas, M. Jeskevic, and V. Sirutkaitis, “Transient interference implications on the subpicosecond laser damage of multidielectrics,” Appl. Phys. Lett. 97, 051112 (2010).
[CrossRef]

Chin. Opt. Lett.

IEEE J. Quantum Electron.

T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings—Part1: experimental,” IEEE J. Quantum Electron. 17, 2041–2052 (1981).
[CrossRef]

N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. 10, 375–386 (1974).
[CrossRef]

J. Appl. Phys.

T. Q. Jia, H. Y. Sun, X. X. Li, D. H. Feng, C. B. Li, S. Z. Xu, R. X. Li, Z. Z. Xu, and H. Kuroda, “The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors,” J. Appl. Phys. 100, 023103(2006).
[CrossRef]

Phys. Rev. B

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63, 045117 (2001).
[CrossRef]

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Proc. SPIE

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]

Sov. Phys. JETP

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Other

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks Cole, 1976).

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Figures (11)

Fig. 1.
Fig. 1.

NEFI distribution in the outer five layer pairs of HfO2/SiO2 mirrors irradiating by 800 nm laser without the repartition consideration [8]. H and L denote the high (HfO2) and low (SiO2) refractive index coatings, respectively. (a) “Standard” and (b) “modified” mirrors with several positions marked by alphabets.

Fig. 2.
Fig. 2.

Measured single-shot LIDT results of two kinds of mirror. The relative error of LIDT determination amounts to about ±9%.

Fig. 3.
Fig. 3.

Typical crater morphologies of mirrors irradiating by single-shot 800 nm, 50 fs laser pulse with the fluence near the LIDT. (a) “Standard” mirror and (b) “modified” mirror.

Fig. 4.
Fig. 4.

Typical crater morphologies of mirrors irradiating by 40-shots 800 nm, 50 fs laser pulse with the fluence near the LIDT. (a) “Standard” mirror and (b) “modified” mirror. The arrow signed with E means the direction of the incident electric field vector.

Fig. 5.
Fig. 5.

Real (n) and imaginary (k) parts of the complex index (N) for hafnia material as a function of free electron density according to Eq. (1). The reduced electron mass m*, 0.5×9.11×1031kg the Drude relaxation time τD is set to 1 fs.

Fig. 6.
Fig. 6.

Schematic profile of single 800 nm, 50 fs laser pulse in our simulation with five different moments marked by t1, t2, t3, t4, and t5.

Fig. 7.
Fig. 7.

Variation in the real and imaginary parts of the complex index (N) as a function of penetration thickness for the “standard” mirror irradiating by single 800 nm, 50 fs, 0.4J/cm2 laser pulse. P1 means the first H/L layer interface. At the moment t5, the electron density reaches to the value of 1021cm3.

Fig. 8.
Fig. 8.

Repartition of NEFI distribution at different moments in the “standard” mirror irradiating by single 800 nm, 50 fs, 0.4J/cm2 laser pulse. (b) shows the regional details in (a).

Fig. 9.
Fig. 9.

Variation in the real and imaginary parts of the complex index (N) as a function of penetration thickness for the “modified” mirror irradiating by single 800 nm, 50 fs, 0.5J/cm2 laser pulse. At the moment t5, the electron density reaches to the value of 1021cm3.

Fig. 10.
Fig. 10.

Repartition of NEFI distribution at different moments in the “modified” mirror irradiating by single 800 nm, 50 fs, 0.5J/cm2 laser pulse. (b) shows the regional details of (a).

Fig. 11.
Fig. 11.

Comparison of experimental threshold results to theoretical prediction (a) without and (b) with feedback effect. The black squares and red circles indicate the measured thresholds, while the black dashed and dash-dot lines stand for the thresholds form theoretical simulation for the “standard” and “modified” mirrors, respectively.

Equations (2)

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

net=WPI_Keldysh(qE)+WAv_Drude(qE,ne)neτr,
N(ne)=N02ne·e2m*ε01ω2+i·ω/τD,

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