Abstract

In order to more exactly predict femtosecond pulse laser induced damage threshold, an accurate theoretical model taking into account photoionization, avalanche ionization and decay of electrons is proposed by comparing respectively several combined ionization models with the published experimental measurements. In addition, the transmittance property and the near-field distribution of the ‘moth eye’ broadband antireflective microstructure directly patterned into the substrate material as a function of the surface structure period and groove depth are performed by a rigorous Fourier model method. It is found that the near-field distribution is strongly dependent on the periodicity of surface structure for TE polarization, but for TM wave it is insensitive to the period. What’s more, the femtosecond pulse laser damage threshold of the surface microstructure on the pulse duration taking into account the local maximum electric field enhancement was calculated using the proposed relatively accurate theoretical ionization model. For the longer incident wavelength of 1064nm, the weak linear damage threshold on the pulse duration is shown, but there is a surprising oscillation peak of breakdown threshold as a function of the pulse duration for the shorter incident wavelength of 532nm.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
    [CrossRef]
  2. B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
    [CrossRef] [PubMed]
  3. M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
    [CrossRef]
  4. A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
    [CrossRef]
  5. 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(4), 045117 (2001).
    [CrossRef]
  6. 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(11), 115109 (2005).
    [CrossRef]
  7. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
    [CrossRef] [PubMed]
  8. D. S. Hobbs, B. D. MacLeod, and J. R. Riccobono, “Update on the development of high performance antireflecting surface relief micro-structures,” Proc. SPIE 6545, 65450Y (2007).
    [CrossRef]
  9. W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
    [CrossRef]
  10. K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
    [CrossRef]
  11. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).
  12. L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
    [CrossRef] [PubMed]
  13. L. Yuan, Y. A. Zhao, G. Q. Shang, C. R. Wang, H. B. He, J. D. Shao, and Z. X. Fan, “Comparison of femtosecond and nanosecond laser-induced damage in HfO2 single-layer film and HfO2–SiO2 high reflector,” J. Opt. Soc. Am. B 24(3), 538–543 (2007).
    [CrossRef]
  14. M. Jupé, L. Jensen, A. Melninkaitis, V. Sirutkaitis, and D. Ristau, “Calculations and experimental demonstration of multi-photon absorption governing fs laser-induced damage in titania,” Opt. Express 17(15), 12269–12278 (2009).
    [CrossRef] [PubMed]
  15. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
    [CrossRef]
  16. B. Rethfeld, “Unified model for the free-electron avalanche in laser-irradiated dielectrics,” Phys. Rev. Lett. 92(18), 187401 (2004).
    [CrossRef] [PubMed]
  17. A. Vaidyanathan, T. W. Walker, and A. H. Guenther, “The relative roles of avalanche multiplication and multiphoton absorption in laser-induced damage of dielectrics,” IEEE J. Quantum Electron. 16(1), 89–93 (1980).
    [CrossRef]
  18. P. N. Saeta and B. I. Greene, “Primary relaxation processes at the band edge of SiO2,” Phys. Rev. Lett. 70(23), 3588–3591 (1993).
    [CrossRef] [PubMed]
  19. M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
    [CrossRef]
  20. T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
    [CrossRef]
  21. L. F. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
    [CrossRef]
  22. S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
    [CrossRef]
  23. J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
    [CrossRef]
  24. L. F. Li, “Note on the S-matrix propagation algorithm,” J. Opt. Soc. Am. A 20(4), 655–660 (2003).
    [CrossRef]
  25. D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
    [CrossRef] [PubMed]
  26. D. Du, X. Liu, and G. Mourou, “Reduction of multi-photon ionization in dielectrics due to collisions,” Appl. Phys. B 63, 617–621 (1996).

2009 (1)

2008 (1)

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

2007 (2)

2006 (1)

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

2005 (1)

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(11), 115109 (2005).
[CrossRef]

2004 (3)

B. Rethfeld, “Unified model for the free-electron avalanche in laser-irradiated dielectrics,” Phys. Rev. Lett. 92(18), 187401 (2004).
[CrossRef] [PubMed]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

2003 (2)

L. F. Li, “Note on the S-matrix propagation algorithm,” J. Opt. Soc. Am. A 20(4), 655–660 (2003).
[CrossRef]

D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
[CrossRef] [PubMed]

2002 (1)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

2001 (1)

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(4), 045117 (2001).
[CrossRef]

1999 (3)

Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999).
[CrossRef] [PubMed]

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
[CrossRef]

1998 (1)

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

1997 (1)

1996 (2)

D. Du, X. Liu, and G. Mourou, “Reduction of multi-photon ionization in dielectrics due to collisions,” Appl. Phys. B 63, 617–621 (1996).

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

1995 (1)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

1994 (1)

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[CrossRef]

1993 (1)

P. N. Saeta and B. I. Greene, “Primary relaxation processes at the band edge of SiO2,” Phys. Rev. Lett. 70(23), 3588–3591 (1993).
[CrossRef] [PubMed]

1980 (2)

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

A. Vaidyanathan, T. W. Walker, and A. H. Guenther, “The relative roles of avalanche multiplication and multiphoton absorption in laser-induced damage of dielectrics,” IEEE J. Quantum Electron. 16(1), 89–93 (1980).
[CrossRef]

1965 (1)

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

Amotchkina, T. V.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

Backus, S.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

Cheng, C. F.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Cheng, Z.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Chirkin, A. S.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

Couairon, A.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Deng, Z. X.

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Du, D.

D. Du, X. Liu, and G. Mourou, “Reduction of multi-photon ionization in dielectrics due to collisions,” Appl. Phys. B 63, 617–621 (1996).

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[CrossRef]

Fan, Z. X.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

L. Yuan, Y. A. Zhao, G. Q. Shang, C. R. Wang, H. B. He, J. D. Shao, and Z. X. Fan, “Comparison of femtosecond and nanosecond laser-induced damage in HfO2 single-layer film and HfO2–SiO2 high reflector,” J. Opt. Soc. Am. B 24(3), 538–543 (2007).
[CrossRef]

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

Feng, D. H.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Franco, M.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Gibson, G. N.

M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
[CrossRef]

Greene, B. I.

P. N. Saeta and B. I. Greene, “Primary relaxation processes at the band edge of SiO2,” Phys. Rev. Lett. 70(23), 3588–3591 (1993).
[CrossRef] [PubMed]

Guenther, A. H.

A. Vaidyanathan, T. W. Walker, and A. H. Guenther, “The relative roles of avalanche multiplication and multiphoton absorption in laser-induced damage of dielectrics,” IEEE J. Quantum Electron. 16(1), 89–93 (1980).
[CrossRef]

Hane, K.

He, H. B.

Herman, S.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

Hobbs, D. S.

D. S. Hobbs, B. D. MacLeod, and J. R. Riccobono, “Update on the development of high performance antireflecting surface relief micro-structures,” Proc. SPIE 6545, 65450Y (2007).
[CrossRef]

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(4), 045117 (2001).
[CrossRef]

Jensen, L.

Jia, T. Q.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Jin, Y. X.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

Jupé, M.

Kanamori, Y.

Kapteyn, H.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

Kautek, W.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Keldysh, L. V.

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

Kong, W. J.

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Korn, G.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[CrossRef]

Krausz, F.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Krüger, J.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Lamouroux, B.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Lee, H.

D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
[CrossRef] [PubMed]

Lenzner, M.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Li, L. F.

Li, M.

M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
[CrossRef]

Li, R. X.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Li, X. X.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

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(11), 115109 (2005).
[CrossRef]

Liu, S. J.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Liu, X.

D. Du, X. Liu, and G. Mourou, “Reduction of multi-photon ionization in dielectrics due to collisions,” Appl. Phys. B 63, 617–621 (1996).

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[CrossRef]

Lowdermilk, W. H.

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

Ma, J. Y.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

MacLeod, B. D.

D. S. Hobbs, B. D. MacLeod, and J. R. Riccobono, “Update on the development of high performance antireflecting surface relief micro-structures,” Proc. SPIE 6545, 65450Y (2007).
[CrossRef]

Melninkaitis, A.

Menon, S.

M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
[CrossRef]

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(11), 115109 (2005).
[CrossRef]

Milam, D.

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

Mourou, G.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

D. Du, X. Liu, and G. Mourou, “Reduction of multi-photon ionization in dielectrics due to collisions,” Appl. Phys. B 63, 617–621 (1996).

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[CrossRef]

Murnane, M.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

Mysyrowicz, A.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

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(4), 045117 (2001).
[CrossRef]

Nibarger, J. P.

M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
[CrossRef]

Perry, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

Prade, B.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Rethfeld, B.

B. Rethfeld, “Unified model for the free-electron avalanche in laser-irradiated dielectrics,” Phys. Rev. Lett. 92(18), 187401 (2004).
[CrossRef] [PubMed]

Riccobono, J. R.

D. S. Hobbs, B. D. MacLeod, and J. R. Riccobono, “Update on the development of high performance antireflecting surface relief micro-structures,” Proc. SPIE 6545, 65450Y (2007).
[CrossRef]

Ristau, D.

M. Jupé, L. Jensen, A. Melninkaitis, V. Sirutkaitis, and D. Ristau, “Calculations and experimental demonstration of multi-photon absorption governing fs laser-induced damage in titania,” Opt. Express 17(15), 12269–12278 (2009).
[CrossRef] [PubMed]

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(11), 115109 (2005).
[CrossRef]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[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(4), 045117 (2001).
[CrossRef]

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

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(11), 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(4), 045117 (2001).
[CrossRef]

Saeta, P. N.

P. N. Saeta and B. I. Greene, “Primary relaxation processes at the band edge of SiO2,” Phys. Rev. Lett. 70(23), 3588–3591 (1993).
[CrossRef] [PubMed]

Sartania, S.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Sasaki, M.

Schwettman, H. A.

D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
[CrossRef] [PubMed]

Shang, G. Q.

Shao, J. D.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

L. Yuan, Y. A. Zhao, G. Q. Shang, C. R. Wang, H. B. He, J. D. Shao, and Z. X. Fan, “Comparison of femtosecond and nanosecond laser-induced damage in HfO2 single-layer film and HfO2–SiO2 high reflector,” J. Opt. Soc. Am. B 24(3), 538–543 (2007).
[CrossRef]

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Shen, J.

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Shen, Z. C.

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Shore, B. W.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

Simanovskii, D. M.

D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
[CrossRef] [PubMed]

Sirutkaitis, V.

Spielmann, Ch.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

Squier, J.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[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(11), 115109 (2005).
[CrossRef]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[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(4), 045117 (2001).
[CrossRef]

Stuart, B. C.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

Sudrie, L.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Sun, H. Y.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Tien, A.-C.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

Tikhonravov, A. A.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

Trubetskov, M.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

Tzortzakis, S.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Vaidyanathan, A.

A. Vaidyanathan, T. W. Walker, and A. H. Guenther, “The relative roles of avalanche multiplication and multiphoton absorption in laser-induced damage of dielectrics,” IEEE J. Quantum Electron. 16(1), 89–93 (1980).
[CrossRef]

Walker, T. W.

A. Vaidyanathan, T. W. Walker, and A. H. Guenther, “The relative roles of avalanche multiplication and multiphoton absorption in laser-induced damage of dielectrics,” IEEE J. Quantum Electron. 16(1), 89–93 (1980).
[CrossRef]

Wang, C. R.

Wang, H. Z.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Welch, A. J.

D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
[CrossRef] [PubMed]

Welling, H.

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

Xu, C.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

Xu, N. S.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Xu, Z. Z.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

Yuan, L.

Zhao, Y. A.

L. Yuan, Y. A. Zhao, G. Q. Shang, C. R. Wang, H. B. He, J. D. Shao, and Z. X. Fan, “Comparison of femtosecond and nanosecond laser-induced damage in HfO2 single-layer film and HfO2–SiO2 high reflector,” J. Opt. Soc. Am. B 24(3), 538–543 (2007).
[CrossRef]

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

Appl. Phys. B (1)

D. Du, X. Liu, and G. Mourou, “Reduction of multi-photon ionization in dielectrics due to collisions,” Appl. Phys. B 63, 617–621 (1996).

Appl. Phys. Lett. (2)

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in Si02 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[CrossRef]

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Vaidyanathan, T. W. Walker, and A. H. Guenther, “The relative roles of avalanche multiplication and multiphoton absorption in laser-induced damage of dielectrics,” IEEE J. Quantum Electron. 16(1), 89–93 (1980).
[CrossRef]

J. Appl. Phys. (1)

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

S. J. Liu, Z. C. Shen, W. J. Kong, J. Shen, Z. X. Deng, Y. A. Zhao, J. D. Shao, and Z. X. Fan, “Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor,” Opt. Commun. 267(1), 50–57 (2006).
[CrossRef]

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281(12), 3295–3300 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (3)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996).
[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(4), 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(11), 115109 (2005).
[CrossRef]

Phys. Rev. Lett. (8)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[CrossRef] [PubMed]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[CrossRef]

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-Pulse Laser Damage in Transparent Materials as a Function of Pulse Duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999).
[CrossRef]

B. Rethfeld, “Unified model for the free-electron avalanche in laser-irradiated dielectrics,” Phys. Rev. Lett. 92(18), 187401 (2004).
[CrossRef] [PubMed]

P. N. Saeta and B. I. Greene, “Primary relaxation processes at the band edge of SiO2,” Phys. Rev. Lett. 70(23), 3588–3591 (1993).
[CrossRef] [PubMed]

M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999).
[CrossRef]

D. M. Simanovskii, H. A. Schwettman, H. Lee, and A. J. Welch, “Midinfrared optical breakdown in transparent dielectrics,” Phys. Rev. Lett. 91(10), 107601 (2003).
[CrossRef] [PubMed]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Proc. SPIE (2)

D. S. Hobbs, B. D. MacLeod, and J. R. Riccobono, “Update on the development of high performance antireflecting surface relief micro-structures,” Proc. SPIE 6545, 65450Y (2007).
[CrossRef]

K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004).
[CrossRef]

Sov. Phys. JETP (1)

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

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 (10)

Fig. 1
Fig. 1

Typical PI rate with respect to electric field with the effective electron masses of 0.635 m e , 0.5 m e and 0.3 m e , respectively, for the both material gap of 9eV and 3.6eV.

Fig. 2
Fig. 2

PI rate on the laser intensity with gap E g = 9  eV from Keldysh’s theory, the incident wavelength is λ = 800 nm , and the multiphoton and tunnel limits are also shown.

Fig. 3
Fig. 3

AI rate as a function of the incident electric field for the AI models of Stuart, Thornber and Sparks, respectively.

Fig. 4
Fig. 4

Total evolution of free electron density based on the Eq. (2) for the combining Keldysh’s PI with the AI models of Thornber, Stuart, Sparks and Drude, respectively. And the evolution of ED produced only by Keldysh’s PI is also shown for reference. A Gaussian pulse of peak intensity I 0 = 23.85  TW/cm 2 with the pulse duration of 100fs and the incident wavelength of 800nm is selected to produce the ED. The material parameters of the refractive index n 0 = 1.46 , band gap E g = 9 eV, the reduced electron mass m e = 0.635 m e and the relaxation time τ r = 100 fs are applied to calculate ED evolution. Besides, the CED n c r = ( ε 0 m e ω 2 ) / e 2 = 1.1 × 10 21 cm 3 is demonstrated as the damage criterion.

Fig. 5
Fig. 5

The schematic diagram of a BAM arrays

Fig. 6
Fig. 6

Parameter scan of transmittance as a function of the groove depth and period for the BAM arrays at normal incidence. (a) and (c) exhibit the incident wavelength of 1064nm and 532nm, respectively, for TE polarization. (b) and (d) indicate the incident wavelength of 1064nm and 532nm, respectively, for TM polarization.

Fig. 7
Fig. 7

The zero order transmission efficiencies as a function of the incident wavelength at normal incidence with the variation of the groove depth and the period, respectively. (a) and (b) for TE polarization. (c) and (d) for TM polarization.

Fig. 8
Fig. 8

The normalized near-field distribution calculated quantitatively by the FMM for both TE and TM polarizations. The periods of 100nm, 200nm, 300nm and 400nm, respectively, with the groove depth of 400nm for the incident wavelength of 1064nm at normal incidence on the basis of the transmittance > 99.8 % are performed in sequence.

Fig. 9
Fig. 9

The normalized near-field distribution with the same parameters of Fig. 8 except for the incident wavelength 532nm. The periods of 100nm, 200nm, 300nm and 350nm, respectively are performed in sequence.

Fig. 10
Fig. 10

(a)(c) The varying characteristic of both the local maximum electric field enhancement q and the corresponding damage threshold as a function of the surface structure period based on the Fig. 8 and Fig. 9 for the laser pulse duration 100fs. (a) for the incident wavelength of 1064nm, (c) for the incident wavelength of 532nm. (b)(d) The calculated damage threshold as a function of the pulse duration taking account of the local maximum electric field enhancement q in the Fig. 8 and Fig. 9, respectively. (b) for the incident wavelength of 1064nm. (d) for the incident wavelength of 532nm.

Equations (12)

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

n c r = ε 0 m e ω 2 e 2 ,
n e ( t ) t = W P I ( I ( t )) + W A v ( I ( t )) n e ( t ) W r e l ( n ( t ) , t ) ,
W P I ( I ( t )) = 2 ω 9 π ( ω m e γ 1 ) 3/2 Q ( γ , x )exp { π x + 1 K ( γ 1 ) E ( γ 1 ) E ( γ 2 ) } ,
Q ( γ , x ) = π 2 K ( γ 2 ) × n = 0 exp { n π K ( γ 2 ) E ( γ 2 ) E ( γ 1 ) } Φ { π 2 (2 x + 1 2 x + n ) K ( γ 2 ) E ( γ 2 ) } , x = 2 π E g ω 1 + γ 2 γ E ( 1 1 + γ 2 ),   Φ ( z ) = 0 z  exp ( y 2 z 2 ) d y ,
W m u l t p t = 2 ω 9 π ( m e ω ) 3/2 Φ ( 2 E g ' / ω + 1 2 E g ' / ω )                                    × exp { 2 E g ' / ω + 1 ( 1 1 4 γ 2 ) } ( 1 16 γ 2 ) E g ' / ω + 1 ,
W t u n n e l = 2 ω 9 π 2 ( m e E g 2 ) 3/2 ( ω E g γ ) 5/2 exp { π 2 E g γ ω ( 1 γ 2 8 ) } .
W A v S t u a r t = α I ( t ) ,
W A v _ S p a r k s = 0.693 e 2 E 2 τ K m e E g ( 1 + ω 2 τ K 2 ) 0.693 ω p E g τ L ,
W A v _ T h o r n b e r = υ s e E E g exp{ E I E ( 1 + E / E p h o n o n ) + E k T },
W A v _ D r u d e = σ E g I ( t ),
σ = e 2 c ε 0 n 0 m e τ c 1 + ω 2 τ c 2 , τ c = 16 π ε 0 2 m e ( 0.1 E g ) 3 2 e 4 n ( t ) ,
W r e l = n ( t ) τ r .

Metrics