Abstract

Thermal conduction model is presented, by which nonlinear absorptivity of ultrashort laser pulses in internal modification of bulk glass is simulated. The simulated nonlinear absorptivity agrees with experimental values with maximum uncertainty of ±3% in a wide range of laser parameters at 10ps pulse duration in borosilicate glass. The nonlinear absorptivity increases with increasing energy and repetition rate of the laser pulse, reaching as high as 90%. The increase in the average absorbed laser power is accompanied by the extension of the laser-absorption region toward the laser source. Transient thermal conduction model for three-dimensional heat source shows that laser energy is absorbed by avalanche ionization seeded by thermally excited free-electrons at locations apart from the focus at pulse repetition rates higher than 100kHz.

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  1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996).
    [CrossRef] [PubMed]
  2. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
    [CrossRef]
  3. T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44, L687–L689 (2005).
    [CrossRef]
  4. I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoengineering 2, 7–14 (2007).
    [CrossRef]
  5. 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 Condens. Matter 53(4), 1749–1761 (1996).
    [CrossRef] [PubMed]
  6. C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76, 351–354 (2003).
    [CrossRef]
  7. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator,” Opt. Express 13(2), 612–620 (2005).
    [CrossRef] [PubMed]
  8. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
    [CrossRef]
  9. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005).
    [CrossRef] [PubMed]
  10. M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
    [CrossRef]
  11. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  12. J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficient and energy density,” IEEE J. Quantum Electron. 35, 1156–1167 (1999).
    [CrossRef]
  13. C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells,” Opt. Express 15(16), 10303–10317 (2007).
    [CrossRef] [PubMed]
  14. K. Nahen and A. Vogel, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses – part II: transmission, scattering, and reflection,” J. Sel. Top. Quant. Electron. 2, 861–871 (1996).
    [CrossRef]
  15. I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
    [CrossRef]
  16. J. Bovatsek, A. Araia, and C. B. Schaffer, “Three-dimensional micromachining inside transparent materials using femtosecond laser pulses: new applications,” Proceedings of CLEO/Europe - EQEC2005 (2005).
  17. http://www.schott.com/special_applications/english/download/d263te.pdf .
  18. http://www.schott.com/special_applications/english/download/af45e.pdf .
  19. http://psec.uchicago.edu/glass/Schott%20B270%20Properties%20%20Knight%20Optical.pdf .
  20. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 353 (Oxford at the Clarendon Press, 1959).
  21. http://www.coresix.com/images/0211.pdf .
  22. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
    [CrossRef] [PubMed]
  23. A. E. Siegman and S. W. Townsent, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
    [CrossRef]
  24. I. Miyamoto and T. Hermann, “Characteristics of internal melting of glass for fusion welding using ps laser pulses with average power up to 8W,” Proc. 8th Int. Symp. On Laser Precision Microfabrication- LPM2007 (2007).
  25. D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
    [CrossRef]
  26. P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: part I – theory,” IEEE J. Quantum Electron. 31, 2241–2249 (1995).
    [CrossRef]
  27. K. Morigaki, Physics of Amorphous Semiconductors (Imperial College Press, 1999).

2008 (1)

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[CrossRef]

2007 (3)

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells,” Opt. Express 15(16), 10303–10317 (2007).
[CrossRef] [PubMed]

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoengineering 2, 7–14 (2007).
[CrossRef]

2005 (3)

2004 (1)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

2003 (1)

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76, 351–354 (2003).
[CrossRef]

2001 (1)

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

1999 (2)

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficient and energy density,” IEEE J. Quantum Electron. 35, 1156–1167 (1999).
[CrossRef]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[CrossRef]

1996 (3)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996).
[CrossRef] [PubMed]

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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

K. Nahen and A. Vogel, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses – part II: transmission, scattering, and reflection,” J. Sel. Top. Quant. Electron. 2, 861–871 (1996).
[CrossRef]

1995 (1)

P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: part I – theory,” IEEE J. Quantum Electron. 31, 2241–2249 (1995).
[CrossRef]

1994 (1)

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

1993 (1)

A. E. Siegman and S. W. Townsent, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Aiello, L.

Arai, A.

Arnold, C. L.

Bergé, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Borrelli, N. F.

Bovatsek, J.

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Cerullo, G.

Chiodo, N.

Couairon, A.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Davis, K. M.

De Nicola, S.

Du, D.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Eaton, S. M.

Ertmer, W.

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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Ferraro, P.

Finizio, A.

Franco, M.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Gaeta, A. L.

Garcia, J. F.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76, 351–354 (2003).
[CrossRef]

Gottmann, J.

I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoengineering 2, 7–14 (2007).
[CrossRef]

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

Heisterkamp, A.

Herman, P. R.

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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Hirao, K.

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996).
[CrossRef] [PubMed]

Homoelle, D.

Horn, A.

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoengineering 2, 7–14 (2007).
[CrossRef]

Itoh, K.

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44, L687–L689 (2005).
[CrossRef]

Kennedy, P. K.

P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: part I – theory,” IEEE J. Quantum Electron. 31, 2241–2249 (1995).
[CrossRef]

Korn, G.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Laporta, P.

Liu, X.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Lubatschowski, H.

Maselli, V.

Mazur, E.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76, 351–354 (2003).
[CrossRef]

Miura, K.

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996).
[CrossRef] [PubMed]

Miyamoto, I.

I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoengineering 2, 7–14 (2007).
[CrossRef]

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

Mourou, G.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Mysyrowicz, A.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Nahen, K.

K. Nahen and A. Vogel, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses – part II: transmission, scattering, and reflection,” J. Sel. Top. Quant. Electron. 2, 861–871 (1996).
[CrossRef]

Nishii, J.

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44, L687–L689 (2005).
[CrossRef]

Noack, J.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficient and energy density,” IEEE J. Quantum Electron. 35, 1156–1167 (1999).
[CrossRef]

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Osellame, R.

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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Pierattini, G.

Prade, B.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Sakakura, M.

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[CrossRef]

Schaffer, C. B.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76, 351–354 (2003).
[CrossRef]

Shah, L.

Shimizu, M.

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[CrossRef]

Shimotsuma, Y.

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman and S. W. Townsent, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Smith, C.

Squier, J.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Sudrie, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Sugimoto, N.

Tamaki, T.

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44, L687–L689 (2005).
[CrossRef]

Townsent, S. W.

A. E. Siegman and S. W. Townsent, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Tünnermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Tzortzakis, S.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Vogel, A.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficient and energy density,” IEEE J. Quantum Electron. 35, 1156–1167 (1999).
[CrossRef]

K. Nahen and A. Vogel, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses – part II: transmission, scattering, and reflection,” J. Sel. Top. Quant. Electron. 2, 861–871 (1996).
[CrossRef]

Watanabe, W.

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44, L687–L689 (2005).
[CrossRef]

Wielandy, S.

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Wortmann, D.

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

Yin, A.

Yoshino, F.

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005).
[CrossRef] [PubMed]

Zavelani-Rossi, M.

Zhang, H.

Appl. Phys. Lett. (2)

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett. 93, 231112 (2008).
[CrossRef]

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76, 351–354 (2003).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficient and energy density,” IEEE J. Quantum Electron. 35, 1156–1167 (1999).
[CrossRef]

P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: part I – theory,” IEEE J. Quantum Electron. 31, 2241–2249 (1995).
[CrossRef]

A. E. Siegman and S. W. Townsent, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

J. Laser Micro/Nanoengineering (2)

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoengineering 2, 57-63 (2007).
[CrossRef]

I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoengineering 2, 7–14 (2007).
[CrossRef]

J. Mod. Opt. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

J. Sel. Top. Quant. Electron. (1)

K. Nahen and A. Vogel, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses – part II: transmission, scattering, and reflection,” J. Sel. Top. Quant. Electron. 2, 861–871 (1996).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44, L687–L689 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B Condens. Matter (1)

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 Condens. Matter 53(4), 1749–1761 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[CrossRef] [PubMed]

Other (9)

K. Morigaki, Physics of Amorphous Semiconductors (Imperial College Press, 1999).

I. Miyamoto and T. Hermann, “Characteristics of internal melting of glass for fusion welding using ps laser pulses with average power up to 8W,” Proc. 8th Int. Symp. On Laser Precision Microfabrication- LPM2007 (2007).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

J. Bovatsek, A. Araia, and C. B. Schaffer, “Three-dimensional micromachining inside transparent materials using femtosecond laser pulses: new applications,” Proceedings of CLEO/Europe - EQEC2005 (2005).

http://www.schott.com/special_applications/english/download/d263te.pdf .

http://www.schott.com/special_applications/english/download/af45e.pdf .

http://psec.uchicago.edu/glass/Schott%20B270%20Properties%20%20Knight%20Optical.pdf .

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 353 (Oxford at the Clarendon Press, 1959).

http://www.coresix.com/images/0211.pdf .

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Figures (11)

Fig. 1
Fig. 1

Cross-sections obtained at different pulse energies Q0 at pulse repetition rates f of (a) 50kHz, (b) 200kHz and (c) 500kHz at 20mm/s in D263. Geometrical focus is assumed to be at the bottom edge of internal modification at threshold pulse energy shown by a horizontal line. (NA0.55, τ = 10ps). (d) Coordinate and direction of laser beam (the sample is translated along x-axis, which is perpendicular to the paper plane).

Fig. 2
Fig. 2

Focused laser beam was irradiated at the interface of two glass plates of D263 (thickness: 1mm, v = 20mm/s. The glass plates are welded together within the outer structure of the modified region.

Fig. 3
Fig. 3

Nonlinear absorptivity vs. pulse energy at different pulse repetition rates. Solid lines show experimental values, and closed circles simulated values.

Fig. 4
Fig. 4

(a) Cross-sectional area S within isothermal line of Tm vs. laser pulse energy Q0 at different pulse repetition rates f. (b) S vs. AExfQ0 . Closed circles are experimental values and solid line simulated.

Fig. 5
Fig. 5

Isothermal lines of 1,051°C and 3,600°C at f = 500kHz simulated at different values of m. In this calculation, b = 73W/cm (independently of m) and a for m = 0.5, 1.0 and 2.0 are 1032W/cm 1.5, 19500W/cm2 and 1.95*104 W/cm3 , respectively (Q0 = 1.59µJ, v = 20mm/s, T0 = 25°C).

Fig. 6
Fig. 6

Isothermal lines of 1,051°C and 3,600°C simulated at f = 50kHz (Q0 = 10.3µJ, v = 20mm/s, m = 1, T0 = 25°C).

Fig. 7
Fig. 7

Ratio of ACal/AEx plotted vs. average absorbed laser power Wab (K = 0.0096W/cmK).

Fig. 8
Fig. 8

Simulated and experimental length of laser absorbed region vs. pulse energy at different pulse repetition rates. Relationship between Q0 and z for different values of I given by Eq. (9) is plotted by solid lines, where ω0 = 2.26µm is used.

Fig. 9
Fig. 9

Length of laser absorbed region l and average absorbed laser power per unit length Wab/l vs. averaged absorbed laser power of Wab ( = ACalfQ0 ) at different energies Q0 and repetition rates of laser pulse f.

Fig. 10
Fig. 10

Transient temperature on the laser beam axis at z = 2.5µm and z = l/2 at 20mm/s at pulse repetition rates of (a) 50kHz (Q0 = 3.72µJ, l = 22µm) and (b) 300kHz (Q0 = 3.9µJ, l = 72µm).

Fig. 11
Fig. 11

(a) Temperature TBS (0,0,z;tf ) attained at steady condition at z = 2.5µm and z = l/2. (b) Thermally excited free electron density at TBS (0,0,z;tf ) (Q0 = 3.9±0.18µJ, Eg = 3.7eV, v = 20mm/s).

Equations (12)

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A E x = 1 Q t Q 0 1 ( 1 R ) 2 ,
T ( x , y , z ) = 1 4 π K 0 l w ( z ' ) s e x p { v 2 α ( x + s ) } d z ' + T 0 ,
0 l w ( z ' ) s e x p { v 2 α ( x + s ) } { x r 3 v 2 α ( x r 1 ) } d z ' = 0
A C a l = 1 f Q 0 0 l w ( z ) d z ,
w ( z ) = a z m + b ,
A C a l = 1 f Q 0 ( a m + 1 l m + 1 + b l )
ω ( z ) = ω 0 1 + ( M 2 λ z π ω 0 2 n g ) 2 ; ω 0 = M 2 λ π N A ,
I ( z ) = 2 Q 0 π τ ω 2 ( z ) .
z = n g N A 2 Q 0 π τ I ω 0 2 ,
T ( x , y , z ; t ) = 1 8 c ρ i = 0 N 1 q ( x ' + v ( t + i f 1 ) , y ' , z ' ) { π α ( t + i f 1 ) } 3 / 2 e x p [ { x x ' + v ( t + i f 1 ) } 2 + ( y y ' ) 2 + ( z z ' ) 2 4 α ( t + i f 1 ) ] d x ' d y ' d z '
q ( r , z ) = 2 w ( z ) π ω 2 ( z ) f exp { 2 r 2 ω 2 ( z ) } ; 0 z l ,
T ( x , y , z ; t ) = 1 π c ρ f 0 N 1 1 π α ( t i f 1 ) 0 l w ( z ' ) ω 2 ( z ' ) + 8 α ( t i f 1 ) exp [ 2 { ( x + v ( t i f 1 ) ) 2 + y 2 } ω 2 ( z ' ) + 8 α ( t i f 1 ) ( z z ' ) 2 4 α t ] d z ' .

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