Abstract

Evolution of free-electron density in internal modification of glass by fs-laser pulses at high pulse repetition rates is simulated based on rate equation model, which is coupled with thermal conduction model in order to incorporate the effect of thermal ionization. Model shows that highly absorbing small plasma generated near the geometrical focus moves toward the laser source periodically to cover the region, which is much larger than focus volume. The simulated results agree qualitatively with dynamic motion of plasma produced in internal modification of borosilicate glass by fs-laser pulses at 1 MHz through the observation using high-speed video camera. The paper also reveals the physical mechanism of the internal modification of glass when heat accumulation is significant.

© 2016 Optical Society of America

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References

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    [Crossref]

2016 (1)

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

2015 (2)

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[Crossref]

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[Crossref]

2014 (2)

I. Miyamoto, Y. Okamoto, R. Tanabe, and Y. Ito, “Characterization of plasma in microwelding of glass using ultrashort laser pulse at high pulse repetition rates,” Phys. Procedia 56, 973–982 (2014).
[Crossref]

I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014).
[Crossref]

2013 (3)

2012 (1)

K. Cvecek, I. Miyamoto, M. Adam, and M. Schmidt, “Effects of spherical aberrations on micro welding of glass using ultra short laser pulses,” Phys. Procedia 39, 563–568 (2012).
[Crossref]

2011 (4)

2009 (1)

2008 (1)

2005 (4)

L. Shah, A. Arai, S. Eaton, and P. Herman, “Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate,” Opt. Express 13(6), 1999–2006 (2005).
[Crossref] [PubMed]

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

A. Vogel, J. Novak, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005).
[Crossref]

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44(22), L687–L689 (2005).
[Crossref]

2003 (2)

X. Mao, S. S. Mao, and R. E. Russo, “Imaging femtosecond laser-induced electronic excitation in glass,” Appl. Phys. Lett. 82(5), 697–699 (2003).
[Crossref]

J. F. G. Schaffer and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 187–208 (2003).
[Crossref]

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 (4)

C. B. Schaffer, A. Brodeur, and E. Mazur, “Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses,” Meas. Sci. Technol. 12(11), 1784–1794 (2001).
[Crossref]

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]

C. H. Fan and J. P. Longtin, “Modeling optical breakdown in dielectrics during ultrafast laser processing,” Appl. Opt. 40(18), 3124–3131 (2001).
[Crossref] [PubMed]

K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26(19), 1516–1518 (2001).
[Crossref] [PubMed]

1996 (1)

M. D. 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)

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(12), 2241–2249 (1995).
[Crossref]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1207–1314 (1965).

Adam, M.

K. Cvecek, I. Miyamoto, M. Adam, and M. Schmidt, “Effects of spherical aberrations on micro welding of glass using ultra short laser pulses,” Phys. Procedia 39, 563–568 (2012).
[Crossref]

Alexeev, I.

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[Crossref]

Arai, A.

Araki, R.

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

Arriola, A.

Audouard, E.

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]

Brandt, N.

Brodeur, A.

C. B. Schaffer, A. Brodeur, and E. Mazur, “Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses,” Meas. Sci. Technol. 12(11), 1784–1794 (2001).
[Crossref]

Charles, N.

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]

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]

Cvecek, K.

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[Crossref]

I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014).
[Crossref]

K. Cvecek, I. Miyamoto, M. Adam, and M. Schmidt, “Effects of spherical aberrations on micro welding of glass using ultra short laser pulses,” Phys. Procedia 39, 563–568 (2012).
[Crossref]

I. Miyamoto, K. Cvecek, and M. Schmidt, “Characteristics of laser absorption and welding in FOTURAN glass by ultrashort laser pulses,” Opt. Express 19, 22961–22973 (2011).

I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express 19(11), 10714–10727 (2011).
[Crossref] [PubMed]

Dai, Y.

Döring, S.

S. Richter, S. Döring, A. Tünnermann, and S. Nolte, “Bonding of glass with femtosecond laser pulses at high repetition rates,” Appl. Phys., A Mater. Sci. Process. 103(2), 257–261 (2011).
[Crossref]

Eaton, S.

Eppelt, U.

Fan, C. H.

Feit, M. D.

M. D. 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]

Fernandez, P.

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[Crossref]

Fernandez, T. T.

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[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]

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]

Fuerbach, A.

Fujimoto, J. G.

Fujita, K.

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

Gottmann, J.

Gross, S.

Hartl, I.

Hartmann, C.

Heberle, J.

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[Crossref]

Herman, P.

Herman, S.

M. D. 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]

Hertel, I. V.

Hirao, K

Hirao, K.

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

Horn-Solle, H.

Hoyo, J.

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[Crossref]

Huot, N.

Hüttman, G.

A. Vogel, J. Novak, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005).
[Crossref]

Ippen, E. P.

Ito, Y.

I. Miyamoto, Y. Okamoto, R. Tanabe, and Y. Ito, “Characterization of plasma in microwelding of glass using ultrashort laser pulse at high pulse repetition rates,” Phys. Procedia 56, 973–982 (2014).
[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(22), L687–L689 (2005).
[Crossref]

Jovanovic, N.

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1207–1314 (1965).

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(12), 2241–2249 (1995).
[Crossref]

Kowalevicz, A. M.

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]

Landon, S.

Liu, Y.

Longtin, J. P.

Mao, S. S.

X. Mao, S. S. Mao, and R. E. Russo, “Imaging femtosecond laser-induced electronic excitation in glass,” Appl. Phys. Lett. 82(5), 697–699 (2003).
[Crossref]

Mao, X.

X. Mao, S. S. Mao, and R. E. Russo, “Imaging femtosecond laser-induced electronic excitation in glass,” Appl. Phys. Lett. 82(5), 697–699 (2003).
[Crossref]

Mauclair, C.

Mazur, E.

J. F. G. Schaffer and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 187–208 (2003).
[Crossref]

C. B. Schaffer, A. Brodeur, and E. Mazur, “Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses,” Meas. Sci. Technol. 12(11), 1784–1794 (2001).
[Crossref]

Mermillod-Blondin, A.

Minoshima, K.

Miura, K.

Y. Liu, M. Shimizu, B. Zhu, Y. Dai, B. Qian, J. Qiu, Y Shimotsuma, K. Miura, and K Hirao, “Micromodification of element distribution in glass using femtosecond laser irradiatio,” Opt. Lett. 34, 136–138 (2009).
[Crossref] [PubMed]

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

Miyamoto, I.

I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014).
[Crossref]

I. Miyamoto, Y. Okamoto, R. Tanabe, and Y. Ito, “Characterization of plasma in microwelding of glass using ultrashort laser pulse at high pulse repetition rates,” Phys. Procedia 56, 973–982 (2014).
[Crossref]

K. Cvecek, I. Miyamoto, M. Adam, and M. Schmidt, “Effects of spherical aberrations on micro welding of glass using ultra short laser pulses,” Phys. Procedia 39, 563–568 (2012).
[Crossref]

I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express 19(11), 10714–10727 (2011).
[Crossref] [PubMed]

I. Miyamoto, K. Cvecek, and M. Schmidt, “Characteristics of laser absorption and welding in FOTURAN glass by ultrashort laser pulses,” Opt. Express 19, 22961–22973 (2011).

Myiamoto, I.

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]

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]

Nagulin, K. Yu.

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[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(22), L687–L689 (2005).
[Crossref]

Nolte, S.

S. Richter, S. Döring, A. Tünnermann, and S. Nolte, “Bonding of glass with femtosecond laser pulses at high repetition rates,” Appl. Phys., A Mater. Sci. Process. 103(2), 257–261 (2011).
[Crossref]

Nordin, I. H. W.

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

Novak, J.

A. Vogel, J. Novak, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005).
[Crossref]

Okada, A.

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

Okamoto, Y.

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

I. Miyamoto, Y. Okamoto, R. Tanabe, and Y. Ito, “Characterization of plasma in microwelding of glass using ultrashort laser pulse at high pulse repetition rates,” Phys. Procedia 56, 973–982 (2014).
[Crossref]

I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014).
[Crossref]

Olaizola, S. M.

Paltauf, G.

A. Vogel, J. Novak, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005).
[Crossref]

Perry, M. D.

M. D. 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]

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]

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]

Qian, B.

Qiu, J.

Richter, S.

S. Richter, S. Döring, A. Tünnermann, and S. Nolte, “Bonding of glass with femtosecond laser pulses at high repetition rates,” Appl. Phys., A Mater. Sci. Process. 103(2), 257–261 (2011).
[Crossref]

Rosenfeld, A.

Rubenchik, A. M.

M. D. 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]

Russ, S.

Russo, R. E.

X. Mao, S. S. Mao, and R. E. Russo, “Imaging femtosecond laser-induced electronic excitation in glass,” Appl. Phys. Lett. 82(5), 697–699 (2003).
[Crossref]

Sakagawa, T.

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

Schaffer, C. B.

C. B. Schaffer, A. Brodeur, and E. Mazur, “Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses,” Meas. Sci. Technol. 12(11), 1784–1794 (2001).
[Crossref]

Schaffer, J. F. G.

J. F. G. Schaffer and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 187–208 (2003).
[Crossref]

Schmidt, M.

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[Crossref]

I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014).
[Crossref]

K. Cvecek, I. Miyamoto, M. Adam, and M. Schmidt, “Effects of spherical aberrations on micro welding of glass using ultra short laser pulses,” Phys. Procedia 39, 563–568 (2012).
[Crossref]

I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express 19(11), 10714–10727 (2011).
[Crossref] [PubMed]

I. Miyamoto, K. Cvecek, and M. Schmidt, “Characteristics of laser absorption and welding in FOTURAN glass by ultrashort laser pulses,” Opt. Express 19, 22961–22973 (2011).

Schulz, W.

Shah, L.

Shimizu, M.

Shimotsuma, Y

Shore, B. W.

M. D. 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]

Siebert, C.

Siegel, J.

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[Crossref]

Solis, J.

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[Crossref]

Sotillo, B.

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[Crossref]

Stoian, R.

Stuart, M. D.

M. D. 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]

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]

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]

Sun, M.

Takekuni, T.

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

Tamaki, T.

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44(22), L687–L689 (2005).
[Crossref]

Tanabe, R.

I. Miyamoto, Y. Okamoto, R. Tanabe, and Y. Ito, “Characterization of plasma in microwelding of glass using ultrashort laser pulse at high pulse repetition rates,” Phys. Procedia 56, 973–982 (2014).
[Crossref]

Tünnermann, A.

S. Richter, S. Döring, A. Tünnermann, and S. Nolte, “Bonding of glass with femtosecond laser pulses at high repetition rates,” Appl. Phys., A Mater. Sci. Process. 103(2), 257–261 (2011).
[Crossref]

Tuthill, P. G.

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]

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.

A. Vogel, J. Novak, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005).
[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(22), L687–L689 (2005).
[Crossref]

Withford, M. J.

Wortmann, D.

Yonesaki, Y.

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

Zhu, B.

Zhu, J.

Appl. Opt. (1)

Appl. Phys. B (1)

A. Vogel, J. Novak, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005).
[Crossref]

Appl. Phys. Lett. (1)

X. Mao, S. S. Mao, and R. E. Russo, “Imaging femtosecond laser-induced electronic excitation in glass,” Appl. Phys. Lett. 82(5), 697–699 (2003).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (4)

S. Richter, S. Döring, A. Tünnermann, and S. Nolte, “Bonding of glass with femtosecond laser pulses at high repetition rates,” Appl. Phys., A Mater. Sci. Process. 103(2), 257–261 (2011).
[Crossref]

J. F. G. Schaffer and E. Mazur, “Bulk heating of transparent materials using high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 187–208 (2003).
[Crossref]

I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014).
[Crossref]

I. H. W. Nordin, Y. Okamoto, A. Okada, T. Takekuni, and T. Sakagawa, “Effect of focusing condition on molten area characteristics in micro-welding of borosilicate glass by picosecond pulsed laser,” Appl. Phys., A Mater. Sci. Process. 122(5), 492 (2016).
[Crossref]

IEEE J. Quantum Electron. (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(12), 2241–2249 (1995).
[Crossref]

J. Non-Cryst. Solids (1)

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351(10-11), 885–892 (2005).
[Crossref]

J. Phys. D Appl. Phys. (1)

T. T. Fernandez, J. Siegel, J. Hoyo, B. Sotillo, P. Fernandez, and J. Solis, “Controlling plasma distributions as driving forces for ion migration during fs laser writing,” J. Phys. D Appl. Phys. 48(15), 155101 (2015).
[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(22), L687–L689 (2005).
[Crossref]

Meas. Sci. Technol. (1)

C. B. Schaffer, A. Brodeur, and E. Mazur, “Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses,” Meas. Sci. Technol. 12(11), 1784–1794 (2001).
[Crossref]

Micromach. (1)

I. Alexeev, J. Heberle, K. Cvecek, K. Yu. Nagulin, and M. Schmidt, “High speed pump-probe apparatus for observation of transitional effects in ultrafast laser micromachining processes,” Micromach. 6(12), 1914–1922 (2015).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Opt. Mater. Express (1)

Phys. Procedia (2)

K. Cvecek, I. Miyamoto, M. Adam, and M. Schmidt, “Effects of spherical aberrations on micro welding of glass using ultra short laser pulses,” Phys. Procedia 39, 563–568 (2012).
[Crossref]

I. Miyamoto, Y. Okamoto, R. Tanabe, and Y. Ito, “Characterization of plasma in microwelding of glass using ultrashort laser pulse at high pulse repetition rates,” Phys. Procedia 56, 973–982 (2014).
[Crossref]

Phys. Rev. B (1)

M. D. 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]

Phys. Rev. Lett. (2)

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]

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]

Sov. Phys. JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1207–1314 (1965).

Other (4)

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

A. E. Siegman, Lasers (University Science, 1986), Chap. 17.

N. Linz, S. Freidank, X. Liang, J. Noack, G. Paltauf, and A. Vogel, “Roles of tunneling, multiphoton ionization, and cascade ionization for femtosecond optical breakdown in aqueous media,” AFORS International Research Initiative Project SPC 053010 / EOARD, 2009. http://www.dtic.mil/dtic/tr/fulltext/u2/a521817.pdf .

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

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Figures (11)

Fig. 1
Fig. 1 (a) Experimental setup and coordinates. Laser beam (τp = 550 fs, f = 1 MHz, Q = 2.5 µJ) is focused into moving glass sample (v = 20 mm/s) at a depth of zf = 250 µm. (b) Cross-section of internal modification (y-z plane). (c) Side-view of the modified glass sample (x-z plane). The starting position is indicated by an arrow, and horizontal distance of 20 µm corresponds to 1,000 laser pulses. (d) Snap shot of laser-induced plasma taken in y-direction. GF is shown by a dotted line.
Fig. 2
Fig. 2 High-speed pictures taken at 50,000 frames per second under conditions of τp = 550 fs, f = 1MHz, Q = 2.5 µJ, zf = 250 µm, v = 20 mm/s in D263. Figures indicate relative frame number. #2 ~#31 correspond to 6th cycle in Fig. 3 where steady condition is nearly reached.
Fig. 3
Fig. 3 Vertical positions of the bright region at the top and bottom with respect to the GF are shown by closed and open circles, respectively, and are plotted from the first laser pulse (f = 1 MHz, Q = 2.5 µJ and v = 20 mm/s).
Fig. 4
Fig. 4 Time-dependent free-electron density ρ(z,t) at different values of z by single laser pulse. Maximum value of ρ(z,t) at z is designated by ρmax (τp = 550 fs, Q = 2.5 µJ, zR = 15 µm, zf = 250 µm).
Fig. 5
Fig. 5 Waveform of laser intensity simulated without and with plasma, I0(z,t) and I(z,t), respectively, at z = (a) 202 µm, (b) 211 µm, (c) 224 µm and (d) 239 µm.
Fig. 6
Fig. 6 Free-electron density ρmax, laser intensity (Imax: in plasma, I0max: without absorption) plotted vs. z by single laser pulse irradiation. Laser beam propagates from left to right.
Fig. 7
Fig. 7 Temperature variation at x = 0 and z = 240 µm, when five laser pulses (Q = 2.5 µJ) are irradiated. Temperature just before and after 4th laser pulse are represented by TJBP and TJAP, respectively.
Fig. 8
Fig. 8 Distribution of TJBP along z-axis at different pulse numbers simulated with simple heat accumulation model. Dotted line shows T = 3,600 °C, which is the temperature at the contour of the inner structure (laser absorption region). Locations where TJBP reaches 3,600 °C at 65th pulse, for instance, are shown by A0 and B0.
Fig. 9
Fig. 9 Distribution of TJBP along z-axis at different pulse numbers simulated with incorporating the effect of thermal ionization in the model. The locations whereTJBP reaches 3,600 °C in each cycle is shown by Ath and Bth.
Fig. 10
Fig. 10 (a) Location of maximum temperature TJBP with thermal ionization. (b) The region where temperature exceeds 3,600 °C, without (black line) and with (dashed red line) thermal ionization. Location of maximum temperature is also plotted by blue line.
Fig. 11
Fig. 11 Free-electron densities (ρtherm & ρmax), temperature TJBP, laser intensity (Imax: with plasma, I0max: without plasma) and absorption coefficient α max are plotted vs. z at every two pulses. Laser beam propagating from left to right is focused at GF zf = 250 µm.

Equations (9)

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ρ(z,t) t = η photo I K ( z,t )+ η casc I(z,t)ρ(z,t) η rec ρ (z,t) 2
η casc = 1 ω L 2 τ 2 +1 e 2 τ c n 0 ε 0 m(3/2) E g
I(z,t)= 2Q 1.06× τ p πω (z) 2 exp[ 2 r 2 ω (z) 2 ]exp[ 4ln2 ( t n 0 (z z f )/c2 τ p τ p ) 2 0 z α(z,t)dz ]
ω(z)= ω 0 1+ ( z z f z R ) 2 ,
α(z,t)I( z,t )=[ η photo I K ( z,t )+ η casc I(z,t)ρ(z,t) ]×(3/2) E g
T(x,y,z,t)= 1 π c g ρ g i=1 n 1 πk{ t( i1 )/f } q(z') ω 2 (z')+8k{ t( i1 )/f } ×exp[ 2{ ( x+v{ t( i1 )/f } ) 2 + y 2 } ω 2 (z')+8k{ t( i1 )/f } (zz') 2 4k{ t( i1 )/f } ]dz',
q(z')= π 2 ω (z') 2 α(z',t)I(z',t)dt .
ρ therm = ρ bound 3 π 2 ( kT E g ) 3/2 exp( E g 2kT ) 1+3 π 2 ( kT E g ) 3/2 exp( E g 2kT )
ρ[z,0]= ρ therm

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