Abstract

The spatial distribution of the laser energy absorbed by nonlinear absorption process in bulk glass w(z) is determined and thermal cycles due to the successive ultrashort laser pulse (USLP) is simulated using w(z) based on the transient thermal conduction model. The thermal stress produced in internal melting of bulk glass by USLP is qualitatively analyzed based on a simple thermal stress model, and crack-free conditions are studied in glass having large coefficient of thermal expansion. In heating process, cracks are prevented when the laser pulse impinges into glass with temperatures higher than the softening temperature of glass. In cooling process, shrinkage stress is suppressed to prevent cracks, because the embedded molten pool produced by nonlinear absorption process behaves like an elastic body under the compressive stress field unlike the case of CW-laser welding where the molten pool having a free surface produced by linear absorption process is plastically deformed under the compressive stress field.

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    [CrossRef]

2012 (1)

2011 (4)

2010 (1)

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

2009 (2)

2008 (1)

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

2007 (3)

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 MicroNanoeng.2(1), 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 Nanoeng.2(1), 57–63 (2007).
[CrossRef]

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. Express15(16), 10303–10317 (2007).
[CrossRef] [PubMed]

2006 (2)

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

2005 (3)

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]

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express13(12), 4708–4716 (2005).
[CrossRef] [PubMed]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

2004 (2)

C. B. Schaffer, A. O. Jamison, and E. Mazur, “Morphology of femtosecond laser-induced structural changes in bulk transparent materials,” Appl. Phys. Lett.84(9), 1441–1443 (2004).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt.51(16-18), 2533–2542 (2004).
[CrossRef]

1999 (1)

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: Calculation of thresholds, absorption coefficients and energy density,” IEEE J. Quantum Electron.35(8), 1156–1167 (1999).
[CrossRef]

1998 (1)

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

1996 (1)

1993 (1)

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron.29(4), 1212–1217 (1993).
[CrossRef]

Arai, A. Y.

Arnold, C. L.

Bhardwaj, V. R.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

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(16-18), 2533–2542 (2004).
[CrossRef]

Corkum, P. B.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

Cournoyer, A.

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

Cvecek, K.

Dai, Y.

Davis, K. M.

Deshaies, S.

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

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. M.

Ertmer, W.

Forest, R.

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

Frick, T.

Gottmann, J.

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 Nanoeng.2(1), 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 MicroNanoeng.2(1), 7–14 (2007).
[CrossRef]

Hanada, Y.

Heisterkamp, A.

Helvajian, H.

Herman, P. R.

Hirao, K.

Hnatovsky, C.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

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 Nanoeng.2(1), 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 MicroNanoeng.2(1), 7–14 (2007).
[CrossRef]

Itoh, K.

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

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]

Jamison, A. O.

C. B. Schaffer, A. O. Jamison, and E. Mazur, “Morphology of femtosecond laser-induced structural changes in bulk transparent materials,” Appl. Phys. Lett.84(9), 1441–1443 (2004).
[CrossRef]

Juodkazis, S.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Labrnche, B.

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

Levesque, M.

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

Liu, Y.

Lubatschowski, H.

Makimura, T.

Matsuo, S.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Mazur, E.

C. B. Schaffer, A. O. Jamison, and E. Mazur, “Morphology of femtosecond laser-induced structural changes in bulk transparent materials,” Appl. Phys. Lett.84(9), 1441–1443 (2004).
[CrossRef]

Midorikawa, K.

Misawa, H.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Miura, K.

Miyamoto, I.

Nishii, J.

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

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]

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Noack, J.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: Calculation of thresholds, absorption coefficients and energy density,” IEEE J. Quantum Electron.35(8), 1156–1167 (1999).
[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]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt.51(16-18), 2533–2542 (2004).
[CrossRef]

Okamoto, Y.

Onda, S.

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

Qian, B.

Qiu, J.

Rajeev, P. P.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

Rayner, D. M.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

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]

Sakakura, M.

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

Savard, E.

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

Schaffer, C. B.

C. B. Schaffer, A. O. Jamison, and E. Mazur, “Morphology of femtosecond laser-induced structural changes in bulk transparent materials,” Appl. Phys. Lett.84(9), 1441–1443 (2004).
[CrossRef]

Schmidt, M.

Shah, L.

Shimizu, M.

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 irradiation,” Opt. Lett.34(2), 136–138 (2009).
[CrossRef] [PubMed]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

Shimotsuma, Y.

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 irradiation,” Opt. Lett.34(2), 136–138 (2009).
[CrossRef] [PubMed]

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

Siegman, A. E.

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron.29(4), 1212–1217 (1993).
[CrossRef]

Simova, E.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

Strauss, J.

Suganuma, R.

Sugimoto, N.

Sugioka, K.

Sun, H.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Suzuki, Y.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Takahashi, T.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Tamaki, T.

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

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]

Taylor, R. S.

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

Terasaki, T.

T. Terasaki, “Welding distortion and residual stress,” J. Jpn. Welding Soc.78, 139–146 (2009).

Townsend, S. W.

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron.29(4), 1212–1217 (1993).
[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]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt.51(16-18), 2533–2542 (2004).
[CrossRef]

Vogel, A.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: Calculation of thresholds, absorption coefficients and energy density,” IEEE J. Quantum Electron.35(8), 1156–1167 (1999).
[CrossRef]

Wang, H.

Watanabe, M.

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[CrossRef]

Watanabe, W.

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

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]

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(16-18), 2533–2542 (2004).
[CrossRef]

Wolf, M.

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 Nanoeng.2(1), 57–63 (2007).
[CrossRef]

Wu, D.

Wu, S.

Xu, J.

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 Nanoeng.2(1), 57–63 (2007).
[CrossRef]

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express13(12), 4708–4716 (2005).
[CrossRef] [PubMed]

Zhang, H.

Zhu, B.

Appl. Opt. (1)

Appl. Phys. Lett. (4)

M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, “Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett.89, 021106 (2006).

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett.87(1), 014104 (2005).
[CrossRef]

C. B. Schaffer, A. O. Jamison, and E. Mazur, “Morphology of femtosecond laser-induced structural changes in bulk transparent materials,” Appl. Phys. Lett.84(9), 1441–1443 (2004).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (2)

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]

C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: Calculation of thresholds, absorption coefficients and energy density,” IEEE J. Quantum Electron.35(8), 1156–1167 (1999).
[CrossRef]

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron.29(4), 1212–1217 (1993).
[CrossRef]

J. Jpn. Welding Soc. (1)

T. Terasaki, “Welding distortion and residual stress,” J. Jpn. Welding Soc.78, 139–146 (2009).

J. Laser Micro Nanoeng. (1)

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 Nanoeng.2(1), 57–63 (2007).
[CrossRef]

J. Laser MicroNanoeng. (1)

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 MicroNanoeng.2(1), 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(16-18), 2533–2542 (2004).
[CrossRef]

Jpn. J. Appl. Phys. (2)

M. Watanabe, H. Sun, S. Juodkazis, T. Takahashi, S. Matsuo, Y. Suzuki, J. Nishii, and H. Misawa, “Three-dimensional optical data storage in vitreous silica,” Jpn. J. Appl. Phys.37(Part 2, No. 12B), L1527–L1530 (1998).
[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]

Opt. Express (5)

Opt. Lett. (2)

Physics Procedia (1)

M. Levesque, B. Labrnche, R. Forest, E. Savard, S. Deshaies, and A. Cournoyer, “Welding of glass pieces,” Physics Procedia5, 139–144 (2010).
[CrossRef]

Other (5)

Y. Arata, H. Maruo, I. Miyamoto, and S. Tackuchi, “Dynamic behavior of laser welding and cutting,” Proc Symp. Electron and ion beam Science and technologies, 7th Int. Conf. 111–128 (1976)

M. Watanabe and K. Satoh, Welding Mechanics and its Applications (Asakura, 1965), Chap. 8.

I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, I. Mingareev, F. Yoshino, M. Schmidt, Y. Okamoto, Y. Uno, and T. Hermann, “Novel fusion welding technology of glass using ultrashort pulse lasers,” Proc. 27th International Congress on Applications of Lasers and Electro-Optics (ICALEO) 112–121 (2010).
[CrossRef]

D. O. MacCallum, G. A. Knorovsky, and S. T. Reed, “CO2 laser welding fused silica,” Proc. 24th Int. Cong. on Application of Lasers and Electro-Optics (ICALEO) 687–695 (2005)

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley and Sons, 1984), Chap. 27.

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Figures (12)

Fig. 1
Fig. 1

Cross-sections of internally melted D263 at 20mm/s at Q0 = 1.63µJ. Experimental values of nonlinear absorptivity Aex are (a) 45%, (b) 52%, (c) 66% (d) 76% and (e) 81%.

Fig. 2
Fig. 2

Crack-free and cracking conditions at v = 20mm/s in D263. Crack-free internal melting is available at average laser power higher than 0.25W.

Fig. 3
Fig. 3

(a) Instantaneous Gaussian heat source with radius of ω(z) and intensity of q(r,z) at repetition rate of f. (b) Line heat source of continuous heat delivery with average intensity distribution w(z).

Fig. 4
Fig. 4

Simulated w(z) at different pulse repetition rates corresponding to Fig. 5.

Fig. 5
Fig. 5

Simulated isothermal lines of Tout = 1051°C (blue line). (a) The outer structure (500°C) is shown by a green line (Aex = 45%), (b) Tin = 3000°C (Aex = 52%,), (c) Tin = 3000°C (Acal = 64.1%), (d) Tin = 3300°C (Acal = 74.2%), (e) Tin = 3800°C (Acal = 79.9%). (D263, m = 2 and M2 = 3.5).

Fig. 6
Fig. 6

Temperature variations on the laser axis TN(0,0,z;t) at z = 1µm and 12µm are plotted until N = 12, and thereafter only TNB(0,0,z;τ) is plotted. Pulse repetition rates f (kHz): (a) 50, (b) 200 and (c) 500 (v = 20mm/s, Q0 = 1.63µJ, M2 = 3.6)

Fig. 7
Fig. 7

Distribution of TSB(z) and TSP(z) plotted by thick and thin lines, respectively, at f = 50kHz, 200kHz and 500kHz (N→∞).

Fig. 8
Fig. 8

Thermal stress produced in CW-laser welding of glass where molten pool contains free surface. Tensile stress is produced in bar A when bar A is cooled down to room temperature ( + and represent tensile and compressive stress, respectively).

Fig. 9
Fig. 9

Thermal stress in USLP welding of glass where molten pool contains no free surface. While tensile stress is developed in heating period in bar B, no tensile is produced in Bar A, when bar A is cooled down to room temperature.

Fig. 10
Fig. 10

Relationship between ΔT and TSB at Q0 = 1.63µJ at different pulse repetition rates in D263. The region highlighted by green color corresponds to the crack-free condition in heating process.

Fig. 11
Fig. 11

(a) Experimental set up (f = 1MHz, Q0 = 1.6µJ). (b) Laser-irradiated region showing in region i internal melting (no cracks), (ii) cracks with melt region appeared at the rear surface and iii) no melting.

Fig. 12
Fig. 12

Top view of overlap welding at 20mm/s with varied gap distance between glass plates in D263 with irradiating green light (λ = 530nm) was irradiated

Equations (10)

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A ex =1 Q t Q 0 1 (1R) 2 ,
ω(z)= ω 0 1+ ( M 2 λz π ω 0 2 n g ) 2 ; ω 0 = M 2 λ πNA ,
q(r,z)= 2w(z) π ω 2 (z)f exp{ 2 r 2 ω 2 (z) }; 0zl,
T N (x,y,z;t)= 1 πcρf i=0 N1 1 πα( ti f 1 ) 0 l w(z') ω 2 (z')+8α( ti f 1 ) × exp[ 2{ ( x+v( ti f 1 ) ) 2 + y 2 } ω 2 (z')+8α( ti f 1 ) (zz') 2 4αt ]dz'.
T(x,y,z)= 1 4πK 0 l w(z') s exp{ v 2α ( x+s ) }dz'+ T 0 ,
w(z)=a z m +b; 0<z<l,
W ab = A cal W= 0 l w(z)dz ,
ΔT(z)= T N (0,0,z;0) T N1 (0,0,z;τ)= q(0,z) cρ ; (τ=1/f),
T SB (z)= lim N T N (0,0,z;τ), T SP (z)= lim N T N (0,0,z;0).
T SB > T soft

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