Abstract

Local melting and modulation of elemental distributions can be induced inside a glass by focusing femtosecond (fs) laser pulses at high repetition rate (>100 kHz). Using only a single beam of fs laser pulses, the shape of the molten region is ellipsoidal, so the induced elemental distributions are often circular and elongate in the laser propagation direction. In this study, we show that the elongation of the fs laser-induced elemental distributions inside a soda-lime glass could be suppressed by parallel fsing of 250 kHz and 1 kHz fs laser pulses. The thickness of a Si-rich region became about twice thinner than that of a single 250 kHz laser irradiation. Interestingly, the position of the Si-rich region depended on the relative positions between 1 kHz and 250 kHz photoexcited regions. The observation of glass melt during laser exposure showed that the vortex flow of glass melt occurred and it induced the formation of a Si-rich region. Based on the simulation of the transient temperature and viscosity distributions during laser exposure, we temporally interpreted the origin of the vortex flow of glass melt and the mechanism of the formation of the Si-rich region.

© 2014 Optical Society of America

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    [CrossRef]

2013 (3)

2012 (4)

2011 (4)

2010 (3)

F. Luo, B. Qian, G. Lin, J. Xu, Y. Liao, J. Song, H. Sun, B. Zhu, J. Qiu, Q. Zhao, and Z. Xu, “Redistribution of elements in glass induced by a high-repetition-rate femtosecond laser,” Opt. Express18(6), 6262–6269 (2010).
[CrossRef] [PubMed]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

2009 (1)

2008 (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(23), 231112 (2008).
[CrossRef]

S. Kanehira, K. Miura, and K. Hirao, “Ion exchange in glass using femtosecond laser irradiation,” Appl. Phys. Lett.93(2), 023112 (2008).
[CrossRef]

2007 (2)

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

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

2005 (6)

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B81(8), 1015–1047 (2005).
[CrossRef]

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Phys. Rev. B71(2), 024113 (2005).
[CrossRef]

D. Rayner, A. Naumov, and P. Corkum, “Ultrashort pulse non-linear optical absorption in transparent media,” Opt. Express13(9), 3208–3217 (2005).
[CrossRef] [PubMed]

S. K. Lee, “Microscopic origins of macroscopic properties of silicate melts and glasses at ambient and high pressure: Implications for melt generation and dynamics,” Geochim. Cosmochim. Acta69(14), 3695–3710 (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]

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett.87(3), 031101 (2005).
[CrossRef]

2003 (1)

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process.76(3), 351–354 (2003).
[CrossRef]

1998 (1)

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng.19(3), 193297 (1980).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Arai, A. Y.

Bellec, M.

Bellouard, Y.

Booth, M. J.

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

Bourhis, K.

Bovatsek, J.

Burmeister, F.

Canioni, L.

Cardinal, T.

Chen, G.

Choi, J.

Corkum, P.

Cvecek, K.

Dai, Y.

Dierolf, V.

Döring, S.

Du, Y.

Eaton, S. M.

Erraji-Chahid, A.

Fan, C.

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng.19(3), 193297 (1980).
[CrossRef]

Fukuda, N.

Garcia, J. F.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process.76(3), 351–354 (2003).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

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

Gupta, P.

Han, Y.

Hayasaki, Y.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett.87(3), 031101 (2005).
[CrossRef]

He, X.

Herman, P. R.

Hirao, K.

M. Sakakura, T. Kurita, M. Shimizu, K. Yoshimura, Y. Shimotsuma, N. Fukuda, K. Hirao, and K. Miura, “Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots,” Opt. Lett.38(23), 4939–4942 (2013).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, “Directionally controlled 3D ferroelectric single crystal growth in LaBGeO5 glass by femtosecond laser irradiation,” Opt. Express17(25), 23284–23289 (2009).
[CrossRef] [PubMed]

S. Kanehira, K. Miura, and K. Hirao, “Ion exchange in glass using femtosecond laser irradiation,” Appl. Phys. Lett.93(2), 023112 (2008).
[CrossRef]

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(23), 231112 (2008).
[CrossRef]

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

Hongler, M.-O.

Horn, A.

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

Hüttman, G.

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B81(8), 1015–1047 (2005).
[CrossRef]

Iida, M.

Jain, H.

Kanehira, S.

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

S. Kanehira, K. Miura, and K. Hirao, “Ion exchange in glass using femtosecond laser irradiation,” Appl. Phys. Lett.93(2), 023112 (2008).
[CrossRef]

Kurita, T.

Lancry, M.

Lee, S. K.

S. K. Lee, “Microscopic origins of macroscopic properties of silicate melts and glasses at ambient and high pressure: Implications for melt generation and dynamics,” Geochim. Cosmochim. Acta69(14), 3695–3710 (2005).
[CrossRef]

Liao, Y.

Lin, G.

Liu, Q.

Lu, B.

Luo, F.

Ma, H.

Makimura, T.

Mazur, E.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process.76(3), 351–354 (2003).
[CrossRef]

Micorikawa, K.

Midorikawa, K.

Miura, K.

M. Sakakura, T. Kurita, M. Shimizu, K. Yoshimura, Y. Shimotsuma, N. Fukuda, K. Hirao, and K. Miura, “Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots,” Opt. Lett.38(23), 4939–4942 (2013).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, “Directionally controlled 3D ferroelectric single crystal growth in LaBGeO5 glass by femtosecond laser irradiation,” Opt. Express17(25), 23284–23289 (2009).
[CrossRef] [PubMed]

S. Kanehira, K. Miura, and K. Hirao, “Ion exchange in glass using femtosecond laser irradiation,” Appl. Phys. Lett.93(2), 023112 (2008).
[CrossRef]

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(23), 231112 (2008).
[CrossRef]

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

Miyamoto, I.

I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express19(11), 10714–10727 (2011).
[CrossRef] [PubMed]

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

Nakaya, T.

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

Naumov, A.

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

Nishi, M.

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

Nishida, N.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett.87(3), 031101 (2005).
[CrossRef]

Noack, J.

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B81(8), 1015–1047 (2005).
[CrossRef]

Nolte, S.

Ohnishi, M.

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

Paltauf, G.

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B81(8), 1015–1047 (2005).
[CrossRef]

Papon, G.

Poumellec, B.

Qian, B.

Qiu, J.

Rayner, D.

Richardson, M.

Richter, S.

Royon, A.

Sakakura, M.

M. Sakakura, T. Kurita, M. Shimizu, K. Yoshimura, Y. Shimotsuma, N. Fukuda, K. Hirao, and K. Miura, “Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots,” Opt. Lett.38(23), 4939–4942 (2013).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, “Directionally controlled 3D ferroelectric single crystal growth in LaBGeO5 glass by femtosecond laser irradiation,” Opt. Express17(25), 23284–23289 (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 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Phys. Rev. B71(2), 024113 (2005).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Schaffer, C. B.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process.76(3), 351–354 (2003).
[CrossRef]

Schmidt, M.

Shah, L.

Shimizu, M.

M. Sakakura, T. Kurita, M. Shimizu, K. Yoshimura, Y. Shimotsuma, N. Fukuda, K. Hirao, and K. Miura, “Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots,” Opt. Lett.38(23), 4939–4942 (2013).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

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(23), 231112 (2008).
[CrossRef]

Shimotsuma, Y.

M. Sakakura, T. Kurita, M. Shimizu, K. Yoshimura, Y. Shimotsuma, N. Fukuda, K. Hirao, and K. Miura, “Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots,” Opt. Lett.38(23), 4939–4942 (2013).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, “Formation mechanism of element distribution in glass under femtosecond laser irradiation,” Opt. Lett.36(11), 2161–2163 (2011).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, “Directionally controlled 3D ferroelectric single crystal growth in LaBGeO5 glass by femtosecond laser irradiation,” Opt. Express17(25), 23284–23289 (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 250kHz irradiation of femtosecond laser pulses,” Appl. Phys. Lett.93(23), 231112 (2008).
[CrossRef]

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

Song, J.

Stone, A.

Stone, G.

Sugimoto, T.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett.87(3), 031101 (2005).
[CrossRef]

Sugioka, K.

Sun, H.

Takai, H.

Takita, A.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett.87(3), 031101 (2005).
[CrossRef]

Terazima, M.

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Phys. Rev. B71(2), 024113 (2005).
[CrossRef]

Tünnermann, A.

Vogel, A.

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B81(8), 1015–1047 (2005).
[CrossRef]

Wang, H.

Wilson, T.

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

Wu, D.

Wu, S.

Xu, J.

Xu, Z.

Yamaji, M.

Yoshimura, K.

Yoshino, F.

Zeng, H.

Zeng, X.

Zhang, H.

Zhao, Q.

Zhong, M.

Zhu, B.

Zimmermann, F.

Appl. Phys. B (1)

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B81(8), 1015–1047 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

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(23), 231112 (2008).
[CrossRef]

S. Kanehira, K. Miura, and K. Hirao, “Ion exchange in glass using femtosecond laser irradiation,” Appl. Phys. Lett.93(2), 023112 (2008).
[CrossRef]

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett.87(3), 031101 (2005).
[CrossRef]

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

M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, “Space-selective phase separation inside a glass by controlling compositional distribution with femtosecond-laser irradiation,” Appl. Phys., A Mater. Sci. Process.100(4), 1001–1005 (2010).
[CrossRef]

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process.76(3), 351–354 (2003).
[CrossRef]

Geochim. Cosmochim. Acta (1)

S. K. Lee, “Microscopic origins of macroscopic properties of silicate melts and glasses at ambient and high pressure: Implications for melt generation and dynamics,” Geochim. Cosmochim. Acta69(14), 3695–3710 (2005).
[CrossRef]

J. Appl. Phys. (1)

M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys.108(7), 073533 (2010).
[CrossRef]

J. Laser Micro. Nanoeng. (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 Micro. Nanoeng.2(1), 7–14 (2007).
[CrossRef]

J. Microsc. (1)

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192(2), 90–98 (1998).
[CrossRef]

Opt. Eng. (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng.19(3), 193297 (1980).
[CrossRef]

Opt. Express (10)

F. Luo, B. Qian, G. Lin, J. Xu, Y. Liao, J. Song, H. Sun, B. Zhu, J. Qiu, Q. Zhao, and Z. Xu, “Redistribution of elements in glass induced by a high-repetition-rate femtosecond laser,” Opt. Express18(6), 6262–6269 (2010).
[CrossRef] [PubMed]

M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express15(25), 16800–16807 (2007).
[CrossRef] [PubMed]

S. Richter, S. Döring, F. Burmeister, F. Zimmermann, A. Tünnermann, and S. Nolte, “Formation of periodic disruptions induced by heat accumulation of femtosecond laser pulses,” Opt. Express21(13), 15452–15463 (2013).
[CrossRef] [PubMed]

D. Rayner, A. Naumov, and P. Corkum, “Ultrashort pulse non-linear optical absorption in transparent media,” Opt. Express13(9), 3208–3217 (2005).
[CrossRef] [PubMed]

I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express19(11), 10714–10727 (2011).
[CrossRef] [PubMed]

M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, “Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates,” Opt. Express20(2), 934–940 (2012).
[CrossRef] [PubMed]

S. Wu, D. Wu, J. Xu, H. Wang, T. Makimura, K. Sugioka, and K. Midorikawa, “Absorption mechanism of the second pulse in double-pulse femtosecond laser glass microwelding,” Opt. Express21(20), 24049–24059 (2013).
[CrossRef] [PubMed]

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]

A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, “Directionally controlled 3D ferroelectric single crystal growth in LaBGeO5 glass by femtosecond laser irradiation,” Opt. Express17(25), 23284–23289 (2009).
[CrossRef] [PubMed]

Y. Bellouard and M.-O. Hongler, “Femtosecond-laser generation of self-organized bubble patterns in fused silica,” Opt. Express19(7), 6807–6821 (2011).
[CrossRef] [PubMed]

Opt. Lett. (5)

Opt. Mater. Express (1)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Phys. Rev. B (1)

M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Phys. Rev. B71(2), 024113 (2005).
[CrossRef]

Other (4)

R. Dennemeyer, Introduction to Partial Differential Equations and Boundary Value Problems (McGraw-Hill, 1968), p. 294.

G. R. Fowles, Introduction to Modern Optics (Dover, 1975), Chap. 5.

Glass data sheet from Schott: http://psec.uchicago.edu/glass/Schott%20B270%20Properties%20-%20Knight%20Optical.pdf

A. K. Varshneya, Fundamentals of Inorganic Glasses (Academic, 1993), Chaps. 1, 3, and 9.

Supplementary Material (2)

» Media 1: MP4 (2061 KB)     
» Media 2: MP4 (1980 KB)     

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Figures (6)

Fig. 1
Fig. 1

(a) Parallel laser irradiation system with two fs laser sources and a spatial light modulator. BS: a polarization beam splitter; DM: dichroic mirror, which reflects light around 800 nm; OL is an objective lens; L1, L2: lenses of focal lengths of 220 mm and 90 mm, respectively; CCDs: charge coupled device camera. (b) Schematic illustration of focusing of 250 kHz and 1 kHz laser pulses at multiple spots.

Fig. 2
Fig. 2

(a) Simulated intensity distributions along the beam axis of 250 kHz and 1 kHz laser pulses. The red broken line indicates the geometrical focus of the laser beam. (b) Light intensity at the maximum plotted against along z. Red dots are simulated intensities, and the black lines are fitting by Eq. (3).

Fig. 3
Fig. 3

(a), (b) Optical microscope images of the fs laser-induced modifications inside a soda-lime glass observed perpendicular to the laser propagation axis. (a) The modification by 250 kHz laser beam at a single spot and (b) that by multi-spots’ irradiation, respectively. (c), (d) The EPMA images of Si, Ca and K along the beam axis in the modifications of (a) and (b), respectively. The color bars indicate the relative signal intensity of Si and Ca in the EPMA. The signal intensity in the unmodified region is 100.

Fig. 4
Fig. 4

Distributions of Si and Ca of different relative depth (Δd) between the focal positions of 250 kHz and 1 kHz fs laser pulses. The broken line is the geometrically calculated focal plane of 250 kHz pulses and the cross marks ( × ) are the focal positions of the 1 kHz pulses. These focal positions were calculated based on the geometrical optics and Fresnel lens patterns added to the phase hologram.

Fig. 5
Fig. 5

(a), (b) Snap shot of the transmission optical microscope images of glass melt during laser exposure viewed perpendicular to the laser propagation direction by the CCD-2. The differences in focal depth of 250 kHz and 1 kHz laser pulses in (a) and (b) were Δd = + 15 μm (Media 1) and −15 μm (Media 2), respectively. The cross marks ( × ) at 0.1 s indicate the focused positions of 1 kHz pulses, which were calculated using geometrical optics. The observed flows of melt were drawn by red arrows in the images at 2.0 s. (c) Proposed model of Si condensation upper in the molten region in the case of Δd = + 15 μm. The arrows indicate flow of melts. η means viscosity.

Fig. 6
Fig. 6

(a) Simulated temperature distribution during laser exposure at Δd = + 15 μm. (b) Viscosity distributions calculated by the temperature distribution of (a) and temperature dependent viscosity of a soda-lime glass. (c) Viscosity distributions with the regions of 103-103.5 Pa∙s drawn in black. The blown lines indicate the expected flow of glass melt through the transiently formed channels.

Tables (2)

Tables Icon

Table 1 Parameters for expressing the heat sources in the temperature simulation.

Tables Icon

Table 2 Parameters for the temperature and diffusion simulation [19]. λt does not include the thermal conduction by radiation. Q250kHz was estimated by the modification by irradiation with a single 250 kHz laser pulses, and Q1kHz was estimated by the absorptivity (75%) and pulse energy just after the objective lens (10 μJ at each spot).

Equations (3)

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T( t,r ) t = λ t ρ C p ( 2 x 2 + 2 y 2 + 2 z 2 )T( t,r )+ 1 ρ C p Q ( t,r )
Q ( t,r )= n=0 N 250kHz 1 Q 250Hz δ(tnΔ t 250kHz ) f 250kHz (r) + k=1 4 n=0 N 1kHz 1 Q 1kHz δ(tnΔ t 1kHz ) f 1kHz (r- R k )
f X ( r ) = A X * exp ( x 2 + y 2 ( w th / 2 ) 2 ) [ p X * exp { ( z Z X1 L X1 / 2 ) 2 } + ( 1 p X ) * exp { ( z Z X2 L X2 / 2 ) 2 } ]

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