Abstract

By continuously scanning a femtosecond laser beam across a fused silica specimen, we demonstrate the formation of self-organized bubbles buried in the material. Rather than using high intensity pulses and high numerical aperture to induce explosions in the material, here bubbles form as a consequence of cumulative energy deposits. We observe a transition between chaotic and self-organized patterns at high scanning rate (above 10 mm/s). Through modeling the energy exchange, we outline the similarities of this phenomenon with other non-linear dynamical systems. Furthermore, we demonstrate with this method the high-speed writing of two- and three- dimensional bubble “crystals” in bulk silica.

© 2011 OSA

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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. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
    [CrossRef]
  3. G. Della Valle, S. Taccheo, R. Osellame, A. Festa, G. Cerullo, and P. Laporta, “1.5 mum single longitudinal mode waveguide laser fabricated by femtosecond laser writing,” Opt. Express 15(6), 3190–3194 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-6-3190 .
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

2010 (2)

2009 (1)

M. C. Ruzicka, “Dripping faucet and bubbling faucet: an analogy,” Chem. Eng. Res. Des. 87(10), 1366–1370 (2009).
[CrossRef]

2008 (5)

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008).
[CrossRef]

B. Poumellec, M. Lancry, J. C. Poulin, and S. Ani-Joseph, “Non reciprocal writing and chirality in femtosecond laser irradiated silica,” Opt. Express 16(22), 18354–18361 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-18354 .
[CrossRef] [PubMed]

Q. Sun, F. Liang, R. Vallée, and S. L. Chin, “Nanograting formation on the surface of silica glass by scanning focused femtosecond laser pulses,” Opt. Lett. 33(22), 2713–2715 (2008).
[CrossRef] [PubMed]

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

2007 (3)

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void formation in glasses,” N. J. Phys. 9(8), 253 (2007).
[CrossRef]

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

G. Della Valle, S. Taccheo, R. Osellame, A. Festa, G. Cerullo, and P. Laporta, “1.5 mum single longitudinal mode waveguide laser fabricated by femtosecond laser writing,” Opt. Express 15(6), 3190–3194 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-6-3190 .
[CrossRef] [PubMed]

2006 (1)

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

S. Juodkazis, H. Misawa, and I. Maksimov, “Thermal accumulation effect in three-dimensional recording by picosecond pulses,” Appl. Phys. Lett. 85(22), 5239–5241 (2004).
[CrossRef]

2003 (3)

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[CrossRef]

C. Schaffer, J. García, 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]

2002 (1)

X. Xu and D. A. Willis, “Non-equilibrium phase change in metal induced by nanosecond pulsed laser irradiation,” J. Heat Transfer 124(2), 293–298 (2002).
[CrossRef]

1997 (1)

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71(7), 882–884 (1997).
[CrossRef]

1996 (1)

1974 (1)

V. I. Goryunov, A. V. Dondoshanskaya, V. S. Metrikin, and R. F. Nagaev, “Periodic motions of an object above a surface vibrating according to an anharmonic law,” Prikl. Mekh. 10, 65–71 (1974).

Adams, D. E.

Ani-Joseph, S.

Apolonski, A.

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

Arai, A.

Backus, S.

Bellouard, Y.

Bian, H.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

Block, E.

Bovatsek, J.

Brueckner, H.

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[CrossRef]

Cerullo, G.

Chen, F.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

Cheng, Y.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Chichkov, B.

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

Chin, S. L.

Dai, Y.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Davis, K. M.

Della Valle, G.

Dondoshanskaya, A. V.

V. I. Goryunov, A. V. Dondoshanskaya, V. S. Metrikin, and R. F. Nagaev, “Periodic motions of an object above a surface vibrating according to an anharmonic law,” Prikl. Mekh. 10, 65–71 (1974).

Dubov, M.

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

Durfee, C. G.

Eaton, S.

Fernandez, A.

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

Festa, A.

Gamaly, E. G.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

García, J.

C. Schaffer, J. García, 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]

Glezer, E. N.

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71(7), 882–884 (1997).
[CrossRef]

Goryunov, V. I.

V. I. Goryunov, A. V. Dondoshanskaya, V. S. Metrikin, and R. F. Nagaev, “Periodic motions of an object above a surface vibrating according to an anharmonic law,” Prikl. Mekh. 10, 65–71 (1974).

Graf, R.

R. Graf, A. Fernandez, M. Dubov, H. Brueckner, B. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87(1), 21–27 (2007).
[CrossRef]

Hallo, L.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

Hashimoto, T.

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void formation in glasses,” N. J. Phys. 9(8), 253 (2007).
[CrossRef]

Herman, P.

Hirao, K.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[CrossRef] [PubMed]

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]

Hou, X.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

Hu, X.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Juodkazis, S.

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void formation in glasses,” N. J. Phys. 9(8), 253 (2007).
[CrossRef]

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

S. Juodkazis, H. Misawa, and I. Maksimov, “Thermal accumulation effect in three-dimensional recording by picosecond pulses,” Appl. Phys. Lett. 85(22), 5239–5241 (2004).
[CrossRef]

Kamata, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Kazansky, P. G.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008).
[CrossRef]

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[CrossRef] [PubMed]

Kleinfeld, D.

Lancry, M.

Laporta, P.

Liang, F.

Liu, H.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

Luther-Davies, B.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

Maksimov, I.

S. Juodkazis, H. Misawa, and I. Maksimov, “Thermal accumulation effect in three-dimensional recording by picosecond pulses,” Appl. Phys. Lett. 85(22), 5239–5241 (2004).
[CrossRef]

Mazur, E.

C. Schaffer, J. García, 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]

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71(7), 882–884 (1997).
[CrossRef]

Metrikin, V. S.

V. I. Goryunov, A. V. Dondoshanskaya, V. S. Metrikin, and R. F. Nagaev, “Periodic motions of an object above a surface vibrating according to an anharmonic law,” Prikl. Mekh. 10, 65–71 (1974).

Misawa, H.

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void formation in glasses,” N. J. Phys. 9(8), 253 (2007).
[CrossRef]

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

S. Juodkazis, H. Misawa, and I. Maksimov, “Thermal accumulation effect in three-dimensional recording by picosecond pulses,” Appl. Phys. Lett. 85(22), 5239–5241 (2004).
[CrossRef]

Miura, K.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (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]

Nagaev, R. F.

V. I. Goryunov, A. V. Dondoshanskaya, V. S. Metrikin, and R. F. Nagaev, “Periodic motions of an object above a surface vibrating according to an anharmonic law,” Prikl. Mekh. 10, 65–71 (1974).

Nicolai, P.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

Nishimura, K.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[CrossRef]

Obara, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Osellame, R.

Poulin, J. C.

Poumellec, B.

Qiu, J.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[CrossRef] [PubMed]

Rajesh, S.

Ruzicka, M. C.

M. C. Ruzicka, “Dripping faucet and bubbling faucet: an analogy,” Chem. Eng. Res. Des. 87(10), 1366–1370 (2009).
[CrossRef]

Sakakura, M.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

Schaffer, C.

C. Schaffer, J. García, 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]

Shah, L.

Shimotsuma, Y.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[CrossRef] [PubMed]

Si, J.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

Song, J.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Squier, J. A.

Sugimoto, N.

Sun, Q.

Svirko, Y. P.

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008).
[CrossRef]

Taccheo, S.

Tanaka, S.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

Tikhonchuk, V. T.

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

Toratani, E.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Tuennermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[CrossRef]

Vallée, R.

Vitek, D. N.

Wang, X.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[CrossRef]

Willis, D. A.

X. Xu and D. A. Willis, “Non-equilibrium phase change in metal induced by nanosecond pulsed laser irradiation,” J. Heat Transfer 124(2), 293–298 (2002).
[CrossRef]

Xu, X.

X. Xu and D. A. Willis, “Non-equilibrium phase change in metal induced by nanosecond pulsed laser irradiation,” J. Heat Transfer 124(2), 293–298 (2002).
[CrossRef]

Xu, Z.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Yang, Q.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

Yang, W.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008).
[CrossRef]

Yoshino, F.

Zhang, H.

Appl. Phys. B (1)

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[CrossRef]

Appl. Phys. Lett. (5)

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
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[CrossRef]

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (3)

C. Schaffer, J. García, 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]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys., A Mater. Sci. Process. 77(1), 109–111 (2003).
[CrossRef]

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys., A Mater. Sci. Process. 102(1), 39–44 (2011).
[CrossRef]

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M. C. Ruzicka, “Dripping faucet and bubbling faucet: an analogy,” Chem. Eng. Res. Des. 87(10), 1366–1370 (2009).
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J. Heat Transfer (1)

X. Xu and D. A. Willis, “Non-equilibrium phase change in metal induced by nanosecond pulsed laser irradiation,” J. Heat Transfer 124(2), 293–298 (2002).
[CrossRef]

N. J. Phys. (1)

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void formation in glasses,” N. J. Phys. 9(8), 253 (2007).
[CrossRef]

Nat. Photonics (1)

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[CrossRef] [PubMed]

S. Juodkazis, K. Nishimura, S. Tanaka, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Laser-induced microexplosion confined in the bulk of a sapphire crystal: evidence of multimegabar pressures,” Phys. Rev. Lett. 96(16), 166101 (2006).
[CrossRef] [PubMed]

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V. I. Goryunov, A. V. Dondoshanskaya, V. S. Metrikin, and R. F. Nagaev, “Periodic motions of an object above a surface vibrating according to an anharmonic law,” Prikl. Mekh. 10, 65–71 (1974).

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Figures (11)

Fig. 1
Fig. 1

Effect of increasing writing speeds: top-view microscopic images (bright field, bottom illumination). All the lines are written with the same pulse energy (300 nJ). The repetition rate is 9.4 MHz. The images on the right are lines written in the opposite direction from the ones shown on the left side and for the same velocity parameters. (The writing direction is indicated by an arrow at the bottom of the figure.) Lines are located 190 +/− 10µm below the surface. The images are taken with a bottom illumination.

Fig. 2
Fig. 2

Left: Effect of writing speeds, side view of bubble patterns. The patterns were written at increasing higher speeds. The pulse energy was 250 nJ. The NA was 0.3. Right: Typical ‘single bubble pattern’ as observed in a SEM. The specimen is viewed at an angle in the SEM and therefore, looks smaller than it is in reality. Pulse energy was 210 nJ. The laser affected zone has a comet shape in which bubbles are found.

Fig. 3
Fig. 3

Effect of increasing the pulse energy at a constant writing speed (30 mm/s). The patterns were written approximately 200 µm below the surface. The thermally affected zones surrounding bubbles are clearly visible (in particular at low energies where they are isolated one from another). The gradual increase of the laser affected zone width with the pulse energy is a clear signature of a thermal process.

Fig. 4
Fig. 4

Two-dimensional array of bubbles. Each line is written at 30mm/s and along the same direction.

Fig. 5
Fig. 5

Transmission optical microscope images of a large array of bubbles. The total area covered is 25 mm2 and was written in less than a minute. The writing speed was 30 mm/s. The pattern here consists of a large bubble and a smaller one. The spacing between bubbles patterns is 31 μm. The inset shows a few bubbles seen at higher magnification. The image is focused on the smaller bubble illustrating the fact that large and small bubbles lie on different planes (a few µm apart).

Fig. 6
Fig. 6

Three-dimensional network of bubbles. Images are taken with an optical microscope (20X objective). The three images on the left are taken using dark-field microscopy and illustrate the regularity of the spatial arrangement. The bottom-right image shows the cross section of the 3D assembly and the top-right image a portion of the structure seen from the top surface. Scale bar is 100 µm.

Fig. 7
Fig. 7

Evidences of ‘frozen-in’ bubble coalescence events. These patterns were written with the conditions described in Fig. 1 (speed were 27 mm/s to 29 mm/s). The pattern length is shown. This parameter will be used in Fig. 11.

Fig. 8
Fig. 8

Illustration of the deposition of energy in the system.

Fig. 9
Fig. 9

Qualitative fluid analogy of the laser energy accumulation-discharge process. When the water level in the vessel fills the siphon elbow, (i.e high Wcr), auto-siphoning is triggered. For high elbows, (i.e. high Wcr), the auto-siphoning purge of the system is triggered. For high elbows, random stationary fluctuations in the faucet flow are smoothed out due to the law of large numbers.

Fig. 10
Fig. 10

Qualitative sketch of the iterative mapping (see Eq. (2)).

Fig. 11
Fig. 11

Pattern length distributions as a function of the laser writing velocity for the two sets of experiments presented in Fig. 1. We define the pattern length as the length measured along the writing direction of the bubble patterns (see Fig. 7). Each point corresponds to the average of measured pattern length separated by less than three times the standard deviation of the measurement methods. The various regimes are highlighted and the figure illustrates a series of cascade of bifurcations as theoretically predicted.

Equations (17)

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J = η exp ( E b k B T ) w i t h η = N ( 3 σ π m )
ε ( t ) = k a k δ ( t k Δ )
ε x ( t ) k = K min K max a k δ ( t k Δ )
K min = [ ( x w 0 ) v t ] a n d K max = [ ( x + w 0 ) v t ]
{ τ n + 1 = τ n + Ξ α ( φ n ) + S α ( τ n , φ n ) + D α ( τ n , φ n ) φ n + 1 = γ φ n + Θ α [ Ξ α ( φ n ) ]
( τ n + 1 φ n + 1 ) = ( 1 α 0 1 ) : = M ( τ n φ n ) + ( S + D 0 )
Ξ α ( φ n ) = α φ n , Θ α [ Ξ α ( φ n ) ] = [ ( 1 γ ) / α ] Ξ α ( φ n ) , S α ( τ n , φ n ) = S , D α ( τ n , φ n ) = D .
τ n = τ 0 + n P , φ n φ s = ( P S D ) / α
{ t n + 1 = t n + 1 α Ξ α ( φ n ) + D α φ n + 1 = γ φ n + Θ [ 1 α Ξ α ( φ n ) ]
φ n + 1 = γ φ n + Θ [ 1 α Ξ α ( φ n ) ] > 0 t n .
Θ [ P + 1 α Ξ α ( φ n ) ] = Θ [ 1 α Ξ α ( φ n ) ]
{ t n + 1 = t n + φ n + D α φ n + 1 = γ φ n + Θ α ( t n + 1 )
t n = t 0 + k P , k a n d φ n = φ s , n
Θ ( t 0 + φ s ) + ( γ 1 ) φ s = 0
L α ( t 0 , φ s ) = ( 1 1 Θ α t γ + Θ α φ ) ( φ = φ s , t = t 0 ) = ( 1 1 Θ ' α γ + Θ ' α )
| λ ± | = | 1 2 { [ 1 + γ + Θ α ' ] ± [ 1 + γ + Θ α ' ] 2 4 γ } | < 1
| λ + + λ | = | [ 1 + γ + Θ α ' ] | < 2 a n d λ + . λ = γ .

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