Abstract

We report on a systematic investigation of selective etching of fs-laser inscribed microstructures in Y3Al5O12 (YAG). The resulting microchannels are up to 8.9 mm long and exhibit cross sections from below 10 µm to more than 100 µm. Aspect ratios of up to 593 were achieved. Investigations with different structuring and etching parameters revealed that the etching process is mainly diffusion determined. The etching depth depends on the square root of time, similar to the well-known Brownian motion. In addition, we could enhance the etching diffusion constant by a factor of two, reducing the time to etch the longest channel by an order of magnitude, using a 1:1 mixture of sulfuric and phosphoric acid instead of pure phosphoric acid. The observed fundamental time dependence in conjunction with diffusion coefficients up to 160 µm/h1/2 makes the etching behavior highly predictable and paves the way toward arbitrary three-dimensional micro- and nanostructuring over long distances in crystalline materials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

2018 (1)

2017 (1)

2015 (2)

K. Hasse, T. Calmano, B. Deppe, C. Liebald, and C. Kränkel, “Efficient Yb3+:CaGdAlO4 bulk and femtosecond-laser-written waveguide lasers,” Opt. Lett. 40(15), 3552 (2015).
[Crossref]

T. Calmano and S. Müller, “Crystalline Waveguide Lasers in the Visible and Near-Infrared Spectral Range,” IEEE J. Sel. Top. Quantum Electron. 21(1), 401–413 (2015).
[Crossref]

2014 (4)

F. Chen and J. R. V. de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond- laser micromachining,” Laser Photonics Rev. 8(2), 251–275 (2014).
[Crossref]

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

K. Sugioka and Y. Cheng, “Femtosecond laser three-dimensional micro- and nanofabrication,” Appl. Phys. Rev. 1(4), 041303 (2014).
[Crossref]

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

2013 (1)

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

2012 (1)

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

2011 (1)

C. Grivas, “Optically pumped planar waveguide lasers, Part I : Fundamentals and fabrication techniques,” Prog. Quantum Electron. 35(6), 159–239 (2011).
[Crossref]

2010 (2)

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

2009 (2)

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femtosecond laser microfabrication of channels inside vitreous silica substrates,” J. Phys. Chem. C 113(27), 11560–11566 (2009).
[Crossref]

J. Siebenmorgen and K. Petermann, “Femtosecond laser written stress-induced Nd: Y3Al5O12 (Nd: YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

2008 (2)

2006 (1)

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

2005 (4)

A. G. Okhrimchuk and A. V. Shestakov, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30(17), 2248–2250 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

1999 (1)

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

1990 (1)

1923 (1)

C. V. Raman, “A theory of the viscosity of liquids,” Nature 111(2790), 532–533 (1923).
[Crossref]

1906 (1)

M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
[Crossref]

1905 (1)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. 322(8), 549–560 (1905).
[Crossref]

Benayas, A.

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Berthou, H.

Bhardwaj, V. R.

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

Brandt, N.

Calmano, T.

Cerullo, G.

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Chapman, H. N.

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

Chen, F.

F. Chen and J. R. V. de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond- laser micromachining,” Laser Photonics Rev. 8(2), 251–275 (2014).
[Crossref]

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Cheng, Y.

K. Sugioka and Y. Cheng, “Femtosecond laser three-dimensional micro- and nanofabrication,” Appl. Phys. Rev. 1(4), 041303 (2014).
[Crossref]

Choudhury, D.

C. A. Ross, D. G. MacLachlan, D. Choudhury, and R. R. Thomson, “Optimisation of ultrafast laser assisted etching in fused silica,” Opt. Express 26(19), 24343 (2018).
[Crossref]

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Corkum, P. B.

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

Corrielli, G.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

de Aldana, J. R. V.

F. Chen and J. R. V. de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond- laser micromachining,” Laser Photonics Rev. 8(2), 251–275 (2014).
[Crossref]

Deponte, D.

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

Deppe, B.

Díaz, F.

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

Ebisui, T.

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Einstein, A.

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. 322(8), 549–560 (1905).
[Crossref]

Förster, S.

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Gong, Q.

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

Gottmann, J.

Grivas, C.

C. Grivas, “Optically pumped planar waveguide lasers, Part I : Fundamentals and fabrication techniques,” Prog. Quantum Electron. 35(6), 159–239 (2011).
[Crossref]

Gu, M.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

Hashimoto, S.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femtosecond laser microfabrication of channels inside vitreous silica substrates,” J. Phys. Chem. C 113(27), 11560–11566 (2009).
[Crossref]

Hasse, K.

Hirao, K.

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

Hnatovsky, C.

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

Horn-Solle, H.

Jaque, D.

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Jiang, H.

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

John, S.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

Jornod, N.

Juodkazis, S.

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Kar, A. K.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Keller, U.

Kiss, R.

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Kiyama, S.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femtosecond laser microfabrication of channels inside vitreous silica substrates,” J. Phys. Chem. C 113(27), 11560–11566 (2009).
[Crossref]

Kondo, Y.

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

Kränkel, C.

Krüger, K.

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

Liebald, C.

Liu, Y.

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

Macdonald, J. R.

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

MacLachlan, D. G.

Matsuo, S.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femtosecond laser microfabrication of channels inside vitreous silica substrates,” J. Phys. Chem. C 113(27), 11560–11566 (2009).
[Crossref]

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Metrangolo, P.

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Misawa, H.

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Mitsuyu, T.

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

Morihira, Y.

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femtosecond laser microfabrication of channels inside vitreous silica substrates,” J. Phys. Chem. C 113(27), 11560–11566 (2009).
[Crossref]

Müller, S.

T. Calmano and S. Müller, “Crystalline Waveguide Lasers in the Visible and Near-Infrared Spectral Range,” IEEE J. Sel. Top. Quantum Electron. 21(1), 401–413 (2015).
[Crossref]

Navarrini, W.

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Nishimura, K.

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Okada, T.

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Okhrimchuk, A. G.

Osellame, R.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Paiè, P.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

Paterson, L.

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Petermann, K.

J. Siebenmorgen and K. Petermann, “Femtosecond laser written stress-induced Nd: Y3Al5O12 (Nd: YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

Qiu, J.

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

Raman, C. V.

C. V. Raman, “A theory of the viscosity of liquids,” Nature 111(2790), 532–533 (1923).
[Crossref]

Ramsay, W. T.

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Rayner, D. M.

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

Resnati, G.

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Ródenas, A.

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

Ross, C. A.

Roth, S. V.

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

Shestakov, A. V.

Siebenmorgen, J.

J. Siebenmorgen and K. Petermann, “Femtosecond laser written stress-induced Nd: Y3Al5O12 (Nd: YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

Simova, E.

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

Südmeyer, T.

Sugioka, K.

K. Sugioka and Y. Cheng, “Femtosecond laser three-dimensional micro- and nanofabrication,” Appl. Phys. Rev. 1(4), 041303 (2014).
[Crossref]

Sun, Q.

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

Tan, Y.

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Taylor, R. S.

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30(14), 1867 (2005).
[Crossref]

Thomson, R. R.

Torchia, G. A.

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Trebbin, M.

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

Vazquez, R. M.

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

Vázquez De Aldana, J. R.

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Venturini, F.

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

von Smoluchowski, M.

M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
[Crossref]

Waki, R.

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Waldburger, D.

Willoughby, N. A.

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Wittwer, V. J.

Wortmann, D.

Yang, H.

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

Yoko, T.

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

Zhou, Y.

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

Adv. Mater. (1)

S. Juodkazis, K. Nishimura, H. Misawa, T. Ebisui, R. Waki, S. Matsuo, and T. Okada, “Control over the crystalline state of sapphire,” Adv. Mater. 18(11), 1361–1364 (2006).
[Crossref]

Ann. Phys. (2)

M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
[Crossref]

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. 322(8), 549–560 (1905).
[Crossref]

Appl. Phys. B: Lasers Opt. (1)

J. Siebenmorgen and K. Petermann, “Femtosecond laser written stress-induced Nd: Y3Al5O12 (Nd: YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

Appl. Phys. Lett. (2)

D. Choudhury, A. Ródenas, L. Paterson, F. Díaz, D. Jaque, and A. K. Kar, “Three-dimensional microstructuring of yttrium aluminum garnet crystals for laser active optofluidic applications,” Appl. Phys. Lett. 103(4), 041101 (2013).
[Crossref]

Y. Tan, F. Chen, J. R. Vázquez De Aldana, G. A. Torchia, A. Benayas, and D. Jaque, “Continuous wave laser generation at 1064 nm in femtosecond laser inscribed Nd: YVO4 channel waveguides,” Appl. Phys. Lett. 97(3), 031119 (2010).
[Crossref]

Appl. Phys. Rev. (1)

K. Sugioka and Y. Cheng, “Femtosecond laser three-dimensional micro- and nanofabrication,” Appl. Phys. Rev. 1(4), 041303 (2014).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Calmano and S. Müller, “Crystalline Waveguide Lasers in the Visible and Near-Infrared Spectral Range,” IEEE J. Sel. Top. Quantum Electron. 21(1), 401–413 (2015).
[Crossref]

J. Appl. Phys. (1)

C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations,” J. Appl. Phys. 98(1), 013517 (2005).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A: Pure Appl. Opt. 7(11), 655–659 (2005).
[Crossref]

J. Phys. Chem. C (2)

F. Venturini, W. Navarrini, G. Resnati, P. Metrangolo, R. M. Vazquez, R. Osellame, and G. Cerullo, “Selective iterative etching of fused silica with gaseous hydrofluoric acid,” J. Phys. Chem. C 114(43), 18712–18716 (2010).
[Crossref]

S. Kiyama, S. Matsuo, S. Hashimoto, and Y. Morihira, “Examination of etching agent and etching mechanism on femtosecond laser microfabrication of channels inside vitreous silica substrates,” J. Phys. Chem. C 113(27), 11560–11566 (2009).
[Crossref]

Jpn. J. Appl. Phys. (1)

Y. Kondo, J. Qiu, T. Mitsuyu, K. Hirao, and T. Yoko, “Three-dimensional microdrilling of glass by multiphoton process and chemical etching,” Jpn. J. Appl. Phys. 38(Part 2), L1146–L1148 (1999).
[Crossref]

Lab Chip (2)

M. Trebbin, K. Krüger, D. Deponte, S. V. Roth, H. N. Chapman, and S. Förster, “Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions,” Lab Chip 14(10), 1733–1745 (2014).
[Crossref]

D. Choudhury, W. T. Ramsay, R. Kiss, N. A. Willoughby, L. Paterson, and A. K. Kar, “A 3D mammalian cell separator biochip,” Lab Chip 12(5), 948–953 (2012).
[Crossref]

Laser Photonics Rev. (2)

F. Chen and J. R. V. de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond- laser micromachining,” Laser Photonics Rev. 8(2), 251–275 (2014).
[Crossref]

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

Nat. Photonics (2)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

A. Ródenas, M. Gu, G. Corrielli, P. Paiè, S. John, A. K. Kar, and R. Osellame, “Three-dimensional femtosecond laser nanolithography of crystals,” Nat. Photonics 13(2), 105–109 (2019).
[Crossref]

Nature (1)

C. V. Raman, “A theory of the viscosity of liquids,” Nature 111(2790), 532–533 (1923).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Prog. Quantum Electron. (1)

C. Grivas, “Optically pumped planar waveguide lasers, Part I : Fundamentals and fabrication techniques,” Prog. Quantum Electron. 35(6), 159–239 (2011).
[Crossref]

Other (2)

Potash Corp “Purified Phosphoric Acid,” Tech. Inf. Bull. (2012).

Landolt-Börnstein, “Part 5a, Viscosity and Diffusion,” in Properties of Matter in its Aggregated States, 2, 6th ed. (Springer-Verlag, 1969).

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Figures (10)

Fig. 1.
Fig. 1. Sketch of the fs-laser structuring setup. The red arrows indicate the E-field vectors of the laser beams used for structuring with respect to the orientation of the inscribed tracks.
Fig. 2.
Fig. 2. (a) Sketch of a sample. The black lines indicate the transversally (1) and longitudinally (2) written tracks. (b) Cross sections of tracks of fs-modified material inscribed transversally (in x-direction) and (c) longitudinally (in z-direction, upwards) to the laser beam before etching.
Fig. 3.
Fig. 3. (a) Etching depth vs. etching time for different etching temperatures and square root fits, (b) fitting parameter D vs. temperature Te and viscosity η and linear fit. The single tracks in the [111] oriented samples were inscribed with 0.45 µJ pulse energy, a σ-polarized beam, 100 µm/s translation velocity and etched in phosphoric acid.
Fig. 4.
Fig. 4. Etching depth vs. etching time for different etching agents. The orientation of the sample was [111]. Inscription data and fitting parameters D for square-root time dependencies are given aside the figure.
Fig. 5.
Fig. 5. Fitting parameter D in dependency of pulse energy (a) and writing velocities (b) for different polarizations of the inscribing beam and etching temperatures in phosphoric acid. The samples were oriented in [111] direction. The dashed lines are guides to the eye.
Fig. 6.
Fig. 6. Fitting parameter D in dependency of pulse energy for different writing velocities. The tracks were written in σ-polarization with a lens of 4.51 mm focal length in an [111] oriented crystal and etched in 85 °C phosphoric acid.
Fig. 7.
Fig. 7. Selectivity in dependency of the etching temperature for different samples etched with phosphoric acid or a 1:1 mixture of phosphoric and sulfuric acid at temperatures between 80 °C and 135 °C.
Fig. 8.
Fig. 8. Quasi-three-dimensional microscopic images taken with a Keyence Vhx-6000 microscope. Microchannels resulting from etching of (1) single tracks written in x-direction (4.51 mm focal length, π-polarization, 100 µm/s, 0.27 µJ) (2) multiple tracks written with 1 µm horizontal distance (same writing parameters like (1)) (3) single tracks with round cross sections written in longitudinal writing mode in z-direction (4.51 mm focal length, π-polarization, 0.5 µJ, from left to right: 100 µm/s, 50 µm/s, 25 µm/s). The scale holds for both images. The artifacts arise from an imperfect surface polishing prior to the etching, which was affected during the etching process.
Fig. 9.
Fig. 9. Side views of selectively etched single tracks, etched at different temperatures in phosphoric acid, structured with identical parameters in [111] oriented YAG crystals. Inset (a) shows the magnified front part inside the red circle.
Fig. 10.
Fig. 10. Channel cross sections at the channels front facet in xz-plane. Channel e) was inscribed in a longitudinal writing scheme, all other channels were inscribed in the transversal scheme. Writing conditions were 0.45 µJ, 100 µm/s, 4.51 mm focal length, π-polarization, the samples were etched in phosphoric acid for 50 d.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

d e = D t 1 / 2 .
D ( T e / η ) 1 / 2 ,   with   η e x p ( E / R T e ) ,
S   = 2 × d e / D w ch .

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