Abstract

Line-shaped femtosecond pulses are well-suited to large-area machining with high throughput in laser cutting, peeling, and grooving of materials. First, we demonstrated the single-shot fabrication of a line structure in a glass surface using a line-shaped pulse generated by a holographic cylindrical lens displayed on a liquid-crystal spatial light modulator. We found the line structure was uniform and smooth near the ends because of the ability to precisely control the intensity distribution and to achieve single-shot fabrication. Second, we demonstrated a line-shaped beam deformed three-dimensionally for showing the potential of holographic line-shaped beam processing. Third, we demonstrated laser peeling of an indium tin oxide film. We found that little debris around the fabricated area was observed, because the debris was removed by the beam itself. Last, we demonstrated laser grooving of stainless steel. We found the swelling of the surface included upwardly growing nanogratings, although many line-shaped pulse irradiations were given. The swelling was caused by the depositions of the debris on the top of the nanogratings.

© 2015 Optical Society of America

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References

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  1. 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]
  2. N. Sanner, N. Huot, E. Audouard, C. Larat, J. P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett. 30(12), 1479–1481 (2005).
    [Crossref] [PubMed]
  3. S. Hasegawa, Y. Hayasaki, and N. Nishida, “Holographic femtosecond laser processing with multiplexed phase Fresnel lenses,” Opt. Lett. 31(11), 1705–1707 (2006).
    [Crossref] [PubMed]
  4. L. Kelemen, S. Valkai, and P. Ormos, “Parallel photopolymerisation with complex light patterns generated by diffractive optical elements,” Opt. Express 15(22), 14488–14497 (2007).
    [Crossref] [PubMed]
  5. H. Takahashi, S. Hasegawa, A. Takita, and Y. Hayasaki, “Sparse-exposure technique in holographic two-photon polymerization,” Opt. Express 16(21), 16592–16599 (2008).
    [PubMed]
  6. K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010).
    [Crossref] [PubMed]
  7. M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2015 (1)

K. Sakuma, S. Hasegawa, H. Takahasi, M. Ota, and Y. Hayasaki, “Holographic laser sweeper for in-process debris removal,” Appl. Phys. B 119(3), 533–538 (2015).
[Crossref]

2014 (1)

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

2013 (2)

2011 (2)

2010 (6)

A. Y. Vorobyev and C. Guo, “Laser turns silicon superwicking,” Opt. Express 18(7), 6455–6460 (2010).
[Crossref] [PubMed]

K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010).
[Crossref] [PubMed]

A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18(20), 21090–21099 (2010).
[Crossref] [PubMed]

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

M. Antkowiak, M. L. Torres-Mapa, F. Gunn-Moore, and K. Dholakia, “Application of dynamic diffractive optics for enhanced femtosecond laser based cell transfection,” J. Biophotonics 3(10-11), 696–705 (2010).
[Crossref] [PubMed]

2009 (1)

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

2005 (2)

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]

N. Sanner, N. Huot, E. Audouard, C. Larat, J. P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett. 30(12), 1479–1481 (2005).
[Crossref] [PubMed]

Antkowiak, M.

M. Antkowiak, M. L. Torres-Mapa, F. Gunn-Moore, and K. Dholakia, “Application of dynamic diffractive optics for enhanced femtosecond laser based cell transfection,” J. Biophotonics 3(10-11), 696–705 (2010).
[Crossref] [PubMed]

Audouard, E.

Baum, A.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Beresna, M.

Bhuyan, M. K.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Bonse, J.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Booth, M. J.

Chichkov, B. N.

Courvoisier, F.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Dearden, G.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Dholakia, K.

M. Antkowiak, M. L. Torres-Mapa, F. Gunn-Moore, and K. Dholakia, “Application of dynamic diffractive optics for enhanced femtosecond laser based cell transfection,” J. Biophotonics 3(10-11), 696–705 (2010).
[Crossref] [PubMed]

Dudley, J. M.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Edwardson, S. P.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Fearon, E.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Furfaro, L.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Gecevicius, M.

Gunn-Moore, F.

M. Antkowiak, M. L. Torres-Mapa, F. Gunn-Moore, and K. Dholakia, “Application of dynamic diffractive optics for enhanced femtosecond laser based cell transfection,” J. Biophotonics 3(10-11), 696–705 (2010).
[Crossref] [PubMed]

Guo, C.

Hartelt, M.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Hasegawa, S.

Hayasaki, Y.

Hinze, U.

Hirao, K.

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Improved phase hologram design for generating symmetric light spots and its application for laser writing of waveguides,” Opt. Lett. 36(7), 1065–1067 (2011).
[Crossref] [PubMed]

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

Höhm, S.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Huignard, J. P.

Huot, N.

Jacquot, M.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Jesacher, A.

Kazansky, P. G.

Kelemen, L.

Koch, J.

Koter, R.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Krüger, J.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Kuang, Z.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Lacourt, P. A.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Larat, C.

Liu, D.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Loiseaux, B.

Miura, K.

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Improved phase hologram design for generating symmetric light spots and its application for laser writing of waveguides,” Opt. Lett. 36(7), 1065–1067 (2011).
[Crossref] [PubMed]

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

Nishida, N.

S. Hasegawa, Y. Hayasaki, and N. Nishida, “Holographic femtosecond laser processing with multiplexed phase Fresnel lenses,” Opt. Lett. 31(11), 1705–1707 (2006).
[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]

Obata, K.

Ormos, P.

Ota, M.

K. Sakuma, S. Hasegawa, H. Takahasi, M. Ota, and Y. Hayasaki, “Holographic laser sweeper for in-process debris removal,” Appl. Phys. B 119(3), 533–538 (2015).
[Crossref]

Pentzien, S.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Perrie, W.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Rosenfeld, A.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

Sakakura, M.

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Improved phase hologram design for generating symmetric light spots and its application for laser writing of waveguides,” Opt. Lett. 36(7), 1065–1067 (2011).
[Crossref] [PubMed]

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

Sakuma, K.

K. Sakuma, S. Hasegawa, H. Takahasi, M. Ota, and Y. Hayasaki, “Holographic laser sweeper for in-process debris removal,” Appl. Phys. B 119(3), 533–538 (2015).
[Crossref]

Salut, R.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[Crossref]

Sanner, N.

Sawano, T.

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Improved phase hologram design for generating symmetric light spots and its application for laser writing of waveguides,” Opt. Lett. 36(7), 1065–1067 (2011).
[Crossref] [PubMed]

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

Scully, P. J.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Shimotsuma, Y.

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Improved phase hologram design for generating symmetric light spots and its application for laser writing of waveguides,” Opt. Lett. 36(7), 1065–1067 (2011).
[Crossref] [PubMed]

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

Spaltmann, D.

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

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]

Takahashi, H.

Takahasi, H.

K. Sakuma, S. Hasegawa, H. Takahasi, M. Ota, and Y. Hayasaki, “Holographic laser sweeper for in-process debris removal,” Appl. Phys. B 119(3), 533–538 (2015).
[Crossref]

Takita, A.

H. Takahashi, S. Hasegawa, A. Takita, and Y. Hayasaki, “Sparse-exposure technique in holographic two-photon polymerization,” Opt. Express 16(21), 16592–16599 (2008).
[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]

Torres-Mapa, M. L.

M. Antkowiak, M. L. Torres-Mapa, F. Gunn-Moore, and K. Dholakia, “Application of dynamic diffractive optics for enhanced femtosecond laser based cell transfection,” J. Biophotonics 3(10-11), 696–705 (2010).
[Crossref] [PubMed]

Valkai, S.

Vorobyev, A. Y.

Watkins, K. G.

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

Appl. Phys. B (2)

D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010).
[Crossref]

K. Sakuma, S. Hasegawa, H. Takahasi, M. Ota, and Y. Hayasaki, “Holographic laser sweeper for in-process debris removal,” Appl. Phys. B 119(3), 533–538 (2015).
[Crossref]

Appl. Phys. Lett. (2)

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010).
[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. (1)

J. Bonse, R. Koter, M. Hartelt, D. Spaltmann, S. Pentzien, S. Höhm, A. Rosenfeld, and J. Krüger, “Femtosecond laser-induced periodic surface structures on steel and titanium alloy for tribological applications,” Appl. Phys., A Mater. Sci. Process. 117(1), 103–110 (2014).
[Crossref]

J. Biophotonics (1)

M. Antkowiak, M. L. Torres-Mapa, F. Gunn-Moore, and K. Dholakia, “Application of dynamic diffractive optics for enhanced femtosecond laser based cell transfection,” J. Biophotonics 3(10-11), 696–705 (2010).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, “Parallel drawing of multiple bent optical waveguides by using a spatial light modulator,” Jpn. J. Appl. Phys. 48(12), 126507 (2009).
[Crossref]

Opt. Express (7)

Opt. Lett. (4)

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Figures (10)

Fig. 1
Fig. 1

Phase distributions of holographic cylindrical lenses with (a) wrect, (b) whann, and (c) wmak, and their computational reconstructions at different distances from the SLM.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

SEM images of structure processed using holographic cylindrical lenses with window functions (a) wrect, (b) whann, and (c) wmak, respectively. E means the irradiation energy on the sample plane.

Fig. 4
Fig. 4

(a) SEM images of structure processed using the line-shaped beam with wmak. Processing was performed with E = 7.1 μJ, a repetition frequency of 1 Hz, and a scanning speed of 2 μm/s. (b) SEM images of structure processed using a scanning focused Gaussian beam. Processing was performed with E = 142 nJ, a repetition frequency of 1 kHz, and a scanning speed of 60 μm/s.

Fig. 5
Fig. 5

Length of fabricated structure versus irradiation energy. The filled triangles and circles show the results obtained with whann and wmak, respectively.

Fig. 6
Fig. 6

Three-dimensional line structure fabricated by single-shot pulse irradiation inside glass. (a) Phase distribution of holographic cylindrical lens with different focal lengths. (b) Transmission optical microscope side view image of the fabricated structure.

Fig. 7
Fig. 7

(a) Phase distribution of holographic cylindrical lens and (b) its optical reconstruction. (c) Line-shaped laser peeling of ITO membrane on glass substrate.

Fig. 8
Fig. 8

(a) Laser grooving of stainless steel with a line-shaped beam and (b) its depth profile. (c)–(e) SEM images of the structures processed with various polarizations.

Fig. 9
Fig. 9

Groove depth versus irradiation energy and scan speed.

Fig. 10
Fig. 10

(a) Confocal laser microscope and (b) SEM images of laser grooving of stainless steel using a line-shaped beam with E = 0.7 μJ and a scan speed of 50 μm/s. The grayscale bar indicates heights of −1.1 to 1.8 μm.

Equations (5)

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u ( x , y ) = w ( x ) ( k y 2 2 f ) m o d ( 2 π ) ,
w r e c t ( x ) = { 1 0 if 0 x < 1 else ,
w h a n n ( x ) = { 1 2 [ 1 cos 2 π x ] if 0 x < 1 0 else .
w m a k ( x ) = { w a k a i k e ( 4 x ) if 0 < x < 0.125 1 if 0.125 < x < 0.875 w a k a i k e { 4 ( x 0.750 ) } if 0.875 < x < 1 0 else ,
u ( x , y ) = w ( x ) [ k y 2 2 f ( x ) ] m o d ( 2 π ) ,

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