Abstract

Time-resolved diffraction microscopy technique has been used to observe the formation of laser-induced periodic surface structures (LIPSS) from the interaction of a single femtosecond laser pulse (pump) with a nano-scale groove mechanically formed on a single-crystal Cu substrate. The interaction dynamics (0–1200 ps) was captured by diffracting a time-delayed, frequency-doubled pulse (probe) from nascent LIPSS formation induced by the pump with an infinity-conjugate microscopy setup. The LIPSS ripples are observed to form asynchronously, with the first one forming after 50 ps and others forming sequentially outward from the groove edge at larger time delays. A 1-D analytical model of electron heating including both the laser pulse and surface plasmon polariton excitation at the groove edge predicts ripple period, melt spot diameter, and qualitatively explains the asynchronous time-evolution of LIPSS formation.

© 2015 Optical Society of America

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2015 (1)

2014 (4)

J. Reif, O. Varlamova, S. Uhlig, S. Varlamov, and M. Bestehorn, “On the physics of self-organized nanostructure formation upon femtosecond laser ablation,” Appl. Phys. A 117, 179–184 (2014).
[Crossref]

K. Miyazaki and G. Miyaji, “Mechanism and control of periodic surface nanostructure formation with femtosecond laser pulses,” Appl. Phys. A 114, 177–185 (2014).
[Crossref]

X. Jia, T. Q. Jia, N. N. Peng, D. H. Feng, S. A. Zhang, and Z. R. Sun, “Dynamics of femtosecond laser-induced periodic surface structures on silicon by high spatial and temporal resolution imaging,” J. Appl. Phys. 115, 143102 (2014).
[Crossref]

O. Varlamova, C. Martens, M. Ratzke, and J. Reif, “Genesis of femtosecond-induced nanostructures on solid surfaces,” Appl. Opt. 53, I10–I15 (2014).
[Crossref] [PubMed]

2013 (4)

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Laser-induced periodic surface structure formation resulting from single-pulse ultrafast irradiation of au microstructures on a si substrate,” Appl. Phys. Lett. 102, 211101 (2013).
[Crossref]

S. Wang, Y. Ren, C. Cheng, J. Chen, and D. Tzou, “Micromachining of copper by femtosecond laser pulses,” Appl. Surf. Sci. 265, 302–308 (2013).
[Crossref]

S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Femtosecond diffraction dynamics of laser-induced periodic surface structures on fused silica,” Appl. Phys. Lett. 102, 054102 (2013).
[Crossref]

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Pump-probe imaging of laser-induced periodic surface structures after ultrafast irradiation of si,” Appl. Phys. Lett. 103, 141104 (2013).
[Crossref]

2011 (1)

2010 (2)

J. Bonse and J. Krüger, “Pulse number dependence of laser-induced periodic surface structures for femtosecond laser irradiation of silicon,” J. Appl. Phys. 108, 034903 (2010).
[Crossref]

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

2009 (2)

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano 3, 4062–4070 (2009).
[Crossref] [PubMed]

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256, 61 – 66 (2009).
[Crossref]

2008 (3)

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett. 92, 041914 (2008).
[Crossref]

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
[Crossref]

2007 (3)

M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
[Crossref]

J. P. McDonald, J. A. Nees, and S. M. Yalisove, “Pump-probe imaging of femtosecond pulsed laser ablation of silicon with thermally grown oxide films,” J. Appl. Phys. 102, 063109 (2007).
[Crossref]

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single- and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci. 253, 8075–8079 (2007). Photon-Assisted Synthesis and Processing of Functional Materials E-MRS-H Symposium.
[Crossref]

2005 (4)

L. Jiang and H. Tsai, “Improved two-temperature model and its application in ultrashort laser heating of metal films,” J. of Heat Transfer 127, 1167–1173 (2005).
[Crossref]

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

J. P. Colombier, P. Combis, F. Bonneau, R. Le Harzic, and E. Audouard, “Hydrodynamic simulations of metal ablation by femtosecond laser irradiation,” Phys. Rev. B 71, 165406 (2005).
[Crossref]

A. Chimmalgi, C. P. Grigoropoulos, and K. Komvopoulos, “Surface nanostructuring by nano-/femtosecond laser-assisted scanning force microscopy,” J. Appl. Phys. 97, 104319 (2005).
[Crossref]

2002 (1)

M. Hashida, A. Semerok, O. Gobert, G. Petite, Y. Izawa, and J.F- Wagner, “Ablation threshold dependence on pulse duration for copper,” Appl. Surf. Sci. 197198, 862 – 867 (2002). COLA’01 {SI}.
[Crossref]

2001 (1)

D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, and S. Eliezer, “Interband and intraband (drude) contributions to femtosecond laser absorption in aluminum,” Phys. Rev. E 65, 016409 (2001).
[Crossref]

1997 (1)

S. Suzuki, Y. Ishikawa, M. Isshiki, and Y. Waseda, “Native oxide layers formed on the surface of ultra high-purity iron and copper investigated by angle resolved xps,” Mater. Trans., JIM 38, 1004–1009 (1997).
[Crossref]

1996 (2)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[Crossref] [PubMed]

Y. F. Lu, W. K. Choi, Y. Aoyagi, A. Kinomura, and K. Fujii, “Controllable laser-induced periodic structures at silicondioxide/silicon interface by excimer laser irradiation,” J. Appl. Phys. 80, 7052 (1996).
[Crossref]

1995 (1)

T. M. Brown and J. B. Adams, “{EAM} calculations of the thermodynamics of amorphous copper,” J. Non-Cryst. Solids 180, 275–284 (1995).
[Crossref]

1993 (1)

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

1984 (1)

Y. T. Lee and R. M. More, “An electron conductivity model for dense plasmas,” Phys. Fluids (1958–1988) 27, 1273–1286 (1984).
[Crossref]

1983 (1)

J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure. i. theory,” Phys. Rev. B 27, 1141–1154 (1983).
[Crossref]

1981 (1)

Adams, D. P.

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Pump-probe imaging of laser-induced periodic surface structures after ultrafast irradiation of si,” Appl. Phys. Lett. 103, 141104 (2013).
[Crossref]

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Laser-induced periodic surface structure formation resulting from single-pulse ultrafast irradiation of au microstructures on a si substrate,” Appl. Phys. Lett. 102, 211101 (2013).
[Crossref]

Adams, J. B.

T. M. Brown and J. B. Adams, “{EAM} calculations of the thermodynamics of amorphous copper,” J. Non-Cryst. Solids 180, 275–284 (1995).
[Crossref]

Agostini, P.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Aoyagi, Y.

Y. F. Lu, W. K. Choi, Y. Aoyagi, A. Kinomura, and K. Fujii, “Controllable laser-induced periodic structures at silicondioxide/silicon interface by excimer laser irradiation,” J. Appl. Phys. 80, 7052 (1996).
[Crossref]

Audouard, E.

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single- and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci. 253, 8075–8079 (2007). Photon-Assisted Synthesis and Processing of Functional Materials E-MRS-H Symposium.
[Crossref]

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

J. P. Colombier, P. Combis, F. Bonneau, R. Le Harzic, and E. Audouard, “Hydrodynamic simulations of metal ablation by femtosecond laser irradiation,” Phys. Rev. B 71, 165406 (2005).
[Crossref]

Bajt, S.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Barty, A.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Bastide, S.

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Bestehorn, M.

J. Reif, O. Varlamova, S. Uhlig, S. Varlamov, and M. Bestehorn, “On the physics of self-organized nanostructure formation upon femtosecond laser ablation,” Appl. Phys. A 117, 179–184 (2014).
[Crossref]

Bogan, M.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Bonneau, F.

J. P. Colombier, P. Combis, F. Bonneau, R. Le Harzic, and E. Audouard, “Hydrodynamic simulations of metal ablation by femtosecond laser irradiation,” Phys. Rev. B 71, 165406 (2005).
[Crossref]

Bonse, J.

S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Femtosecond diffraction dynamics of laser-induced periodic surface structures on fused silica,” Appl. Phys. Lett. 102, 054102 (2013).
[Crossref]

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

J. Bonse and J. Krüger, “Pulse number dependence of laser-induced periodic surface structures for femtosecond laser irradiation of silicon,” J. Appl. Phys. 108, 034903 (2010).
[Crossref]

Bostedt, C.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Bounhalli, M.

Boutet, S.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Breitling, D.

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

Brown, T. M.

T. M. Brown and J. B. Adams, “{EAM} calculations of the thermodynamics of amorphous copper,” J. Non-Cryst. Solids 180, 275–284 (1995).
[Crossref]

Cai, L.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256, 61 – 66 (2009).
[Crossref]

Cavalleri, A.

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B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
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D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, and S. Eliezer, “Interband and intraband (drude) contributions to femtosecond laser absorption in aluminum,” Phys. Rev. E 65, 016409 (2001).
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Feng, D. H.

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D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, and S. Eliezer, “Interband and intraband (drude) contributions to femtosecond laser absorption in aluminum,” Phys. Rev. E 65, 016409 (2001).
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M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
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X. Jia, T. Q. Jia, N. N. Peng, D. H. Feng, S. A. Zhang, and Z. R. Sun, “Dynamics of femtosecond laser-induced periodic surface structures on silicon by high spatial and temporal resolution imaging,” J. Appl. Phys. 115, 143102 (2014).
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M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
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X. Jia, T. Q. Jia, N. N. Peng, D. H. Feng, S. A. Zhang, and Z. R. Sun, “Dynamics of femtosecond laser-induced periodic surface structures on silicon by high spatial and temporal resolution imaging,” J. Appl. Phys. 115, 143102 (2014).
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A. Chimmalgi, C. P. Grigoropoulos, and K. Komvopoulos, “Surface nanostructuring by nano-/femtosecond laser-assisted scanning force microscopy,” J. Appl. Phys. 97, 104319 (2005).
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S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Femtosecond diffraction dynamics of laser-induced periodic surface structures on fused silica,” Appl. Phys. Lett. 102, 054102 (2013).
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J. P. Colombier, P. Combis, F. Bonneau, R. Le Harzic, and E. Audouard, “Hydrodynamic simulations of metal ablation by femtosecond laser irradiation,” Phys. Rev. B 71, 165406 (2005).
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Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
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Y. F. Lu, W. K. Choi, Y. Aoyagi, A. Kinomura, and K. Fujii, “Controllable laser-induced periodic structures at silicondioxide/silicon interface by excimer laser irradiation,” J. Appl. Phys. 80, 7052 (1996).
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T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
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Y. T. Lee and R. M. More, “An electron conductivity model for dense plasmas,” Phys. Fluids (1958–1988) 27, 1273–1286 (1984).
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D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, and S. Eliezer, “Interband and intraband (drude) contributions to femtosecond laser absorption in aluminum,” Phys. Rev. E 65, 016409 (2001).
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Peng, N. N.

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Rosandi, Y.

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S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Femtosecond diffraction dynamics of laser-induced periodic surface structures on fused silica,” Appl. Phys. Lett. 102, 054102 (2013).
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T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Sanner, N.

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single- and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci. 253, 8075–8079 (2007). Photon-Assisted Synthesis and Processing of Functional Materials E-MRS-H Symposium.
[Crossref]

Sarnet, T.

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Schafer, K. J.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Schulz, J.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Schumacher, D. W.

Seibert, M.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Semerok, A.

M. Hashida, A. Semerok, O. Gobert, G. Petite, Y. Izawa, and J.F- Wagner, “Ablation threshold dependence on pulse duration for copper,” Appl. Surf. Sci. 197198, 862 – 867 (2002). COLA’01 {SI}.
[Crossref]

Sentis, M.

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Shymanovich, U.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Sipe, J. E.

J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure. i. theory,” Phys. Rev. B 27, 1141–1154 (1983).
[Crossref]

Soder, H.

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single- and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci. 253, 8075–8079 (2007). Photon-Assisted Synthesis and Processing of Functional Materials E-MRS-H Symposium.
[Crossref]

SokolowskiTinten, K.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Sommer, S.

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

Stojanovic, N.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Sugimoto, N.

Sun, Z. R.

X. Jia, T. Q. Jia, N. N. Peng, D. H. Feng, S. A. Zhang, and Z. R. Sun, “Dynamics of femtosecond laser-induced periodic surface structures on silicon by high spatial and temporal resolution imaging,” J. Appl. Phys. 115, 143102 (2014).
[Crossref]

Suzuki, S.

S. Suzuki, Y. Ishikawa, M. Isshiki, and Y. Waseda, “Native oxide layers formed on the surface of ultra high-purity iron and copper investigated by angle resolved xps,” Mater. Trans., JIM 38, 1004–1009 (1997).
[Crossref]

Tobey, R.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Tonchev, S.

Torralva, B.

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Laser-induced periodic surface structure formation resulting from single-pulse ultrafast irradiation of au microstructures on a si substrate,” Appl. Phys. Lett. 102, 211101 (2013).
[Crossref]

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Pump-probe imaging of laser-induced periodic surface structures after ultrafast irradiation of si,” Appl. Phys. Lett. 103, 141104 (2013).
[Crossref]

Torregrosa, F.

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Torres, R.

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Treusch, R.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Tsai, H.

L. Jiang and H. Tsai, “Improved two-temperature model and its application in ultrashort laser heating of metal films,” J. of Heat Transfer 127, 1167–1173 (2005).
[Crossref]

Tzou, D.

S. Wang, Y. Ren, C. Cheng, J. Chen, and D. Tzou, “Micromachining of copper by femtosecond laser pulses,” Appl. Surf. Sci. 265, 302–308 (2013).
[Crossref]

Uhlig, S.

J. Reif, O. Varlamova, S. Uhlig, S. Varlamov, and M. Bestehorn, “On the physics of self-organized nanostructure formation upon femtosecond laser ablation,” Appl. Phys. A 117, 179–184 (2014).
[Crossref]

Urbassek, H. M.

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Valette, S.

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

van Driel, H. M.

J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure. i. theory,” Phys. Rev. B 27, 1141–1154 (1983).
[Crossref]

Varlamov, S.

J. Reif, O. Varlamova, S. Uhlig, S. Varlamov, and M. Bestehorn, “On the physics of self-organized nanostructure formation upon femtosecond laser ablation,” Appl. Phys. A 117, 179–184 (2014).
[Crossref]

Varlamova, O.

J. Reif, O. Varlamova, S. Uhlig, S. Varlamov, and M. Bestehorn, “On the physics of self-organized nanostructure formation upon femtosecond laser ablation,” Appl. Phys. A 117, 179–184 (2014).
[Crossref]

O. Varlamova, C. Martens, M. Ratzke, and J. Reif, “Genesis of femtosecond-induced nanostructures on solid surfaces,” Appl. Opt. 53, I10–I15 (2014).
[Crossref] [PubMed]

Vervisch, V.

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Vorobyev, A. Y.

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett. 92, 041914 (2008).
[Crossref]

Wagner, J.F-

M. Hashida, A. Semerok, O. Gobert, G. Petite, Y. Izawa, and J.F- Wagner, “Ablation threshold dependence on pulse duration for copper,” Appl. Surf. Sci. 197198, 862 – 867 (2002). COLA’01 {SI}.
[Crossref]

Walker, B.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Wang, S.

S. Wang, Y. Ren, C. Cheng, J. Chen, and D. Tzou, “Micromachining of copper by femtosecond laser pulses,” Appl. Surf. Sci. 265, 302–308 (2013).
[Crossref]

Waseda, Y.

S. Suzuki, Y. Ishikawa, M. Isshiki, and Y. Waseda, “Native oxide layers formed on the surface of ultra high-purity iron and copper investigated by angle resolved xps,” Mater. Trans., JIM 38, 1004–1009 (1997).
[Crossref]

Weber, W. H.

Weikert, M.

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

Wu, B.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256, 61 – 66 (2009).
[Crossref]

Xu, N.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano 3, 4062–4070 (2009).
[Crossref] [PubMed]

Xu, N. S.

M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
[Crossref]

Xu, Z.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano 3, 4062–4070 (2009).
[Crossref] [PubMed]

Xu, Z. Z.

M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
[Crossref]

Yalisove, S. M.

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Pump-probe imaging of laser-induced periodic surface structures after ultrafast irradiation of si,” Appl. Phys. Lett. 103, 141104 (2013).
[Crossref]

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Laser-induced periodic surface structure formation resulting from single-pulse ultrafast irradiation of au microstructures on a si substrate,” Appl. Phys. Lett. 102, 211101 (2013).
[Crossref]

J. P. McDonald, J. A. Nees, and S. M. Yalisove, “Pump-probe imaging of femtosecond pulsed laser ablation of silicon with thermally grown oxide films,” J. Appl. Phys. 102, 063109 (2007).
[Crossref]

Yang, B.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Ye, X.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256, 61 – 66 (2009).
[Crossref]

Young, J. F.

J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure. i. theory,” Phys. Rev. B 27, 1141–1154 (1983).
[Crossref]

Zhang, S. A.

X. Jia, T. Q. Jia, N. N. Peng, D. H. Feng, S. A. Zhang, and Z. R. Sun, “Dynamics of femtosecond laser-induced periodic surface structures on silicon by high spatial and temporal resolution imaging,” J. Appl. Phys. 115, 143102 (2014).
[Crossref]

Zhao, F.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano 3, 4062–4070 (2009).
[Crossref] [PubMed]

Zhao, F. L.

M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
[Crossref]

Zhigilei, L. V.

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
[Crossref]

Zhou, M.

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256, 61 – 66 (2009).
[Crossref]

ACS Nano (1)

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano 3, 4062–4070 (2009).
[Crossref] [PubMed]

AIP Conference Proceedings (1)

K. SokolowskiTinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. HauRiege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Dsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Shortpulse laser induced transient structure formation and ablation studied with timeresolved coherent xuvscattering,” AIP Conference Proceedings 1278, 373–379 (2010).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (2)

K. Miyazaki and G. Miyaji, “Mechanism and control of periodic surface nanostructure formation with femtosecond laser pulses,” Appl. Phys. A 114, 177–185 (2014).
[Crossref]

J. Reif, O. Varlamova, S. Uhlig, S. Varlamov, and M. Bestehorn, “On the physics of self-organized nanostructure formation upon femtosecond laser ablation,” Appl. Phys. A 117, 179–184 (2014).
[Crossref]

Appl. Phys. Lett. (4)

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett. 92, 041914 (2008).
[Crossref]

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Laser-induced periodic surface structure formation resulting from single-pulse ultrafast irradiation of au microstructures on a si substrate,” Appl. Phys. Lett. 102, 211101 (2013).
[Crossref]

R. D. Murphy, B. Torralva, D. P. Adams, and S. M. Yalisove, “Pump-probe imaging of laser-induced periodic surface structures after ultrafast irradiation of si,” Appl. Phys. Lett. 103, 141104 (2013).
[Crossref]

S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Femtosecond diffraction dynamics of laser-induced periodic surface structures on fused silica,” Appl. Phys. Lett. 102, 054102 (2013).
[Crossref]

Appl. Surf. Sci. (5)

S. Wang, Y. Ren, C. Cheng, J. Chen, and D. Tzou, “Micromachining of copper by femtosecond laser pulses,” Appl. Surf. Sci. 265, 302–308 (2013).
[Crossref]

M. Hashida, A. Semerok, O. Gobert, G. Petite, Y. Izawa, and J.F- Wagner, “Ablation threshold dependence on pulse duration for copper,” Appl. Surf. Sci. 197198, 862 – 867 (2002). COLA’01 {SI}.
[Crossref]

R. L. Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249, 322 – 331 (2005).
[Crossref]

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single- and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci. 253, 8075–8079 (2007). Photon-Assisted Synthesis and Processing of Functional Materials E-MRS-H Symposium.
[Crossref]

B. Wu, M. Zhou, J. Li, X. Ye, G. Li, and L. Cai, “Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser,” Appl. Surf. Sci. 256, 61 – 66 (2009).
[Crossref]

J. Appl. Phys. (5)

A. Chimmalgi, C. P. Grigoropoulos, and K. Komvopoulos, “Surface nanostructuring by nano-/femtosecond laser-assisted scanning force microscopy,” J. Appl. Phys. 97, 104319 (2005).
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J. Bonse and J. Krüger, “Pulse number dependence of laser-induced periodic surface structures for femtosecond laser irradiation of silicon,” J. Appl. Phys. 108, 034903 (2010).
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Y. F. Lu, W. K. Choi, Y. Aoyagi, A. Kinomura, and K. Fujii, “Controllable laser-induced periodic structures at silicondioxide/silicon interface by excimer laser irradiation,” J. Appl. Phys. 80, 7052 (1996).
[Crossref]

X. Jia, T. Q. Jia, N. N. Peng, D. H. Feng, S. A. Zhang, and Z. R. Sun, “Dynamics of femtosecond laser-induced periodic surface structures on silicon by high spatial and temporal resolution imaging,” J. Appl. Phys. 115, 143102 (2014).
[Crossref]

J. P. McDonald, J. A. Nees, and S. M. Yalisove, “Pump-probe imaging of femtosecond pulsed laser ablation of silicon with thermally grown oxide films,” J. Appl. Phys. 102, 063109 (2007).
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T. M. Brown and J. B. Adams, “{EAM} calculations of the thermodynamics of amorphous copper,” J. Non-Cryst. Solids 180, 275–284 (1995).
[Crossref]

J. of Heat Transfer (1)

L. Jiang and H. Tsai, “Improved two-temperature model and its application in ultrashort laser heating of metal films,” J. of Heat Transfer 127, 1167–1173 (2005).
[Crossref]

Mater. Trans., JIM (1)

S. Suzuki, Y. Ishikawa, M. Isshiki, and Y. Waseda, “Native oxide layers formed on the surface of ultra high-purity iron and copper investigated by angle resolved xps,” Mater. Trans., JIM 38, 1004–1009 (1997).
[Crossref]

Nanotechnology (1)

M. Huang, F. L. Zhao, T. Q. Jia, Y. Cheng, N. S. Xu, and Z. Z. Xu, “A uniform 290 nm periodic square structure on zno fabricated by two-beam femtosecond laser ablation,” Nanotechnology 18, 505301 (2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Fluids (1958–1988) (1)

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Phys. Rev. B (3)

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
[Crossref]

J. P. Colombier, P. Combis, F. Bonneau, R. Le Harzic, and E. Audouard, “Hydrodynamic simulations of metal ablation by femtosecond laser irradiation,” Phys. Rev. B 71, 165406 (2005).
[Crossref]

J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure. i. theory,” Phys. Rev. B 27, 1141–1154 (1983).
[Crossref]

Phys. Rev. E (1)

D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, and S. Eliezer, “Interband and intraband (drude) contributions to femtosecond laser absorption in aluminum,” Phys. Rev. E 65, 016409 (2001).
[Crossref]

Phys. Rev. Lett. (1)

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Proc. SPIE (1)

T. Sarnet, M. Halbwax, R. Torres, P. Delaporte, M. Sentis, S. Martinuzzi, V. Vervisch, F. Torregrosa, H. Etienne, L. Roux, and S. Bastide, “Femtosecond laser for black silicon and photovoltaic cells,” Proc. SPIE 6881, 688119 (2008).
[Crossref]

Other (1)

A. M. Fox and M. Fox, Optical Properties of Solids (Oxford University, 2001), vol. 2010.

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Figures (4)

Fig. 1
Fig. 1

(a) Depth profile (Wyko) of machined groove: 1 μm wide, 100 nm peak-to-valley. Depth is averaged over a 10 μm length. (b) Time-resolved diffraction microscopy experimental setup. A single pulse from the pump beam at 45° AOI forms LIPSS on the Cu target near a machined nano-groove. A microscope objective images LIPSS formation under illumination of the diffracted frequency-doubled probe beam at specified time delay. The objective lens is oriented at 12° from normal to gather more diffracted signal. Sample is translated along groove structure to a fresh site for the next pump pulse.

Fig. 2
Fig. 2

Time-resolved diffraction microscopy images and corresponding lineouts. Images are in false color with pre-fabricated groove edge marked (red line to guide the eye), and averaged horizontal lineout location shown (gray rectangle). LIPSS are observed to form asynchronously, where the first LIPSS ridge (nearest the groove) is beginning to form by 50 ps, but not until 75–100 ps for the second ridge and longer for the third. A melt zone is also observed which is centered on the laser’s Gaussian maximum.

Fig. 3
Fig. 3

Study of damage site resulting from femtosecond pulse interaction with grooved single crystal Cu substrate, profiled with optical profiler. (a) 3D profile rendered with depth dimension exaggerated by ∼300×. Incident laser k (45°) and E (p-pol.) shown. Damaged area is raised (crater formation absent), and mostly flat, which is consistent with the dark central spots observed forming in TRDM images. (b) 2D false color depth profile, with faint gray bar indicating width and arrow indicating direction of lineout shown in Fig. 4. LIPSS period 2.3 μm. Peak at far right (red arrow) marks the location of the initial groove edge, but it clearly has also been modified by the laser.

Fig. 4
Fig. 4

Results of Eq. (1) the 1D electron heating model (lines, right vertical axis), and experimental depth profile lineout from Fig. 3 (blue filled circles, left vertical axis). The left edge of the nano-groove is positioned near 0 μm along the horizontal axis, corresponding to the feature at ∼15 μm in Fig. 3(b). The fluence axis (right vertical) was scaled by setting the peak of the calculated laser heating (red) in the absence of an SPP (η = 0) equal to the experimental peak fluence. A central raised spot is formed with or without a scratch where the η = 0 curve it is above the measured fluence threshold (red dashed line) of melting. For SPP parameters determined by εcold, η = 1 (cyan), neither the hot-groove temperature gradient, nor the laser spot profile are reproduced. The experimental results are better represented using εhot (blue), with temperature gradient toward the groove, and the correct number of ripples are predicted (curve oscillations above and below threshold fluence are correlated with the depth profile) before they are washed out by the central melt zone.

Equations (5)

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F ( x ) = I ( x ) d t ( E Laser + η E SPP ) 2 d t
E Laser = exp [ ( x v L t v L τ ) 2 ( x d w 0 sin θ ) 2 + i ( k sin θ x i ω t ) ]
E SPP = exp [ ( x v s t v s τ ) 2 ( d w 0 sin θ ) 2 + i ( Re [ k s ] x i ω t ) ] Im [ k s ] x ]
η 2 = E SPP 2 E Laser 2 = T el = 2 | ε | 2 cos θ ( 1 R ) ε ( | ε | 1 ) 1 / 2
Γ e e E F ( k B T e E F ) 2 for k B T e < E F

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