Abstract

A comparative study on reflection of nanosecond Nd-YAG laser pulses in ablation of aluminum in air and in vacuum under the same other experimental conditions is performed. We find that, hemispherical total reflectivity of aluminum undergoes a sharp drop at the plasma formation threshold both in the air and in vacuum. The initial large value (0.8) of aluminum reflectivity decreases to a level of about 0.14 and 0.24 for ablation in the air and in vacuum, respectively. These decreased reflectivity values remain virtually unchanged with further increasing laser fluence. The reflectivity drop in the air is observed to be sharper than in vacuum. Our study indicates that the reflectivity drop is predominantly caused by absorption of the laser light in plasma. Nano/micro-structural defects present on practical sample surfaces play the important role in the plasma formation, especially for the ablation in the air, where the plasma formation threshold is found to be by a factor of 3 smaller than in vacuum.

© 2013 OSA

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  7. V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
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  13. J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
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    [CrossRef]
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  18. A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett.92(4), 041914 (2008).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. A. Ya. Vorob’ev, “Reflection of the pulsed ruby laser radiation by a copper target in air and in vacuum,” Sov. J. Quantum Electron.15(4), 490–493 (1985).
    [CrossRef]
  28. A. Y. Vorobyev and C. Guo, “Reflection of femtosecond laser light in multipulse ablation of metals,” J. Appl. Phys.110(4), 043102 (2011).
    [CrossRef]
  29. A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. S. J. Tan and D. K. Gramotnev, “Heating effects in nanofocusing metal wedges,” J. Appl. Phys.110(3), 034310 (2011).
    [CrossRef]
  34. N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
    [CrossRef]
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2013 (1)

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev.7(3), 385–407 (2013).
[CrossRef]

2012 (3)

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

G. Tang, A. C. Hourd, and A. Abdolvand, “Nanosecond pulsed laser blackening of copper,” Appl. Phys. Lett.101(23), 231902 (2012).
[CrossRef]

S. C. Singh and H. Zeng, “Nanomaterials and nanopartterns based on laser processing: A brief review on current state of art,” Sci. Adv. Mater.4(3), 368–390 (2012).
[CrossRef]

2011 (4)

D. Marla, U. V. Bhandarkar, and S. S. Joshi, “Critical assessment of the issues in the modeling of ablation and plasma expansion processes in the pulsed laser deposition of metals,” J. Appl. Phys.109(2), 021101 (2011).
[CrossRef]

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Reflection of femtosecond laser light in multipulse ablation of metals,” J. Appl. Phys.110(4), 043102 (2011).
[CrossRef]

S. J. Tan and D. K. Gramotnev, “Heating effects in nanofocusing metal wedges,” J. Appl. Phys.110(3), 034310 (2011).
[CrossRef]

2010 (4)

S. T. Hendow and S. A. Shakir, “Structuring materials with nanosecond laser pulses,” Opt. Express18(10), 10188–10199 (2010).
[CrossRef] [PubMed]

S. G. Gorny, G. V. Odintsova, A. V. Otkeeva, and V. P. Veiko, “Laser induced multicolor image formation on metal,” Proc. SPIE7996, 799605, 799605-7 (2010).
[CrossRef]

N. M. Bulgakova, A. N. Panchenko, A. E. Tel’minov, and M. A. Shulepov, “Formation of microtower structures in nanosecond laser ablation of liquid metals,” Appl. Phys., A Mater. Sci. Process.98(2), 393–400 (2010).
[CrossRef]

S. Amoruso, J. Schou, and J. G. Lunney, “Energy balance of a laser ablation plume expanding in a background gas,” Appl. Phys., A Mater. Sci. Process.101(1), 209–214 (2010).
[CrossRef]

2009 (1)

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

2008 (2)

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett.92(4), 041914 (2008).
[CrossRef]

N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
[CrossRef]

2007 (1)

S.-B. Wen, X. Mao, R. Greif, and R. E. Russo, “Laser ablation induced vapor plume expansion into a background gas,” J. Appl. Phys.101(2), 023115 (2007).
[CrossRef]

2006 (2)

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

2005 (3)

A. Kurella and N. B. Dahotre, “Review paper: Surface modification for bioimplants: The role of laser surface engineering,” J. Biomater. Appl.20(1), 5–50 (2005).
[CrossRef] [PubMed]

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Enhanced absorptance of gold following multi-pulse femtosecond laser ablation,” Phys. Rev. B72(19), 195422 (2005).
[CrossRef]

2004 (1)

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

2003 (2)

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

A. J. Pedraza, J. D. Fowlkes, and Y.-F. Guan, “Surface nanostructuring of silicon,” Appl. Phys., A Mater. Sci. Process.77(2), 277–284 (2003).

1995 (1)

S. Proyer and E. Stangle, “Time-integrated photography of laser-induced plumes,” Appl. Phys., A Mater. Sci. Process.60(6), 573–580 (1995).
[CrossRef]

1985 (1)

A. Ya. Vorob’ev, “Reflection of the pulsed ruby laser radiation by a copper target in air and in vacuum,” Sov. J. Quantum Electron.15(4), 490–493 (1985).
[CrossRef]

1978 (1)

C. T. Walters, R. H. Barns, and R. E. Beverly, “Initiation of laser-supported-detonation (LSD) waves,” J. Appl. Phys.49(5), 2937–2949 (1978).
[CrossRef]

1977 (1)

Yu. I. Dymshits, “Reflection of intense radiation from a thin metal film,” Sov. Phys. Tech. Phys.22(7), 901–902 (1977).

1975 (1)

T. E. Zavecz, M. A. Saifi, and M. Notis, “Metal reflectivity under high-intensity optical radiation,” Appl. Phys. Lett.26(4), 165–168 (1975).
[CrossRef]

1969 (2)

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

M. N. Libenson, G. S. Romanov, and Ya. A. Imas, “Temperature dependence of the optical constants of a metal in heating by laser radiation,” Sov. Phys. Tech. Phys.13(7), 925–927 (1969).

Abdolvand, A.

G. Tang, A. C. Hourd, and A. Abdolvand, “Nanosecond pulsed laser blackening of copper,” Appl. Phys. Lett.101(23), 231902 (2012).
[CrossRef]

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

Amoruso, S.

S. Amoruso, J. Schou, and J. G. Lunney, “Energy balance of a laser ablation plume expanding in a background gas,” Appl. Phys., A Mater. Sci. Process.101(1), 209–214 (2010).
[CrossRef]

Barns, R. H.

C. T. Walters, R. H. Barns, and R. E. Beverly, “Initiation of laser-supported-detonation (LSD) waves,” J. Appl. Phys.49(5), 2937–2949 (1978).
[CrossRef]

Basov, N. G.

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

Beverly, R. E.

C. T. Walters, R. H. Barns, and R. E. Beverly, “Initiation of laser-supported-detonation (LSD) waves,” J. Appl. Phys.49(5), 2937–2949 (1978).
[CrossRef]

Bhandarkar, U. V.

D. Marla, U. V. Bhandarkar, and S. S. Joshi, “Critical assessment of the issues in the modeling of ablation and plasma expansion processes in the pulsed laser deposition of metals,” J. Appl. Phys.109(2), 021101 (2011).
[CrossRef]

Boiko, V. A.

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

Bourham, M. A.

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

Bulgakova, N. M.

N. M. Bulgakova, A. N. Panchenko, A. E. Tel’minov, and M. A. Shulepov, “Formation of microtower structures in nanosecond laser ablation of liquid metals,” Appl. Phys., A Mater. Sci. Process.98(2), 393–400 (2010).
[CrossRef]

N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
[CrossRef]

Cheng, J.-Y.

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

Chong, T. C.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Chuang, Y.-C.

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

Dahotre, N. B.

A. Kurella and N. B. Dahotre, “Review paper: Surface modification for bioimplants: The role of laser surface engineering,” J. Biomater. Appl.20(1), 5–50 (2005).
[CrossRef] [PubMed]

Dai, J.

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

Diwakar, P. K.

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

Duscher, G.

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

Dymshits, Yu. I.

Yu. I. Dymshits, “Reflection of intense radiation from a thin metal film,” Sov. Phys. Tech. Phys.22(7), 901–902 (1977).

Fotakis, C.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Fowlkes, J. D.

A. J. Pedraza, J. D. Fowlkes, and Y.-F. Guan, “Surface nanostructuring of silicon,” Appl. Phys., A Mater. Sci. Process.77(2), 277–284 (2003).

Freeman, J. R.

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

Gorny, S. G.

S. G. Gorny, G. V. Odintsova, A. V. Otkeeva, and V. P. Veiko, “Laser induced multicolor image formation on metal,” Proc. SPIE7996, 799605, 799605-7 (2010).
[CrossRef]

Gramotnev, D. K.

S. J. Tan and D. K. Gramotnev, “Heating effects in nanofocusing metal wedges,” J. Appl. Phys.110(3), 034310 (2011).
[CrossRef]

Greif, R.

S.-B. Wen, X. Mao, R. Greif, and R. E. Russo, “Laser ablation induced vapor plume expansion into a background gas,” J. Appl. Phys.101(2), 023115 (2007).
[CrossRef]

Guan, Y.-F.

A. J. Pedraza, J. D. Fowlkes, and Y.-F. Guan, “Surface nanostructuring of silicon,” Appl. Phys., A Mater. Sci. Process.77(2), 277–284 (2003).

Guo, C.

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev.7(3), 385–407 (2013).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Reflection of femtosecond laser light in multipulse ablation of metals,” J. Appl. Phys.110(4), 043102 (2011).
[CrossRef]

N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett.92(4), 041914 (2008).
[CrossRef]

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Enhanced absorptance of gold following multi-pulse femtosecond laser ablation,” Phys. Rev. B72(19), 195422 (2005).
[CrossRef]

Harilal, S. S.

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

Hassanein, A.

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

Haverkamp, J.

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

Hendow, S. T.

Hong, M.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

Hong, M. H.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Hourd, A. C.

G. Tang, A. C. Hourd, and A. Abdolvand, “Nanosecond pulsed laser blackening of copper,” Appl. Phys. Lett.101(23), 231902 (2012).
[CrossRef]

Huang, S. M.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Imas, Ya. A.

M. N. Libenson, G. S. Romanov, and Ya. A. Imas, “Temperature dependence of the optical constants of a metal in heating by laser radiation,” Sov. Phys. Tech. Phys.13(7), 925–927 (1969).

In’tveld, B. H.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

Jin, C.

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

Joshi, S. S.

D. Marla, U. V. Bhandarkar, and S. S. Joshi, “Critical assessment of the issues in the modeling of ablation and plasma expansion processes in the pulsed laser deposition of metals,” J. Appl. Phys.109(2), 021101 (2011).
[CrossRef]

Kohns, P.

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

Kokody, N. G.

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

Kovalenko, V.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

Krokhin, O. N.

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

Kurella, A.

A. Kurella and N. B. Dahotre, “Review paper: Surface modification for bioimplants: The role of laser surface engineering,” J. Biomater. Appl.20(1), 5–50 (2005).
[CrossRef] [PubMed]

Kuzmichev, V. M.

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

Li, L.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

Libenson, M. N.

M. N. Libenson, G. S. Romanov, and Ya. A. Imas, “Temperature dependence of the optical constants of a metal in heating by laser radiation,” Sov. Phys. Tech. Phys.13(7), 925–927 (1969).

Liu, Z.

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

Lloyd, R. W.

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

Luk’yanchuk, B. S.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Lunney, J. G.

S. Amoruso, J. Schou, and J. G. Lunney, “Energy balance of a laser ablation plume expanding in a background gas,” Appl. Phys., A Mater. Sci. Process.101(1), 209–214 (2010).
[CrossRef]

Malshe, A.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

Mao, X.

S.-B. Wen, X. Mao, R. Greif, and R. E. Russo, “Laser ablation induced vapor plume expansion into a background gas,” J. Appl. Phys.101(2), 023115 (2007).
[CrossRef]

Marla, D.

D. Marla, U. V. Bhandarkar, and S. S. Joshi, “Critical assessment of the issues in the modeling of ablation and plasma expansion processes in the pulsed laser deposition of metals,” J. Appl. Phys.109(2), 021101 (2011).
[CrossRef]

Mayo, R. M.

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

Narayan, J.

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

Notis, M.

T. E. Zavecz, M. A. Saifi, and M. Notis, “Metal reflectivity under high-intensity optical radiation,” Appl. Phys. Lett.26(4), 165–168 (1975).
[CrossRef]

Odintsova, G. V.

S. G. Gorny, G. V. Odintsova, A. V. Otkeeva, and V. P. Veiko, “Laser induced multicolor image formation on metal,” Proc. SPIE7996, 799605, 799605-7 (2010).
[CrossRef]

Otkeeva, A. V.

S. G. Gorny, G. V. Odintsova, A. V. Otkeeva, and V. P. Veiko, “Laser induced multicolor image formation on metal,” Proc. SPIE7996, 799605, 799605-7 (2010).
[CrossRef]

Panchenko, A. N.

N. M. Bulgakova, A. N. Panchenko, A. E. Tel’minov, and M. A. Shulepov, “Formation of microtower structures in nanosecond laser ablation of liquid metals,” Appl. Phys., A Mater. Sci. Process.98(2), 393–400 (2010).
[CrossRef]

Papazoglou, D. G.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Pedraza, A. J.

A. J. Pedraza, J. D. Fowlkes, and Y.-F. Guan, “Surface nanostructuring of silicon,” Appl. Phys., A Mater. Sci. Process.77(2), 277–284 (2003).

Proyer, S.

S. Proyer and E. Stangle, “Time-integrated photography of laser-induced plumes,” Appl. Phys., A Mater. Sci. Process.60(6), 573–580 (1995).
[CrossRef]

Romanov, G. S.

M. N. Libenson, G. S. Romanov, and Ya. A. Imas, “Temperature dependence of the optical constants of a metal in heating by laser radiation,” Sov. Phys. Tech. Phys.13(7), 925–927 (1969).

Russo, R. E.

S.-B. Wen, X. Mao, R. Greif, and R. E. Russo, “Laser ablation induced vapor plume expansion into a background gas,” J. Appl. Phys.101(2), 023115 (2007).
[CrossRef]

Saifi, M. A.

T. E. Zavecz, M. A. Saifi, and M. Notis, “Metal reflectivity under high-intensity optical radiation,” Appl. Phys. Lett.26(4), 165–168 (1975).
[CrossRef]

Schmidt, M.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

Schmidt, M. J. J.

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

Schou, J.

S. Amoruso, J. Schou, and J. G. Lunney, “Energy balance of a laser ablation plume expanding in a background gas,” Appl. Phys., A Mater. Sci. Process.101(1), 209–214 (2010).
[CrossRef]

Semenov, O. G.

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

Shakir, S. A.

Shil, L. P.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Shulepov, M. A.

N. M. Bulgakova, A. N. Panchenko, A. E. Tel’minov, and M. A. Shulepov, “Formation of microtower structures in nanosecond laser ablation of liquid metals,” Appl. Phys., A Mater. Sci. Process.98(2), 393–400 (2010).
[CrossRef]

Singh, S. C.

S. C. Singh and H. Zeng, “Nanomaterials and nanopartterns based on laser processing: A brief review on current state of art,” Sci. Adv. Mater.4(3), 368–390 (2012).
[CrossRef]

Sklizkov, G. V.

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

Spanakis, E.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Stangle, E.

S. Proyer and E. Stangle, “Time-integrated photography of laser-induced plumes,” Appl. Phys., A Mater. Sci. Process.60(6), 573–580 (1995).
[CrossRef]

Stratakis, E.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Tan, S. J.

S. J. Tan and D. K. Gramotnev, “Heating effects in nanofocusing metal wedges,” J. Appl. Phys.110(3), 034310 (2011).
[CrossRef]

Tang, G.

G. Tang, A. C. Hourd, and A. Abdolvand, “Nanosecond pulsed laser blackening of copper,” Appl. Phys. Lett.101(23), 231902 (2012).
[CrossRef]

Tel’minov, A. E.

N. M. Bulgakova, A. N. Panchenko, A. E. Tel’minov, and M. A. Shulepov, “Formation of microtower structures in nanosecond laser ablation of liquid metals,” Appl. Phys., A Mater. Sci. Process.98(2), 393–400 (2010).
[CrossRef]

Tzanetakis, P.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Veiko, V. P.

S. G. Gorny, G. V. Odintsova, A. V. Otkeeva, and V. P. Veiko, “Laser induced multicolor image formation on metal,” Proc. SPIE7996, 799605, 799605-7 (2010).
[CrossRef]

Verhoff, B.

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

Vorob’ev, A. Ya.

A. Ya. Vorob’ev, “Reflection of the pulsed ruby laser radiation by a copper target in air and in vacuum,” Sov. J. Quantum Electron.15(4), 490–493 (1985).
[CrossRef]

Vorobyev, A. Y.

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev.7(3), 385–407 (2013).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Reflection of femtosecond laser light in multipulse ablation of metals,” J. Appl. Phys.110(4), 043102 (2011).
[CrossRef]

N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett.92(4), 041914 (2008).
[CrossRef]

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Enhanced absorptance of gold following multi-pulse femtosecond laser ablation,” Phys. Rev. B72(19), 195422 (2005).
[CrossRef]

Walters, C. T.

C. T. Walters, R. H. Barns, and R. E. Beverly, “Initiation of laser-supported-detonation (LSD) waves,” J. Appl. Phys.49(5), 2937–2949 (1978).
[CrossRef]

Wang, Q. F.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Wang, Z. B.

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

Wei, C.-W.

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

Wen, S.-B.

S.-B. Wen, X. Mao, R. Greif, and R. E. Russo, “Laser ablation induced vapor plume expansion into a background gas,” J. Appl. Phys.101(2), 023115 (2007).
[CrossRef]

Whitehead, D. J.

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

Yen, M.-H.

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

Young, T.-H.

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

Zavecz, T. E.

T. E. Zavecz, M. A. Saifi, and M. Notis, “Metal reflectivity under high-intensity optical radiation,” Appl. Phys. Lett.26(4), 165–168 (1975).
[CrossRef]

Zeng, H.

S. C. Singh and H. Zeng, “Nanomaterials and nanopartterns based on laser processing: A brief review on current state of art,” Sci. Adv. Mater.4(3), 368–390 (2012).
[CrossRef]

Zergioti, I.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Zhong, M.

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

Zhukov, V. P.

N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
[CrossRef]

Zorba, V.

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Appl. Phys. Lett. (4)

G. Tang, A. C. Hourd, and A. Abdolvand, “Nanosecond pulsed laser blackening of copper,” Appl. Phys. Lett.101(23), 231902 (2012).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett.92(4), 041914 (2008).
[CrossRef]

T. E. Zavecz, M. A. Saifi, and M. Notis, “Metal reflectivity under high-intensity optical radiation,” Appl. Phys. Lett.26(4), 165–168 (1975).
[CrossRef]

V. Zorba, P. Tzanetakis, C. Fotakis, E. Spanakis, E. Stratakis, D. G. Papazoglou, and I. Zergioti, “Silicon electron emitters fabricated by ultraviolet laser pulses,” Appl. Phys. Lett.88(8), 081103 (2006).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (8)

Z. B. Wang, M. H. Hong, B. S. Luk’yanchuk, S. M. Huang, Q. F. Wang, L. P. Shil, and T. C. Chong, “Parallel nanostructuring of GeSbTe film with particle mask,” Appl. Phys., A Mater. Sci. Process.79(4–6), 1603–1606 (2004).
[CrossRef]

A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process.82(2), 357–362 (2006).
[CrossRef]

S. Proyer and E. Stangle, “Time-integrated photography of laser-induced plumes,” Appl. Phys., A Mater. Sci. Process.60(6), 573–580 (1995).
[CrossRef]

N. M. Bulgakova, V. P. Zhukov, A. Y. Vorobyev, and C. Guo, “Modeling of residual thermal effect in femtosecond laser ablation of metals. Role of gas environment,” Appl. Phys., A Mater. Sci. Process.92(4), 883–889 (2008).
[CrossRef]

S. Amoruso, J. Schou, and J. G. Lunney, “Energy balance of a laser ablation plume expanding in a background gas,” Appl. Phys., A Mater. Sci. Process.101(1), 209–214 (2010).
[CrossRef]

A. Abdolvand, R. W. Lloyd, M. J. J. Schmidt, D. J. Whitehead, Z. Liu, and L. Li, “Formation of highly organized, periodic microstructures on steel surfaces upon pulsed laser irradiation,” Appl. Phys., A Mater. Sci. Process.95(2), 447–452 (2009).
[CrossRef]

N. M. Bulgakova, A. N. Panchenko, A. E. Tel’minov, and M. A. Shulepov, “Formation of microtower structures in nanosecond laser ablation of liquid metals,” Appl. Phys., A Mater. Sci. Process.98(2), 393–400 (2010).
[CrossRef]

A. J. Pedraza, J. D. Fowlkes, and Y.-F. Guan, “Surface nanostructuring of silicon,” Appl. Phys., A Mater. Sci. Process.77(2), 277–284 (2003).

CIRP Annals Manufacturing Technology (1)

L. Li, M. Hong, M. Schmidt, M. Zhong, A. Malshe, B. H. In’tveld, and V. Kovalenko, “Laser nano-manufacturing – State of the art and challenges,” CIRP Annals Manufacturing Technology60(2), 735–755 (2011).
[CrossRef]

J. Appl. Phys. (7)

D. Marla, U. V. Bhandarkar, and S. S. Joshi, “Critical assessment of the issues in the modeling of ablation and plasma expansion processes in the pulsed laser deposition of metals,” J. Appl. Phys.109(2), 021101 (2011).
[CrossRef]

A. Y. Vorobyev and C. Guo, “Reflection of femtosecond laser light in multipulse ablation of metals,” J. Appl. Phys.110(4), 043102 (2011).
[CrossRef]

C. T. Walters, R. H. Barns, and R. E. Beverly, “Initiation of laser-supported-detonation (LSD) waves,” J. Appl. Phys.49(5), 2937–2949 (1978).
[CrossRef]

S. J. Tan and D. K. Gramotnev, “Heating effects in nanofocusing metal wedges,” J. Appl. Phys.110(3), 034310 (2011).
[CrossRef]

S.-B. Wen, X. Mao, R. Greif, and R. E. Russo, “Laser ablation induced vapor plume expansion into a background gas,” J. Appl. Phys.101(2), 023115 (2007).
[CrossRef]

J. Haverkamp, R. M. Mayo, M. A. Bourham, J. Narayan, C. Jin, and G. Duscher, “Plasma plume characteristics and properties of pulsed laser deposited diamond-like carbon films,” J. Appl. Phys.93(6), 3627–3634 (2003).
[CrossRef]

B. Verhoff, S. S. Harilal, J. R. Freeman, P. K. Diwakar, and A. Hassanein, “Dynamics of femto- and nanosecond laser ablation plumes investigated using optical emission spectroscopy,” J. Appl. Phys.112(9), 093303 (2012).
[CrossRef]

J. Biomater. Appl. (1)

A. Kurella and N. B. Dahotre, “Review paper: Surface modification for bioimplants: The role of laser surface engineering,” J. Biomater. Appl.20(1), 5–50 (2005).
[CrossRef] [PubMed]

J. Micromech. Microeng. (1)

J.-Y. Cheng, M.-H. Yen, C.-W. Wei, Y.-C. Chuang, and T.-H. Young, “Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip,” J. Micromech. Microeng.15(6), 1147–1156 (2005).
[CrossRef]

Laser Photon. Rev. (1)

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev.7(3), 385–407 (2013).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

A. Y. Vorobyev and C. Guo, “Enhanced absorptance of gold following multi-pulse femtosecond laser ablation,” Phys. Rev. B72(19), 195422 (2005).
[CrossRef]

Proc. SPIE (1)

S. G. Gorny, G. V. Odintsova, A. V. Otkeeva, and V. P. Veiko, “Laser induced multicolor image formation on metal,” Proc. SPIE7996, 799605, 799605-7 (2010).
[CrossRef]

Sci. Adv. Mater. (1)

S. C. Singh and H. Zeng, “Nanomaterials and nanopartterns based on laser processing: A brief review on current state of art,” Sci. Adv. Mater.4(3), 368–390 (2012).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. Ya. Vorob’ev, “Reflection of the pulsed ruby laser radiation by a copper target in air and in vacuum,” Sov. J. Quantum Electron.15(4), 490–493 (1985).
[CrossRef]

Sov. Phys. Tech. Phys. (3)

M. N. Libenson, G. S. Romanov, and Ya. A. Imas, “Temperature dependence of the optical constants of a metal in heating by laser radiation,” Sov. Phys. Tech. Phys.13(7), 925–927 (1969).

N. G. Basov, V. A. Boiko, O. N. Krokhin, O. G. Semenov, and G. V. Sklizkov, “Reduction of reflection coefficient for intense laser radiation on solid surfaces,” Sov. Phys. Tech. Phys.13(1), 1581–1582 (1969).

Yu. I. Dymshits, “Reflection of intense radiation from a thin metal film,” Sov. Phys. Tech. Phys.22(7), 901–902 (1977).

Other (4)

L. J. Radziemski and D. A. Cremers, eds., Laser-Induced Plasmas and Applications (Marcel Dekker, Inc., 1989).

C. R. Phipps, ed., Laser Ablation and Its Applications (Springer, 2007).

J. F. Ready, Effects of High-Power Laser Radiation (Academic Press, 1971).

R. Eason, ed., Pulsed Laser Deposition of Thin Films (Wiley, 2007).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for studying reflection of the laser light in ablation of a metal sample.

Fig. 2
Fig. 2

Hemispherical total reflectivity of aluminum as function of laser fluence for ablation in 1-atm air and in vacuum.

Fig. 3
Fig. 3

Time-integrated photographs of plasma plumes produced in air (a) and vacuum (b) at F = 21.5 J/cm2. The laser spot diameter on the sample surface is 1.0 mm. The photographs were taken in the direction parallel to the sample surface. The exposure time after the laser pulse is 1 s.

Fig. 4
Fig. 4

Reflection of the laser pulse from the sample-plasma system: P(t) is the incident laser pulse power; P(t)exp[-θ(t)] is the laser pulse power that arrives at the sample surface, here θ(t) is the total optical thickness of the plasma; P(t)Rs(t))exp[-θ(t)] is the laser pulse power reflected from the sample surface, here Rs(t) is the reflectivity of the sample surface; P(t) Rs(t))exp[-2θ(t)] is the laser pulse power that comes out from the sample-plasma system.

Equations (3)

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

T surf (t)= (1R) a k π 0 t I(tτ) τ dτ+ T 0 ,
R=( 0 τ L P(t) R s (t)exp[2θ(t)]dt)/ 0 τ L P(t)dt ,
R s (T)1 ω p 2π σ 0 (T) ,

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