Abstract

This work is a presentation of a modeling approach aimed at describing laser–matter interaction under laser-induced breakdown spectroscopy operating conditions. In order to set up a simple numerical tool to compute our model, only the most relevant processes appearing during the interaction were considered. This allowed us to develop a quick and rather accurate idea about how some physical parameters evolve during the interaction, so that the optimization of the laser beam parameters for better analytical results would be possible. For a basic understanding we used for our numerical computation a nanosecond laser pulse with an ideal Gaussian temporal profile and a pure Cu target. In order to optimize the interaction parameters, this study was focused on the effect of some of the laser parameters such as the wavelength (UV, Vis, IR), the pulse duration, and the irradiation on the results of the interaction. An investigation of the influence of some processes such as the vaporization effects and the plasma shielding was also included. The processes occuring on the material surface were closely examined as well. A comparison between the use of temperature-dependent and temperature-independent optical parameters was conducted, and their influence on the results was investigated. The use of variable optical parameters is revealed to be a means to correct the values of the temperature distribution inside the material and convert them into more realistic ones. Our code was first validated when operating under the same conditions used by other authors, and then it was used to present our proper contributions, as previously stated.

© 2013 Optical Society of America

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  3. R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
    [CrossRef]
  4. D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

J. D. Parisse, M. Sentis, and D. E. Zeitoun, “Modeling and numerical simulation of laser matter interaction and ablation with 193 nanometer laser for nanosecond pulse,” Int. J. Numer. Methods Heat Fluid Flow 2, 173–194 (2011).

2010 (3)

N. A. Vasantgadkar, U. V. Bhandarkar, and S. S. Joshi, “A finite element model to predict the ablation depth in pulsed laser ablation,” Thin Solid Films 519, 1421–1430 (2010).
[CrossRef]

M. Stafe, C. Negutu, N. N. Puscas, and I. M. Popescu, “Pulsed laser ablation of solids,” Roman. Rep. Phys. 62, 758–770 (2010).

F. E. M. Silveira and S. M. Kurcbart, “Hagen-Rubens relation beyond far-infrared region,” Europhys. Lett. 90, 44004 (2010).
[CrossRef]

2009 (1)

S. E.-S. Abd El-Ghany, “A theoretical study of the evaporation induced by a pulsed laser in a finite slab,” Opt. Commun. 282, 284–290 (2009).
[CrossRef]

2008 (1)

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

2006 (2)

M. Stafe, C. Negutu, and I. M. Popescu, “Combined experimental and theoretical investigation of multiple-nanosecond laser ablation of metals,” J. Optoelectron. Adv. Mater. 8, 1180–1186 (2006).

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

2005 (3)

A. F. H. Kaplan, “Model of the absorption variation during pulsed heating applied to welding of electronic Au/Ni coated Cu-lead frames,” Appl. Surf. Sci. 241, 362–370 (2005).
[CrossRef]

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

A. Bogaerts and Z. Chen, “Effect of laser parameters on laser ablation and laser-induced plasma formation: a numerical modeling investigation,” Spectrochim. Acta B 60, 1280–1307 (2005).
[CrossRef]

2004 (1)

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

2003 (1)

A. Bogaerts and Z. Chen, “Laser ablation for analytical sampling: what can we learn from modeling?” Spectrochim. Acta B 58, 1867–1893 (2003).
[CrossRef]

2002 (3)

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

Q. M. Lu, S. Mao, X. L. Mao, and R. E. Russo, “Delayed phase explosion during high-power nanosecond laser ablation of silicon,” Appl. Phys. Lett. 80, 3072–3074 (2002).
[CrossRef]

X. Xu, “Phase explosion and its time lag in nanosecond laser ablation,” Appl. Surf. Sci. 197–198, 61–66 (2002).
[CrossRef]

2001 (4)

G. Colonna, L. D. Pietnaza, and M. Capitelli, “Coupled solution of a time dependent collisional-radiative model and Boltzmann equation for atomic hydrogen plasmas: possible implications with LIBS plasmas,” Spectrochem. Acta. B 56, 587–598 (2001).
[CrossRef]

N. M. Bulgakova and A. V. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[CrossRef]

Z. H. Shen, S. Y. Zhang, J. Lu, and X. W. Ni, “Mathematical modeling of laser induced heating and melting in solids,” Opt. Laser Technol. 33, 533–537 (2001).
[CrossRef]

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429, 269–278 (2001).
[CrossRef]

2000 (1)

M. Capitelli, F. Capitelli, and A. Elatski, “Non-equilibrium and equilibrium problems in laser induced plasmas,” Spectrochim. Acta B 55, 559–574 (2000).
[CrossRef]

1997 (1)

1996 (1)

X. Mao and R. E. Russo, “Observation of plasma shielding by measuring transmitted and reflected laser pulse temporal profiles,” Appl. Phys. A 64, 1–6 (1996).
[CrossRef]

1994 (1)

A. Peterlongo, A. Miotello, and R. Kelly, “Laser-pulse sputtering of aluminum: vaporization, boiling, superheating, and gas-dynamic effects,” Phys. Rev. E 50, 4716–4727 (1994).

1993 (1)

A. F. Hassan, M. M. El-Nicklawy, and M. K. El-Adawi, “A general problem of pulse laser heating of a slab,” Opt. Laser Technol. 25, 155–162 (1993).
[CrossRef]

1991 (1)

L. Balazs, R. Gijbels, and A. Vertes, “Expansion of laser-generated plumes near the plasma ignition threshold,” Anal. Chem. 63, 314–320 (1991).
[CrossRef]

1986 (1)

M. K. El Adawi and E. F. El Shehawey, “Heating a slab induced by a time-dependent laser irradiation—an exact solution,” J. Appl. Phys. 60, 2250–2255 (1986).
[CrossRef]

Abd El-Ghany, S. E.-S.

S. E.-S. Abd El-Ghany, “A theoretical study of the evaporation induced by a pulsed laser in a finite slab,” Opt. Commun. 282, 284–290 (2009).
[CrossRef]

Balazs, L.

L. Balazs, R. Gijbels, and A. Vertes, “Expansion of laser-generated plumes near the plasma ignition threshold,” Anal. Chem. 63, 314–320 (1991).
[CrossRef]

Barthlemy, O.

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

Bhandarkar, U. V.

N. A. Vasantgadkar, U. V. Bhandarkar, and S. S. Joshi, “A finite element model to predict the ablation depth in pulsed laser ablation,” Thin Solid Films 519, 1421–1430 (2010).
[CrossRef]

Blatter, A.

M. von Allemen and A. Blatter, Laser Beam Interaction with Materials (Springer, 1995).

Bogaerts, A.

A. Bogaerts and Z. Chen, “Effect of laser parameters on laser ablation and laser-induced plasma formation: a numerical modeling investigation,” Spectrochim. Acta B 60, 1280–1307 (2005).
[CrossRef]

A. Bogaerts and Z. Chen, “Laser ablation for analytical sampling: what can we learn from modeling?” Spectrochim. Acta B 58, 1867–1893 (2003).
[CrossRef]

Buerle, D.

D. Buerle, Laser Processing and Chemistry (Springer, 2011).

Bulgakov, A. V.

N. M. Bulgakova and A. V. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[CrossRef]

Bulgakova, N. M.

N. M. Bulgakova and A. V. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[CrossRef]

Camacho, J. J.

J. J. Camacho, L. Diaz, M. Santos, L. J. Juan, and J. M. L. Poyato, “Optical breakdown in gases induced by high-power IR Co2 pulsed lasers,” in Laser Beams: Theory, Properties and Applications, M. Thys and E. Desmet, eds. (Nova Science, 2011), pp. 415–500.

Capitelli, F.

M. Capitelli, F. Capitelli, and A. Elatski, “Non-equilibrium and equilibrium problems in laser induced plasmas,” Spectrochim. Acta B 55, 559–574 (2000).
[CrossRef]

Capitelli, M.

G. Colonna, L. D. Pietnaza, and M. Capitelli, “Coupled solution of a time dependent collisional-radiative model and Boltzmann equation for atomic hydrogen plasmas: possible implications with LIBS plasmas,” Spectrochem. Acta. B 56, 587–598 (2001).
[CrossRef]

M. Capitelli, F. Capitelli, and A. Elatski, “Non-equilibrium and equilibrium problems in laser induced plasmas,” Spectrochim. Acta B 55, 559–574 (2000).
[CrossRef]

Carlslaw, J. H.

J. H. Carlslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University, 1959).

Chaker, M.

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

Chen, Z.

A. Bogaerts and Z. Chen, “Effect of laser parameters on laser ablation and laser-induced plasma formation: a numerical modeling investigation,” Spectrochim. Acta B 60, 1280–1307 (2005).
[CrossRef]

A. Bogaerts and Z. Chen, “Laser ablation for analytical sampling: what can we learn from modeling?” Spectrochim. Acta B 58, 1867–1893 (2003).
[CrossRef]

Chikhcov, B. N.

Colonna, G.

G. Colonna, L. D. Pietnaza, and M. Capitelli, “Coupled solution of a time dependent collisional-radiative model and Boltzmann equation for atomic hydrogen plasmas: possible implications with LIBS plasmas,” Spectrochem. Acta. B 56, 587–598 (2001).
[CrossRef]

Correll, T.

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

Cremers, D. A.

D. A. Cremers and L. J. Radziemski, Handbook of Laser Induced Breakdown Spectroscopy (Wiley, 2006).

L. J. Rakziemski and D. A. Cremers, Laser-Induced Plasmas and Applications (CRC Press, 1989).

Diaz, L.

J. J. Camacho, L. Diaz, M. Santos, L. J. Juan, and J. M. L. Poyato, “Optical breakdown in gases induced by high-power IR Co2 pulsed lasers,” in Laser Beams: Theory, Properties and Applications, M. Thys and E. Desmet, eds. (Nova Science, 2011), pp. 415–500.

El Adawi, M. K.

M. K. El Adawi and E. F. El Shehawey, “Heating a slab induced by a time-dependent laser irradiation—an exact solution,” J. Appl. Phys. 60, 2250–2255 (1986).
[CrossRef]

El Shehawey, E. F.

M. K. El Adawi and E. F. El Shehawey, “Heating a slab induced by a time-dependent laser irradiation—an exact solution,” J. Appl. Phys. 60, 2250–2255 (1986).
[CrossRef]

El-Adawi, M. K.

A. F. Hassan, M. M. El-Nicklawy, and M. K. El-Adawi, “A general problem of pulse laser heating of a slab,” Opt. Laser Technol. 25, 155–162 (1993).
[CrossRef]

Elatski, A.

M. Capitelli, F. Capitelli, and A. Elatski, “Non-equilibrium and equilibrium problems in laser induced plasmas,” Spectrochim. Acta B 55, 559–574 (2000).
[CrossRef]

El-Nicklawy, M. M.

A. F. Hassan, M. M. El-Nicklawy, and M. K. El-Adawi, “A general problem of pulse laser heating of a slab,” Opt. Laser Technol. 25, 155–162 (1993).
[CrossRef]

Fang, R.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

Fichet, P.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429, 269–278 (2001).
[CrossRef]

Gibb, E.

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

Gijbels, R.

L. Balazs, R. Gijbels, and A. Vertes, “Expansion of laser-generated plumes near the plasma ignition threshold,” Anal. Chem. 63, 314–320 (1991).
[CrossRef]

Gornushkin, I. B.

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

Guan, L.

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Hassan, A. F.

A. F. Hassan, M. M. El-Nicklawy, and M. K. El-Adawi, “A general problem of pulse laser heating of a slab,” Opt. Laser Technol. 25, 155–162 (1993).
[CrossRef]

Hou, S.

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Hu, D.

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

Itina, T.

T. Itina, “Etudes numériques des mécanismes d’interaction d’un laser impulsionnel avec des matériaux: application à la sythèse de nano agrégats,” HDR document (Universite de la Mediterranee Aix-Marseille II, 2008).

Jacobs, H.

Jaeger, J. C.

J. H. Carlslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University, 1959).

Johnston, T. W.

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

Joshi, S. S.

N. A. Vasantgadkar, U. V. Bhandarkar, and S. S. Joshi, “A finite element model to predict the ablation depth in pulsed laser ablation,” Thin Solid Films 519, 1421–1430 (2010).
[CrossRef]

Juan, L. J.

J. J. Camacho, L. Diaz, M. Santos, L. J. Juan, and J. M. L. Poyato, “Optical breakdown in gases induced by high-power IR Co2 pulsed lasers,” in Laser Beams: Theory, Properties and Applications, M. Thys and E. Desmet, eds. (Nova Science, 2011), pp. 415–500.

Kaplan, A. F. H.

A. F. H. Kaplan, “Model of the absorption variation during pulsed heating applied to welding of electronic Au/Ni coated Cu-lead frames,” Appl. Surf. Sci. 241, 362–370 (2005).
[CrossRef]

Kelly, R.

A. Peterlongo, A. Miotello, and R. Kelly, “Laser-pulse sputtering of aluminum: vaporization, boiling, superheating, and gas-dynamic effects,” Phys. Rev. E 50, 4716–4727 (1994).

Kurcbart, S. M.

F. E. M. Silveira and S. M. Kurcbart, “Hagen-Rubens relation beyond far-infrared region,” Europhys. Lett. 90, 44004 (2010).
[CrossRef]

Laville, S.

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

Li, L.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Li, Z.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Liu, D.

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Liu, G.

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

Lu, J.

Z. H. Shen, S. Y. Zhang, J. Lu, and X. W. Ni, “Mathematical modeling of laser induced heating and melting in solids,” Opt. Laser Technol. 33, 533–537 (2001).
[CrossRef]

Lu, Q. M.

Q. M. Lu, S. Mao, X. L. Mao, and R. E. Russo, “Delayed phase explosion during high-power nanosecond laser ablation of silicon,” Appl. Phys. Lett. 80, 3072–3074 (2002).
[CrossRef]

Mao, S.

Q. M. Lu, S. Mao, X. L. Mao, and R. E. Russo, “Delayed phase explosion during high-power nanosecond laser ablation of silicon,” Appl. Phys. Lett. 80, 3072–3074 (2002).
[CrossRef]

Mao, X.

X. Mao and R. E. Russo, “Observation of plasma shielding by measuring transmitted and reflected laser pulse temporal profiles,” Appl. Phys. A 64, 1–6 (1996).
[CrossRef]

Mao, X. L.

Q. M. Lu, S. Mao, X. L. Mao, and R. E. Russo, “Delayed phase explosion during high-power nanosecond laser ablation of silicon,” Appl. Phys. Lett. 80, 3072–3074 (2002).
[CrossRef]

Mauchien, P.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429, 269–278 (2001).
[CrossRef]

Miotello, A.

A. Peterlongo, A. Miotello, and R. Kelly, “Laser-pulse sputtering of aluminum: vaporization, boiling, superheating, and gas-dynamic effects,” Phys. Rev. E 50, 4716–4727 (1994).

Momma, C.

Moulin, C.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429, 269–278 (2001).
[CrossRef]

Negutu, C.

M. Stafe, C. Negutu, N. N. Puscas, and I. M. Popescu, “Pulsed laser ablation of solids,” Roman. Rep. Phys. 62, 758–770 (2010).

M. Stafe, C. Negutu, and I. M. Popescu, “Combined experimental and theoretical investigation of multiple-nanosecond laser ablation of metals,” J. Optoelectron. Adv. Mater. 8, 1180–1186 (2006).

Ni, X. W.

Z. H. Shen, S. Y. Zhang, J. Lu, and X. W. Ni, “Mathematical modeling of laser induced heating and melting in solids,” Opt. Laser Technol. 33, 533–537 (2001).
[CrossRef]

Nolte, S.

Omenetto, N.

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

Parisse, J. D.

J. D. Parisse, M. Sentis, and D. E. Zeitoun, “Modeling and numerical simulation of laser matter interaction and ablation with 193 nanometer laser for nanosecond pulse,” Int. J. Numer. Methods Heat Fluid Flow 2, 173–194 (2011).

Peterlongo, A.

A. Peterlongo, A. Miotello, and R. Kelly, “Laser-pulse sputtering of aluminum: vaporization, boiling, superheating, and gas-dynamic effects,” Phys. Rev. E 50, 4716–4727 (1994).

Pietnaza, L. D.

G. Colonna, L. D. Pietnaza, and M. Capitelli, “Coupled solution of a time dependent collisional-radiative model and Boltzmann equation for atomic hydrogen plasmas: possible implications with LIBS plasmas,” Spectrochem. Acta. B 56, 587–598 (2001).
[CrossRef]

Popescu, I. M.

M. Stafe, C. Negutu, N. N. Puscas, and I. M. Popescu, “Pulsed laser ablation of solids,” Roman. Rep. Phys. 62, 758–770 (2010).

M. Stafe, C. Negutu, and I. M. Popescu, “Combined experimental and theoretical investigation of multiple-nanosecond laser ablation of metals,” J. Optoelectron. Adv. Mater. 8, 1180–1186 (2006).

Poyato, J. M. L.

J. J. Camacho, L. Diaz, M. Santos, L. J. Juan, and J. M. L. Poyato, “Optical breakdown in gases induced by high-power IR Co2 pulsed lasers,” in Laser Beams: Theory, Properties and Applications, M. Thys and E. Desmet, eds. (Nova Science, 2011), pp. 415–500.

Puscas, N. N.

M. Stafe, C. Negutu, N. N. Puscas, and I. M. Popescu, “Pulsed laser ablation of solids,” Roman. Rep. Phys. 62, 758–770 (2010).

Radziemski, L. J.

D. A. Cremers and L. J. Radziemski, Handbook of Laser Induced Breakdown Spectroscopy (Wiley, 2006).

Rakziemski, L. J.

L. J. Rakziemski and D. A. Cremers, Laser-Induced Plasmas and Applications (CRC Press, 1989).

Ready, J. F.

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

Russo, R. E.

Q. M. Lu, S. Mao, X. L. Mao, and R. E. Russo, “Delayed phase explosion during high-power nanosecond laser ablation of silicon,” Appl. Phys. Lett. 80, 3072–3074 (2002).
[CrossRef]

X. Mao and R. E. Russo, “Observation of plasma shielding by measuring transmitted and reflected laser pulse temporal profiles,” Appl. Phys. A 64, 1–6 (1996).
[CrossRef]

Santos, M.

J. J. Camacho, L. Diaz, M. Santos, L. J. Juan, and J. M. L. Poyato, “Optical breakdown in gases induced by high-power IR Co2 pulsed lasers,” in Laser Beams: Theory, Properties and Applications, M. Thys and E. Desmet, eds. (Nova Science, 2011), pp. 415–500.

Sentis, M.

J. D. Parisse, M. Sentis, and D. E. Zeitoun, “Modeling and numerical simulation of laser matter interaction and ablation with 193 nanometer laser for nanosecond pulse,” Int. J. Numer. Methods Heat Fluid Flow 2, 173–194 (2011).

Shen, Z. H.

Z. H. Shen, S. Y. Zhang, J. Lu, and X. W. Ni, “Mathematical modeling of laser induced heating and melting in solids,” Opt. Laser Technol. 33, 533–537 (2001).
[CrossRef]

Silveira, F. E. M.

F. E. M. Silveira and S. M. Kurcbart, “Hagen-Rubens relation beyond far-infrared region,” Europhys. Lett. 90, 44004 (2010).
[CrossRef]

Singh, J. P.

J. P. Singh and S. N. Thakur, Laser Induced Breakdown Spectroscopy (Elsevier, 2007).

Smith, B. W.

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

Stafe, M.

M. Stafe, C. Negutu, N. N. Puscas, and I. M. Popescu, “Pulsed laser ablation of solids,” Roman. Rep. Phys. 62, 758–770 (2010).

M. Stafe, C. Negutu, and I. M. Popescu, “Combined experimental and theoretical investigation of multiple-nanosecond laser ablation of metals,” J. Optoelectron. Adv. Mater. 8, 1180–1186 (2006).

Sun, M.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

Tan, X.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Thakur, S. N.

J. P. Singh and S. N. Thakur, Laser Induced Breakdown Spectroscopy (Elsevier, 2007).

Tunnermann, A.

Vasantgadkar, N. A.

N. A. Vasantgadkar, U. V. Bhandarkar, and S. S. Joshi, “A finite element model to predict the ablation depth in pulsed laser ablation,” Thin Solid Films 519, 1421–1430 (2010).
[CrossRef]

Vertes, A.

L. Balazs, R. Gijbels, and A. Vertes, “Expansion of laser-generated plumes near the plasma ignition threshold,” Anal. Chem. 63, 314–320 (1991).
[CrossRef]

Vidal, F.

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

von Allemen, M.

M. von Allemen and A. Blatter, Laser Beam Interaction with Materials (Springer, 1995).

Wagner, J. F.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429, 269–278 (2001).
[CrossRef]

Wellgehaussen, B.

Welling, H.

Winefordner, J.

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

Xu, X.

X. Xu, “Phase explosion and its time lag in nanosecond laser ablation,” Appl. Surf. Sci. 197–198, 61–66 (2002).
[CrossRef]

Yang, F.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

Yu, B.

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Zeitoun, D. E.

J. D. Parisse, M. Sentis, and D. E. Zeitoun, “Modeling and numerical simulation of laser matter interaction and ablation with 193 nanometer laser for nanosecond pulse,” Int. J. Numer. Methods Heat Fluid Flow 2, 173–194 (2011).

Zhang, D.

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Zhang, S. Y.

Z. H. Shen, S. Y. Zhang, J. Lu, and X. W. Ni, “Mathematical modeling of laser induced heating and melting in solids,” Opt. Laser Technol. 33, 533–537 (2001).
[CrossRef]

Anal. Chem. (1)

L. Balazs, R. Gijbels, and A. Vertes, “Expansion of laser-generated plumes near the plasma ignition threshold,” Anal. Chem. 63, 314–320 (1991).
[CrossRef]

Anal. Chim. Acta (1)

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429, 269–278 (2001).
[CrossRef]

Appl. Phys. A (2)

X. Mao and R. E. Russo, “Observation of plasma shielding by measuring transmitted and reflected laser pulse temporal profiles,” Appl. Phys. A 64, 1–6 (1996).
[CrossRef]

N. M. Bulgakova and A. V. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

Q. M. Lu, S. Mao, X. L. Mao, and R. E. Russo, “Delayed phase explosion during high-power nanosecond laser ablation of silicon,” Appl. Phys. Lett. 80, 3072–3074 (2002).
[CrossRef]

Appl. Surf. Sci. (2)

A. F. H. Kaplan, “Model of the absorption variation during pulsed heating applied to welding of electronic Au/Ni coated Cu-lead frames,” Appl. Surf. Sci. 241, 362–370 (2005).
[CrossRef]

X. Xu, “Phase explosion and its time lag in nanosecond laser ablation,” Appl. Surf. Sci. 197–198, 61–66 (2002).
[CrossRef]

Europhys. Lett. (1)

F. E. M. Silveira and S. M. Kurcbart, “Hagen-Rubens relation beyond far-infrared region,” Europhys. Lett. 90, 44004 (2010).
[CrossRef]

Int. J. Numer. Methods Heat Fluid Flow (1)

J. D. Parisse, M. Sentis, and D. E. Zeitoun, “Modeling and numerical simulation of laser matter interaction and ablation with 193 nanometer laser for nanosecond pulse,” Int. J. Numer. Methods Heat Fluid Flow 2, 173–194 (2011).

J. Anal. At. Spectrom. (1)

J. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectroscopy, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061–1083 (2004).
[CrossRef]

J. Appl. Phys. (1)

M. K. El Adawi and E. F. El Shehawey, “Heating a slab induced by a time-dependent laser irradiation—an exact solution,” J. Appl. Phys. 60, 2250–2255 (1986).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Optoelectron. Adv. Mater. (1)

M. Stafe, C. Negutu, and I. M. Popescu, “Combined experimental and theoretical investigation of multiple-nanosecond laser ablation of metals,” J. Optoelectron. Adv. Mater. 8, 1180–1186 (2006).

Opt. Commun. (1)

S. E.-S. Abd El-Ghany, “A theoretical study of the evaporation induced by a pulsed laser in a finite slab,” Opt. Commun. 282, 284–290 (2009).
[CrossRef]

Opt. Laser Technol. (2)

A. F. Hassan, M. M. El-Nicklawy, and M. K. El-Adawi, “A general problem of pulse laser heating of a slab,” Opt. Laser Technol. 25, 155–162 (1993).
[CrossRef]

Z. H. Shen, S. Y. Zhang, J. Lu, and X. W. Ni, “Mathematical modeling of laser induced heating and melting in solids,” Opt. Laser Technol. 33, 533–537 (2001).
[CrossRef]

Phys. B (1)

D. Zhang, D. Liu, Z. Li, S. Hou, B. Yu, L. Guan, X. Tan, and L. Li, “A new model of pulsed laser ablation and plasma shielding,” Phys. B 362, 82–87 (2005).

Phys. Rev. E (2)

S. Laville, F. Vidal, T. W. Johnston, O. Barthlemy, and M. Chaker, “Fluid modeling of laser ablation depth as a function of pulse duration for conductors,” Phys. Rev. E 66, 066415 (2002).
[CrossRef]

A. Peterlongo, A. Miotello, and R. Kelly, “Laser-pulse sputtering of aluminum: vaporization, boiling, superheating, and gas-dynamic effects,” Phys. Rev. E 50, 4716–4727 (1994).

Physica B (1)

L. Li, D. Zhang, Z. Li, L. Guan, X. Tan, R. Fang, D. Hu, and G. Liu, “The investigation of optical characteristics of metal target in high power laser ablation,” Physica B 383, 194–201 (2006).
[CrossRef]

Roman. Rep. Phys. (1)

M. Stafe, C. Negutu, N. N. Puscas, and I. M. Popescu, “Pulsed laser ablation of solids,” Roman. Rep. Phys. 62, 758–770 (2010).

Solid State Commun. (1)

R. Fang, D. Zhang, Z. Li, F. Yang, L. Li, X. Tan, and M. Sun, “Improved thermal model and its application in UV high-power pulsed laser ablation of metal target,” Solid State Commun. 145, 556–560 (2008).
[CrossRef]

Spectrochem. Acta. B (1)

G. Colonna, L. D. Pietnaza, and M. Capitelli, “Coupled solution of a time dependent collisional-radiative model and Boltzmann equation for atomic hydrogen plasmas: possible implications with LIBS plasmas,” Spectrochem. Acta. B 56, 587–598 (2001).
[CrossRef]

Spectrochim. Acta B (3)

M. Capitelli, F. Capitelli, and A. Elatski, “Non-equilibrium and equilibrium problems in laser induced plasmas,” Spectrochim. Acta B 55, 559–574 (2000).
[CrossRef]

A. Bogaerts and Z. Chen, “Laser ablation for analytical sampling: what can we learn from modeling?” Spectrochim. Acta B 58, 1867–1893 (2003).
[CrossRef]

A. Bogaerts and Z. Chen, “Effect of laser parameters on laser ablation and laser-induced plasma formation: a numerical modeling investigation,” Spectrochim. Acta B 60, 1280–1307 (2005).
[CrossRef]

Thin Solid Films (1)

N. A. Vasantgadkar, U. V. Bhandarkar, and S. S. Joshi, “A finite element model to predict the ablation depth in pulsed laser ablation,” Thin Solid Films 519, 1421–1430 (2010).
[CrossRef]

Other (9)

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

J. J. Camacho, L. Diaz, M. Santos, L. J. Juan, and J. M. L. Poyato, “Optical breakdown in gases induced by high-power IR Co2 pulsed lasers,” in Laser Beams: Theory, Properties and Applications, M. Thys and E. Desmet, eds. (Nova Science, 2011), pp. 415–500.

J. P. Singh and S. N. Thakur, Laser Induced Breakdown Spectroscopy (Elsevier, 2007).

D. A. Cremers and L. J. Radziemski, Handbook of Laser Induced Breakdown Spectroscopy (Wiley, 2006).

L. J. Rakziemski and D. A. Cremers, Laser-Induced Plasmas and Applications (CRC Press, 1989).

M. von Allemen and A. Blatter, Laser Beam Interaction with Materials (Springer, 1995).

D. Buerle, Laser Processing and Chemistry (Springer, 2011).

T. Itina, “Etudes numériques des mécanismes d’interaction d’un laser impulsionnel avec des matériaux: application à la sythèse de nano agrégats,” HDR document (Universite de la Mediterranee Aix-Marseille II, 2008).

J. H. Carlslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University, 1959).

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Figures (12)

Fig. 1.
Fig. 1.

Variation of the thermal penetration depth of a pure Cu target irradiated with a pulse duration of 30 ns.

Fig. 2.
Fig. 2.

Organization chart of the numerical computation procedure. FEM, finite element method.

Fig. 3.
Fig. 3.

Temperature distribution inside the target for (a) λ=266nm, (b) λ=532nm, and (c) λ=1064nm, with τ=10ns and I=1013W/m2.

Fig. 4.
Fig. 4.

Pressure variation above the target surface for λ=266nm, with τ=10ns and I=1013W/m2.

Fig. 5.
Fig. 5.

Temperature distribution inside the target for λ=266nm for (a) 5 and (b) 15 ns pulse durations, with I=1013W/m2.

Fig. 6.
Fig. 6.

Temperature distribution inside the target for λ=532nm for (a) 5 and (b) 15 ns pulse durations, with I=1013W/m2.

Fig. 7.
Fig. 7.

Temperature distribution inside the target for λ=1064nm for (a) 2 and (b) 15 ns pulse durations, with I=1013W/m2.

Fig. 8.
Fig. 8.

Temperature distribution inside the target for (a) 1012W/m2 and (b) 1013W/m2.

Fig. 9.
Fig. 9.

Surface temperature variation using variable and constant optical parameters, for λ=266nm, τ=10ns, and I=1013W/m2.

Fig. 10.
Fig. 10.

Vaporization effects and plasma shielding for (a) λ=266nm, (b) λ=532nm, and (c) λ=1064nm, for τ=10ns and I=1013W/m2.

Fig. 11.
Fig. 11.

Spatial variation of the vapor temperature and density for (a) t=10ns, (b) t=18ns, and (c) t=20ns, for λ=266nm, τ=10ns, and I=1013W/m2.

Fig. 12.
Fig. 12.

Variation of the different species in the plume, for λ=266nm, τ=10ns, and I=1013W/m2.

Equations (20)

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

lαalTw,e.
β(T)=24πcϵ0(1+αT(T(x,t)Ta))λσ0,
αa(T)=4πσ0ϵ0λ(1+αT(T(x,t)Ta)).
σϵ0ω,
ρCpTtu(t)Txk2Tx2=(1βpl)βαaI(t)exp(αax).
kTt|x=0=ΔHvρu(t)
T(l,t)=Ta.
u(t)=0.32PρmkBTs(t).
P=Pbexp[ΔHvR(1Tv1Ts(t))].
ρt=(ρv)x,
(ρv)t=x[p+ρv2],
t[ρ(E+v22)]=x[ρv(E+Pρ+v22)]+Ep,
E=CvPρR,
Ep=βplIϵrad.
αIB,ei=[1exp(hcλkBT)]4e6λ3ne3hc4me2π3mekBT(Z12ni1+Z22ni2),
αIB,en=[1exp(hcλkbT)]ϕnen0.
xexijxj1=1nvap(2πmekBTh2)32exp(IPjkBT),j=1p.
x0+xi1+xi2++xip=1,
xi1+xi2++xip=xe.
kTt|x=0=ΔHvρu(t)BI(t).

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