Abstract

In this paper, the effect of laser pulse energy on orthogonal double femtosecond pulse laser induced breakdown spectroscopy (LIBS) in air is studied. In the experiment, the energy of the probe pulse is changeable, while the pump pulse energy is held constant. At the same time, a systematic study of the laser induced breakdown spectroscopy signal dependence on the inter-pulse delay between the two pulses is performed. It is noted that the double pulse orthogonal configuration yields 2–32 times signal enhancement for the ionic and atomic lines as compared to the single pulse LIBS spectra when an optimum temporal separation between the two pulses is used, while there is no significant signal enhancement for the molecular lines in the studied range of the delay. It is also noted that the dependence of the enhancement factor for ionic and atomic lines on the inter-pulse delay can be fitted by Gaussian function. Furthermore, the electron temperature obtained by the relative line-to-continuum intensity ratio method was used to explain the LIBS signal enhancement.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (2)

2010 (2)

K. Shimizu, T. Ishii, M. Blajan, “Emission spectroscopy of pulsed power microplasma for atmospheric pollution control,” IEEE Trans. Ind. Appl. 46, 1125–1131 (2010).
[CrossRef]

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

2009 (7)

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

Z. Zhang, X. Lu, W. X. Liang, Z. Q. Hao, M. L. Zhou, Z. H. Wang, X. Liu, J. Zhang, “Triggering and guiding HV discharge in air by filamentation of single and dual fs pulses,” Opt. Express,  17, 3461–3468 (2009).
[CrossRef] [PubMed]

B. Zhou, S. Akturk, B. Prade, Y. B. Andr, A. Houard, Y. Liu, M. Franco, C. D. Amico, E. Salmon, Z. Q. Hao, N. Lascoux, A. Mysyrowicz, “Revival of femtosecond laser plasma filaments in air by a nanosecond laser,” Opt. Express,  17, 11450–11456 (2009).
[CrossRef] [PubMed]

V. Piñon, D. Anglos, “Optical emission studies of plasma induced by single and double femtosecond laser pulses,” Spectrochim. Acta, Part B 64, 950–960 (2009).
[CrossRef]

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

G Cristoforettim, “Orthogonal double-pulse versus single-pulse laser ablation at different air pressures: a comparison of the mass removal mechanisms,” Spectrochim. Acta, Part B 64, 26–34 (2009).
[CrossRef]

M. A. Gondal, T. Hussain, Z. H. Yamani, M. A. Baig, “On-line monitoring of remediation process of chromium polluted soil using LIBS,” J. Hazard. Mater. 163, 1265–1271 (2009).
[CrossRef]

2008 (3)

T. Hussain, M. A. Gondal, “Monitoring and assessment of toxic metals in gulf war oil spill contaminated soil using laser-induced breakdown spectroscopy,” Environ. Monit. Assess. 136, 391–399 (2008).
[CrossRef]

A. Bogaerts, Z. Chen, D. Autrique, “Double pulse laser ablation and laser induced breakdown spectroscopy: A modeling investigation,” Spectrochim. Acta, Part B 63, 746–754 (2008).
[CrossRef]

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

2007 (3)

H. Luna, J. Dardis, D. Doria, J. T. Costello, “Analysis of time-resolved laser plasma ablation using an imaging spectra technique,” Braz.J. Phys. 37, 1301–1305 (2007).
[CrossRef]

A. D. Giacomo, M. DellAglio, O. D. Pascale, M. Capitelli, “From single pulse to double pulse ns-laser induced breakdown spectroscopy under water: Elemental analysis of aqueous,” Spectrochim. Acta, Part B 62, 721–738 (2007).
[CrossRef]

C. Pasquini, J. Cortez, L. M. C. Silva, F. B. Gonzaga, “Laser induced breakdown spectroscopy,” J. Braz. Chem. Soc. 18, 463–512 (2007).
[CrossRef]

2006 (4)

K. H. Kurniawan, K. Kagawa, “Hydrogen and deuterium analysis using laser-induced plasma spectroscopy,” Appl. Spectrosc. Rev. 41, 99–130 (2006).
[CrossRef]

J. Scaffidi, S. M. Angel, D. A. Cremers, “Emission enhancement mechanisms in dual-pulse LIBS,” Anal. Chem. 78, 24–32 (2006).
[CrossRef] [PubMed]

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

2005 (2)

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

G. Galbacs, V. Budavari, Z. Geretovszky, “Multi-pulse laser-induced plasma spectroscopy using a single laser source and a compact spectrometer,” J. Anal. At. Spectrom. 20, 974–980 (2005).
[CrossRef]

2004 (4)

T. Kim, Z. G. Specht, P. S. Vary, C. T. Lin, “Spectral fingerprints of bacterial strains by laser-induced breakdown spectroscopy,” J. Phys. Chem. B 108, 5477–5482 (2004).
[CrossRef]

W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser induced breakdown spectroscopy: a review of material approaches,” Appl. Spectrosc. Rev. 39, 27–97 (2004).
[CrossRef]

J. M. Vadillo, J. J. Laserna, “Laser-induced plasma spectrometry: truly a surface analytical tool,” Spectrochim. Acta, Part B 59, 147–161 (2004).
[CrossRef]

A. Semerok, C. Dutouquet, “Ultrashort double pulse laser ablation of metals,” Thin Solid Films 453–454,501–505 (2004).
[CrossRef]

2003 (1)

2002 (2)

L. St-Onge, V. Detalle, M. Sabsabi, “Enhanced laser-induced breakdown spectroscopy using the combination of fourth-harmonic and fundamental Nd:YAG laser pulses,” Spectrochim. Acta, Part B 57, 121–135 (2002).
[CrossRef]

K. Song, Y. I. Lee, J. Sneddon, “Recent developments in instrumentation for laser induced breakdown spectroscopy,” Appl. Spectrosc. Rev. 37, 89–117 (2002).
[CrossRef]

2001 (1)

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

1999 (1)

H. C. Liu, X. L. Mao, J. H. Yoo, R. E. Russo, “Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon,” Spectrochim. Acta, Part B 54, 1607–1624 (1999).
[CrossRef]

1996 (1)

1985 (1)

G. J. Bastiaans, R. A. Mangold, “The calculation of electron density and temperature in Ar spectroscopic plasmas from continuum and line spectra,” Spectrochim. Acta. 40B,885–892 (1985).

1982 (1)

Akturk, S.

Amico, C. D.

Amodeo, T.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Andr, Y. B.

Angel, S. M.

J. Scaffidi, S. M. Angel, D. A. Cremers, “Emission enhancement mechanisms in dual-pulse LIBS,” Anal. Chem. 78, 24–32 (2006).
[CrossRef] [PubMed]

Anglos, D.

V. Piñon, D. Anglos, “Optical emission studies of plasma induced by single and double femtosecond laser pulses,” Spectrochim. Acta, Part B 64, 950–960 (2009).
[CrossRef]

Anthony, V.

Autrique, D.

A. Bogaerts, Z. Chen, D. Autrique, “Double pulse laser ablation and laser induced breakdown spectroscopy: A modeling investigation,” Spectrochim. Acta, Part B 63, 746–754 (2008).
[CrossRef]

Babushok, V. I.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

Baig, M. A.

M. A. Gondal, T. Hussain, Z. H. Yamani, M. A. Baig, “On-line monitoring of remediation process of chromium polluted soil using LIBS,” J. Hazard. Mater. 163, 1265–1271 (2009).
[CrossRef]

Bastiaans, G. J.

G. J. Bastiaans, R. A. Mangold, “The calculation of electron density and temperature in Ar spectroscopic plasmas from continuum and line spectra,” Spectrochim. Acta. 40B,885–892 (1985).

Baudelet, M.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Berg, M. A.

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

Blajan, M.

K. Shimizu, T. Ishii, M. Blajan, “Emission spectroscopy of pulsed power microplasma for atmospheric pollution control,” IEEE Trans. Ind. Appl. 46, 1125–1131 (2010).
[CrossRef]

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

Bogaerts, A.

A. Bogaerts, Z. Chen, D. Autrique, “Double pulse laser ablation and laser induced breakdown spectroscopy: A modeling investigation,” Spectrochim. Acta, Part B 63, 746–754 (2008).
[CrossRef]

Bruno, D.

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

Budavari, V.

G. Galbacs, V. Budavari, Z. Geretovszky, “Multi-pulse laser-induced plasma spectroscopy using a single laser source and a compact spectrometer,” J. Anal. At. Spectrom. 20, 974–980 (2005).
[CrossRef]

Capitelli, M.

A. D. Giacomo, M. DellAglio, O. D. Pascale, M. Capitelli, “From single pulse to double pulse ns-laser induced breakdown spectroscopy under water: Elemental analysis of aqueous,” Spectrochim. Acta, Part B 62, 721–738 (2007).
[CrossRef]

Chen, Z.

A. Bogaerts, Z. Chen, D. Autrique, “Double pulse laser ablation and laser induced breakdown spectroscopy: A modeling investigation,” Spectrochim. Acta, Part B 63, 746–754 (2008).
[CrossRef]

Chin, S. L.

Choi, S. C.

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

Collins, L.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

Cortez, J.

C. Pasquini, J. Cortez, L. M. C. Silva, F. B. Gonzaga, “Laser induced breakdown spectroscopy,” J. Braz. Chem. Soc. 18, 463–512 (2007).
[CrossRef]

Costello, J. T.

H. Luna, J. Dardis, D. Doria, J. T. Costello, “Analysis of time-resolved laser plasma ablation using an imaging spectra technique,” Braz.J. Phys. 37, 1301–1305 (2007).
[CrossRef]

Cremers, D. A.

J. Scaffidi, S. M. Angel, D. A. Cremers, “Emission enhancement mechanisms in dual-pulse LIBS,” Anal. Chem. 78, 24–32 (2006).
[CrossRef] [PubMed]

Cristoforettim, G

G Cristoforettim, “Orthogonal double-pulse versus single-pulse laser ablation at different air pressures: a comparison of the mass removal mechanisms,” Spectrochim. Acta, Part B 64, 26–34 (2009).
[CrossRef]

Daigle, J. F.

Dardis, J.

H. Luna, J. Dardis, D. Doria, J. T. Costello, “Analysis of time-resolved laser plasma ablation using an imaging spectra technique,” Braz.J. Phys. 37, 1301–1305 (2007).
[CrossRef]

DellAglio, M.

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

A. D. Giacomo, M. DellAglio, O. D. Pascale, M. Capitelli, “From single pulse to double pulse ns-laser induced breakdown spectroscopy under water: Elemental analysis of aqueous,” Spectrochim. Acta, Part B 62, 721–738 (2007).
[CrossRef]

Delong, K. W.

DeLucia, F. C.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

Detalle, V.

L. St-Onge, V. Detalle, M. Sabsabi, “Enhanced laser-induced breakdown spectroscopy using the combination of fourth-harmonic and fundamental Nd:YAG laser pulses,” Spectrochim. Acta, Part B 57, 121–135 (2002).
[CrossRef]

Doria, D.

H. Luna, J. Dardis, D. Doria, J. T. Costello, “Analysis of time-resolved laser plasma ablation using an imaging spectra technique,” Braz.J. Phys. 37, 1301–1305 (2007).
[CrossRef]

Dubessy, J.

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

Dutouquet, C.

A. Semerok, C. Dutouquet, “Ultrashort double pulse laser ablation of metals,” Thin Solid Films 453–454,501–505 (2004).
[CrossRef]

Eland, K. L.

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

Fichet, P.

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

Fittinghoff, D. N.

Franco, M.

Frejafon, E.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Galbacs, G.

G. Galbacs, V. Budavari, Z. Geretovszky, “Multi-pulse laser-induced plasma spectroscopy using a single laser source and a compact spectrometer,” J. Anal. At. Spectrom. 20, 974–980 (2005).
[CrossRef]

Gao, X.

Garten, C. T.

Gaudiuso, R.

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

Gautier, C.

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

Geretovszky, Z.

G. Galbacs, V. Budavari, Z. Geretovszky, “Multi-pulse laser-induced plasma spectroscopy using a single laser source and a compact spectrometer,” J. Anal. At. Spectrom. 20, 974–980 (2005).
[CrossRef]

Giacomo, A. D.

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

A. D. Giacomo, M. DellAglio, O. D. Pascale, M. Capitelli, “From single pulse to double pulse ns-laser induced breakdown spectroscopy under water: Elemental analysis of aqueous,” Spectrochim. Acta, Part B 62, 721–738 (2007).
[CrossRef]

Gold, D. M.

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

Gondal, M. A.

M. A. Gondal, T. Hussain, Z. H. Yamani, M. A. Baig, “On-line monitoring of remediation process of chromium polluted soil using LIBS,” J. Hazard. Mater. 163, 1265–1271 (2009).
[CrossRef]

T. Hussain, M. A. Gondal, “Monitoring and assessment of toxic metals in gulf war oil spill contaminated soil using laser-induced breakdown spectroscopy,” Environ. Monit. Assess. 136, 391–399 (2008).
[CrossRef]

Gonzaga, F. B.

C. Pasquini, J. Cortez, L. M. C. Silva, F. B. Gonzaga, “Laser induced breakdown spectroscopy,” J. Braz. Chem. Soc. 18, 463–512 (2007).
[CrossRef]

Gottfried, J. L.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

Guo, K. M.

Guyon, L.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Hao, Z. Q.

Harmon, R. S.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

Houard, A.

Hussain, T.

M. A. Gondal, T. Hussain, Z. H. Yamani, M. A. Baig, “On-line monitoring of remediation process of chromium polluted soil using LIBS,” J. Hazard. Mater. 163, 1265–1271 (2009).
[CrossRef]

T. Hussain, M. A. Gondal, “Monitoring and assessment of toxic metals in gulf war oil spill contaminated soil using laser-induced breakdown spectroscopy,” Environ. Monit. Assess. 136, 391–399 (2008).
[CrossRef]

Ishii, T.

K. Shimizu, T. Ishii, M. Blajan, “Emission spectroscopy of pulsed power microplasma for atmospheric pollution control,” IEEE Trans. Ind. Appl. 46, 1125–1131 (2010).
[CrossRef]

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

Kagawa, K.

K. H. Kurniawan, K. Kagawa, “Hydrogen and deuterium analysis using laser-induced plasma spectroscopy,” Appl. Spectrosc. Rev. 41, 99–130 (2006).
[CrossRef]

Killinger, D. K.

Kim, T.

T. Kim, Z. G. Specht, P. S. Vary, C. T. Lin, “Spectral fingerprints of bacterial strains by laser-induced breakdown spectroscopy,” J. Phys. Chem. B 108, 5477–5482 (2004).
[CrossRef]

Ko, D. K.

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

Krumbgel, M. A.

Kurniawan, K. H.

K. H. Kurniawan, K. Kagawa, “Hydrogen and deuterium analysis using laser-induced plasma spectroscopy,” Appl. Spectrosc. Rev. 41, 99–130 (2006).
[CrossRef]

L’Hermite, D.

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

Lacour, J.-L.

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

Lai, T.

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

Laloi, P.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Lascoux, N.

Laserna, J. J.

J. M. Vadillo, J. J. Laserna, “Laser-induced plasma spectrometry: truly a surface analytical tool,” Spectrochim. Acta, Part B 59, 147–161 (2004).
[CrossRef]

Lee, J.

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

Lee, W. B.

W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser induced breakdown spectroscopy: a review of material approaches,” Appl. Spectrosc. Rev. 39, 27–97 (2004).
[CrossRef]

Lee, Y.

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

Lee, Y. I.

W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser induced breakdown spectroscopy: a review of material approaches,” Appl. Spectrosc. Rev. 39, 27–97 (2004).
[CrossRef]

K. Song, Y. I. Lee, J. Sneddon, “Recent developments in instrumentation for laser induced breakdown spectroscopy,” Appl. Spectrosc. Rev. 37, 89–117 (2002).
[CrossRef]

Li, B. Z.

Liang, W. X.

Lin, C. T.

T. Kim, Z. G. Specht, P. S. Vary, C. T. Lin, “Spectral fingerprints of bacterial strains by laser-induced breakdown spectroscopy,” J. Phys. Chem. B 108, 5477–5482 (2004).
[CrossRef]

Lin, J. Q.

Liu, H. C.

H. C. Liu, X. L. Mao, J. H. Yoo, R. E. Russo, “Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon,” Spectrochim. Acta, Part B 54, 1607–1624 (1999).
[CrossRef]

Liu, X.

Liu, Y.

Lu, X.

Luna, H.

H. Luna, J. Dardis, D. Doria, J. T. Costello, “Analysis of time-resolved laser plasma ablation using an imaging spectra technique,” Braz.J. Phys. 37, 1301–1305 (2007).
[CrossRef]

Mangold, R. A.

G. J. Bastiaans, R. A. Mangold, “The calculation of electron density and temperature in Ar spectroscopic plasmas from continuum and line spectra,” Spectrochim. Acta. 40B,885–892 (1985).

Mao, X. L.

H. C. Liu, X. L. Mao, J. H. Yoo, R. E. Russo, “Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon,” Spectrochim. Acta, Part B 54, 1607–1624 (1999).
[CrossRef]

Martin, M. Z.

McManus, C.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

McMillan, N. J.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

Menut, D.

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

Menyuk, C. R.

Menyuk, N.

Michael Angel, S.

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

Mimura, H.

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

Miziolek, A. W.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

Munson, C. A.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

Muramatsu, S.

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

Mysyrowicz, A.

Nam, S.

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

Oh, M. K.

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

Pascale, O. D.

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

A. D. Giacomo, M. DellAglio, O. D. Pascale, M. Capitelli, “From single pulse to double pulse ns-laser induced breakdown spectroscopy under water: Elemental analysis of aqueous,” Spectrochim. Acta, Part B 62, 721–738 (2007).
[CrossRef]

Pasquini, C.

C. Pasquini, J. Cortez, L. M. C. Silva, F. B. Gonzaga, “Laser induced breakdown spectroscopy,” J. Braz. Chem. Soc. 18, 463–512 (2007).
[CrossRef]

Piñon, V.

V. Piñon, D. Anglos, “Optical emission studies of plasma induced by single and double femtosecond laser pulses,” Spectrochim. Acta, Part B 64, 950–960 (2009).
[CrossRef]

Prade, B.

Remus, J.

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

Russo, R. E.

H. C. Liu, X. L. Mao, J. H. Yoo, R. E. Russo, “Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon,” Spectrochim. Acta, Part B 54, 1607–1624 (1999).
[CrossRef]

Sabsabi, M.

L. St-Onge, V. Detalle, M. Sabsabi, “Enhanced laser-induced breakdown spectroscopy using the combination of fourth-harmonic and fundamental Nd:YAG laser pulses,” Spectrochim. Acta, Part B 57, 121–135 (2002).
[CrossRef]

Salmon, E.

Scaffidi, J.

J. Scaffidi, S. M. Angel, D. A. Cremers, “Emission enhancement mechanisms in dual-pulse LIBS,” Anal. Chem. 78, 24–32 (2006).
[CrossRef] [PubMed]

Semerok, A.

A. Semerok, C. Dutouquet, “Ultrashort double pulse laser ablation of metals,” Thin Solid Films 453–454,501–505 (2004).
[CrossRef]

Shimizu, K.

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

K. Shimizu, T. Ishii, M. Blajan, “Emission spectroscopy of pulsed power microplasma for atmospheric pollution control,” IEEE Trans. Ind. Appl. 46, 1125–1131 (2010).
[CrossRef]

Silva, L. M. C.

C. Pasquini, J. Cortez, L. M. C. Silva, F. B. Gonzaga, “Laser induced breakdown spectroscopy,” J. Braz. Chem. Soc. 18, 463–512 (2007).
[CrossRef]

Sneddon, J.

W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser induced breakdown spectroscopy: a review of material approaches,” Appl. Spectrosc. Rev. 39, 27–97 (2004).
[CrossRef]

K. Song, Y. I. Lee, J. Sneddon, “Recent developments in instrumentation for laser induced breakdown spectroscopy,” Appl. Spectrosc. Rev. 37, 89–117 (2002).
[CrossRef]

Song, K.

K. Song, Y. I. Lee, J. Sneddon, “Recent developments in instrumentation for laser induced breakdown spectroscopy,” Appl. Spectrosc. Rev. 37, 89–117 (2002).
[CrossRef]

Specht, Z. G.

T. Kim, Z. G. Specht, P. S. Vary, C. T. Lin, “Spectral fingerprints of bacterial strains by laser-induced breakdown spectroscopy,” J. Phys. Chem. B 108, 5477–5482 (2004).
[CrossRef]

Sridharan, A.

St-Onge, L.

L. St-Onge, V. Detalle, M. Sabsabi, “Enhanced laser-induced breakdown spectroscopy using the combination of fourth-harmonic and fundamental Nd:YAG laser pulses,” Spectrochim. Acta, Part B 57, 121–135 (2002).
[CrossRef]

Stratis, D. N.

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

Sun, C. K.

Trebino, R.

Tsang, T.

Vadillo, J. M.

J. M. Vadillo, J. J. Laserna, “Laser-induced plasma spectrometry: truly a surface analytical tool,” Spectrochim. Acta, Part B 59, 147–161 (2004).
[CrossRef]

Vary, P. S.

T. Kim, Z. G. Specht, P. S. Vary, C. T. Lin, “Spectral fingerprints of bacterial strains by laser-induced breakdown spectroscopy,” J. Phys. Chem. B 108, 5477–5482 (2004).
[CrossRef]

Wang, T. J.

Wang, Z. H.

Wolf, J. P.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Wu, J. Y.

W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser induced breakdown spectroscopy: a review of material approaches,” Appl. Spectrosc. Rev. 39, 27–97 (2004).
[CrossRef]

Wullschleger, S. D.

Xu, H. L.

Yamani, Z. H.

M. A. Gondal, T. Hussain, Z. H. Yamani, M. A. Baig, “On-line monitoring of remediation process of chromium polluted soil using LIBS,” J. Hazard. Mater. 163, 1265–1271 (2009).
[CrossRef]

Yoo, J. H.

H. C. Liu, X. L. Mao, J. H. Yoo, R. E. Russo, “Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon,” Spectrochim. Acta, Part B 54, 1607–1624 (1999).
[CrossRef]

Yu, J.

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

Yuan, S.

Zhang, J.

Zhang, Z.

Zhao, Z. M.

Zhou, B.

Zhou, M. L.

Anal. Chem. (1)

J. Scaffidi, S. M. Angel, D. A. Cremers, “Emission enhancement mechanisms in dual-pulse LIBS,” Anal. Chem. 78, 24–32 (2006).
[CrossRef] [PubMed]

Appl. Geochem. (1)

R. S. Harmon, J. Remus, N. J. McMillan, C. McManus, L. Collins, J. L. Gottfried, F. C. DeLucia, A. W. Miziolek, “LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals,” Appl. Geochem. 24, 1125–1411 (2009).
[CrossRef]

Appl. Opt. (2)

Appl. Spectrosc. Rev. (3)

K. H. Kurniawan, K. Kagawa, “Hydrogen and deuterium analysis using laser-induced plasma spectroscopy,” Appl. Spectrosc. Rev. 41, 99–130 (2006).
[CrossRef]

W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser induced breakdown spectroscopy: a review of material approaches,” Appl. Spectrosc. Rev. 39, 27–97 (2004).
[CrossRef]

K. Song, Y. I. Lee, J. Sneddon, “Recent developments in instrumentation for laser induced breakdown spectroscopy,” Appl. Spectrosc. Rev. 37, 89–117 (2002).
[CrossRef]

Braz.J. Phys. (1)

H. Luna, J. Dardis, D. Doria, J. T. Costello, “Analysis of time-resolved laser plasma ablation using an imaging spectra technique,” Braz.J. Phys. 37, 1301–1305 (2007).
[CrossRef]

Environ. Monit. Assess. (1)

T. Hussain, M. A. Gondal, “Monitoring and assessment of toxic metals in gulf war oil spill contaminated soil using laser-induced breakdown spectroscopy,” Environ. Monit. Assess. 136, 391–399 (2008).
[CrossRef]

Fresen. J. Anal. Chem. (1)

S. Michael Angel, D. N. Stratis, K. L. Eland, T. Lai, M. A. Berg, D. M. Gold, “LIBS using dual- and ultra-short laser pulses,” Fresen. J. Anal. Chem. 369, 320–327 (2001).
[CrossRef]

IEEE Trans. Ind. Appl. (1)

K. Shimizu, T. Ishii, M. Blajan, “Emission spectroscopy of pulsed power microplasma for atmospheric pollution control,” IEEE Trans. Ind. Appl. 46, 1125–1131 (2010).
[CrossRef]

J. Anal. At. Spectrom. (1)

G. Galbacs, V. Budavari, Z. Geretovszky, “Multi-pulse laser-induced plasma spectroscopy using a single laser source and a compact spectrometer,” J. Anal. At. Spectrom. 20, 974–980 (2005).
[CrossRef]

J. Appl. Phys. (1)

M. Baudelet, L. Guyon, J. Yu, J. P. Wolf, T. Amodeo, E. Frejafon, P. Laloi, “Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: a comparison to the nanosecond regime,” J. Appl. Phys. 99, 084701–084701-9(2006).
[CrossRef]

J. Braz. Chem. Soc. (1)

C. Pasquini, J. Cortez, L. M. C. Silva, F. B. Gonzaga, “Laser induced breakdown spectroscopy,” J. Braz. Chem. Soc. 18, 463–512 (2007).
[CrossRef]

J. Hazard. Mater. (1)

M. A. Gondal, T. Hussain, Z. H. Yamani, M. A. Baig, “On-line monitoring of remediation process of chromium polluted soil using LIBS,” J. Hazard. Mater. 163, 1265–1271 (2009).
[CrossRef]

J. Inst. Electrostat. Jpn. (1)

M. Blajan, S. Muramatsu, T. Ishii, H. Mimura, K. Shimizu, “Emission spectroscopy of microplasma driven by a pulsed power supply,” J. Inst. Electrostat. Jpn. 34, 99–104 (2010).

J. Phys. Chem. B (1)

T. Kim, Z. G. Specht, P. S. Vary, C. T. Lin, “Spectral fingerprints of bacterial strains by laser-induced breakdown spectroscopy,” J. Phys. Chem. B 108, 5477–5482 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Spectrochim. Acta, Part B (11)

H. C. Liu, X. L. Mao, J. H. Yoo, R. E. Russo, “Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon,” Spectrochim. Acta, Part B 54, 1607–1624 (1999).
[CrossRef]

C. Gautier, P. Fichet, D. Menut, J.-L. Lacour, D. L’Hermite, J. Dubessy, “Quantification of the intensity enhancement for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry,” Spectrochim. Acta, Part B 60, 265–276 (2005).
[CrossRef]

L. St-Onge, V. Detalle, M. Sabsabi, “Enhanced laser-induced breakdown spectroscopy using the combination of fourth-harmonic and fundamental Nd:YAG laser pulses,” Spectrochim. Acta, Part B 57, 121–135 (2002).
[CrossRef]

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, A. W. Miziolek, “Double pulse laser ablation and plasma: laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta, Part B 61, 999–1014 (2006).
[CrossRef]

G Cristoforettim, “Orthogonal double-pulse versus single-pulse laser ablation at different air pressures: a comparison of the mass removal mechanisms,” Spectrochim. Acta, Part B 64, 26–34 (2009).
[CrossRef]

A. D. Giacomo, M. DellAglio, D. Bruno, R. Gaudiuso, O. D. Pascale, “Experimental and theoretical comparison of single-pulse and double-pulse laser induced breakdown spectroscopy on metallic samples,” Spectrochim. Acta, Part B 63, 805–816 (2008).
[CrossRef]

S. C. Choi, M. K. Oh, Y. Lee, S. Nam, D. K. Ko, J. Lee, “Dynamic effects of a pre-ablation spark in the orthogonal dual-pulse laser induced breakdown spectroscopy,” Spectrochim. Acta, Part B 64, 427–435 (2009).
[CrossRef]

J. M. Vadillo, J. J. Laserna, “Laser-induced plasma spectrometry: truly a surface analytical tool,” Spectrochim. Acta, Part B 59, 147–161 (2004).
[CrossRef]

V. Piñon, D. Anglos, “Optical emission studies of plasma induced by single and double femtosecond laser pulses,” Spectrochim. Acta, Part B 64, 950–960 (2009).
[CrossRef]

A. D. Giacomo, M. DellAglio, O. D. Pascale, M. Capitelli, “From single pulse to double pulse ns-laser induced breakdown spectroscopy under water: Elemental analysis of aqueous,” Spectrochim. Acta, Part B 62, 721–738 (2007).
[CrossRef]

A. Bogaerts, Z. Chen, D. Autrique, “Double pulse laser ablation and laser induced breakdown spectroscopy: A modeling investigation,” Spectrochim. Acta, Part B 63, 746–754 (2008).
[CrossRef]

Spectrochim. Acta. (1)

G. J. Bastiaans, R. A. Mangold, “The calculation of electron density and temperature in Ar spectroscopic plasmas from continuum and line spectra,” Spectrochim. Acta. 40B,885–892 (1985).

Thin Solid Films (1)

A. Semerok, C. Dutouquet, “Ultrashort double pulse laser ablation of metals,” Thin Solid Films 453–454,501–505 (2004).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup, BS, beam-splitter; M1–8, 810 nm high-reflection mirrors; M9, 270 nm high-reflection mirrors; WP, 1/2 wave plate; GP, Glan polarizer; L1–4, focusing lenses; BBO, Beta-Bariume Borate Crystal.

Fig. 2
Fig. 2

The LIBS spectra from air spark, in the case of the DP and SP scheme.

Fig. 3
Fig. 3

The DP-LIBS spectra from air spark with different inter-pulse delays at the fixed probe pulse energy E2=1.0 mJ.

Fig. 4
Fig. 4

Lorentzian fitting of the stark broadened profile for N II 500.5 nm at inter-pulse delay 0 fs in the DP-LIBS scheme. The ratio of the integrated spectral line intensity (A) and continuum intensity (y0) at the center wavelength were used for the calculation of electron temperature.

Fig. 5
Fig. 5

Influence of the inter-pulse delay, on the signal enhancement factor for several emission lines in the DP-LIBS measurements with all cases of probe pulse energy. (a), (b), (c) and (d) indicate the results of the spectra of 777.2, 746.8, 656.2 and 500.5 nm, respectively.

Fig. 6
Fig. 6

The variation of signal enhancement factor (IDP/ISP) as a function of laser pulses energies ratio (E2/E1). With the inter-pulse delay between the two pulses is 0 fs in all the cases.

Fig. 7
Fig. 7

The time-averaged electron temperature as a function of the inter-pulse delay between the two laser pulses in the DP-LIBS measurements with the probe pulse energy E2 = 1.0 mJ. The insert shows the relation between the signal enhancement factor of N II 500.5 nm line and the electron temperature within the inter-pulse delay range of −200 fs to 0 fs.

Tables (1)

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Table 1 The FWHM for various emission lines observed in the LIBS spectra corresponding to different probe pulse energies.

Equations (3)

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y = y 0 + 2 A π w 4 ( x x c ) + w 2
ε l ε c = C r A k i g k U i λ c 2 λ l T e exp [ ( E i E k Δ E i ) / k T e ] ξ [ 1 exp ( h c / λ k T e ) ] + G [ exp ( h c / λ k T e ) ]
I D P I S P = N D P N S P U ( T S P ) U ( T D P ) exp ( E k * k ( 1 T D P 1 T S P ) )

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