Abstract

Ultrafast laser filament induced breakdown spectroscopy is a very promising method for remote material detection. We present characteristics of plasmas generated in a metal target by laser filaments in air. Our measurements show that the temperature of the ablation plasma is clamped along the filament channel due to intensity clamping in a filament. Nevertheless, significant changes in radiation intensity are noticeable, and this is essentially due to variation in the number density of emitting atoms. The present results also explain the near absence of ion emission but strong atomic neutral emission from plumes produced during fs LIBS in air.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  27. R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
    [Crossref]
  28. M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
    [Crossref]

2015 (3)

S. S. Harilal, P. K. Diwakar, N. L. LaHaye, and M. C. Phillips, “Spatio-temporal evolution of uranium emission in laser-produced plasmas,” Spectrochem. Acta B 111, 1–7 (2015).
[Crossref]

S. S. Harilal, B. E. Brumfield, and M. C. Phillips, “Lifecycle of laser-produced air sparks,” Phys. Plasmas 22(6), 063301 (2015).
[Crossref]

S. S. Harilal, P. K. Diwakar, M. P. Polek, and M. C. Phillips, “Morphological changes in ultrafast laser ablation plumes with varying spot size,” Opt. Express 23(12), 15608–15615 (2015).
[Crossref] [PubMed]

2014 (3)

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

2013 (1)

2012 (1)

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

2011 (1)

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

E. J. Judge, G. Heck, E. B. Cerkez, and R. J. Levis, “Discrimination of Composite Graphite Samples Using Remote Filament-Induced Breakdown Spectroscopy,” Anal. Chem. 81(7), 2658–2663 (2009).
[Crossref] [PubMed]

2008 (2)

J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express 16(1), 466–493 (2008).
[Crossref] [PubMed]

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

2007 (3)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

E. L. Gurevich and R. Hergenröder, “Femtosecond laser-induced breakdown spectroscopy: physics, applications, and perspectives,” Appl. Spectrosc. 61(10), 233–242 (2007).
[Crossref] [PubMed]

2006 (2)

2004 (3)

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

2000 (1)

R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
[Crossref]

1999 (2)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

M. S. Dimitrijevic and S. Sahal-Brechot, “Stark broadening of neutral zinc spectral lines,” Astron. Astrophys. Sup. 140, 193–196 (1999).
[Crossref]

1998 (1)

R. F. W. Herrmann, J. Gerlach, and E. E. B. Campbell, “Ultrashort pulse laser ablation of silicon: an MD simulation study,” Appl. Phys., A Mater. Sci. Process. 66(1), 35–42 (1998).
[Crossref]

Ackermann, R.

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

Afonasenko, A. V.

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Anglos, D.

Apeksimov, D. V.

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Arnold, C. L.

Ashkenasi, D.

R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
[Crossref]

Ayyalasomayajula, K. K.

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

Bagchi, S.

Baudelet, M.

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Bernhardt, J.

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Borchert, H.

Bourayou, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Brumfield, B. E.

S. S. Harilal, B. E. Brumfield, and M. C. Phillips, “Lifecycle of laser-produced air sparks,” Phys. Plasmas 22(6), 063301 (2015).
[Crossref]

Campbell, E. E. B.

R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
[Crossref]

R. F. W. Herrmann, J. Gerlach, and E. E. B. Campbell, “Ultrashort pulse laser ablation of silicon: an MD simulation study,” Appl. Phys., A Mater. Sci. Process. 66(1), 35–42 (1998).
[Crossref]

Cerkez, E. B.

E. J. Judge, G. Heck, E. B. Cerkez, and R. J. Levis, “Discrimination of Composite Graphite Samples Using Remote Filament-Induced Breakdown Spectroscopy,” Anal. Chem. 81(7), 2658–2663 (2009).
[Crossref] [PubMed]

Chateauneuf, M.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Chin, S. L.

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors 11(1), 32–53 (2010).
[Crossref] [PubMed]

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Couairon, A.

Daigle, J. F.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Diener, K.

Dikshit, V.

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

Dimitrijevic, M. S.

M. S. Dimitrijevic and S. Sahal-Brechot, “Stark broadening of neutral zinc spectral lines,” Astron. Astrophys. Sup. 140, 193–196 (1999).
[Crossref]

Diwakar, P. K.

S. S. Harilal, P. K. Diwakar, N. L. LaHaye, and M. C. Phillips, “Spatio-temporal evolution of uranium emission in laser-produced plasmas,” Spectrochem. Acta B 111, 1–7 (2015).
[Crossref]

S. S. Harilal, P. K. Diwakar, M. P. Polek, and M. C. Phillips, “Morphological changes in ultrafast laser ablation plumes with varying spot size,” Opt. Express 23(12), 15608–15615 (2015).
[Crossref] [PubMed]

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Dubois, J.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Durand, M.

Durécu, A.

Eislöffel, J.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Farid, N.

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Fleury, D.

Freeman, J. F.

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Geints, Y. E.

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Gerlach, J.

R. F. W. Herrmann, J. Gerlach, and E. E. B. Campbell, “Ultrashort pulse laser ablation of silicon: an MD simulation study,” Appl. Phys., A Mater. Sci. Process. 66(1), 35–42 (1998).
[Crossref]

Golik, S. S.

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Gray, D.

Gurevich, E. L.

E. L. Gurevich and R. Hergenröder, “Femtosecond laser-induced breakdown spectroscopy: physics, applications, and perspectives,” Appl. Spectrosc. 61(10), 233–242 (2007).
[Crossref] [PubMed]

Harilal, S. S.

S. S. Harilal, B. E. Brumfield, and M. C. Phillips, “Lifecycle of laser-produced air sparks,” Phys. Plasmas 22(6), 063301 (2015).
[Crossref]

S. S. Harilal, P. K. Diwakar, N. L. LaHaye, and M. C. Phillips, “Spatio-temporal evolution of uranium emission in laser-produced plasmas,” Spectrochem. Acta B 111, 1–7 (2015).
[Crossref]

S. S. Harilal, P. K. Diwakar, M. P. Polek, and M. C. Phillips, “Morphological changes in ultrafast laser ablation plumes with varying spot size,” Opt. Express 23(12), 15608–15615 (2015).
[Crossref] [PubMed]

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Hassanein, A.

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Hatzes, A. P.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Heck, G.

E. J. Judge, G. Heck, E. B. Cerkez, and R. J. Levis, “Discrimination of Composite Graphite Samples Using Remote Filament-Induced Breakdown Spectroscopy,” Anal. Chem. 81(7), 2658–2663 (2009).
[Crossref] [PubMed]

Hergenröder, R.

E. L. Gurevich and R. Hergenröder, “Femtosecond laser-induced breakdown spectroscopy: physics, applications, and perspectives,” Appl. Spectrosc. 61(10), 233–242 (2007).
[Crossref] [PubMed]

Herrmann, R. F. W.

R. F. W. Herrmann, J. Gerlach, and E. E. B. Campbell, “Ultrashort pulse laser ablation of silicon: an MD simulation study,” Appl. Phys., A Mater. Sci. Process. 66(1), 35–42 (1998).
[Crossref]

Houard, A.

Judge, E. J.

E. J. Judge, G. Heck, E. B. Cerkez, and R. J. Levis, “Discrimination of Composite Graphite Samples Using Remote Filament-Induced Breakdown Spectroscopy,” Anal. Chem. 81(7), 2658–2663 (2009).
[Crossref] [PubMed]

Kabanov, A. M.

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Kasparian, J.

J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express 16(1), 466–493 (2008).
[Crossref] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Kiran, P. P.

Kolesik, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Krishnan, S. R.

Kumar, G. R.

LaHaye, N. L.

S. S. Harilal, P. K. Diwakar, N. L. LaHaye, and M. C. Phillips, “Spatio-temporal evolution of uranium emission in laser-produced plasmas,” Spectrochem. Acta B 111, 1–7 (2015).
[Crossref]

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Laux, U.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Levis, R. J.

E. J. Judge, G. Heck, E. B. Cerkez, and R. J. Levis, “Discrimination of Composite Graphite Samples Using Remote Filament-Induced Breakdown Spectroscopy,” Anal. Chem. 81(7), 2658–2663 (2009).
[Crossref] [PubMed]

Lim, K.

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

Liu, W.

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Mejean, G.

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

Méjean, G.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Mlejnek, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Moloney, J. V.

J. V. Moloney, “Intense femtosecond pulse propagation with applications,” Proc. SPIE 6261, 626102 (2006).
[Crossref]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Moreau, B.

Munson, C.

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

Mysyrowicz, A.

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Phillips, M. C.

S. S. Harilal, P. K. Diwakar, N. L. LaHaye, and M. C. Phillips, “Spatio-temporal evolution of uranium emission in laser-produced plasmas,” Spectrochem. Acta B 111, 1–7 (2015).
[Crossref]

S. S. Harilal, P. K. Diwakar, M. P. Polek, and M. C. Phillips, “Morphological changes in ultrafast laser ablation plumes with varying spot size,” Opt. Express 23(12), 15608–15615 (2015).
[Crossref] [PubMed]

S. S. Harilal, B. E. Brumfield, and M. C. Phillips, “Lifecycle of laser-produced air sparks,” Phys. Plasmas 22(6), 063301 (2015).
[Crossref]

Polek, M. P.

Porwitzky, A.

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

Prade, B.

Ramme, M.

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

Richardson, M.

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

Rodriguez, M.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Rohwetter, P.

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

Rosenfeld, A.

R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
[Crossref]

Sahal-Brechot, S.

M. S. Dimitrijevic and S. Sahal-Brechot, “Stark broadening of neutral zinc spectral lines,” Astron. Astrophys. Sup. 140, 193–196 (1999).
[Crossref]

Salmon, E.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

Sauerbrey, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Schmitt, R.

Scholz, A.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Singh, J. P.

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Smith, L. T.

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

Stecklum, B.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Stelmaszczyk, K.

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

Stoian, R.

R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
[Crossref]

Theberge, F.

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Théberge, F.

Tzortzakis, S.

Valenzuela, A.

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

Vasseur, O.

Weidman, M.

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

Wolf, J. P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Wolf, J.-P.

Woste, L.

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

Wöste, L.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Wright, E. M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Xu, H. L.

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors 11(1), 32–53 (2010).
[Crossref] [PubMed]

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Yu, J.

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Yueh, F. Y.

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

Zemlyanov, A. A.

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Anal. Bioanal. Chem. (1)

K. K. Ayyalasomayajula, V. Dikshit, F. Y. Yueh, J. P. Singh, and L. T. Smith, “Quantitative analysis of slurry sample by laser-induced breakdown spectroscopy,” Anal. Bioanal. Chem. 400(10), 3315–3322 (2011).
[Crossref] [PubMed]

Anal. Chem. (1)

E. J. Judge, G. Heck, E. B. Cerkez, and R. J. Levis, “Discrimination of Composite Graphite Samples Using Remote Filament-Induced Breakdown Spectroscopy,” Anal. Chem. 81(7), 2658–2663 (2009).
[Crossref] [PubMed]

Appl. Phys. B (1)

A. Valenzuela, C. Munson, A. Porwitzky, M. Weidman, and M. Richardson, “Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys,” Appl. Phys. B 116(2), 485–491 (2014).
[Crossref]

Appl. Phys. Lett. (2)

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004).
[Crossref]

M. Weidman, K. Lim, M. Ramme, M. Durand, M. Baudelet, and M. Richardson, “Stand-off filament-induced ablation of gallium arsenide,” Appl. Phys. Lett. 101(3), 034101 (2012).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (2)

R. F. W. Herrmann, J. Gerlach, and E. E. B. Campbell, “Ultrashort pulse laser ablation of silicon: an MD simulation study,” Appl. Phys., A Mater. Sci. Process. 66(1), 35–42 (1998).
[Crossref]

S. S. Harilal, N. Farid, J. F. Freeman, P. K. Diwakar, N. L. LaHaye, and A. Hassanein, “Background gas collisional effects on expanding fs and ns laser ablation plumes,” Appl. Phys., A Mater. Sci. Process. 117(1), 319–326 (2014).
[Crossref]

Appl. Spectrosc. (1)

E. L. Gurevich and R. Hergenröder, “Femtosecond laser-induced breakdown spectroscopy: physics, applications, and perspectives,” Appl. Spectrosc. 61(10), 233–242 (2007).
[Crossref] [PubMed]

Astron. Astrophys. Sup. (1)

M. S. Dimitrijevic and S. Sahal-Brechot, “Stark broadening of neutral zinc spectral lines,” Astron. Astrophys. Sup. 140, 193–196 (1999).
[Crossref]

J. Anal. At. Spectrom. (1)

P. Rohwetter, J. Yu, G. Mejean, K. Stelmaszczyk, E. Salmon, J. Kasparian, J. P. Wolf, and L. Woste, “Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes,” J. Anal. At. Spectrom. 19, 437–444 (2004).
[Crossref]

J. Opt. (1)

A. V. Afonasenko, D. V. Apeksimov, Y. E. Geints, S. S. Golik, A. M. Kabanov, and A. A. Zemlyanov, “Study of filamentation dynamics of ultrashort laser radiation in air: beam diameter effect,” J. Opt. 16(10), 105204 (2014).
[Crossref]

Opt. Commun. (1)

J. Bernhardt, W. Liu, F. Theberge, H. L. Xu, J. F. Daigle, M. Chateauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281(5), 1268–1274 (2008).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Plasmas (1)

S. S. Harilal, B. E. Brumfield, and M. C. Phillips, “Lifecycle of laser-produced air sparks,” Phys. Plasmas 22(6), 063301 (2015).
[Crossref]

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

Phys. Rev. B (1)

R. Stoian, D. Ashkenasi, A. Rosenfeld, and E. E. B. Campbell, “Coulomb explosion in ultrashort pulsed laser ablation of Al2O3,” Phys. Rev. B 62(19), 13167–13173 (2000).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Proc. SPIE (1)

J. V. Moloney, “Intense femtosecond pulse propagation with applications,” Proc. SPIE 6261, 626102 (2006).
[Crossref]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Sensors (1)

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors 11(1), 32–53 (2010).
[Crossref] [PubMed]

Spectrochem. Acta B (1)

S. S. Harilal, P. K. Diwakar, N. L. LaHaye, and M. C. Phillips, “Spatio-temporal evolution of uranium emission in laser-produced plasmas,” Spectrochem. Acta B 111, 1–7 (2015).
[Crossref]

Other (2)

H. R. Griem, Principles of Plasma Spectroscopy (Cambridge University Press, Cambridge, 1997).

E. G. Gamaly, Femtosecond Laser-Matter Interaction: Theory, Experiments and Applications (Pan Stanford, Singapore, 2011).

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Figures (7)

Fig. 1
Fig. 1 The spectral features recorded from plasmas by fs filament ablation of brass sample at various locations along the filament channel are given. The identified spectral lines are marked. All spectra were acquired at a delay of 100 ns gate delay after the onset of plasma formation and with a gate width of 2 µs and accumulated for 39 events.
Fig. 2
Fig. 2 The intensity of Cu I emission at 510 nm along the filament channel.
Fig. 3
Fig. 3 The measured temperature of the ablation plume generated along the filament channel. The measurements were taken with 100 ns delay after the onset of plasma generation and with 2 μs integration time. The distance given corresponds to the distance away from the 4 m lens to the target.
Fig. 4
Fig. 4 The measured electron density of the ablation plumes generated along the filamentation channel. The measurements were taken with 100 ns delay after the onset of plasma generation and with 2 μs integration time.
Fig. 5
Fig. 5 Time evolution of (a) plasma temperature and (b) density of ablation plasma at certain locations along the filament channel length. The gate width used was 10% of the gate delay.
Fig. 6
Fig. 6 The intensity of Cu I emission at 510 nm with time for filament LIBS recorded at 345 cm and sharply focused LIBS.
Fig. 7
Fig. 7 The time evolution of temperature and density of plasma generated by sharply focused laser beam. A laser energy of 17 mJ was focused using a 20 cm focal length lens for generating the plasma.

Equations (5)

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P c r = 3.72 λ 2 8 π n 0 n 2
Δ n p = ω p 2 2 ω 2 = e 2 ρ e 2 m e ε 0 ω 2
n 2 I + Δ n p = 0
I = e 2 ρ e 2 n 2 m e ε 0 ω 2
I m n A n m N g m h c λ m n e _ E m k B T

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