Abstract

We perform optical emission spectroscopy of ultrafast laser filament-produced air plasmas in the multiple filament regime at driving wavelengths of 400 nm and 800 nm. The spatiotemporal structure of the emission from the plasmas are observed and the emission spectra are used to estimate plasma temperature and density for a range of laser parameters. Plasma temperatures are determined from the molecular nitrogen fluorescence, while the electron densities are estimated from Stark broadening of the oxygen-I 777.19-nm line. Electron temperatures are determined to be in the range of 5000–5200 K and they do not vary significantly along the length of the filament, nor are they sensitive to incident laser energy or wavelength. Electron densities are on order of 1016 cm−3 and show a greater variation with axial position, laser energy, and laser wavelength. We discuss mechanisms responsible for spatial localization of emitting species within the filament. Optical emission spectroscopy offers a simple, non-perturbing method to measure filament properties, that allows the information on the associated molecular transitions and excitation/ionization mechanisms to be extracted.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

2017 (4)

P. J. Skrodzki, M. Burger, and I. Jovanovic, “Transition of femtosecond-filament-solid interactions from single to multiple filament regime,” Sci. Rep. 7, 12740 (2017).
[Crossref] [PubMed]

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

J.-P. Wolf, “Short-pulse lasers for weather control,” Rep. Prog. Phys. 81(2), 026001 (2017).
[Crossref] [PubMed]

S. Chen, X.-L. Liu, X. Lu, J. Ma, J. Wang, B. Zhu, L. Chen, and Y. Li, “Temporal evolution of femtosecond laser filament detected via magnetic field around plasma current,” Opt. Express 25(26), 32514–32521 (2017).
[Crossref]

2016 (3)

2015 (4)

F. V. Potemkin, E. I. Mareev, A. A. Podshivalov, and V. M. Gordienko, “Highly extended high density filaments in tight focusing geometry in water: from femtoseconds to microseconds,” New J. Phys. 17, 053010 (2015).
[Crossref]

Z. Farooq, D. A. Chestakov, B. Yan, G. C. Groenenboom, W. J. van der Zande, and D. H. Parker, “Photodissociation of singlet oxygen in the UV region,” Phys. Chem. Chem. Phys. 16, 3305–3316 (2015).
[Crossref]

A. A. Ilyn, S. S. Golik, F. Lederer, and K. A. Shmirko, “Absorption and emission characteristics of femtosecond laser plasma filaments in the air,” Spectrochim. Acta B 112, 16–22 (2015).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
[Crossref]

2014 (3)

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
[Crossref]

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
[Crossref]

J. Papeer, M. Botton, D. Gordon, A. Zigler, and Z. Henis, “Corrigendum: Extended lifetime of high density plasma filament generated by a dual femto-nanosecond laser pulse,” New J. Phys. 17, 089501 (2014).

2012 (1)

2011 (4)

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
[Crossref] [PubMed]

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

Z. Sun, J. Chen, L. Zuo-Ye, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
[Crossref]

2010 (3)

J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
[Crossref]

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

2009 (4)

G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B 96, 185–191 (2009).
[Crossref]

D. Faccio, A. Lotti, A. Matijosius, F. Bragheri, V. Degiorgio, A. Couairon, and P. Di Trapani, “Experimental energy-density flux characterization of ultrashort laser pulse filaments,” Opt. Express 17(10), 8193–8200 (2009).
[Crossref] [PubMed]

G. Cristoforetti, A. De Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, and N. Omenetto, “Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: Beyond the McWhirter criterion,” Spectrochim. Acta B 65, 86–95 (2009).
[Crossref]

H. L. Xu, A. Azarm, J. Bernhardt, Y. Kamali, and S. L. Chin, “The mechanism of nitrogen fluorescence inside a femtosecond laser filament in air,” Chem. Phys. 360, 171–175 (2009).
[Crossref]

2008 (3)

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

D. G. Papazoglou and S. Tzortzakis, “In-line holography for the characterization of ultrafast laser filamentation in transparent media,” Appl. Phys. Lett. 93, 041120 (2008).
[Crossref]

D. Mirell, O. Chalus, K. Peterson, and J.-C. Diels, “Remote sensing of explosives using infrared and ultraviolet filaments,” J. Opt. Sci. Am. B 25(7), B108–B111 (2008).
[Crossref]

2007 (2)

W. Liu, J. Bernhardt, F. Theberge, S. L. Chin, M. Chateauneuf, and J. Dubois, “Spectroscopic characterization of femtosecond laser filament in argon gas,” J. Appl. Phys. 102(15), 033111 (2007).
[Crossref]

J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
[Crossref]

2006 (2)

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[Crossref]

S. Tzortzakis, D. Anglos, and D. Gray, “Ultraviolet laser filaments for remote laser-induced breakdown spectroscopy (LIBS) analysis: applications in cultural heritage monitoring,” Opt. Lett. 31(8), 1139–1141 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (1)

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

2003 (2)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Q. Luo, W. Liu, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76(3), 337–340 (2003).
[Crossref]

2001 (1)

A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

1999 (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]

1995 (1)

1966 (1)

V. I. Bespalov and V. I. Talanov, “Filamentary Structure of Light Beams in Nonlinear Liquids,” JETP Lett. 3, 307 (1966).

1958 (1)

K. F. Herzfeld, “The rate and mechanism of the thermal dissociation of oxygen,” Symposium (International) on Combustion 7(1), 27–33 (1958).
[Crossref]

Aközbek, N.

A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Ališauskas, S.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
[Crossref]

André, Y.-B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Andriukaitis, G.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
[Crossref]

Anglos, D.

Antonsen, T. M.

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

Atkins, P.

P. Atkins and J. De Paula, Physical Chemistry Thermodynamics, Structure, and Change (Oxford University, 2014), pp. 605–623.

Azarm, A.

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F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
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W. Liu, J. Bernhardt, F. Theberge, S. L. Chin, M. Chateauneuf, and J. Dubois, “Spectroscopic characterization of femtosecond laser filament in argon gas,” J. Appl. Phys. 102(15), 033111 (2007).
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A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
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Braun, A.

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W. Liu, J. Bernhardt, F. Theberge, S. L. Chin, M. Chateauneuf, and J. Dubois, “Spectroscopic characterization of femtosecond laser filament in argon gas,” J. Appl. Phys. 102(15), 033111 (2007).
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J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Châteauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268–1274 (2008).
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Chen, Y.

H. Xu, Y. Chen, Z. Xu, S. L. Chin, and K. Yamanouchi, Progress in Ultrafast Intense Laser Science (Springer-Verlag Berlin Heidelberg, 2012), pp. 145–160.

Chen, Y. P.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

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Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
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S. Xu, X. Sun, B. Zeng, W. Chu, J. Zhao, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Simple method of measuring laser peak intensity inside femtosecond laser filament in air,” Opt. Express 20(1), 299–307 (2012).
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J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

H. L. Xu, A. Azarm, J. Bernhardt, Y. Kamali, and S. L. Chin, “The mechanism of nitrogen fluorescence inside a femtosecond laser filament in air,” Chem. Phys. 360, 171–175 (2009).
[Crossref]

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

W. Liu, J. Bernhardt, F. Theberge, S. L. Chin, M. Chateauneuf, and J. Dubois, “Spectroscopic characterization of femtosecond laser filament in argon gas,” J. Appl. Phys. 102(15), 033111 (2007).
[Crossref]

J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
[Crossref]

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13, 5750–5755 (2005).
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A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

H. Xu, Y. Chen, Z. Xu, S. L. Chin, and K. Yamanouchi, Progress in Ultrafast Intense Laser Science (Springer-Verlag Berlin Heidelberg, 2012), pp. 145–160.

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Couairon, A.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
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J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Châteauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268–1274 (2008).
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S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Daigle, J.-F.

J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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Dell’Aglio, M.

G. Cristoforetti, A. De Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, and N. Omenetto, “Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: Beyond the McWhirter criterion,” Spectrochim. Acta B 65, 86–95 (2009).
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Diels, J.-C.

D. Mirell, O. Chalus, K. Peterson, and J.-C. Diels, “Remote sensing of explosives using infrared and ultraviolet filaments,” J. Opt. Sci. Am. B 25(7), B108–B111 (2008).
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Du, S.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

Dubois, J.

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

W. Liu, J. Bernhardt, F. Theberge, S. L. Chin, M. Chateauneuf, and J. Dubois, “Spectroscopic characterization of femtosecond laser filament in argon gas,” J. Appl. Phys. 102(15), 033111 (2007).
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G. Cristoforetti, A. De Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, and N. Omenetto, “Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: Beyond the McWhirter criterion,” Spectrochim. Acta B 65, 86–95 (2009).
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A. A. Ilyn, S. S. Golik, F. Lederer, and K. A. Shmirko, “Absorption and emission characteristics of femtosecond laser plasma filaments in the air,” Spectrochim. Acta B 112, 16–22 (2015).
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F. V. Potemkin, E. I. Mareev, A. A. Podshivalov, and V. M. Gordienko, “Highly extended high density filaments in tight focusing geometry in water: from femtoseconds to microseconds,” New J. Phys. 17, 053010 (2015).
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J. Papeer, M. Botton, D. Gordon, A. Zigler, and Z. Henis, “Corrigendum: Extended lifetime of high density plasma filament generated by a dual femto-nanosecond laser pulse,” New J. Phys. 17, 089501 (2014).

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Z. Farooq, D. A. Chestakov, B. Yan, G. C. Groenenboom, W. J. van der Zande, and D. H. Parker, “Photodissociation of singlet oxygen in the UV region,” Phys. Chem. Chem. Phys. 16, 3305–3316 (2015).
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Hao, Z.

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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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Henis, Z.

J. Papeer, M. Botton, D. Gordon, A. Zigler, and Z. Henis, “Corrigendum: Extended lifetime of high density plasma filament generated by a dual femto-nanosecond laser pulse,” New J. Phys. 17, 089501 (2014).

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J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
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Houard, A.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
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A. A. Ilyn, S. S. Golik, F. Lederer, and K. A. Shmirko, “Absorption and emission characteristics of femtosecond laser plasma filaments in the air,” Spectrochim. Acta B 112, 16–22 (2015).
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Jarón-Becker, A.

J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
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S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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Ju, J.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
[Crossref]

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G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
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J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Kamali, Y.

H. L. Xu, A. Azarm, J. Bernhardt, Y. Kamali, and S. L. Chin, “The mechanism of nitrogen fluorescence inside a femtosecond laser filament in air,” Chem. Phys. 360, 171–175 (2009).
[Crossref]

J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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Kasparian, J.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

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]

Korn, G.

Kosareva, O.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Kraft, S. D.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

Krushelnick, K.

Lascoux, N.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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A. A. Ilyn, S. S. Golik, F. Lederer, and K. A. Shmirko, “Absorption and emission characteristics of femtosecond laser plasma filaments in the air,” Spectrochim. Acta B 112, 16–22 (2015).
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L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

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G. Cristoforetti, A. De Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, and N. Omenetto, “Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: Beyond the McWhirter criterion,” Spectrochim. Acta B 65, 86–95 (2009).
[Crossref]

Li, R.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
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S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Li, Y.

Liang, H.

Lin, J.

Liu, J.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

Liu, J. S.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Liu, W.

S. Xu, X. Sun, B. Zeng, W. Chu, J. Zhao, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Simple method of measuring laser peak intensity inside femtosecond laser filament in air,” Opt. Express 20(1), 299–307 (2012).
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J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Châteauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268–1274 (2008).
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W. Liu, J. Bernhardt, F. Theberge, S. L. Chin, M. Chateauneuf, and J. Dubois, “Spectroscopic characterization of femtosecond laser filament in argon gas,” J. Appl. Phys. 102(15), 033111 (2007).
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J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13, 5750–5755 (2005).
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Q. Luo, W. Liu, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76(3), 337–340 (2003).
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Liu, W. W.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Liu, X.

Liu, X.-L.

Liu, Y.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

Lotti, A.

Lu, H.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

Lu, X.

Luo, Q.

Q. Luo, W. Liu, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76(3), 337–340 (2003).
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Mao, X.

Marceau, C.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Mareev, E. I.

F. V. Potemkin, E. I. Mareev, A. A. Podshivalov, and V. M. Gordienko, “Highly extended high density filaments in tight focusing geometry in water: from femtoseconds to microseconds,” New J. Phys. 17, 053010 (2015).
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J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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Mauger, S.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
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J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
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Milchberg, H. M.

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
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P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
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G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
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D. Mirell, O. Chalus, K. Peterson, and J.-C. Diels, “Remote sensing of explosives using infrared and ultraviolet filaments,” J. Opt. Sci. Am. B 25(7), B108–B111 (2008).
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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.

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).
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Mourou, G.

Mysyrowicz, A.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
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J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
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S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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Omenetto, N.

G. Cristoforetti, A. De Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, and N. Omenetto, “Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: Beyond the McWhirter criterion,” Spectrochim. Acta B 65, 86–95 (2009).
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Oral, E.

A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
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Palleschi, V.

G. Cristoforetti, A. De Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, and N. Omenetto, “Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: Beyond the McWhirter criterion,” Spectrochim. Acta B 65, 86–95 (2009).
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S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

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D. G. Papazoglou and S. Tzortzakis, “In-line holography for the characterization of ultrafast laser filamentation in transparent media,” Appl. Phys. Lett. 93, 041120 (2008).
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Parker, D. H.

Z. Farooq, D. A. Chestakov, B. Yan, G. C. Groenenboom, W. J. van der Zande, and D. H. Parker, “Photodissociation of singlet oxygen in the UV region,” Phys. Chem. Chem. Phys. 16, 3305–3316 (2015).
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G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B 96, 185–191 (2009).
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D. Mirell, O. Chalus, K. Peterson, and J.-C. Diels, “Remote sensing of explosives using infrared and ultraviolet filaments,” J. Opt. Sci. Am. B 25(7), B108–B111 (2008).
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Petit, Y.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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Phillips, M. C.

Podshivalov, A. A.

F. V. Potemkin, E. I. Mareev, A. A. Podshivalov, and V. M. Gordienko, “Highly extended high density filaments in tight focusing geometry in water: from femtoseconds to microseconds,” New J. Phys. 17, 053010 (2015).
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G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milían, J. Carbonnel, A. Couairon, and A. Mysyrowicz, “Superfilamentation in air,” Phys. Rev. Lett. 112 (223902), 1–5, (2014).
[Crossref]

Polynkin, P.

P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
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P. Polynkin and Y. Cheng, Air Lasing (Springer International Publishing, 2018).
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Potemkin, F. V.

F. V. Potemkin, E. I. Mareev, A. A. Podshivalov, and V. M. Gordienko, “Highly extended high density filaments in tight focusing geometry in water: from femtoseconds to microseconds,” New J. Phys. 17, 053010 (2015).
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Pugžlys, A.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
[Crossref]

Queisser, M.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
[Crossref]

Ran, P.

Richardson, M.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Rodriguez, M.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Rohwetter, P.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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Roy, G.

J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
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J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
[Crossref]

Rudolph, W.

Z. Sun, J. Chen, L. Zuo-Ye, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
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Russo, R. E.

Salame, R.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
[Crossref]

Salmon, E.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Sauerbrey, R.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
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S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
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Seideman, T.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Shim, B.

Shmirko, K. A.

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Siebert, T.

P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
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Simard, P. Tr.

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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M. Burger, P. J. Skrodzki, J. Lin, J. Nees, K. Krushelnick, and I. Jovanovic, “Intense laser filament-solid interactions from near-ultraviolet to mid-infrared,” Opt. Express 26(13), 16456–16669 (2018).
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S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
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S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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Spindler, G.

G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B 96, 185–191 (2009).
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P. R. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, “Standoff spectroscopy via remote generation of a backward-propagating laser beam,” Proc. Natl. Acad. Sci. 108(8), 3130–3134 (2011).
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Stelmasczcyk, K.

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
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Sun, Q.

J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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Sun, Z.

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Théberge, F.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Châteauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268–1274 (2008).
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J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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Voronin, A. A.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
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Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

Wang, J.

Wang, T.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

Wang, T.-J.

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
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S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

J.-F. Daigle, A. Jarón-Becker, S. Hosseini, T.-J. Wang, Y Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
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Weerawarne, D. L.

Wei, Y.

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
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L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010).
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J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
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S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
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L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
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J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
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Xu, H.

H. Xu, Y. Chen, Z. Xu, S. L. Chin, and K. Yamanouchi, Progress in Ultrafast Intense Laser Science (Springer-Verlag Berlin Heidelberg, 2012), pp. 145–160.

Xu, H. L.

H. L. Xu, A. Azarm, J. Bernhardt, Y. Kamali, and S. L. Chin, “The mechanism of nitrogen fluorescence inside a femtosecond laser filament in air,” Chem. Phys. 360, 171–175 (2009).
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J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Châteauneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268–1274 (2008).
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J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
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Xu, S.

Xu, Z.

Y. Liu, T. Wang, N. Chen, S. Du, J. Ju, H. Sun, C. Wang, J. Liu, H. Lu, S. L. Chin, R. Li, Z. Xu, and Z. Wang, “Probing the effective length of plasma inside a filament,” J. Appl. Phys. 25(10), 11078–11087 (2017).

T.-J. Wang, J. Ju, Y. Wei, R. Li, Z. Xu, and S. L. Chin, “Longitudinally resolved measurement of plasma density along femtosecond laser filament via terahertz spectroscopy,” Appl. Phys. Lett. 105, 051101 (2014).
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S. Xu, X. Sun, B. Zeng, W. Chu, J. Zhao, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Simple method of measuring laser peak intensity inside femtosecond laser filament in air,” Opt. Express 20(1), 299–307 (2012).
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H. Xu, Y. Chen, Z. Xu, S. L. Chin, and K. Yamanouchi, Progress in Ultrafast Intense Laser Science (Springer-Verlag Berlin Heidelberg, 2012), pp. 145–160.

Xu, Z. Z.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Yamanouchi, K.

H. Xu, Y. Chen, Z. Xu, S. L. Chin, and K. Yamanouchi, Progress in Ultrafast Intense Laser Science (Springer-Verlag Berlin Heidelberg, 2012), pp. 145–160.

Yan, B.

Z. Farooq, D. A. Chestakov, B. Yan, G. C. Groenenboom, W. J. van der Zande, and D. H. Parker, “Photodissociation of singlet oxygen in the UV region,” Phys. Chem. Chem. Phys. 16, 3305–3316 (2015).
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Yang, B.

Yeak, J.

Yu, J.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
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Yuan, S.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

Zeng, B.

Zeng, H. P.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J. -F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Las. Phys. Rev. 22(1), 1–53 (2011).

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T. Zeng, S. Zhu, S. Zhou, and Y. He, “Spatial evolution of laser filaments in turbulent air,” Opt. Commun. 412161–165 (2018).
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Zheltikov, A. M.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 08368 (2015).
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Zhu, S.

T. Zeng, S. Zhu, S. Zhou, and Y. He, “Spatial evolution of laser filaments in turbulent air,” Opt. Commun. 412161–165 (2018).
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Zorba, V.

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Z. Sun, J. Chen, L. Zuo-Ye, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma filament,” Phys. Rev. E 83, 046408 (2011).
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Appl. Phys. B (5)

Q. Luo, W. Liu, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76(3), 337–340 (2003).
[Crossref]

G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B 96, 185–191 (2009).
[Crossref]

S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jockman, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmasczcyk, P. Rohwetter, L. Woste, C.-L. Soulez, S. Mauger, L. Berge, and S. Skupin, “Saturation of the filament density of ultrashort intense laser pulses in air,” Appl. Phys. B 100, 77–84 (2011).
[Crossref]

J.-F. Daigle, G. Méjean, F. Théberge, W. Liu, H. L. Xu, Y. Kamali, J. Bernhardt, A. Azarm, Q. Sun, P. Mathieu, G. Roy, J.-R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remote filament-induced breakdown spectroscopy,” Appl. Phys. B 87, 749–754 (2007).
[Crossref]

A. Becker, N. Aközbek, K. Vijay Alakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
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Figures (8)

Fig. 1
Fig. 1 Schematic of the experimental setup. The inset image shows an example radial profile of the multiple filament cores (bright spots) observed from the damage on a copper target (3 mJ, 400 nm). The copper target is placed near the geometric focus of the spherical mirror. The damage pattern is from a single laser shot.
Fig. 2
Fig. 2 Measured emission spectrum of the N2 second positive system and the N 2 + first negative system for 3-mJ pulses at 400 nm (blue) and 800 nm (red) 20 mm measured before the geometric focus in the direction of beam propagation. The ICCD delay and gate width were 0 ns and 10 ns, respectively, measured with respect to arrival the incident laser pulse at the filament region. The shaded regions highlight the two molecular band-heads primarily discussed.
Fig. 3
Fig. 3 Time evolution of the filament plasma measured by side imaging for 3-mJ, 800-nm pulses. The gate widths for each time step were 1 ns with 100 accumulations. The white dashed line represents the geometric focus of the spherical mirror.
Fig. 4
Fig. 4 Side imaging of the total and N 2 + emission from the 800-nm filament with 3 mJ (a)–(c) and 12 mJ (d)–(f) laser energies. Profiles (a) and (d) show the vertically-integrated emission. Images (b) and (e) show the total emission. Images (c) and (f) show 391 nm emission with a FWHM of 1.4 nm band pass (BP) filter. The white dashed line represents the geometric focus of the spherical mirror. Images were recorded at a delay of 0 ns with respect to the incident laser pulse, gate width of 10 ns, and accumulated for 100 laser shots.
Fig. 5
Fig. 5 Measured peak intensities for the N2(337 nm) and N 2 + (391 nm) band-heads, and O I (777.19 nm) line from the (a) 800-nm and (b) 400-nm filament spectra and axial gradients (dI/dz) for the measured intensities of each band and line for the (c) 800-nm and (d) 400-nm filaments. Driving laser pulse energy was 3 mJ for both wavelengths. Geometric focus of the spherical mirror is denoted as 0 mm. Data is fit with a spline curve to help guide the eye.
Fig. 6
Fig. 6 Spectrum measured with 3-mJ, 800-nm pulses and simulated by SPECAIR for the (1,3) and (0,2) N2 emission bands.
Fig. 7
Fig. 7 Sample multi-Voigt fit for the O I 777.19-, 777.42-, and 777.54-nm lines used to determine the degree of Stark broadening. The spectrum shown is taken for 800-nm with driving laser energy of 12 mJ.
Fig. 8
Fig. 8 Axially-resolved (a) rotational temperatures (Tr), (b) vibrational temperatures (Tv), (c) electronic temperatures (Te), and (d) electron densities (ne) along the filament length. Geometric focus of the spherical mirror is at 0 mm. Results shown are for 3 mJ energies with both 400- and 800-nm beam wavelengths.

Tables (1)

Tables Icon

Table 1 Driving laser energy- (Eλ) and wavelength- (λ) dependence of filament optical emission and plasma properties. Energy is given in mJ. Intensity ratios ( I N 2 / I N 2 + ) and peak emission (Ipeak) compare the emissions from N2(337 nm) and N 2 + (391 nm) (0,0) band-heads at the axial peak of the optical emission. Plasma temperatures are also given at the axial peak of the optical emission in units of K. Electron densities are calculated from Stark width parameters measured for filaments [27] and given in units of cm−3.

Equations (4)

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P c r = 3.77 λ 2 8 π n 0 n 2 ,
n e = ( Δ λ s 2 a ) × 10 16 ( cm 3 ) ,
T v = h c v k ,
q v = 1 1 exp ( h v / k T v ) ,

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