Abstract

Extending the length of femtosecond laser filamentation has always been desired for practical applications. Here, we demonstrate that significant extending of a single filament in BK7 glass can be achieved by constructing phase-nested beams. The filamentation and the following energy replenishment are assembled in a single phase-nested beam. The central part of the phase-nested beam is an apertured Gaussian beam, which is focused into one focal spot to produce a short filament. In contrast, the rest of the annular part converges gradually towards the central axis to continuously replenish the energy for supporting the regeneration of filaments. The common-path generating system ensures the stability of generated filaments and easily optimizes the beam parameters to obtain the longest high-quality filament due to its flexibility. In addition, we discuss the significance of continuous replenishment for extending filaments and the potential for generating more extended filaments based on this method.

© 2018 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  33. A. Horn, E. W. Kreutz, and R. Poprawe, “Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica,” Appl. Phys. A 79, 923–925 (2004).
    [Crossref]
  34. J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
    [Crossref]

2018 (1)

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
[Crossref]

2016 (2)

2015 (2)

Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
[Crossref]

X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
[Crossref]

2014 (1)

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

2010 (1)

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (2)

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

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

2006 (1)

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

2005 (5)

D. Aumiler, T. Ban, and G. Pichler, “Femtosecond laser-induced cone emission in dense cesium vapor,” Phys. Rev. A 71, 063803 (2005).
[Crossref]

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

W. Liu, J. F. Gravel, F. Théberge, A. Becker, and S. L. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

W. Liu, F. Théberge, E. Arévalo, J. F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref]

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71, 063811 (2005).
[Crossref]

2004 (4)

L. Bergé, “Boosted propagation of femtosecond filaments in air by double-pulse combination,” Phys. Rev. E 69, 065601 (2004).
[Crossref]

A. Horn, E. W. Kreutz, and R. Poprawe, “Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica,” Appl. Phys. A 79, 923–925 (2004).
[Crossref]

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

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

2003 (4)

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

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, 61–64 (2003).
[Crossref]

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A. 68, 015801 (2003).
[Crossref]

2002 (1)

2001 (2)

2000 (2)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” App. Phys. B 71, 877–879 (2000).
[Crossref]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[Crossref]

1999 (1)

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

1996 (1)

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[Crossref]

1995 (2)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
[Crossref]

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[Crossref]

Aközbek, N.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[Crossref]

Ali Rezvani, S.

André, Y. B.

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

Ange, G.

Arévalo, E.

Aumiler, D.

D. Aumiler, T. Ban, and G. Pichler, “Femtosecond laser-induced cone emission in dense cesium vapor,” Phys. Rev. A 71, 063803 (2005).
[Crossref]

Ban, T.

D. Aumiler, T. Ban, and G. Pichler, “Femtosecond laser-induced cone emission in dense cesium vapor,” Phys. Rev. A 71, 063803 (2005).
[Crossref]

Becker, A.

W. Liu, J. F. Gravel, F. Théberge, A. Becker, and S. L. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

W. Liu, F. Théberge, E. Arévalo, J. F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref]

Bergé, L.

L. Bergé, “Boosted propagation of femtosecond filaments in air by double-pulse combination,” Phys. Rev. E 69, 065601 (2004).
[Crossref]

Biegert, J.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

Bondiou-Clergerie, A.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Bourayou, R.

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, 61–64 (2003).
[Crossref]

Bowden, C. M.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[Crossref]

Braun, A.

Centurion, M.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71, 063811 (2005).
[Crossref]

Chen, S.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

Cheng, W.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Cheng, Y.

Chien, C.-Y.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Chin, S. L.

Y. Fu, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett. 34, 3752–3754 (2009).
[Crossref]

W. Liu, F. Théberge, E. Arévalo, J. F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref]

W. Liu, J. F. Gravel, F. Théberge, A. Becker, and S. L. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[Crossref]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” App. Phys. B 71, 877–879 (2000).
[Crossref]

Cho, S. H.

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
[Crossref]

Choi, W.

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
[Crossref]

Christodoulides, D. N.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Chu, W.

Comtois, D.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Couairon, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

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

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A. 68, 015801 (2003).
[Crossref]

Couture, P.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

D’Amico, C.

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G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
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D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
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Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
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C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
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G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
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G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (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, 61–64 (2003).
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Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
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Fujii, T.

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J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
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D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
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X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
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W. Liu, F. Théberge, E. Arévalo, J. F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
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A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
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Helbing, F. W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
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Hong, Z. F.

Horn, A.

A. Horn, E. W. Kreutz, and R. Poprawe, “Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica,” Appl. Phys. A 79, 923–925 (2004).
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Houard, A.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
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Jeon, J. W.

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
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Ji, S. Y.

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
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D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Kalkner, W.

Kasparian, J.

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

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
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J. Yu, D. Mondelain, G. Ange, R. Volk, S. Niedermeier, J. P. Wolf, J. Kasparian, and R. Sauerbrey, “Backward supercontinuum emission from a filament generated by ultrashort laser pulses in air,” Opt. Lett. 26, 533–535 (2001).
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J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” App. Phys. B 71, 877–879 (2000).
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A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

Kieffer, J. C.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Kim, H. Y.

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
[Crossref]

Klingbeil, L.

Kolesik, M.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express 16, 15733–15740 (2008).
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M. Mlejnek, M. Kolesik, J. Moloney, and E. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
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Kong, L. J.

Korn, G.

Kornelis, W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

Kreutz, E. W.

A. Horn, E. W. Kreutz, and R. Poprawe, “Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica,” Appl. Phys. A 79, 923–925 (2004).
[Crossref]

Lalande, P.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Lan, P. F.

Li, S. M.

Li, W.

Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
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Liu, J.

Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
[Crossref]

Liu, W.

Liu, W. W.

X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
[Crossref]

Liu, X.

Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
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Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

Lu, P. X.

Martin, F.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Méchain, G.

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

Méjean, G.

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

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

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, 61–64 (2003).
[Crossref]

Mercure, H. P.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Mills, M. S.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Miri, M. A.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Mlejnek, M.

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

Moloney, J.

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express 16, 15733–15740 (2008).
[Crossref]

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

Moloney, J. V.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Mondelain, D.

Mourou, G.

Mysyrowicz, A.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

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

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

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, 61–64 (2003).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

Niedermeier, S.

Patalano, G.

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

Pepin, H.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Pichler, G.

D. Aumiler, T. Ban, and G. Pichler, “Femtosecond laser-induced cone emission in dense cesium vapor,” Phys. Rev. A 71, 063803 (2005).
[Crossref]

Polynkin, P.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express 16, 15733–15740 (2008).
[Crossref]

Poprawe, R.

A. Horn, E. W. Kreutz, and R. Poprawe, “Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica,” Appl. Phys. A 79, 923–925 (2004).
[Crossref]

Potvin, C.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Prade, B.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

Psaltis, D.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71, 063811 (2005).
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Pu, Y.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71, 063811 (2005).
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Qian, S. X.

Ranka, J. K.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[Crossref]

Ren, Z. C.

Rethmeier, K.

Rizk, F. A. M.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Roberts, A.

Rodriguez, M.

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

Rohwetter, P.

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

Salmon, E.

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

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

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

Sauerbrey, R.

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

J. Yu, D. Mondelain, G. Ange, R. Volk, S. Niedermeier, J. P. Wolf, J. Kasparian, and R. Sauerbrey, “Backward supercontinuum emission from a filament generated by ultrashort laser pulses in air,” Opt. Lett. 26, 533–535 (2001).
[Crossref]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” App. Phys. B 71, 877–879 (2000).
[Crossref]

Scheller, M.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Schirmer, R. W.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[Crossref]

Shin, Y. G.

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
[Crossref]

Squier, J.

Stelmaszczyk, K.

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

Sun, X. D.

X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
[Crossref]

Talebpour, A.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[Crossref]

Théberge, F.

W. Liu, J. F. Gravel, F. Théberge, A. Becker, and S. L. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

W. Liu, F. Théberge, E. Arévalo, J. F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref]

Tikhonchuk, V. T.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Tsang, M.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71, 063811 (2005).
[Crossref]

Tu, C. H.

Tzortzakis, S.

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

Vidal, F.

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

Volk, R.

Wang, C. Y.

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[Crossref]

Wang, H. T.

Wei, Z. Y.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406 (2001).
[Crossref]

Wille, H.

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

Wolf, J. P.

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

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

J. Yu, D. Mondelain, G. Ange, R. Volk, S. Niedermeier, J. P. Wolf, J. Kasparian, and R. Sauerbrey, “Backward supercontinuum emission from a filament generated by ultrashort laser pulses in air,” Opt. Lett. 26, 533–535 (2001).
[Crossref]

Wöste, L.

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

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

Wright, E.

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

Xiong, H.

Xu, H.

Xu, Z.

Yang, H.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406 (2001).
[Crossref]

Yao, J.

Yu, C. X.

Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
[Crossref]

Yu, J.

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

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

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, 61–64 (2003).
[Crossref]

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wöste, T. Fujii, Y. B. André, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J. P. Wolf, “Triggering and guiding megavolt discharges by use of laser-induced ionized filaments,” Opt. Lett. 27, 772–774 (2002).
[Crossref]

J. Yu, D. Mondelain, G. Ange, R. Volk, S. Niedermeier, J. P. Wolf, J. Kasparian, and R. Sauerbrey, “Backward supercontinuum emission from a filament generated by ultrashort laser pulses in air,” Opt. Lett. 26, 533–535 (2001).
[Crossref]

Yu, W.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406 (2001).
[Crossref]

Zeng, B.

Zeng, T.

X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
[Crossref]

Zhang, J.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406 (2001).
[Crossref]

Zhang, Q. B.

Zhang, S. W.

X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
[Crossref]

Zhao, X. M.

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[Crossref]

App. Phys. B (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” App. Phys. B 71, 877–879 (2000).
[Crossref]

Appl. Phys. A (1)

A. Horn, E. W. Kreutz, and R. Poprawe, “Ultrafast time-resolved photography of femtosecond laser induced modifications in BK7 glass and fused silica,” Appl. Phys. A 79, 923–925 (2004).
[Crossref]

Appl. Phys. B (3)

W. Liu, J. F. Gravel, F. Théberge, A. Becker, and S. L. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, M. Franco, B. Prade, and A. Mysyrowicz, “Concatenation of plasma filaments created in air by femtosecond infrared laser pulses,” Appl. Phys. B 76, 609–612 (2003).
[Crossref]

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, “Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system,” Appl. Phys. B 78, 535–537 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[Crossref]

IEEE Trans. Plasma Sci. (1)

D. Comtois, H. Pepin, F. Vidal, F. A. M. Rizk, C.-Y. Chien, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, “Triggering and guiding of an upward positive leader from a ground rod with an ultrashort laser pulse. I. Experimental results,” IEEE Trans. Plasma Sci. 31, 377–386 (2003).
[Crossref]

J. Anal. At. Spectrom. (1)

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

J. Mod. Opt. (1)

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006).
[Crossref]

J. Phys. B (1)

X. D. Sun, T. Zeng, H. Gao, S. W. Zhang, and W. W. Liu, “Power dependent filamentation of a femtosecond laser pulse in air by focusing with an axicon,” J. Phys. B 48, 094004 (2015).
[Crossref]

Nat. Photonics (1)

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photonics 8, 297–301 (2014).
[Crossref]

Opt. Commun. (1)

G. Méchain, C. D’Amico, Y. B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247, 171–180 (2005).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Photon. Res. (1)

Phys. Rep. (1)

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

Phys. Rev. A (3)

D. Aumiler, T. Ban, and G. Pichler, “Femtosecond laser-induced cone emission in dense cesium vapor,” Phys. Rev. A 71, 063803 (2005).
[Crossref]

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71, 063811 (2005).
[Crossref]

Z. F. Feng, W. Li, C. X. Yu, X. Liu, J. Liu, and L. B. Fu, “Extended laser filamentation in air generated by femtosecond annular Gaussian beams,” Phys. Rev. A 91, 033839 (2015).
[Crossref]

Phys. Rev. A. (1)

A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A. 68, 015801 (2003).
[Crossref]

Phys. Rev. E (3)

L. Bergé, “Boosted propagation of femtosecond filaments in air by double-pulse combination,” Phys. Rev. E 69, 065601 (2004).
[Crossref]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[Crossref]

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406 (2001).
[Crossref]

Phys. Rev. Lett. (4)

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

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

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[Crossref]

Res. Rev. J. Mater. Sci. (1)

J. W. Jeon, S. Y. Ji, H. Y. Kim, W. Choi, Y. G. Shin, and S. H. Cho, “Formation of permanent brown-colored patterns in transparent BK7 glass upon irradiation with a tightly focused femtosecond laser,” Res. Rev. J. Mater. Sci. 6, 35–38 (2018).
[Crossref]

Science (1)

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, 61–64 (2003).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Generation of a phase-nested beam for prolonging the filament. (a) Experimental setup, (b) phase distribution of the generated phase-nested beam behind lens L3, (c) simulated interference pattern of the phase-nested beam behind lens L3 with the Gaussian beam, and (d) the experimentally measured result corresponding to (c).
Fig. 2.
Fig. 2. Equivalent focal length F of the phase-nested beam for different γ, ρc, and ρ1 in BK7 glass, as a function of the normalized radial coordinate.
Fig. 3.
Fig. 3. Simulated nonlinear propagation behaviors of different beams under the conditions of P=10Pc, ϵ104, f=0.0125Ld, γ=γ0, ρc=0.35, ρ1=0.32, and ϕ0=0. Simulated on-axis intensity of nonlinear propagation of (a) the whole phase-nested beam, (b) the central part (ρρc) of the phase-nested beam, (c) the annular part (ρ>ρc) of the phase-nested beam, and (d) the Gaussian beam with the same input power and size as the phase-nested beam. (e)–(h) show the intensity in cross-sections as a function of propagation distance corresponding to (a)–(d), respectively.
Fig. 4.
Fig. 4. Experimental results of the filament extended by the phase-nested beam. (a) Filament produced by the phase-nested beam. (b) Filament produced by the central part of only the phase-nested beam. (c) No filament is formed by the annular part of the phase-nested beam. (d) Filament generated by the Gaussian beam with same pulse energy and beam width as the whole phase-nested beam. The corresponding input beams are shown in the left side, while the corresponding far-field patterns are shown in the right side. (e) The output spectra of the above beams. The ruler is also captured simultaneously as the filaments to measure the filamentation length.
Fig. 5.
Fig. 5. Filaments produced by the phase-nested beams with different phase shifts. The parameters remain unchanged as r0=1.2  mm, γ=1/18, ρc=0.35, ρ1=0.32, and E=13  μJ. The exposure time of the digital camera stays at 20 s.
Fig. 6.
Fig. 6. Filaments produced by the phase-nested beams with the different parameter sets γ, ρc, ρ1, and ϕ0. The pulse energy of all of the input fields is kept at E=13  μJ, and the exposure time of the digital camera stays at 20 s.
Fig. 7.
Fig. 7. Filaments produced by the partially blocked phase-nested beams. The intensity profiles of the input beams are shown on the left. (a), (c), (e) The filaments produced by the phase-nested beams blocked by a specific ring-like band-stop filter, whose normalized internal radius and width are ρa and d, respectively. (b), (d), (f) The filaments produced by the phase-nested beams blocked by a low-passing circular aperture with a normalized radius of ρb.

Equations (5)

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

t={eiπ2[1+cos(2πf0x)],(0ρρc)eiπ2[1+cos(2πf0x+ϕa)],(ρc<ρ1),
ϕa=2πγ[(ρρ1)2(ρcρ1)2]+ϕ0.
E(ρ)={A0eρ2w2,(0ρρc)A0eρ2w2+iϕa,(ρc<ρ1).
E(ρ)={A0eρ2w2i2πr02ρ2λf,(0ρρc)A0eρ2w2i2πr02ρ2λf+iϕa,(ρc<ρ1).
dΨdζ=i(2ρ2+ρρ+2ρ2ϕ2)Ψ+i(PPc|Ψ|2ϵP2Pc2|Ψ|4)Ψβ(K)|Ψ|2K2Ψ,