Abstract

We report on the direct experimental observation of pulse-splitting dynamics along a femtosecond filament. The fundamental pulse experiences a significant self-shortening during the propagation leading to pulse durations of 5.3 fs, corresponding to sub-3 cycles, which is measured without external pulse compression. A compression factor of eight could be achieved in a single filamentary stage. Theoretical modeling of the fundamental pulse propagation confirms our observed pulse structures and durations and gives further insight into the nonlinear dynamics during filamentation.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  37. A. A. Zozulya, S. A. Diddams, A. G. V. Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430 (1999).
    [Crossref]
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    [Crossref]
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    [Crossref]
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  41. M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
    [Crossref]
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    [Crossref]
  44. A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
    [Crossref]
  45. C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
    [Crossref] [PubMed]
  46. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16, 17626–17636 (2008).
    [Crossref] [PubMed]

2014 (2)

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

2012 (5)

D. S. Steingrube, M. Kretschmar, D. Hoff, E. Schulz, T. Binhammer, P. Hansinger, G. G. Paulus, U. Morgner, and M. Kovacev, “Sub-1.5-cycle pulses from a single filament,” Opt. Express 20, 24049–24058 (2012).
[Crossref] [PubMed]

E. O. Smetanina, A. E. Dormidonov, and V. P. Kandidov, “Spatio-temporal evolution scenarios of femtosecond laser pulse filamentation in fused silica,” Laser Phys. 22, 1189–1198 (2012).
[Crossref]

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

J. Odhner and R. J. Levis, “Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air,” Opt. Lett. 37, 1775–1777 (2012).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in n2, o2, n2o, and ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

2011 (6)

B. Alonso, I. J. Sola, J. S. Roman, O. Varela, and L. Roso, “Spatiotemporal evolution of light during propagation in filamentation regime,” J. Opt. Soc. Am. B 28, 1807–1816 (2011).
[Crossref]

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

E. Schulz, D. S. Steingrube, T. Vockerodt, T. Binhammer, U. Morgner, and M. Kovačev, “Gradient enhanced third harmonic generation in a femtosecond filament,” Opt. Lett. 36, 4389–4391 (2011).
[Crossref] [PubMed]

D. S. Steingrube, E. Schulz, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “High-order harmonic generation directly from a filament,” New J. Phys. 13, 043022 (2011).
[Crossref]

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

E. Schulz, D. S. Steingrube, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “Tracking spectral shapes and temporal dynamics along a femtosecond filament,” Opt. Express 19, 19495–19507 (2011).
[Crossref] [PubMed]

2010 (3)

J. Odhner, D. Romanov, and R. J. Levis, “Self-shortening dynamics measured along a femtosecond laser filament in air,” Phys. Rev. Lett. 105, 125001 (2010).
[Crossref] [PubMed]

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

2009 (5)

S. Minardi, A. Gopal, A. Couairon, G. Tamoauskas, R. Piskarskas, A. Dubietis, and P. D. Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34, 3020–3022 (2009).
[Crossref] [PubMed]

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[Crossref]

E. Schulz, T. Binhammer, D. Steingrube, S. Rausch, M. Kovacev, and U. Morgner, “Intense few-cycle laser pulses from self-compression in a self-guiding filament,” Appl. Phys. B 95, 269–272 (2009).
[Crossref]

M. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: Diagnostics and application,” Phys. Rev. Lett. 103, 043901 (2009).
[Crossref] [PubMed]

C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
[Crossref] [PubMed]

2008 (5)

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16, 17626–17636 (2008).
[Crossref] [PubMed]

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[Crossref]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10, 025023 (2008).
[Crossref]

2007 (6)

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

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

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Supercontinuum and third-harmonic generation accompanying optical filamentation as first-order scattering processes,” Opt. Lett. 32, 2816–2818 (2007).
[Crossref] [PubMed]

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. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15, 5394–5405 (2007).
[Crossref] [PubMed]

2006 (4)

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[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. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006).
[Crossref] [PubMed]

2005 (1)

2001 (1)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

1999 (1)

A. A. Zozulya, S. A. Diddams, A. G. V. Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430 (1999).
[Crossref]

1998 (1)

1995 (1)

1966 (2)

Dalgarno and Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. Roy. Soc. London Ser. A 259, 424–429 (1966).
[Crossref]

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Adams, D. E.

D. E. Adams, T. A. Planchon, J. A. Squier, and C. G. Durfee, “Spatiotemporal dynamics of ionizing filaments in air,” Proceedings of IEEE Conference on Lasers and Electro-OpticsJThE119 (2010).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Quantum Electronics Principles and Applications Series, 1989).

Ahmad, I.

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

Akturk, S.

Akzbek, N.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Alonso, B.

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Arrell, C.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Austin, D.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Baltuska, A.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Becker, A.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Berg, L.

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

Bergé, L.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
[Crossref] [PubMed]

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

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

Bethge, J.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

Biegert, J.

Binhammer, T.

Bloemer, M.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Bragheri, F.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Braun, A.

Breé, C.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
[Crossref] [PubMed]

Brée, C.

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

Chakraborty, H. S.

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

Chang, Y.-Y.

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

Chateauneuf, M.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Chen, Y.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in n2, o2, n2o, and ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

Chin, S. L.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

S. L. Chin, Femtosecond Laser Filamentation (Springer, 2010).
[Crossref]

Clement, T. S.

A. A. Zozulya, S. A. Diddams, A. G. V. Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430 (1999).
[Crossref]

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Couairon, A.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

D. S. Steingrube, E. Schulz, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “High-order harmonic generation directly from a filament,” New J. Phys. 13, 043022 (2011).
[Crossref]

E. Schulz, D. S. Steingrube, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “Tracking spectral shapes and temporal dynamics along a femtosecond filament,” Opt. Express 19, 19495–19507 (2011).
[Crossref] [PubMed]

M. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: Diagnostics and application,” Phys. Rev. Lett. 103, 043901 (2009).
[Crossref] [PubMed]

S. Minardi, A. Gopal, A. Couairon, G. Tamoauskas, R. Piskarskas, A. Dubietis, and P. D. Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34, 3020–3022 (2009).
[Crossref] [PubMed]

A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10, 025023 (2008).
[Crossref]

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16, 17626–17636 (2008).
[Crossref] [PubMed]

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15, 5394–5405 (2007).
[Crossref] [PubMed]

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

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]

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]

D’Amico, C.

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]

Daigle, J. F.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Dalgarno,

Dalgarno and Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. Roy. Soc. London Ser. A 259, 424–429 (1966).
[Crossref]

Degiorgio, V.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Demircan, A.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
[Crossref] [PubMed]

Di Trapani, P.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Diddams, S. A.

A. A. Zozulya, S. A. Diddams, A. G. V. Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430 (1999).
[Crossref]

Dormidonov, A. E.

E. O. Smetanina, A. E. Dormidonov, and V. P. Kandidov, “Spatio-temporal evolution scenarios of femtosecond laser pulse filamentation in fused silica,” Laser Phys. 22, 1189–1198 (2012).
[Crossref]

Downer, M. C.

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

Drescher, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Du, D.

Dubietis, A.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

S. Minardi, A. Gopal, A. Couairon, G. Tamoauskas, R. Piskarskas, A. Dubietis, and P. D. Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34, 3020–3022 (2009).
[Crossref] [PubMed]

Dubois, J.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Durfee, C. G.

D. E. Adams, T. A. Planchon, J. A. Squier, and C. G. Durfee, “Spatiotemporal dynamics of ionizing filaments in air,” Proceedings of IEEE Conference on Lasers and Electro-OpticsJThE119 (2010).
[Crossref]

Eckle, P.

Engen, A. G. V.

A. A. Zozulya, S. A. Diddams, A. G. V. Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430 (1999).
[Crossref]

Faccio, D.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Franco, M.

Frank, F.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Fu, W.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Gaarde, M.

M. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: Diagnostics and application,” Phys. Rev. Lett. 103, 043901 (2009).
[Crossref] [PubMed]

Gaarde, M. B.

D. S. Steingrube, E. Schulz, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “High-order harmonic generation directly from a filament,” New J. Phys. 13, 043022 (2011).
[Crossref]

E. Schulz, D. S. Steingrube, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “Tracking spectral shapes and temporal dynamics along a femtosecond filament,” Opt. Express 19, 19495–19507 (2011).
[Crossref] [PubMed]

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[Crossref]

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Gallmann, L.

Gopal, A.

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Guandalini, A.

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Hansinger, P.

Hauri, C. P.

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]

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, “Generation of intense few-cycle laser pulses through filamentation parameter dependence,” Opt. Express 13, 7541–7547 (2005).
[Crossref] [PubMed]

Haworth, C.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Heinzmann, U.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

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).
[Crossref]

Hentschel, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Hoff, D.

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Holler, M.

Houard, A.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[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]

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[Crossref]

Jarnac, A.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

Kandidov, V. P.

E. O. Smetanina, A. E. Dormidonov, and V. P. Kandidov, “Spatio-temporal evolution scenarios of femtosecond laser pulse filamentation in fused silica,” Laser Phys. 22, 1189–1198 (2012).
[Crossref]

Karsch, S.

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

Kasparian, J.

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

Keller, U.

A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10, 025023 (2008).
[Crossref]

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15, 5394–5405 (2007).
[Crossref] [PubMed]

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]

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, “Generation of intense few-cycle laser pulses through filamentation parameter dependence,” Opt. Express 13, 7541–7547 (2005).
[Crossref] [PubMed]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Kingston,

Dalgarno and Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. Roy. Soc. London Ser. A 259, 424–429 (1966).
[Crossref]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Kolesik, M.

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]

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, “Generation of intense few-cycle laser pulses through filamentation parameter dependence,” Opt. Express 13, 7541–7547 (2005).
[Crossref] [PubMed]

Kosma, K.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Kovacev, M.

Krausz, F.

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[Crossref]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Kretschmar, M.

Lederer, F.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

Levis, R. J.

J. Odhner and R. J. Levis, “Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air,” Opt. Lett. 37, 1775–1777 (2012).
[Crossref] [PubMed]

J. Odhner, D. Romanov, and R. J. Levis, “Self-shortening dynamics measured along a femtosecond laser filament in air,” Phys. Rev. Lett. 105, 125001 (2010).
[Crossref] [PubMed]

Li, Z.

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

Liu, X.

Major, Z.

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

Majus, D.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

Marangos, J.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Marceau, C.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Matijosius, A.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

McKenna, J.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Milchberg, H. M.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in n2, o2, n2o, and ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

Milosevic, N.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Minardi, S.

Mlejnek, M.

Moloney, J. V.

Morgner, U.

Mourou, G.

Mysyrowicz, A.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10, 025023 (2008).
[Crossref]

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16, 17626–17636 (2008).
[Crossref] [PubMed]

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15, 5394–5405 (2007).
[Crossref] [PubMed]

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]

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]

Nibbering, E.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

Nuter, R.

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

Odhner, J.

J. Odhner and R. J. Levis, “Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air,” Opt. Lett. 37, 1775–1777 (2012).
[Crossref] [PubMed]

J. Odhner, D. Romanov, and R. J. Levis, “Self-shortening dynamics measured along a femtosecond laser filament in air,” Phys. Rev. Lett. 105, 125001 (2010).
[Crossref] [PubMed]

Okell, W.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Panja, S.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Paulus, G. G.

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Piskarskas, A.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Piskarskas, R.

Planchon, T. A.

D. E. Adams, T. A. Planchon, J. A. Squier, and C. G. Durfee, “Spatiotemporal dynamics of ionizing filaments in air,” Proceedings of IEEE Conference on Lasers and Electro-OpticsJThE119 (2010).
[Crossref]

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Prade, B.

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]

Rausch, S.

E. Schulz, T. Binhammer, D. Steingrube, S. Rausch, M. Kovacev, and U. Morgner, “Intense few-cycle laser pulses from self-compression in a self-guiding filament,” Appl. Phys. B 95, 269–272 (2009).
[Crossref]

Reider, G. A.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Robinson, J.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Roman, J. S.

Romanov, D.

J. Odhner, D. Romanov, and R. J. Levis, “Self-shortening dynamics measured along a femtosecond laser filament in air,” Phys. Rev. Lett. 105, 125001 (2010).
[Crossref] [PubMed]

Roso, L.

Scalora, M.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Schafer, K. J.

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[Crossref]

Schapper, F.

Schmid, W. E.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Schnuerer, M.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Schulz, E.

Skupin, S.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
[Crossref] [PubMed]

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

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

Smetanina, E. O.

E. O. Smetanina, A. E. Dormidonov, and V. P. Kandidov, “Spatio-temporal evolution scenarios of femtosecond laser pulse filamentation in fused silica,” Laser Phys. 22, 1189–1198 (2012).
[Crossref]

Sokollik, T.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

Sola, I. J.

Spielmann, C.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Squier, J.

Squier, J. A.

D. E. Adams, T. A. Planchon, J. A. Squier, and C. G. Durfee, “Spatiotemporal dynamics of ionizing filaments in air,” Proceedings of IEEE Conference on Lasers and Electro-OpticsJThE119 (2010).
[Crossref]

Steingrube, D.

E. Schulz, T. Binhammer, D. Steingrube, S. Rausch, M. Kovacev, and U. Morgner, “Intense few-cycle laser pulses from self-compression in a self-guiding filament,” Appl. Phys. B 95, 269–272 (2009).
[Crossref]

Steingrube, D. S.

Steinmeyer, G.

C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
[Crossref]

C. Breé, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Self-pinching of pulsed laser beams during filamentary propagation,” Opt. Express 17, 16429–16435 (2009).
[Crossref] [PubMed]

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006).
[Crossref] [PubMed]

Stibenz, G.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006).
[Crossref] [PubMed]

Tamoauskas, G.

Tamosauskas, G.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
[Crossref]

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Tate, J. L.

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[Crossref]

Teng, H.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Terentev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Theberge, F.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[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]

Tisch, J. W. G.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Trapani, P. D.

Truschin, S.

I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
[Crossref]

Trushin, S. A.

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
[Crossref]

Varanavicius, A.

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

Varela, O.

Vockerodt, T.

Wahlstrand, J. K.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in n2, o2, n2o, and ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

Walmsley, I.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Wang, T. J.

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Wang, X.

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

Witting, T.

F. Frank, C. Arrell, T. Witting, W. Okell, J. McKenna, J. Robinson, C. Haworth, D. Austin, H. Teng, I. Walmsley, J. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref] [PubMed]

Wolf, J.-P.

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

Wright, E. M.

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614 (2008).
[Crossref] [PubMed]

Zaïr, A.

Zgadzaj, R.

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

Zhavoronkov, N.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
[Crossref]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006).
[Crossref] [PubMed]

Zozulya, A. A.

A. A. Zozulya, S. A. Diddams, A. G. V. Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: Multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430 (1999).
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Appl. Phys. B (1)

E. Schulz, T. Binhammer, D. Steingrube, S. Rausch, M. Kovacev, and U. Morgner, “Intense few-cycle laser pulses from self-compression in a self-guiding filament,” Appl. Phys. B 95, 269–272 (2009).
[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. Opt. Soc. Am. B (1)

J. Phys. B: At. Mol. Opt. Phys. (1)

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[Crossref]

Laser Phys. (1)

E. O. Smetanina, A. E. Dormidonov, and V. P. Kandidov, “Spatio-temporal evolution scenarios of femtosecond laser pulse filamentation in fused silica,” Laser Phys. 22, 1189–1198 (2012).
[Crossref]

Laser Phys. Lett. (1)

T. J. Wang, J. F. Daigle, Y. Chen, C. Marceau, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “High energy thz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7, 517–521 (2010).
[Crossref]

Nat. Commun. (1)

Z. Li, R. Zgadzaj, X. Wang, Y.-Y. Chang, and M. C. Downer, “Single-shot tomographic movies of evolving light-velocity objects,” Nat. Commun. 5, 3085 (2014).
[Crossref] [PubMed]

Nature (1)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
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New J. Phys. (5)

D. S. Steingrube, E. Schulz, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner, and M. Kovačev, “High-order harmonic generation directly from a filament,” New J. Phys. 13, 043022 (2011).
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A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10, 025023 (2008).
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N. Akzbek, S. A. Trushin, A. Baltuska, W. Fu, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, “Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses,” New J. Phys. 8, 177 (2006).
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C. Brée, J. Bethge, S. Skupin, L. Berg, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12, 093046 (2010).
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I. Ahmad, L. Bergé, Z. Major, F. Krausz, S. Karsch, and S. Truschin, “Redshift of few-cycle infrared pulses in the filamentation regime,” New J. Phys. 13, 093005 (2011).
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Opt. Express (6)

Opt. Lett. (7)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
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Phys. Rev. A (5)

F. Bragheri, D. Faccio, A. Couairon, A. Matijosius, G. Tamosauskas, A. Varanavicius, V. Degiorgio, A. Piskarskas, and P. Di Trapani, “Conical-emission and shock-front dynamics in femtosecond laser-pulse filamentation,” Phys. Rev. A 76, 025801 (2007).
[Crossref]

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
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C. Breé, A. Demircan, J. Bethge, E. Nibbering, S. Skupin, L. Bergé, and G. Steinmeyer, “Filamentary pulse self-compression: The impact of the cell windows,” Phys. Rev. A 83, 043803 (2011).
[Crossref]

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008).
[Crossref]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in n2, o2, n2o, and ar,” Phys. Rev. A 85, 043820 (2012).
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Phys. Rev. E (1)

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, “Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006).
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L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633 (2007).
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[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Sketch of the experimental setup. The fundamental beam is focused by a curved mirror into a gas-cell while surpassing a translation stage. The propagating filament is truncated by means of a laser-drilled pinhole stage. Moving the translation stage allows for the extraction of the fundamental pulses at different propagation lengths of the filament. The emerging pulses are characterized directly in the subsequent all-vacuum chamber by a SHG-FROG setup, enabling a unperturbed observation of the fundamental pulse-shape.
Fig. 2
Fig. 2 Evolution of the measured (a) and simulated (b) spectrum along the propagation direction of the filament. The red lines display the central frequency in dependence of the filament’s length. A significant spectral broadening is observed with ongoing propagation of the filament. From each spectrum, the Fourier-limited pulse duration is determined and displayed below the spectral evolution in (c) and (d).
Fig. 3
Fig. 3 Spectral evolution measured after the SHG-FROG device. The red-dotted lines display exemplary points along the propagation direction of the filament at which the fundamental pulse shapes have been determined using a SHG-FROG device. The obtained traces are shown in panels (b)–(d) with their corresponding reconstructed traces, spectra and pulse shapes. The ongoing change of the pulse shape can be traced along the propagation direction. The shortest measured pulse at position 212 cm has a duration of 5.30 fs.
Fig. 4
Fig. 4 Experimentally obtained and simulated dependence of the fundamental pulse shape on the propagation distance of the filament. The pulse duration of the reconstructed pulse shapes is displayed below. The inlets in panels c) and d) present a zoom to propagation distances with the shortest pulse durations.
Fig. 5
Fig. 5 Comparison of the near field pulse-shape to the vacuum-propagated pulse-shape after a double pinhole setup.

Tables (1)

Tables Icon

Table 1 Comparison of experiments and simulations using key-values derived from the evolution of the spectrum as well as the pulse shapes along the filament.

Equations (2)

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z E = i 2 k 0 T 1 Δ E + i D E + i ω 0 c n 2 T | E | 2 E i k 0 2 ρ c T 1 ρ E σ 2 ρ E U i W ( I ) ( ρ n t ρ ) 2 I E
t ρ = W ( I ) ( ρ n t ρ ) + σ U i ρ I .

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