Abstract

We report on numerical simulations and experiments of pulse self-compression by filamentation. Spectral and temporal evolution during ultrashort-pulse laser filamentation can be intuitively represented using spectrograms, which display spectra at different time delays of a gate pulse. This representation makes evident the features of self-compression by filamentation, namely spectral broadening and pulse shortening. In addition, it allows for an analysis of the spectral phase during the nonlinear propagation. In our simulations we observe occurrence of negative chirp over a few cm before the shortest pulse is obtained during filamentation; this provides an important basis for the understanding of the mechanisms leading to self-compressed filaments. We attribute the negative chirp to spatio-temporal reshaping due to the competition between self-phase modulation and group velocity dispersion. We show that the plasma induced dispersion plays a minor role in establishing the negative chirp.

© 2008 Optical Society of America

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  1. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
    [CrossRef] [PubMed]
  2. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the "Single-Cycle" Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
    [CrossRef]
  3. P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
    [CrossRef] [PubMed]
  4. T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
    [CrossRef]
  5. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
    [CrossRef] [PubMed]
  6. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
    [CrossRef] [PubMed]
  7. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
    [CrossRef]
  8. A. Zair, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5404 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5394.
    [CrossRef] [PubMed]
  9. 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]
  10. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (2006).
    [CrossRef]
  11. A. Mysyrowicz, A. Couairon, and U. Keller, "Self-compression of optical laser pulses by filamentation," New J. Phys. 10, 025023 (2008).
    [CrossRef]
  12. A. Couairon, and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
    [CrossRef]
  13. S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "A simple method for determination of nonlinear propagation regimes in gases," Opt. Express 15, 15260-15267 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15260.
    [CrossRef] [PubMed]
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    [CrossRef]
  15. A. L. Gaeta, "Catastrophic Collapse of Ultrashort Pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
    [CrossRef] [PubMed]
  16. 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).
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  17. I. G. Koprinkov, "Ionization variation of the group velocity dispersion by high-intensity optical pulses," Appl. Phys. B 76, 359-361 (2004).
    [CrossRef]
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    [CrossRef]
  19. 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]
  20. 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] [PubMed]
  21. D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X-Wave formation in air," Opt. Express 16, 1565-1570 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-3-1565.
    [CrossRef] [PubMed]
  22. A. Couairon, S. Tzortzakis, L. Berge, M. Franco, B. Prade, and A. Mysyrowicz, "Infrared femtosecond light filaments in air: simulations and experiments," J. Opt. Soc. Am. B 19, 1117-1131 (2002).
    [CrossRef]
  23. L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, "Spectral reshaping and pulse compression via sequential filamentation in gases," Opt. Express 16, 390-401 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-1-390.
    [CrossRef] [PubMed]
  24. R. A. Altes, "Detection, estimation, and classification with spectrograms," J. Acoust. Soc. Am. 67, 1232-1248 (1980).
    [CrossRef]
  25. L. Cohen, "Time-Frequency Distributions-A Review," Proceedings of the IEEE 77, 941-981 (1989).
    [CrossRef]
  26. R. Trebino, Frequency-Resolved Optical Gating (Kluwer Academic Publishers, Boston, 2002).
    [CrossRef]
  27. H. S. Nawab, T. F. Quatieri, and J. S. Lim, "Signal reconstruction from short-time fourier transform magnitude," IEEE Trans. Acoust. Speech. Signal. Process. ASSP-31, 986-998 (1983).
    [CrossRef]
  28. S. Linden, J. Kuhl, and H. Giessen, "Amplitude and phase characterization of weak blue ultrashort pulses by downconversion," Opt. Lett. 24, 569-571 (1999).
    [CrossRef]
  29. R. Trebino and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101-1111 (1993).
    [CrossRef]
  30. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
    [CrossRef]
  31. Q4. S. Akturk, C. D'Amico, and A. Mysyrowicz, "Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating," J. Opt. Soc. Am. B 25 (2008).
    [CrossRef]
  32. A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-Harmonic Generation Frequency-Resolved Optical Gating in the Single-Cycle Regime," IEEE J. Quantum Electron. 35, 459-478 (1999).
    [CrossRef]
  33. A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. S. J. Russel, "Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling," Opt. Express 12, 6498-6507 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-26-6498.
    [CrossRef] [PubMed]
  34. R. W. Boyd, Nonlinear Optics (Academic Press, 2003).
  35. T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
    [CrossRef]
  36. J. Liu, H. Schroeder, S. L. Chin, R. Li, W. Yu, and Z. Xu, "Space-frequency coupling, conical waves and small-scale filamentation in water," Phys. Rev. A 72, 053817 (2005).
    [CrossRef]
  37. A. Couairon, "Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses," Phys. Rev. A 68, 015801 (2003).
    [CrossRef]
  38. D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
    [CrossRef]
  39. S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
    [CrossRef]

2008

2007

A. Couairon, and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[CrossRef]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "A simple method for determination of nonlinear propagation regimes in gases," Opt. Express 15, 15260-15267 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15260.
[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. Zair, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5404 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5394.
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

2006

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]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (2006).
[CrossRef]

C. P. Hauri, A. Trisorio, M. Merano, G. Rey, R. B. Lopez-Martens, and G. Mourou, "Generation of high-fidelity, down-chirped sub-10 fs mJ pulses through filamentation for driving relativistic laser-matter interactions at 1 kHz," Appl. Phys. Lett. 89 151125 (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

J. Liu, H. Schroeder, S. L. Chin, R. Li, W. Yu, and Z. Xu, "Space-frequency coupling, conical waves and small-scale filamentation in water," Phys. Rev. A 72, 053817 (2005).
[CrossRef]

2004

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. S. J. Russel, "Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling," Opt. Express 12, 6498-6507 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-26-6498.
[CrossRef] [PubMed]

I. G. Koprinkov, "Ionization variation of the group velocity dispersion by high-intensity optical pulses," Appl. Phys. B 76, 359-361 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

2003

2002

2001

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

2000

T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

A. L. Gaeta, "Catastrophic Collapse of Ultrashort Pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

1999

A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-Harmonic Generation Frequency-Resolved Optical Gating in the Single-Cycle Regime," IEEE J. Quantum Electron. 35, 459-478 (1999).
[CrossRef]

S. Linden, J. Kuhl, and H. Giessen, "Amplitude and phase characterization of weak blue ultrashort pulses by downconversion," Opt. Lett. 24, 569-571 (1999).
[CrossRef]

1997

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the "Single-Cycle" Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

1996

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] [PubMed]

1993

1989

L. Cohen, "Time-Frequency Distributions-A Review," Proceedings of the IEEE 77, 941-981 (1989).
[CrossRef]

1983

H. S. Nawab, T. F. Quatieri, and J. S. Lim, "Signal reconstruction from short-time fourier transform magnitude," IEEE Trans. Acoust. Speech. Signal. Process. ASSP-31, 986-998 (1983).
[CrossRef]

1980

R. A. Altes, "Detection, estimation, and classification with spectrograms," J. Acoust. Soc. Am. 67, 1232-1248 (1980).
[CrossRef]

1975

J. H. Marburger, "Self-focusing: Theory," Prog. Quantum. Electron. 4, 35-110 (1975).
[CrossRef]

Akturk, S.

Q4. S. Akturk, C. D'Amico, and A. Mysyrowicz, "Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating," J. Opt. Soc. Am. B 25 (2008).
[CrossRef]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "A simple method for determination of nonlinear propagation regimes in gases," Opt. Express 15, 15260-15267 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15260.
[CrossRef] [PubMed]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

Altes, R. A.

R. A. Altes, "Detection, estimation, and classification with spectrograms," J. Acoust. Soc. Am. 67, 1232-1248 (1980).
[CrossRef]

Averchi, A.

Baltuska, A.

A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-Harmonic Generation Frequency-Resolved Optical Gating in the Single-Cycle Regime," IEEE J. Quantum Electron. 35, 459-478 (1999).
[CrossRef]

Berge, L.

Biancalana, F.

Biegert, J.

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

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]

Chin, S. L.

J. Liu, H. Schroeder, S. L. Chin, R. Li, W. Yu, and Z. Xu, "Space-frequency coupling, conical waves and small-scale filamentation in water," Phys. Rev. A 72, 053817 (2005).
[CrossRef]

Christov, I. P.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the "Single-Cycle" Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

Cohen, L.

L. Cohen, "Time-Frequency Distributions-A Review," Proceedings of the IEEE 77, 941-981 (1989).
[CrossRef]

Corkum, P. B.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

Couairon, A.

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

D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X-Wave formation in air," Opt. Express 16, 1565-1570 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-3-1565.
[CrossRef] [PubMed]

A. Couairon, and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[CrossRef]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "A simple method for determination of nonlinear propagation regimes in gases," Opt. Express 15, 15260-15267 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15260.
[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. Zair, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5404 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5394.
[CrossRef] [PubMed]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (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]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

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

A. Couairon, S. Tzortzakis, L. Berge, M. Franco, B. Prade, and A. Mysyrowicz, "Infrared femtosecond light filaments in air: simulations and experiments," J. Opt. Soc. Am. B 19, 1117-1131 (2002).
[CrossRef]

D'Amico, C.

Q4. S. Akturk, C. D'Amico, and A. Mysyrowicz, "Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating," J. Opt. Soc. Am. B 25 (2008).
[CrossRef]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "A simple method for determination of nonlinear propagation regimes in gases," Opt. Express 15, 15260-15267 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15260.
[CrossRef] [PubMed]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

De Silvestri, S.

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]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Di Trapani, P.

D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X-Wave formation in air," Opt. Express 16, 1565-1570 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-3-1565.
[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]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

Drescher, D.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Dubietis, A.

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

Efimov, A.

Faccio, D.

D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X-Wave formation in air," Opt. Express 16, 1565-1570 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-3-1565.
[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]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

Ferencz, K.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Franco, M.

Gaeta, A. L.

L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, "Spectral reshaping and pulse compression via sequential filamentation in gases," Opt. Express 16, 390-401 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-1-390.
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A. L. Gaeta, "Catastrophic Collapse of Ultrashort Pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

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] [PubMed]

Gallmann, L.

Giessen, H.

Guandalini, A.

Hauri, C. P.

L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, "Spectral reshaping and pulse compression via sequential filamentation in gases," Opt. Express 16, 390-401 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-1-390.
[CrossRef] [PubMed]

C. P. Hauri, A. Trisorio, M. Merano, G. Rey, R. B. Lopez-Martens, and G. Mourou, "Generation of high-fidelity, down-chirped sub-10 fs mJ pulses through filamentation for driving relativistic laser-matter interactions at 1 kHz," Appl. Phys. Lett. 89 151125 (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]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Heinzmann, U.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. 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]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Hentschel, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
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Holler, M.

Joly, N. Y.

Kane, D. J.

Kapteyn, H. C.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the "Single-Cycle" Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
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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. Zair, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5404 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5394.
[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]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (2006).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
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Kienberger, R.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

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Koprinkov, I. G.

I. G. Koprinkov, "Ionization variation of the group velocity dispersion by high-intensity optical pulses," Appl. Phys. B 76, 359-361 (2004).
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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, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Krausz, F.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
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M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

Krumbugel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Kucinskas, E.

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

Kuhl, J.

Li, R.

J. Liu, H. Schroeder, S. L. Chin, R. Li, W. Yu, and Z. Xu, "Space-frequency coupling, conical waves and small-scale filamentation in water," Phys. Rev. A 72, 053817 (2005).
[CrossRef]

Lim, J. S.

H. S. Nawab, T. F. Quatieri, and J. S. Lim, "Signal reconstruction from short-time fourier transform magnitude," IEEE Trans. Acoust. Speech. Signal. Process. ASSP-31, 986-998 (1983).
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Linden, S.

Liu, J.

J. Liu, H. Schroeder, S. L. Chin, R. Li, W. Yu, and Z. Xu, "Space-frequency coupling, conical waves and small-scale filamentation in water," Phys. Rev. A 72, 053817 (2005).
[CrossRef]

Lopez-Martens, R. B.

L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, "Spectral reshaping and pulse compression via sequential filamentation in gases," Opt. Express 16, 390-401 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-1-390.
[CrossRef] [PubMed]

C. P. Hauri, A. Trisorio, M. Merano, G. Rey, R. B. Lopez-Martens, and G. Mourou, "Generation of high-fidelity, down-chirped sub-10 fs mJ pulses through filamentation for driving relativistic laser-matter interactions at 1 kHz," Appl. Phys. Lett. 89 151125 (2006).
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Lotti, A.

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J. H. Marburger, "Self-focusing: Theory," Prog. Quantum. Electron. 4, 35-110 (1975).
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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]

Merano, M.

C. P. Hauri, A. Trisorio, M. Merano, G. Rey, R. B. Lopez-Martens, and G. Mourou, "Generation of high-fidelity, down-chirped sub-10 fs mJ pulses through filamentation for driving relativistic laser-matter interactions at 1 kHz," Appl. Phys. Lett. 89 151125 (2006).
[CrossRef]

Milosevic, N.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Mourou, G.

C. P. Hauri, A. Trisorio, M. Merano, G. Rey, R. B. Lopez-Martens, and G. Mourou, "Generation of high-fidelity, down-chirped sub-10 fs mJ pulses through filamentation for driving relativistic laser-matter interactions at 1 kHz," Appl. Phys. Lett. 89 151125 (2006).
[CrossRef]

Murnane, M. M.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the "Single-Cycle" Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

Mysyrowicz, A.

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

Q4. S. Akturk, C. D'Amico, and A. Mysyrowicz, "Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating," J. Opt. Soc. Am. B 25 (2008).
[CrossRef]

A. Couairon, and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[CrossRef]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "A simple method for determination of nonlinear propagation regimes in gases," Opt. Express 15, 15260-15267 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15260.
[CrossRef] [PubMed]

A. Zair, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5404 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5394.
[CrossRef] [PubMed]

S. Akturk, C. D'Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (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]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (2006).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

A. Couairon, S. Tzortzakis, L. Berge, M. Franco, B. Prade, and A. Mysyrowicz, "Infrared femtosecond light filaments in air: simulations and experiments," J. Opt. Soc. Am. B 19, 1117-1131 (2002).
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Nawab, H. S.

H. S. Nawab, T. F. Quatieri, and J. S. Lim, "Signal reconstruction from short-time fourier transform magnitude," IEEE Trans. Acoust. Speech. Signal. Process. ASSP-31, 986-998 (1983).
[CrossRef]

Nisoli, M.

Omenetto, F. G.

Papazoglou, D.

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]

Porras, M. A.

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

Prade, B.

Pshenichnikov, M. S.

A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-Harmonic Generation Frequency-Resolved Optical Gating in the Single-Cycle Regime," IEEE J. Quantum Electron. 35, 459-478 (1999).
[CrossRef]

Quatieri, T. F.

H. S. Nawab, T. F. Quatieri, and J. S. Lim, "Signal reconstruction from short-time fourier transform magnitude," IEEE Trans. Acoust. Speech. Signal. Process. ASSP-31, 986-998 (1983).
[CrossRef]

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] [PubMed]

Reider, G. A.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Rey, G.

C. P. Hauri, A. Trisorio, M. Merano, G. Rey, R. B. Lopez-Martens, and G. Mourou, "Generation of high-fidelity, down-chirped sub-10 fs mJ pulses through filamentation for driving relativistic laser-matter interactions at 1 kHz," Appl. Phys. Lett. 89 151125 (2006).
[CrossRef]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Russel, P. S. J.

Sansone, G.

Sartania, S.

Schapper, F.

Schenkel, B.

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] [PubMed]

Schroeder, H.

J. Liu, H. Schroeder, S. L. Chin, R. Li, W. Yu, and Z. Xu, "Space-frequency coupling, conical waves and small-scale filamentation in water," Phys. Rev. A 72, 053817 (2005).
[CrossRef]

Skryabin, D. V.

Spielmann, C.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, D. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
[CrossRef] [PubMed]

Stagira, S.

Steinmeyer, G.

Stibenz, G.

Svelto, O.

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997).
[CrossRef]

Szipocs, R.

Tamosauskas, G.

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]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, "Angular and chromatic dispersion in Kerr-driven conical emission," Opt. Commun. 265, 672-677 (2007).
[CrossRef]

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Supplementary Material (1)

» Media 1: AVI (1507 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Spectrograms of transform limited (a), linearly (positive) chirped (b) and quadratically (positive) chirped ultrashort laser pulses (c).

Fig. 2.
Fig. 2.

Simulation results of on axis intensity and electron density during filamentation in argon (input parameters given in text).

Fig. 3.
Fig. 3.

(Media 1) Movie of simulated spectrograms showing temporal pulse evolution during filamentation. Note the appearance of negative chirp starting at ~100 cm and, and a self compressed pulse (with duration <5 fs) at ~110 cm. The x-axes represent the delay; hence the traces are centered at the maximum intensity.

Fig. 4.
Fig. 4.

The evolution of the pulse duration (at the radius of the peak intensity) during the filamentary propagation. The minimum duration, (4.9 fs), occurs at ~110 cm.

Fig. 5.
Fig. 5.

Left column: Simulated on-axis intensity (red) and instantaneous frequency (black) vs. time. Right column: Spatio-temporal intensity profiles. Positions indicated at top of the figures.

Fig. 6.
Fig. 6.

Measured temporal intensity and phase profiles before and after filamentation. The output duration (~10 fs) is significantly shorter with respect to the initial pulse duration (~70fs).

Equations (8)

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P ( τ , ω ) = 1 2 π e i ω t S ( t ) h ( t τ ) dt 2
ε ω z = i 2 κ ( ω ) [ Δ + D ( ω ) ] ε ω + F [ N ( ε t , ρ ) ]
N ( ε t , ρ ) = T 2 i ω 0 c n 2 ε t 2 ε t k 0 ρ 2 n 0 ρ c ( 1 + i ω τ c ) ω 0 τ c ( 1 + ω 2 τ c 2 ) ε t T W ( ε t 2 ) U i 2 ε t 2 ( ρ at ρ ) ε t
T ( 1 + i ω 0 t )
k eff SPM = 3 3 2 ( ω 0 c ) n 2 I sat τ 2
I sat ( 0.76 n 2 ρ c σ K τ ρ at ) 1 ( K 1 )
k eff plasma = ρ sat ρ c n 0 3 k 0 v g 2
ρ sat = σ K I sat K ρ at τ = 2.3 × 10 16 cm 3

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