Abstract

We study the possibility to obtain high-intensity pulses that maintain a constant Carrier Envelope Phase (CEP) during propagation in dispersive media, i.e. pulses such that the carrier-wave offset with respect to the main intensity peak remains fixed. Our numerical experiments strongly suggest that pulse splitting and X-wave formation within femtosecond laser pulse filamentation leads to the formation of “constant-CEP” within well-defined regions inside the filament.We study the creation of “constant- CEP” pulses in both gasseous and condensed media showing that this is a generic feature of filaments.

© 2008 Optical Society of America

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  2. A. de Bohan, P. Antoine, D. B. Milo¡sevic, and B. Piraux,"Phase-dependent harmonic emission with ultrashort laser pulse," Phys. Rev. Lett. 81, 1837-1840 (1998).
    [CrossRef]
  3. T. Brabec and F. Krausz,"Intense few-cycle laser fields: frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  4. P. B. Corkum and F. Krausz, "Attosecond Science," Nature Phys. 3, 381-387 (2007).
    [CrossRef]
  5. L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
    [CrossRef] [PubMed]
  6. A. Baltu¡ska, T. Fuji, and T. Kobayashi,"Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifier," Phys. Rev. Lett. 88, 133901 (2002).
    [CrossRef] [PubMed]
  7. X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
    [CrossRef]
  8. A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with Pulsed Bessel Beams for High Harmonic Generation," Phys. Rev. A. 77, 021802(R) (2008).
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    [CrossRef]
  10. N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
    [CrossRef]
  11. M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (2008).
    [CrossRef] [PubMed]
  12. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
    [CrossRef]
  13. 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, 1633-1713 (2007).
    [CrossRef]
  14. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression of ultra-short laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
    [CrossRef]
  15. 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 (2005).
    [CrossRef] [PubMed]
  16. L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
    [CrossRef]
  17. A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
    [CrossRef]
  18. H. S. Chakraborty, M. B. Gaarde, and A. Couairon, "Single attosecond pulses from high harmonics driven by self-compressed filaments," Opt. Lett. 31, 3662-3664 (2006).
    [CrossRef] [PubMed]
  19. 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]
  20. 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]
  21. A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
    [CrossRef]
  22. E. R. Peck and K. Reeder, "Dispersion of Air," J. Opt. Soc. Am. 62, 958-962 (1972).
    [CrossRef]
  23. D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
    [CrossRef]
  24. M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
    [CrossRef] [PubMed]
  25. M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 2839021-4 (2002).
    [CrossRef]
  26. M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell??s to unidirectional equations," Phys. Rev. E 70, 0366041-4 (2004).
  27. M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X-waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
    [CrossRef] [PubMed]
  28. D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
    [CrossRef] [PubMed]
  29. 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).
    [CrossRef] [PubMed]
  30. D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
    [CrossRef] [PubMed]
  31. C. Conti, "Generation and nonlinear dynamics of X waves of the Schrodinger equation," Phys. Rev. E 70, 0466131-4 (2004).
  32. M. Kolesik and J. V. Moloney, "Self-healing light filaments," Opt. Lett. 29, 590-592 (2004).
    [CrossRef] [PubMed]

2008 (3)

M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (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]

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).
[CrossRef] [PubMed]

2007 (8)

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

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

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, 1633-1713 (2007).
[CrossRef]

P. B. Corkum and F. Krausz, "Attosecond Science," Nature Phys. 3, 381-387 (2007).
[CrossRef]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

2006 (5)

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

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

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, "Single attosecond pulses from high harmonics driven by self-compressed filaments," Opt. Lett. 31, 3662-3664 (2006).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

2005 (3)

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

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 (2005).
[CrossRef] [PubMed]

2004 (5)

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]

C. Conti, "Generation and nonlinear dynamics of X waves of the Schrodinger equation," Phys. Rev. E 70, 0466131-4 (2004).

M. Kolesik and J. V. Moloney, "Self-healing light filaments," Opt. Lett. 29, 590-592 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell??s to unidirectional equations," Phys. Rev. E 70, 0366041-4 (2004).

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X-waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

2002 (2)

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 2839021-4 (2002).
[CrossRef]

A. Baltu¡ska, T. Fuji, and T. Kobayashi,"Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifier," Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

2000 (1)

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

1998 (1)

A. de Bohan, P. Antoine, D. B. Milo¡sevic, and B. Piraux,"Phase-dependent harmonic emission with ultrashort laser pulse," Phys. Rev. Lett. 81, 1837-1840 (1998).
[CrossRef]

1996 (1)

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

1972 (1)

E. R. Peck and K. Reeder, "Dispersion of Air," J. Opt. Soc. Am. 62, 958-962 (1972).
[CrossRef]

Abel, M. J.

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

Adams, M.

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Anscombe, M. P.

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

Antoine, P.

A. de Bohan, P. Antoine, D. B. Milo¡sevic, and B. Piraux,"Phase-dependent harmonic emission with ultrashort laser pulse," Phys. Rev. Lett. 81, 1837-1840 (1998).
[CrossRef]

Averchi, A.

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).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

Baltu¡ska, A.

A. Baltu¡ska, T. Fuji, and T. Kobayashi,"Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifier," Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

Bergé, L.

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

Biegert, J.

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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 (2005).
[CrossRef] [PubMed]

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]

Biegerti, J.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

Brabec, T.

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

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Bragheri, F.

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Bramati, A.

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Brimhall, N.

M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (2008).
[CrossRef] [PubMed]

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[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]

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, "Single attosecond pulses from high harmonics driven by self-compressed filaments," Opt. Lett. 31, 3662-3664 (2006).
[CrossRef] [PubMed]

Christensen, E.

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Cohen, O.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

Conti, C.

C. Conti, "Generation and nonlinear dynamics of X waves of the Schrodinger equation," Phys. Rev. E 70, 0466131-4 (2004).

Corkum, P. B.

P. B. Corkum and F. Krausz, "Attosecond Science," Nature Phys. 3, 381-387 (2007).
[CrossRef]

Couairon, A.

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]

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).
[CrossRef] [PubMed]

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

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, "Single attosecond pulses from high harmonics driven by self-compressed filaments," Opt. Lett. 31, 3662-3664 (2006).
[CrossRef] [PubMed]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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 (2005).
[CrossRef] [PubMed]

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]

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A. de Bohan, P. Antoine, D. B. Milo¡sevic, and B. Piraux,"Phase-dependent harmonic emission with ultrashort laser pulse," Phys. Rev. Lett. 81, 1837-1840 (1998).
[CrossRef]

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D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[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).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Dubietis, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Eckle, P.

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

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).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Franco, M.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (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 (2005).
[CrossRef] [PubMed]

Fuji, T.

A. Baltu¡ska, T. Fuji, and T. Kobayashi,"Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifier," Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

Gaarde, M. B.

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]

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, "Single attosecond pulses from high harmonics driven by self-compressed filaments," Opt. Lett. 31, 3662-3664 (2006).
[CrossRef] [PubMed]

Gallmann, L.

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

Giraud, G.

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Guandalini, A.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

H¨ansch, T. W.

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Hauri, C. P.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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]

Helbing, F. W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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]

Holler, M.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

Kapteyn, H. C.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[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, 1633-1713 (2007).
[CrossRef]

Keller, U.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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 (2005).
[CrossRef] [PubMed]

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]

Kobayashi, T.

A. Baltu¡ska, T. Fuji, and T. Kobayashi,"Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifier," Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

Kolesik, M.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X-waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, "Self-healing light filaments," Opt. Lett. 29, 590-592 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell??s to unidirectional equations," Phys. Rev. E 70, 0366041-4 (2004).

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 2839021-4 (2002).
[CrossRef]

Kornelis, W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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.

P. B. Corkum and F. Krausz, "Attosecond Science," Nature Phys. 3, 381-387 (2007).
[CrossRef]

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

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Leone, S.R.

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

Liberale, C.

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Lotti, A.

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).
[CrossRef] [PubMed]

Lytle, A. L.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

Matijosius, A.

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Minardi, S.

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

Mlejnek, M.

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 2839021-4 (2002).
[CrossRef]

Moloney, J.

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X-waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Moloney, J. V.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, "Self-healing light filaments," Opt. Lett. 29, 590-592 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell??s to unidirectional equations," Phys. Rev. E 70, 0366041-4 (2004).

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 2839021-4 (2002).
[CrossRef]

Murnane, M. M.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

Mysyrowicz, A.

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

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression 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 (2005).
[CrossRef] [PubMed]

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]

Nagel, P. M.

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

Neumark, D. M.

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[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, 1633-1713 (2007).
[CrossRef]

Painter, J. C.

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Papazoglou, 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).
[CrossRef] [PubMed]

Peatross, J.

M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (2008).
[CrossRef] [PubMed]

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
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E. R. Peck and K. Reeder, "Dispersion of Air," J. Opt. Soc. Am. 62, 958-962 (1972).
[CrossRef]

Pfeifer, T.

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

Piskarskas, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

Polesana, P.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

Popmintchev, T.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

Poppe, A.

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Porras, M.

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

Powers, N.

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Reeder, K.

E. R. Peck and K. Reeder, "Dispersion of Air," J. Opt. Soc. Am. 62, 958-962 (1972).
[CrossRef]

Schapper, F.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

Schlup, P.

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

Skupin, S.

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

Spielmann, Ch.

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Tamosauskas, G.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

Turner, M.

M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (2008).
[CrossRef] [PubMed]

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Tzortzakis, S.

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).
[CrossRef] [PubMed]

Ware, M.

M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (2008).
[CrossRef] [PubMed]

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

Wolf, J. P.

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

Wright, E.

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X-waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

Xu, L.

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Zaïr, A.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

Zhang, X.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

Zhou, X.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

App. Phys. B. (1)

L. Gallmann, T. Pfeifer, P. M. Nagel, M. J. Abel, D. M. Neumark, and S.R. Leone, "Comparison of the filamentation and the hollow-core fiber characteristics for pulse compression into the few-cycle regime," App. Phys. B. 86, 2503-2508 (2007).
[CrossRef]

Appl. Phys. B (1)

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]

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. (1)

E. R. Peck and K. Reeder, "Dispersion of Air," J. Opt. Soc. Am. 62, 958-962 (1972).
[CrossRef]

J. Opt. Soc. Am. B (1)

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (2005).
[CrossRef]

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

A. Guandalini, P. Eckle, M. P. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis," J. Phys. B: At. Mol. Opt. Phys. 39, S257-S264 (2006).
[CrossRef]

Nature Phys. (2)

P. B. Corkum and F. Krausz, "Attosecond Science," Nature Phys. 3, 381-387 (2007).
[CrossRef]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen "Quasi-phasematching and quantum-path control of high-harmonic generation using counterpropagating light," Nature Phys. 3, 270-275 (2007).
[CrossRef]

Opt. Express (6)

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegerti, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5395-5405 (2007).
[CrossRef]

N. Brimhall, J. C. Painter, N. Powers, G. Giraud, M. Turner, M. Ware, and J. Peatross, "Measured laser-beam evolution during high-order harmonic generation in a semi-infinite gas cell," Opt. Express 15, 16841689 (2007).
[CrossRef]

M. Turner, N. Brimhall, M. Ware, and J. Peatross, "Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell," Opt. Express 16, 1571-1576 (2008).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Opt. Lett (1)

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 (2005).
[CrossRef] [PubMed]

Opt. Lett. (4)

M. Kolesik and J. V. Moloney, "Self-healing light filaments," Opt. Lett. 29, 590-592 (2004).
[CrossRef] [PubMed]

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, "Single attosecond pulses from high harmonics driven by self-compressed filaments," Opt. Lett. 31, 3662-3664 (2006).
[CrossRef] [PubMed]

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 34713473 (2006).
[CrossRef]

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. H¨ansch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Phys. Rep. (1)

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

Phys. Rev. A (1)

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]

Phys. Rev. E (2)

C. Conti, "Generation and nonlinear dynamics of X waves of the Schrodinger equation," Phys. Rev. E 70, 0466131-4 (2004).

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell??s to unidirectional equations," Phys. Rev. E 70, 0366041-4 (2004).

Phys. Rev. Lett. (5)

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X-waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional Optical Pulse Propagation Equation," Phys. Rev. Lett. 89, 2839021-4 (2002).
[CrossRef]

A. Baltu¡ska, T. Fuji, and T. Kobayashi,"Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifier," Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

A. de Bohan, P. Antoine, D. B. Milo¡sevic, and B. Piraux,"Phase-dependent harmonic emission with ultrashort laser pulse," Phys. Rev. Lett. 81, 1837-1840 (1998).
[CrossRef]

Rep. Prog. Phys. (1)

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

Rev. Mod. Phys. (1)

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

Other (2)

P. Wegener, Extreme Nonlinear Optics (Springer 2005).

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with Pulsed Bessel Beams for High Harmonic Generation," Phys. Rev. A. 77, 021802(R) (2008).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Far-field spectrum generated in a femtosecond filament in air. In the filament, the incident pulse undergoes temporal splitting giving rise to two daughter (or split-off) pulses. The white line marks the spectral structure that is generated by the leading split-off pulse. The location of this structure is essentially determined by the group velocity of the peak which in this case is very close to the phase velocity of the carrier. This indicates the possibility of constant carrier-envelope phase in the leading split-off peak.

Fig. 2.
Fig. 2.

Left: Pulse splitting in the air filament as seen in the on-axis intensity vs local time for several propagation distances. The leading peak can exhibit slowly changing carrier-envelope phase. Right: On-axis maximal intensity in the filament. The nearly constant carrier envelope phase occurs just beyond the first maximum and before the second pulse splitting event.

Fig. 3.
Fig. 3.

Snapshot of the on-axis intensity profile (left) after pulse splitting in the filament. The leading split-off pulse is shown in detail in the right-hand-side panel together with the squared electric field intensity (red curve). The maxima of the envelope and carrier are aligned (CEP=0).

Fig. 4.
Fig. 4.

Carrier-envelope phase for the leading peak vs propagation distance (black line) compared to the carrier-envelope phase in the free-propagating Gaussian pulse given by (1).

Fig. 5.
Fig. 5.

Temporal locations, in the local frame of reference co-moving with the pulse, of the envelope maximum of the leading split-off peak (black line), and of the nearest real-field peak (red line). For comparison, the dashed line represents the “movement” of the real-field peak as it would be observed in a freely propagating Gaussian pulse (i.e. this line represents the phase velocity at 800nm).

Fig. 6.
Fig. 6.

Carrier-envelope phase for the leading peak vs propagation distance (black line) compared to the carrier-envelope phase in the free-propagating Gaussian pulse for a filament created in silica. Due to the condensed medium stronger dispersion and nonlinearity, the co-propagation effect is scaled down, but qualitatively similar to that observed in the air filament.

Fig. 7.
Fig. 7.

Envelope and field maximum co-propagation in silica. Temporal locations, in the local frame of reference co-moving with the pulse, of the envelope maximum of the leading split-off peak (black line), and of the nearest real-field peak (red line). For comparison, the dashed line represents the “movement” of the real-field peak as it would be observed in a freely propagating Gaussian pulse (i.e. this line represents the phase velocity at 1050 nm).

Fig. 8.
Fig. 8.

Carrier-envelope phase vs distance for a normal filament (black) and two cases of linear evolution beyond certain chosen distance. The curves immediately separate, but still exhibit relatively slow CEP evolution. The latter is restored very quickly after the sudden switch-off of the nonlinearity.

Fig.9.
Fig.9.

Leading split-off peak inverse velocity difference 1/ν-1/ν G (λ) w.r.t. the group velocity at a given wavelength, that is required to achieve equal peak and phase velocities, ν = νφ (λ), in silica. As the typical splitting rates in femtosecond filaments go, values in the range of 5×10-11s/m are rather high. Therefore, constant CEP pulses are most likely to occur in the vicinity of λ ≈ 1μm.

Equations (1)

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ϕ ( z ) = z [ k ( w ) ω k ( ω ) ω ]

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