Abstract

We report on the first direct observation of carrier-envelope-phase (CEP) effect during the interaction between few-cycle laser pulses and bulk solid materials. Using 2-cycle mid-infrared laser pulses with stabilized CEP, the CEP effect of tunneling ionization during the laser filamentation in a fused silica is revealed. The phase variation of the accompanying supercontinuum (SC) emission with filamentation at different CEPs of laser pulses can be measured by means of spectral interference technique, as a direct manifestation of the strong field tunneling ionization dynamics in transparent solids.

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2011 (5)

A. V. Mitrofanov, A. J. Verhoef, E. E. Serebryannikov, J. Lumeau, L. Glebov, A. M. Zheltikov, and A. Baltuška, “Optical Detection of Attosecond Ionization Induced by a Few-Cycle Laser Field in a Transparent Dielectric Material,” Phys. Rev. Lett.106(14), 147401 (2011).
[CrossRef] [PubMed]

G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
[CrossRef]

C. Li, D. Wang, L. Song, J. Liu, P. Liu, C. Xu, Y. Leng, R. Li, and Z. Xu, “Generation of carrier-envelope phase stabilized intense 1.5 cycle pulses at 1.75 μm,” Opt. Express19(7), 6783–6789 (2011).
[CrossRef] [PubMed]

L. Bergé, C. L. Soulez, C. Köhler, and S. Skupin, “Role of the carrier-envelope phase in laser filamentation,” Appl. Phys. B103(3), 563–570 (2011).
[CrossRef]

G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
[CrossRef]

2010 (4)

Á. Börzsönyi, Z. Heiner, A. P. Kovács, M. P. Kalashnikov, and K. Osvay, “Measurement of pressure dependent nonlinear refractive index of inert gases,” Opt. Express18(25), 25847–25854 (2010).
[CrossRef] [PubMed]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
[CrossRef]

M. Gertsvolf, M. Spanner, D. M. Rayner, and P. B. Corkum, “Demonstration of attosecond ionization dynamics inside transparent solids,” J. Phys. At. Mol. Opt. Phys.43(13), 131002 (2010).
[CrossRef]

T. Popmintchev, M. C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics4(12), 822–832 (2010).
[CrossRef]

2009 (2)

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical Aspects in Above-Threshold Ionization with a Midinfrared Strong Laser Field,” Phys. Rev. Lett.103(9), 093001 (2009).
[CrossRef] [PubMed]

C. Zhang, P. Wei, Y. Huang, Y. Leng, Y. Zheng, Z. Zeng, R. Li, and Z. Xu, “Tunable phase-stabilized infrared optical parametric amplifier for high-order harmonic generation,” Opt. Lett.34(18), 2730–2732 (2009).
[CrossRef] [PubMed]

2008 (1)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (3)

M. Kreß, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few cycle laser pulses with terahertz emission spectroscopy,” Nat. Phys.2(5), 327–331 (2006).

T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, Th. Metzger, A. Baltuška, N. Forger, D. Kaplan, A. Galvanauskas, and F. Krausz, “Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm,” Opt. Lett.31(8), 1103–1105 (2006).

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

2005 (2)

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B71(12), 125435 (2005).
[CrossRef]

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. A72(5), 053817 (2005).
[CrossRef]

2003 (2)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond Synchronization of High-Harmonic Soft X-rays,” Science302(5650), 1540–1543 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle Laser Pulses,” Phys. Rev. Lett.91(25), 253004 (2003).
[CrossRef] [PubMed]

2002 (1)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in Fused silica,” Phys. Rev. Lett.89(18), 186601 (2002).
[CrossRef] [PubMed]

2001 (4)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses From High Harmonic Generation,” Science292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature414(6863), 509–513 (2001).
[CrossRef] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett.87(21), 213902 (2001).
[CrossRef] [PubMed]

2000 (2)

1994 (1)

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP64, 1191–1194 (1986).

1965 (1)

L. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP20, 1037–1314 (1965).

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond Synchronization of High-Harmonic Soft X-rays,” Science302(5650), 1540–1543 (2003).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses From High Harmonic Generation,” Science292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Alexeev, I.

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP64, 1191–1194 (1986).

Antonetti, A.

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Arpin, P.

T. Popmintchev, M. C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics4(12), 822–832 (2010).
[CrossRef]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Audebert, P.

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses From High Harmonic Generation,” Science292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Balcou, Ph.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses From High Harmonic Generation,” Science292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Baltuška, A.

A. V. Mitrofanov, A. J. Verhoef, E. E. Serebryannikov, J. Lumeau, L. Glebov, A. M. Zheltikov, and A. Baltuška, “Optical Detection of Attosecond Ionization Induced by a Few-Cycle Laser Field in a Transparent Dielectric Material,” Phys. Rev. Lett.106(14), 147401 (2011).
[CrossRef] [PubMed]

G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
[CrossRef]

G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
[CrossRef]

T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, Th. Metzger, A. Baltuška, N. Forger, D. Kaplan, A. Galvanauskas, and F. Krausz, “Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm,” Opt. Lett.31(8), 1103–1105 (2006).

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle Laser Pulses,” Phys. Rev. Lett.91(25), 253004 (2003).
[CrossRef] [PubMed]

Béjot, P.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
[CrossRef]

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Bergé, L.

L. Bergé, C. L. Soulez, C. Köhler, and S. Skupin, “Role of the carrier-envelope phase in laser filamentation,” Appl. Phys. B103(3), 563–570 (2011).
[CrossRef]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett.87(21), 213902 (2001).
[CrossRef] [PubMed]

Bisson, E.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
[CrossRef]

Blaga, C. I.

Börzsönyi, Á.

Brabec, T.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature414(6863), 509–513 (2001).
[CrossRef] [PubMed]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond Synchronization of High-Harmonic Soft X-rays,” Science302(5650), 1540–1543 (2003).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses From High Harmonic Generation,” Science292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Carré, B.

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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
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L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in Fused silica,” Phys. Rev. Lett.89(18), 186601 (2002).
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G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle Laser Pulses,” Phys. Rev. Lett.91(25), 253004 (2003).
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G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle Laser Pulses,” Phys. Rev. Lett.91(25), 253004 (2003).
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Milchberg, H.

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M. Kreß, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few cycle laser pulses with terahertz emission spectroscopy,” Nat. Phys.2(5), 327–331 (2006).

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M. Kreß, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few cycle laser pulses with terahertz emission spectroscopy,” Nat. Phys.2(5), 327–331 (2006).

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G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
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Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond Synchronization of High-Harmonic Soft X-rays,” Science302(5650), 1540–1543 (2003).
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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001).
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Paul, P. M.

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Poletto, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
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Power, E. P.

Prade, B.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B71(12), 125435 (2005).
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L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in Fused silica,” Phys. Rev. Lett.89(18), 186601 (2002).
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S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett.87(21), 213902 (2001).
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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001).
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Schultze, M.

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A. V. Mitrofanov, A. J. Verhoef, E. E. Serebryannikov, J. Lumeau, L. Glebov, A. M. Zheltikov, and A. Baltuška, “Optical Detection of Attosecond Ionization Induced by a Few-Cycle Laser Field in a Transparent Dielectric Material,” Phys. Rev. Lett.106(14), 147401 (2011).
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B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
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Skupin, S.

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M. Gertsvolf, M. Spanner, D. M. Rayner, and P. B. Corkum, “Demonstration of attosecond ionization dynamics inside transparent solids,” J. Phys. At. Mol. Opt. Phys.43(13), 131002 (2010).
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M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature414(6863), 509–513 (2001).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001).
[CrossRef] [PubMed]

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A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B71(12), 125435 (2005).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in Fused silica,” Phys. Rev. Lett.89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett.87(21), 213902 (2001).
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Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond Synchronization of High-Harmonic Soft X-rays,” Science302(5650), 1540–1543 (2003).
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Teisset, C. Y.

Thomson, M. D.

M. Kreß, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few cycle laser pulses with terahertz emission spectroscopy,” Nat. Phys.2(5), 327–331 (2006).

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses From High Harmonic Generation,” Science292(5522), 1689–1692 (2001).
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B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
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L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in Fused silica,” Phys. Rev. Lett.89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett.87(21), 213902 (2001).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
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M. Kreß, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few cycle laser pulses with terahertz emission spectroscopy,” Nat. Phys.2(5), 327–331 (2006).

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Velotta, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
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A. V. Mitrofanov, A. J. Verhoef, E. E. Serebryannikov, J. Lumeau, L. Glebov, A. M. Zheltikov, and A. Baltuška, “Optical Detection of Attosecond Ionization Induced by a Few-Cycle Laser Field in a Transparent Dielectric Material,” Phys. Rev. Lett.106(14), 147401 (2011).
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Villeneuve, D. M.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001).
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G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
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G. Cerullo, A. Baltuška, O. D. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser Photonics Rev.5(3), 323–351 (2011).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
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G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle Laser Pulses,” Phys. Rev. Lett.91(25), 253004 (2003).
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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001).
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B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical Aspects in Above-Threshold Ionization with a Midinfrared Strong Laser Field,” Phys. Rev. Lett.103(9), 093001 (2009).
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Xu, H.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical Aspects in Above-Threshold Ionization with a Midinfrared Strong Laser Field,” Phys. Rev. Lett.103(9), 093001 (2009).
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Xu, Z.

C. Li, D. Wang, L. Song, J. Liu, P. Liu, C. Xu, Y. Leng, R. Li, and Z. Xu, “Generation of carrier-envelope phase stabilized intense 1.5 cycle pulses at 1.75 μm,” Opt. Express19(7), 6783–6789 (2011).
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C. Zhang, P. Wei, Y. Huang, Y. Leng, Y. Zheng, Z. Zeng, R. Li, and Z. Xu, “Tunable phase-stabilized infrared optical parametric amplifier for high-order harmonic generation,” Opt. Lett.34(18), 2730–2732 (2009).
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J. Liu, R. Li, Z. Xu, and J. Liu, “ Sub-picosecond resolved investigation of dynamics of laser driven plasma by broad band chirped-pulse spectral interferometry,” AIP Conference641, 328–331 (2002).
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W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical Aspects in Above-Threshold Ionization with a Midinfrared Strong Laser Field,” Phys. Rev. Lett.103(9), 093001 (2009).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
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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. A72(5), 053817 (2005).
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Zheltikov, A. M.

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Appl. Phys. B (1)

L. Bergé, C. L. Soulez, C. Köhler, and S. Skupin, “Role of the carrier-envelope phase in laser filamentation,” Appl. Phys. B103(3), 563–570 (2011).
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B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, “Compression of 1.8μm laser pulses to sub two optical cycles with bulk material,” Appl. Phys. Lett.96(12), 121109 (2010).
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Nat. Photonics (1)

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Nat. Phys. (1)

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Nature (2)

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Opt. Express (3)

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Phys. Rev. A (1)

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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup. The CEP-stabilized laser pulses from the OPA are sent to the argon gas filled hollow fiber (HF) and a dispersion compensator to be compressed down to 12 fs. The CEP of laser pulse is varied by adjusting the thickness of the wedge (W). The laser pulse is then reflected by a white blank (WB) and focused by a concave mirror (CM) into the fused silica (FS) to form the filament, and the transmitted laser spectra are measured by the spectrometer. (b) Measured laser spectra with (solid red line) and without (dash blue line) the supercontinuum generated in the fused silica (FS). (c) The measured spectra with the fused silica as a function of CEP.

Fig. 2
Fig. 2

(a) The results (blue star) obtained by fitting the phase of fringes in Fig. 1(c) with (n(ω)-ng)ωZ/c. The black dashed line and red solid curve are the linear fit and the sin(x) + linear fit to blue stars, respectively. (b) Similar results obtained with the laser filamentation in CaF2.

Fig. 3
Fig. 3

(a1) The remaining part of the phase retrieved from Fig. 1(c) after removing the linear part. (a2) The relative intensity distributions of the spectra vs CEPs of the laser pulse. (b) The detailed results of the phase (blue solid line) and relative intensity (red dash line) in (a) at 0.51 μm vs CEPs. The phase (c1) and the intensity (c2) of the calculated spectra vs CEPs. (d) The detailed results of (c) at 0.51 μm.

Fig. 4
Fig. 4

(a) The amplitude |E| and (b) the wave vector Δk of the third harmonic (0.51μm) as functions of the propagation distance under two different CEP values of laser pulses, the significant difference can be seen at around 100 μm propagation distance.

Equations (6)

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φ 1 ( Δz )= n( ω ) z 0 +( n( ω )1 )Δz c ω+ φ 01 ,
φ 2 ( Δz )= n g z 0 +( n g 1 )Δz c ω+f( CEP )+ φ 02
Δφ= ( n( ω ) n g )ω c ( z 0 +Δz )f( CEP )+ φ 01 φ 02
n( λ )= ( 1+ C 1 1 C 2 2 / λ 2 + C 3 1 C 4 2 / λ 2 + C 5 1 C 6 2 / λ 2 ) 1/2 ,
z E ˜ ( ω )=ik( ω ) E ˜ ( ω )+ i 2k( ω ) 2 E ˜ ( ω ) iω n b n 2 n( ω )c F ^ [ I( t )E( t ) ]+ i 2 ε 0 n( ω )ωc e 2 m F ^ [ n e ( t )E( t ) ] I p 2 ε 0 n( ω )c F ^ [ t n e ( t ) E( t ) ]
n e t = σ K | Ê | 2K ( n at n e )+w(E(t))( n at n e ) n e τ r

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