Abstract

We report a detailed numerical study on the postcompression of high-energy (30mJ) femtosecond laser pulses (40fs), using the spectral broadening induced by optical-field ionization of a low-pressure helium gas in a capillary. Our numerical results are in very good agreement with previously published experimental data on spectral shapes, transmitted energies and recompressed pulse durations in the full range of laser energies and gas pressures investigated. Then, we calculate the performances of the method with shorter input pulses (20fs) and demonstrate that few optical cycles recompressed pulses with 5 to 8.5 mJ energy could then be achieved.

© 2012 Optical Society of America

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  1. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
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    [CrossRef]
  4. F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  23. A. Perelomov and V. Popov, “Ionization of atoms in an alternating electrical field. III,” Sov. Phys. JETP 25, 336–343 (1967).
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  27. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992), pp. 701–740.
  28. R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [CrossRef]

2010

2009

2008

V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10, 083040 (2008).
[CrossRef]

2007

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]

2006

F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
[CrossRef]

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

2005

Y. Oishi, A. Suda, K. Midorikawa, and F. Kannari, “Sub-10 fs, multimillijoule laser system,” Rev. Sci. Instrum. 76, 093114 (2005).
[CrossRef]

2004

C. Hauri, W. Kornelis, F. 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]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

2003

1998

G. Tempea and T. Brabec, “Theory of self-focusing in hollow waveguide,” Opt. Lett. 23, 762–764 (1998).
[CrossRef]

S. P. Nikitin, Yuelin Li, T. M. Antonsen, and H. M. Milchberg, “Ionization-induced pulse shortening and retardation of high intensity femtosecond laser pulses,” Opt. Commun. 157, 139–144 (1998).
[CrossRef]

1997

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

1996

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

1994

1988

E. Yablonovitch, “Energy conservation in the picosecond and subpicosecond photoelectric effect,” Phys. Rev. Lett. 60, 795–796 (1988).
[CrossRef]

1987

1986

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionisation of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

1967

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field. II,” Sov. Phys. JETP 24, 207–217 (1967).

A. Perelomov and V. Popov, “Ionization of atoms in an alternating electrical field. III,” Sov. Phys. JETP 25, 336–343 (1967).

1966

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

1965

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), pp. 45–48.

Akturk, S.

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionisation of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Anscombe, M.

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

Antonsen, T. M.

S. P. Nikitin, Yuelin Li, T. M. Antonsen, and H. M. Milchberg, “Ionization-induced pulse shortening and retardation of high intensity femtosecond laser pulses,” Opt. Commun. 157, 139–144 (1998).
[CrossRef]

Arnold, C. L.

Baltuska, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Bammer, G.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Becker, P.

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. Anscombe, P. Schlup, J. Biegert, and U. Keller, “5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis,” J. Phys. B 39, S257–S264 (2006).
[CrossRef]

C. Hauri, W. Kornelis, F. 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]

Bohman, S.

Borot, A.

Brabec, T.

Brée, C.

C. Brée, A. Demircan, and G. Steinmeyer, “Method for computing the nonlinear refractive index via Keldysh theory,” IEEE J. Quantum Electron. 46, 433–437 (2010).
[CrossRef]

Burnett, N.

Canova, L.

Chen, X.

Constant, E.

C. Fourcade Dutin, A. Dubrouil, S. Petit, E. Mével, E. Constant, and D. Descamps, “Post-compression of high-energy femtosecond pulses using gas ionization,” Opt. Lett. 35, 253–255(2010).
[CrossRef]

V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10, 083040 (2008).
[CrossRef]

Corkum, P.

Couairon, A.

C. Hauri, W. Kornelis, F. 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]

Cruz, C. Brito

De Silvestri, S.

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionisation of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Delong, K.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Demircan, A.

C. Brée, A. Demircan, and G. Steinmeyer, “Method for computing the nonlinear refractive index via Keldysh theory,” IEEE J. Quantum Electron. 46, 433–437 (2010).
[CrossRef]

Descamps, D.

Drescher, M.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Dubrouil, A.

Durfee, C.

Dutin, C. Fourcade

Eckle, P.

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

Fittinghoff, D.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992), pp. 701–740.

Fork, R.

Goulielmakis, E.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Guandalini, A.

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

Hatayama, M.

Hauri, C.

C. Hauri, W. Kornelis, F. 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, F.

C. Hauri, W. Kornelis, F. 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.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Ivanov, M.

Jullien, A.

Kanai, T.

Kane, D.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Kannari, F.

Y. Oishi, A. Suda, K. Midorikawa, and F. Kannari, “Sub-10 fs, multimillijoule laser system,” Rev. Sci. Instrum. 76, 093114 (2005).
[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]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Keller, U.

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

C. Hauri, W. Kornelis, F. 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]

Kienberger, R.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Kleineberg, U.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Kornelis, W.

C. Hauri, W. Kornelis, F. 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]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionisation of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Krausz, F.

F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
[CrossRef]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Krumbügel, M.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Li, Yuelin

S. P. Nikitin, Yuelin Li, T. M. Antonsen, and H. M. Milchberg, “Ionization-induced pulse shortening and retardation of high intensity femtosecond laser pulses,” Opt. Commun. 157, 139–144 (1998).
[CrossRef]

Lopez-Martens, R.

Malvache, A.

Marcinkevicius, A.

Mével, E.

C. Fourcade Dutin, A. Dubrouil, S. Petit, E. Mével, E. Constant, and D. Descamps, “Post-compression of high-energy femtosecond pulses using gas ionization,” Opt. Lett. 35, 253–255(2010).
[CrossRef]

V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10, 083040 (2008).
[CrossRef]

Midorikawa, K.

Milchberg, H. M.

S. P. Nikitin, Yuelin Li, T. M. Antonsen, and H. M. Milchberg, “Ionization-induced pulse shortening and retardation of high intensity femtosecond laser pulses,” Opt. Commun. 157, 139–144 (1998).
[CrossRef]

Mysyrowicz, A.

S. Akturk, C. L. Arnold, B. Zhou, and A. Mysyrowicz, “High-energy ultrashort laser pulse compression in hollow planar waveguides,” Opt. Lett. 34, 1462–1464 (2009).
[CrossRef]

C. Hauri, W. Kornelis, F. 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]

Nagasaka, K.

Nikitin, S. P.

S. P. Nikitin, Yuelin Li, T. M. Antonsen, and H. M. Milchberg, “Ionization-induced pulse shortening and retardation of high intensity femtosecond laser pulses,” Opt. Commun. 157, 139–144 (1998).
[CrossRef]

Nikogosyan, D. N.

D. N. Nikogosyan, Optical and Laser-Related Materials. A Handbook (Wiley, 1997), p. 522.

Nisoli, M.

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

Nurhuda, M.

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]

Oishi, Y.

Y. Oishi, A. Suda, K. Midorikawa, and F. Kannari, “Sub-10 fs, multimillijoule laser system,” Rev. Sci. Instrum. 76, 093114 (2005).
[CrossRef]

Perelomov, A.

A. Perelomov and V. Popov, “Ionization of atoms in an alternating electrical field. III,” Sov. Phys. JETP 25, 336–343 (1967).

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field. II,” Sov. Phys. JETP 24, 207–217 (1967).

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Petit, S.

Popov, V.

A. Perelomov and V. Popov, “Ionization of atoms in an alternating electrical field. III,” Sov. Phys. JETP 25, 336–343 (1967).

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field. II,” Sov. Phys. JETP 24, 207–217 (1967).

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992), pp. 701–740.

Richman, B.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Schlup, P.

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

Scrinzi, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Shank, C.

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]

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C. Brée, A. Demircan, and G. Steinmeyer, “Method for computing the nonlinear refractive index via Keldysh theory,” IEEE J. Quantum Electron. 46, 433–437 (2010).
[CrossRef]

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V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10, 083040 (2008).
[CrossRef]

Suda, A.

Svelto, O.

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

Sweetser, J.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Tavella, F.

Tempea, G.

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field. II,” Sov. Phys. JETP 24, 207–217 (1967).

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992), pp. 701–740.

Trebino, R.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Trisorio, A.

Uiberacker, M.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992), pp. 701–740.

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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

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

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[CrossRef]

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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

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Appl. Phys. B

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[CrossRef]

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M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

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C. Brée, A. Demircan, and G. Steinmeyer, “Method for computing the nonlinear refractive index via Keldysh theory,” IEEE J. Quantum Electron. 46, 433–437 (2010).
[CrossRef]

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J. Phys. B

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

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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, G. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

New J. Phys.

V. V. Strelkov, E. Mével, and E. Constant, “Generation of isolated attosecond pulses by spatial shaping of a femtosecond laser beam,” New J. Phys. 10, 083040 (2008).
[CrossRef]

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Phys. Rev. Lett.

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[CrossRef]

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

Rev. Sci. Instrum.

R. Trebino, K. Delong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

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[CrossRef]

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A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field. II,” Sov. Phys. JETP 24, 207–217 (1967).

A. Perelomov and V. Popov, “Ionization of atoms in an alternating electrical field. III,” Sov. Phys. JETP 25, 336–343 (1967).

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Other

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), pp. 45–48.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992), pp. 701–740.

D. N. Nikogosyan, Optical and Laser-Related Materials. A Handbook (Wiley, 1997), p. 522.

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Figures (10)

Fig. 1.
Fig. 1.

Postcompression setup. M1, focusing mirror with f=3-m; M2, flat mirror; W, wedged window; M3, collimating silver mirror with f=2m; P, iris. The hollow capillary radius is 210 μm and the length is 40 cm.

Fig. 2.
Fig. 2.

2D maps of (a) laser fluence ([J/cm2]) and (b) plasma electron density left behind the pulse, computed for EL=27.3mJ, τL=40fs, and pHe=8mbar.

Fig. 3.
Fig. 3.

Evolution of the spectrum shape with He pressure for EL=27.3mJ (transmitted energy in EH11 mode) and τL=40fs. (a) Experiment. (b) Simulations: black solid curve, reference without gas; red dashed curve, pHe=1mbar; blue dotted curve, pHe=3mbar; green dashed–dotted curve, pHe=8mbar.

Fig. 4.
Fig. 4.

Evolution of the spectrum shape with laser energy for τL=40fs and pHe=8mbar. (a) Experiment. (b) Simulations: black solid curve, reference without gas; red dashed curve, EL=12.4mJ; blue dotted curve, EL=21.6mJ; green dashed–dotted curve, EL=27.3mJ.

Fig. 5.
Fig. 5.

Transmitted energy in the EH11 capillary mode as a function of He pressure for EL=27.3mJ and τL=40fs. The curves are B-spline fits of the data. Solid curve with solid triangles: experiment. Dashed curve with solid squares: simulations.

Fig. 6.
Fig. 6.

Duration of the postcompressed pulse measured and calculated as a function of He pressure, for the same conditions as in Fig. 4. The curves are B-spline fits of the data. Solid curve with solid triangles: experiment. Dashed curve with solid squares: simulations, far field on axis.

Fig. 7.
Fig. 7.

SHG-FROG measurement of the shortest postcompressed pulses. (a) Experimental (gray area) and retrieved (solid curve) FROG spectra of the postcompressed pulse with the residual spectral phase (dashed–dotted curve). (b) Retrieved intensity profile (solid curve) and temporal phase (dashed–dotted curve) of the postcompressed pulses.

Fig. 8.
Fig. 8.

Postcompressed pulse shapes calculated on the laser axis for EL=27.3mJ and τL=40fs. (a) pHe=1mbar, (b) pHe=3mbar, (c) pHe=6mbar, and (d) pHe=8mbar. Solid curve, far field; dashed curve, near field; dashed–dotted curve, Fourier-transform-limited pulse envelope in the far field.

Fig. 9.
Fig. 9.

(a) Spatially resolved spectrum computed at the output of the capillary for EL=27.3mJ, τL=40fs, and pHe=8mbar. (b) Same as (a), 2 m away from the output of the capillary. (c) Temporal shape corresponding to spectrum in (a). (d) Temporal shape for spectrum given in (b).

Fig. 10.
Fig. 10.

(a) On-axis spectrum and spectral phase computed in the far field for EL=13.7mJ (transmitted energy in EH11 mode without gas), τL=20fs and pHe=8mbar. (b) Corresponding postcompressed pulse shape. Solid curve: profile after compensation of the quadratic component of the spectral phase. Dashed curve: Fourier-transform-limited pulse shape. (c) and (d) Same as (a) and (b) for EL=27.3mJ.

Equations (21)

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ω(t)=dφdt=ω0ω0c0Lne(z,t)tdz,
Eξ=i2k0T12Eik22Eτ2+iω0cn2ε0c2T(|E|2E)12iω0cT1(NeNcE)12Z=0Z=Zmax1WZNZIpZε0c2|E|2E,
Eξ=i2k0T12E12iω0cT1(NeNcE)12Z=0Z=Zmax1WZNZIpZε0c2|E|2E.
N0τ=W0N0,N1τ=W0N0W1N1,NZmax1τ=WZmax2NZmax2WZmax1NZmax1,NZmaxτ=WZmax1NZmax1,
{Eξ=LEEξE=N,
{L=i2k0T12N=(12iω0cT1NeNc12Z=0Z=Zmax1WZNZIpZε0c2|E|2)E.
E^(r,ξ+Δξ,ω)=eL^ΔξE^(r,ξ,ω),E^(r,ξ+Δξ,ω)=ξξ+ΔξN^(r,ξ,ω)dξ,
E^=FT(E),L^=FT(L)=i2k0T^12,N^=FT(N)=12iω0cT^1FT(NeENc)12FT(Z=0Z=Zmax1WZNZIpZε0c2|E|2E),T^=FT(T)=1+ωω0,T^11ωω0,
{E^m+12E^mΔξ2=L^2(E^m+12+E^m),E^m+1E^mΔξ=N^m+12,E^m+1E^m+12Δξ2=L^2(E^m+1+E^m+12),withξ=(m1)Δξ.
E^(r,ξ,ω)=Emax,jbj(ξ,ω)J(ρjra0),
Emax=2Imaxε0c
E^(r,z,ω)=Emaxjbj0(z,ω)J0(ρjra0),
bj0(ξ+Δξ2,ω)=exp[i(βj+iαj)Δξ2]×bj0(ξ,ω),
βjk2(ρjka0)2,
αj=12a01+n2n21(ρjka0)2,
βj=k1(ρjka0)2k[112(ρjka0)2].
vgj=dβjdω=c1(ρjka0)2.
eL^Δξ1+Δξ2L^1Δξ2L^
r˜=rr0,ξ˜=2ξk0r02,Δξ˜=2Δξk0r02τ˜=ττL,a˜0=a0r0,E˜=EEmax,δ1=(k0r0)2Na4Nc,δ2=k0r022NaIp0τL(ε0cEmax22),δ3=1(k0r0)2,δ4=1ω0τL,δ5=1k0a0,
(bj0)m+1=1iΔξ˜16(1δ4ω)2(ρja˜0)2(1+δ4ωiδ51+n2n21)1+iΔξ˜16(1δ4ω)2(ρja˜0)2(1+δ4ωiδ51+n2n21)(bj0)m.
N^=iδ1(1δ4ω)F^δ22G^,

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