Abstract

We show that the peak intensity of single attosecond x-ray pulses is enhanced by 1 or 2 orders of magnitude, the pulse duration is greatly compressed, and the optimal propagation distance is shortened by genetic algorithm optimization of the chirp and initial phase of 5 fs laser pulses. However, as the laser intensity increases, more efficient nonadiabatic self-phase matching can lead to a dramatically enhanced harmonic yield, and the efficiency of optimization decreases in the enhancement and compression of the generated attosecond pulses.

© 2006 Optical Society of America

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  1. T. W. Hänsch, "A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators," Opt. Commun. 80, 71-75 (1990).
    [CrossRef]
  2. S. Yoshikawa and T. Imasaka, "A new approach for the generation of ultrashort optical pulses," Opt. Commun. 96, 94-98 (1993).
    [CrossRef]
  3. A. E. Kaplan, "Subfemtosecond pulses in mode-locked 2 pi solitons of the cascade stimulated Raman scattering," Phys. Rev. Lett. 73, 1243-1246 (1994).
    [CrossRef] [PubMed]
  4. S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
    [CrossRef]
  5. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-harmonic generation of attosecond pulses in the 'single-cycle' regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
    [CrossRef]
  6. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
    [CrossRef] [PubMed]
  7. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
    [CrossRef] [PubMed]
  8. I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, "Attosecond time-scale intra-atomic phase matching of high harmonic generation," Phys. Rev. Lett. 86, 5458-5461 (2001).
    [CrossRef] [PubMed]
  9. X. Chu and S. I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403(R) (2001).
    [CrossRef]
  10. A. Ben Haj Yedder and C. Le Bris, "Optimal control of attosecond pulse synthesis from high-order harmonic generation," Phys. Rev. A 69, 041802(R) (2004).
    [CrossRef]
  11. M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
    [CrossRef] [PubMed]
  12. P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
    [CrossRef] [PubMed]
  13. T. Brabec and F. Krausz, "Intense few-cycle laser fields: frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
    [CrossRef]
  14. F. L. Kien, K. Midorikawa, and A. Suda, "Attosecond pulse generation using high harmonics in the multicycle regime of the driver pulse," Phys. Rev. A 58, 3311-3319 (1998).
    [CrossRef]
  15. M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
    [CrossRef]
  16. M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
    [CrossRef]
  17. A. Scrinzi, M. Geissler, and T. Brabec, "Ionization above the Coulomb barrier," Phys. Rev. Lett. 83, 706-709 (1999).
    [CrossRef]
  18. Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
    [CrossRef]
  19. K. J. Schafer and K. C. Kulander, "High harmonic generation from ultrafast pump lasers," Phys. Rev. Lett. 78, 638-641 (1997).
    [CrossRef]
  20. N. H. Shon, A. Suda, and K. Midorikawa, "Generation and propagation of attosecond pulses in He gas with sub-10-fs driver pulses," Phys. Rev. A 60, 2587-2590 (1999).
    [CrossRef]

2004

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

A. Ben Haj Yedder and C. Le Bris, "Optimal control of attosecond pulse synthesis from high-order harmonic generation," Phys. Rev. A 69, 041802(R) (2004).
[CrossRef]

2001

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, "Attosecond time-scale intra-atomic phase matching of high harmonic generation," Phys. Rev. Lett. 86, 5458-5461 (2001).
[CrossRef] [PubMed]

X. Chu and S. I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403(R) (2001).
[CrossRef]

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

2000

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

M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
[CrossRef]

1999

A. Scrinzi, M. Geissler, and T. Brabec, "Ionization above the Coulomb barrier," Phys. Rev. Lett. 83, 706-709 (1999).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

N. H. Shon, A. Suda, and K. Midorikawa, "Generation and propagation of attosecond pulses in He gas with sub-10-fs driver pulses," Phys. Rev. A 60, 2587-2590 (1999).
[CrossRef]

1998

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
[CrossRef]

F. L. Kien, K. Midorikawa, and A. Suda, "Attosecond pulse generation using high harmonics in the multicycle regime of the driver pulse," Phys. Rev. A 58, 3311-3319 (1998).
[CrossRef]

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

1997

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-harmonic generation of attosecond pulses in the 'single-cycle' regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

K. J. Schafer and K. C. Kulander, "High harmonic generation from ultrafast pump lasers," Phys. Rev. Lett. 78, 638-641 (1997).
[CrossRef]

1994

M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

A. E. Kaplan, "Subfemtosecond pulses in mode-locked 2 pi solitons of the cascade stimulated Raman scattering," Phys. Rev. Lett. 73, 1243-1246 (1994).
[CrossRef] [PubMed]

1993

S. Yoshikawa and T. Imasaka, "A new approach for the generation of ultrashort optical pulses," Opt. Commun. 96, 94-98 (1993).
[CrossRef]

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

1990

T. W. Hänsch, "A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators," Opt. Commun. 80, 71-75 (1990).
[CrossRef]

Balcou, Ph.

M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Baltuska, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

Bammer, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

Bartels, R.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, "Attosecond time-scale intra-atomic phase matching of high harmonic generation," Phys. Rev. Lett. 86, 5458-5461 (2001).
[CrossRef] [PubMed]

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," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

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

M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, "Ionization above the Coulomb barrier," Phys. Rev. Lett. 83, 706-709 (1999).
[CrossRef]

Chang, Z.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
[CrossRef]

Christov, I.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
[CrossRef]

Christov, I. P.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, "Attosecond time-scale intra-atomic phase matching of high harmonic generation," Phys. Rev. Lett. 86, 5458-5461 (2001).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-harmonic generation of attosecond pulses in the 'single-cycle' regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

Chu, S. I.

X. Chu and S. I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403(R) (2001).
[CrossRef]

Chu, X.

X. Chu and S. I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403(R) (2001).
[CrossRef]

Corkum, P.

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

Corkum, P. B.

M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

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

Drescher, M.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[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," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Geissler, M.

M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, "Ionization above the Coulomb barrier," Phys. Rev. Lett. 83, 706-709 (1999).
[CrossRef]

Goulielmakis, E.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

Hänsch, T. W.

T. W. Hänsch, "A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators," Opt. Commun. 80, 71-75 (1990).
[CrossRef]

Harris, S. E.

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

Heinzmann, U.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[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," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Hentschel, M.

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

Imasaka, T.

S. Yoshikawa and T. Imasaka, "A new approach for the generation of ultrashort optical pulses," Opt. Commun. 96, 94-98 (1993).
[CrossRef]

Ivanov, M. Yu

M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Kaplan, A. E.

A. E. Kaplan, "Subfemtosecond pulses in mode-locked 2 pi solitons of the cascade stimulated Raman scattering," Phys. Rev. Lett. 73, 1243-1246 (1994).
[CrossRef] [PubMed]

Kapteyn, H. C.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, "Attosecond time-scale intra-atomic phase matching of high harmonic generation," Phys. Rev. Lett. 86, 5458-5461 (2001).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
[CrossRef]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-harmonic generation of attosecond pulses in the 'single-cycle' regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

Kien, F. L.

F. L. Kien, K. Midorikawa, and A. Suda, "Attosecond pulse generation using high harmonics in the multicycle regime of the driver pulse," Phys. Rev. A 58, 3311-3319 (1998).
[CrossRef]

Kienberger, R.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[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," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Kleineberg, U.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

Krausz, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[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," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

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

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

Kulander, K. C.

K. J. Schafer and K. C. Kulander, "High harmonic generation from ultrafast pump lasers," Phys. Rev. Lett. 78, 638-641 (1997).
[CrossRef]

Le Bris, C.

A. Ben Haj Yedder and C. Le Bris, "Optimal control of attosecond pulse synthesis from high-order harmonic generation," Phys. Rev. A 69, 041802(R) (2004).
[CrossRef]

Lewenstein, M.

M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

L'Huillier, A.

M. Lewenstein, Ph. Balcou, M. Yu Ivanov, A. L'Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Midorikawa, K.

N. H. Shon, A. Suda, and K. Midorikawa, "Generation and propagation of attosecond pulses in He gas with sub-10-fs driver pulses," Phys. Rev. A 60, 2587-2590 (1999).
[CrossRef]

F. L. Kien, K. Midorikawa, and A. Suda, "Attosecond pulse generation using high harmonics in the multicycle regime of the driver pulse," Phys. Rev. A 58, 3311-3319 (1998).
[CrossRef]

Milosevic, N.

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

Murnane, M. M.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, "Attosecond time-scale intra-atomic phase matching of high harmonic generation," Phys. Rev. Lett. 86, 5458-5461 (2001).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
[CrossRef]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "High-harmonic generation of attosecond pulses in the 'single-cycle' regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

Reider, G. A.

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

Rundquist, A.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, "Temporal phase control of soft-x-ray harmonic emission," Phys. Rev. A 58, R30-R33 (1998).
[CrossRef]

Schafer, K. J.

K. J. Schafer and K. C. Kulander, "High harmonic generation from ultrafast pump lasers," Phys. Rev. Lett. 78, 638-641 (1997).
[CrossRef]

Schnürer, M.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

Scrinzi, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, "Ionization above the Coulomb barrier," Phys. Rev. Lett. 83, 706-709 (1999).
[CrossRef]

Shon, N. H.

N. H. Shon, A. Suda, and K. Midorikawa, "Generation and propagation of attosecond pulses in He gas with sub-10-fs driver pulses," Phys. Rev. A 60, 2587-2590 (1999).
[CrossRef]

Sokolov, A. V.

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

Spielmann, Ch.

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

Suda, A.

N. H. Shon, A. Suda, and K. Midorikawa, "Generation and propagation of attosecond pulses in He gas with sub-10-fs driver pulses," Phys. Rev. A 60, 2587-2590 (1999).
[CrossRef]

F. L. Kien, K. Midorikawa, and A. Suda, "Attosecond pulse generation using high harmonics in the multicycle regime of the driver pulse," Phys. Rev. A 58, 3311-3319 (1998).
[CrossRef]

Tempea, G.

M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, "Light propagation in field-ionizing media: extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

Uiberacker, M.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

Wang, H.

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Figures (3)

Fig. 1
Fig. 1

Harmonic spectra generated in He gas using (a) the original 5 fs Ti:sapphire laser field and (b) the optimal laser pulse with the wavelength 800 nm and peak intensity 5 × 10 14 W cm 2 after a propagation distance of 1 mm. (c) Original and (d) optimized attosecond pulses obtained by inverse Fourier transform of the spectrum between N = 73 rd and N = 78 th . The insets show the peak intensity of the attosecond pulse versus the propagation length.

Fig. 2
Fig. 2

Harmonic spectra generated in He gas using (a) the original 5 fs Ti:sapphire laser field and (b) the optimal laser pulse with the wavelength 800 nm and peak intensity 1 × 10 15 W cm 2 after a propagation distance of 100 μ m . (c) Original and (d) optimized attosecond pulses obtained by inverse Fourier transform of the spectrum between N = 130 th and N = 140 th . The insets show the peak intensity of the attosecond pulse versus the propagation length.

Fig. 3
Fig. 3

Harmonic spectra generated in He gas using (a) the original 5 fs Ti:sapphire laser field and (b) the optimal laser pulse with the wavelength 800 nm and peak intensity 2 × 10 15 W cm 2 after a propagation distance of 9 μ m . (c) Original and (d) optimized attosecond pulses obtained by inverse Fourier transform of the spectrum between N = 240 th and N = 250 th . The insets show the peak intensity of the attosecond pulse versus the propagation length.

Equations (11)

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ξ E l ( ξ , τ ) = 1 2 c τ ω p 2 ( ξ , τ ) E l ( ξ , τ ) d τ 2 π I p c τ n ( ξ , τ ) E l ( ξ , τ ) ,
ξ E h ( ξ , τ ) = 2 π c τ D [ E l ( ξ , τ ) ] ,
n ( ξ , τ ) = n 0 ( 1 exp { τ d τ w [ E ( ξ , τ ) ] } ) .
r ( τ ) = i 0 τ d t ( π i t 2 ) 3 2 E l ( τ t ) d [ p A ( τ t ) ] exp [ i S ( τ , t ) γ ( τ ) γ ( τ t ) ] d * [ p A ( τ ) ] + c.c. ,
S ( τ , t ) = τ t τ d t { 1 2 [ p A ( t ) ] 2 + I p } ,
γ ( τ ) = w ( τ ) 2 .
d ( p ) = i 2 7 2 α 5 4 π p ( p 2 + α ) 3 ,
I ( ξ , t ) = q min q max E ̃ ( ξ , q ) exp ( i q w t ) d q 2 .
J = I 1 I 2 ,
I 1 = t c t pulse t c + t pulse I ( t ) d t ,
I 2 = 0 t c t pulse I ( t ) d t + t c + t pulse T I ( t ) d t ,

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