Abstract

We present an efficient method to observe the high harmonics generated in individual half-cycle of the driving laser pulse by mixing a weak ultraviolet pulse, and then the cutoff of each half-cycle harmonic is imaged. The simulation shows that the information of the driving laser pulse, including the laser intensity, pulse duration and carrier-envelope phase, can be in situ retrieved from the harmonic spectrogram. In addition, our results show that this method also distinguishes the half-cycle high harmonics for a pulse longer than 10 fs, suggesting a potential to extend the CEP measurement to the multi-cycle regime.

© 2008 Optical Society of America

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  1. T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  2. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature (London) 421, 611 (2003).
    [CrossRef] [PubMed]
  3. D. B. Miloˇsevi’c, G. G. Paulus, and W. Becker, "High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase," Opt. Express 11, 1418 (2003).
    [PubMed]
  4. G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, "Measurement of the Phase of Few-Cycle Laser Pulses," Phys. Rev. Lett. 91, 253004 (2003).
    [CrossRef]
  5. A. D. Bandrauk, S. Chelkowski, and N. H. Shon, "Measuring the electric field of few-cycle laser pulses by attosecond cross correlation," Phys. Rev. Lett. 89, 283903 (2002).
    [CrossRef]
  6. A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgd¨orfer, T. W. H¨ansch, and F. Krausz, "Observation of Light-Phase-Sensitive Photoemission from a Metal," Phys. Rev. Lett. 92, 073902 (2004).
    [CrossRef] [PubMed]
  7. C. Lemell, X. M. Tong, F. Krausz, and J. Burgdorfer, "Electron emission from metal surfaces by ultrashort pulses: Determination of the carrier-envelope phase," Phys. Rev. Lett. 90, 076403 (2003).
    [CrossRef] [PubMed]
  8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, J. W. G. Tisch, and "Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval," Nature Phys. 3, 52 (2007).
    [CrossRef]
  9. M. Kress, T. L¨offler, M. D. Thomson, R. D¨orner, 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 terahertzemission spectroscopy," Nature Phys. 2, 327 (2006).
    [CrossRef]
  10. S. T. Cundiff, "Better by half," Nature Phys. 3, 16 (2007).
    [CrossRef]
  11. P. B. Corkum, "Plasma perspective on stong-field multphoton ionization," Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  12. K. Ishikawa, "Photonemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses," Phys. Rev. Lett. 91, 043002 (2003).
    [CrossRef] [PubMed]
  13. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, "Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses," Phys. Rev. A 76, 051801(R) (2007).
    [CrossRef]
  14. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, "Strong field quantum path control using attosecond pulse trains," Phys. Rev. Lett. 92, 023003 (2004).
    [CrossRef] [PubMed]
  15. P. Lan, P. Lu, W. Cao, and X. Wang, "Efficient generation of an isolated single-cycle attosecond pulse," Phys. Rev. A 76, 043808 (2007).
    [CrossRef]
  16. R. Trebino, and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: using frequency-resolved optical gating," J. Opt. Soc. Am. A,  10, 1011 (1993).
    [CrossRef]
  17. C. Iaconis and I.A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792 (1998).
    [CrossRef]
  18. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605 (2004).
    [CrossRef] [PubMed]
  19. H. Mashiko, A. Suda, and K. Midorikawa, "Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2," Opt. Lett. 29, 1927 (2004).
    [CrossRef] [PubMed]

2007 (3)

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, J. W. G. Tisch, and "Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval," Nature Phys. 3, 52 (2007).
[CrossRef]

S. T. Cundiff, "Better by half," Nature Phys. 3, 16 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, and X. Wang, "Efficient generation of an isolated single-cycle attosecond pulse," Phys. Rev. A 76, 043808 (2007).
[CrossRef]

2006 (1)

M. Kress, T. L¨offler, M. D. Thomson, R. D¨orner, 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 terahertzemission spectroscopy," Nature Phys. 2, 327 (2006).
[CrossRef]

2004 (4)

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgd¨orfer, T. W. H¨ansch, and F. Krausz, "Observation of Light-Phase-Sensitive Photoemission from a Metal," Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, "Strong field quantum path control using attosecond pulse trains," Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef] [PubMed]

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605 (2004).
[CrossRef] [PubMed]

H. Mashiko, A. Suda, and K. Midorikawa, "Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2," Opt. Lett. 29, 1927 (2004).
[CrossRef] [PubMed]

2003 (5)

D. B. Miloˇsevi’c, G. G. Paulus, and W. Becker, "High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase," Opt. Express 11, 1418 (2003).
[PubMed]

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature (London) 421, 611 (2003).
[CrossRef] [PubMed]

K. Ishikawa, "Photonemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses," Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

C. Lemell, X. M. Tong, F. Krausz, and J. Burgdorfer, "Electron emission from metal surfaces by ultrashort pulses: Determination of the carrier-envelope phase," Phys. Rev. Lett. 90, 076403 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, "Measurement of the Phase of Few-Cycle Laser Pulses," Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

2002 (1)

A. D. Bandrauk, S. Chelkowski, and N. H. Shon, "Measuring the electric field of few-cycle laser pulses by attosecond cross correlation," Phys. Rev. Lett. 89, 283903 (2002).
[CrossRef]

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)

1993 (2)

R. Trebino, and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: using frequency-resolved optical gating," J. Opt. Soc. Am. A,  10, 1011 (1993).
[CrossRef]

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

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

R. Trebino, and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: using frequency-resolved optical gating," J. Opt. Soc. Am. A,  10, 1011 (1993).
[CrossRef]

Nature (1)

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605 (2004).
[CrossRef] [PubMed]

Nature (London) (1)

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature (London) 421, 611 (2003).
[CrossRef] [PubMed]

Nature Phys. (3)

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, J. W. G. Tisch, and "Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval," Nature Phys. 3, 52 (2007).
[CrossRef]

M. Kress, T. L¨offler, M. D. Thomson, R. D¨orner, 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 terahertzemission spectroscopy," Nature Phys. 2, 327 (2006).
[CrossRef]

S. T. Cundiff, "Better by half," Nature Phys. 3, 16 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

P. Lan, P. Lu, W. Cao, and X. Wang, "Efficient generation of an isolated single-cycle attosecond pulse," Phys. Rev. A 76, 043808 (2007).
[CrossRef]

Phys. Rev. Lett. (7)

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, "Strong field quantum path control using attosecond pulse trains," Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef] [PubMed]

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

K. Ishikawa, "Photonemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses," Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, "Measurement of the Phase of Few-Cycle Laser Pulses," Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

A. D. Bandrauk, S. Chelkowski, and N. H. Shon, "Measuring the electric field of few-cycle laser pulses by attosecond cross correlation," Phys. Rev. Lett. 89, 283903 (2002).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgd¨orfer, T. W. H¨ansch, and F. Krausz, "Observation of Light-Phase-Sensitive Photoemission from a Metal," Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

C. Lemell, X. M. Tong, F. Krausz, and J. Burgdorfer, "Electron emission from metal surfaces by ultrashort pulses: Determination of the carrier-envelope phase," Phys. Rev. Lett. 90, 076403 (2003).
[CrossRef] [PubMed]

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 (1)

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, "Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses," Phys. Rev. A 76, 051801(R) (2007).
[CrossRef]

Supplementary Material (3)

» Media 1: AVI (1077 KB)     
» Media 2: AVI (766 KB)     
» Media 3: AVI (590 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

(a) Electric fields of the few-cycle pulse (red line) and the uv pulse (blue line). The dotted line shows the dependence of the electron energy (Ip +Ek ) on the ionization time. (b) High harmonic spectrogram as a function of delay between the laser and uv pulses (see the movie for various CEPs). The colorbar shows the harmonic intensity in logarithmic scale. The laser intensity is 4×1014 Wcm-2, pulse duration is 5 fs and the CEP is 0. The uv pulse intensity is 1×1013 Wcm-2 and duration is 1 fs. [Media 1]

Fig. 2.
Fig. 2.

The dependence of HCOs obtained from TDSE (the bars) and classical model (solid lines) on the CEP. Parameters are the same as Fig. 1.

Fig. 3.
Fig. 3.

Retrieved CEPs as a function of “known” ones. Parameters are the same as Fig. 1.

Fig. 4.
Fig. 4.

High harmonic spectrogram as a function of delay between the driving laser and uv pulse in a (a) 8- and 11.5-fs laser pulse. See the movie for a range of CEPs. Other parameters are the same as Fig. 1. [Media 2][Media 3]

Fig. 5.
Fig. 5.

Same as Fig. 2, but for a 11.5-fs laser pulse.

Fig. 6.
Fig. 6.

The half-cycle harmonic cutoff ln [ ( H c I p ) N ] 2 ~ t T for a two- (circles), three- (triangle), four-(square) laser pulse with the CEP of (a) 0 and (b) π/2. The solid line presents the fitted results. Other parameters are the same as Fig. 1.

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