Abstract

We calculate time-frequency representations (TFRs) of high-order short pulse harmonics generated in the interaction between neon atoms and an intense laser field, including macroscopic effects of propagation and phase matching in the non-linear medium. The phase structure of the harmonics is often complicated and the TFR can help to resolve the different components of this structure. The harmonic pulses exhibit an overall negative chirp, which can be attributed in part to the intensity dependence of the harmonic dipole phase. In some cases, the harmonic field separates in the time-frequency domain and clearly exhibits two different chirps. We also compute an experimental realization of a TFR (using Frequency Resolved Optical Gating, FROG) for a high harmonic. Due to the complicated time structure of the harmonics, the FROG trace is visually complex.

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  1. For a review, see A. L'Huillier et al, "High-order harmonics: A coherent source in the XUV range," J. of Nonl. Opt. Phys. and Mat. 4, 647 (1995).
    [CrossRef]
  2. M. Gisselbrecht et al, "Absolute photoionization cross sections of excited He states in the near-threshold region," Phys. Rev. Lett. 82, 4607 (1999).
    [CrossRef]
  3. Z. Chang et al., "Generation of coherent soft X rays at 2.7 nm using high harmonics," Phys. Rev. Lett. 79, 2967 (1997). ; R. Bartels et al., Nature 406, 164 (2000).
    [CrossRef]
  4. C.-G. Wahlstr�m et al., "High-order harmonic generation in rare gases with an intense short-pulse laser," Phys. Rev. A 48, 4709 (1993).
    [CrossRef] [PubMed]
  5. R. Trebino et al, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277 (1997).
    [CrossRef]
  6. B. Sheehy et al, "High Harmonic Generation at Long Wavelengths," Phys. Rev. Lett. 83, 5270 (1999).
    [CrossRef]
  7. T. Sekikawa et al, "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564 (1999).
    [CrossRef]
  8. M. Lewenstein, P. Sali�res, and A. L'Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747 (1995).
    [CrossRef] [PubMed]
  9. M. B. Gaarde et al, "Spatiotemporal separation of high harmonic radiation into two quantum path components," Phys. Rev. A 59, 1367 (1999).
    [CrossRef]
  10. K. C. Kulander, K. J. Schafer, and J. L. Krause, in Atoms in Intense Radiation Fields, Ed. M. Gavrila (Academic Press, New York, 1992).
  11. Ph. Antoine et al, "Theory of high-order harmonic generation by an elliptically polarized laser field," Phys. Rev. A 53, 1725 (1995).
    [CrossRef]
  12. Ph. Balcou et al, "Quantum-path analysis and phase matching of high-order frequency mixing processes in strong laser fields," J. Phys. B 32, 2973 (1999).
    [CrossRef]
  13. P. Sali�res et al, "Studies of the spatial and temporal coherence of high order harmonics," Adv. At. Mol. Opt. Phys. 41, 83 (1999).
    [CrossRef]
  14. M. Bellini et al, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297 (1998).
    [CrossRef]
  15. C. Lyng� et al, "Studies of the temporal coherence of high-order harmonics," Phys. Rev. A 60, 4823 (1999).
    [CrossRef]

Other (15)

For a review, see A. L'Huillier et al, "High-order harmonics: A coherent source in the XUV range," J. of Nonl. Opt. Phys. and Mat. 4, 647 (1995).
[CrossRef]

M. Gisselbrecht et al, "Absolute photoionization cross sections of excited He states in the near-threshold region," Phys. Rev. Lett. 82, 4607 (1999).
[CrossRef]

Z. Chang et al., "Generation of coherent soft X rays at 2.7 nm using high harmonics," Phys. Rev. Lett. 79, 2967 (1997). ; R. Bartels et al., Nature 406, 164 (2000).
[CrossRef]

C.-G. Wahlstr�m et al., "High-order harmonic generation in rare gases with an intense short-pulse laser," Phys. Rev. A 48, 4709 (1993).
[CrossRef] [PubMed]

R. Trebino et al, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

B. Sheehy et al, "High Harmonic Generation at Long Wavelengths," Phys. Rev. Lett. 83, 5270 (1999).
[CrossRef]

T. Sekikawa et al, "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564 (1999).
[CrossRef]

M. Lewenstein, P. Sali�res, and A. L'Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747 (1995).
[CrossRef] [PubMed]

M. B. Gaarde et al, "Spatiotemporal separation of high harmonic radiation into two quantum path components," Phys. Rev. A 59, 1367 (1999).
[CrossRef]

K. C. Kulander, K. J. Schafer, and J. L. Krause, in Atoms in Intense Radiation Fields, Ed. M. Gavrila (Academic Press, New York, 1992).

Ph. Antoine et al, "Theory of high-order harmonic generation by an elliptically polarized laser field," Phys. Rev. A 53, 1725 (1995).
[CrossRef]

Ph. Balcou et al, "Quantum-path analysis and phase matching of high-order frequency mixing processes in strong laser fields," J. Phys. B 32, 2973 (1999).
[CrossRef]

P. Sali�res et al, "Studies of the spatial and temporal coherence of high order harmonics," Adv. At. Mol. Opt. Phys. 41, 83 (1999).
[CrossRef]

M. Bellini et al, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297 (1998).
[CrossRef]

C. Lyng� et al, "Studies of the temporal coherence of high-order harmonics," Phys. Rev. A 60, 4823 (1999).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Time-frequency representations of the 45th (left) and the 89th (right) harmonics emitted from a neon atom subject to a 216 fs laser pulse with a peak intensity of 6×1014 W/cm2.

Fig. 2.
Fig. 2.

(a) TFR trace of the 45th harmonic in neon after propagation through a 1 mm long gas jet. In (b) we show the logarithm of the spectrogram shown in (a).

Fig. 3.
Fig. 3.

Polarization gate FROG trace of the 45th harmonic shown in Fig. 2.

Fig. 4.
Fig. 4.

Time profile of the 45th harmonic after propagation through the gas jet.

Fig. 5.
Fig. 5.

The time-frequency behavior of the harmonic radiation found at (a) the outer edge of the farfield profile, and (b) on-axis in the farfield profile.

Equations (3)

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S ( ω , τ ) = E ( t ) W ( t τ ) e iωt d t 2 ,
S p ( ω , τ ) = 0 r d r E ( r , t ) W ( t τ ) e iωt d t 2 ,
β i α i I 0 π 2 2 T 2 .

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