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.

© 2001 Optical Society of America

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References

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  1. For a review, seeA. L’Huillieret al, “High-order harmonics: A coherent source in the XUV range,” J. of Nonl. Opt. Phys. and Mat. 4, 647 (1995).
    [Crossref]
  2. M. Gisselbrechtet al, “Absolute photoionization cross sections of excited He states in the near-threshold region,” Phys. Rev. Lett. 82, 4607 (1999).
    [Crossref]
  3. Z. Changet al., “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967 (1997).
    [Crossref]
  4. C.-G. Wahlströmet al., “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
    [Crossref] [PubMed]
  5. R. Trebinoet al, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277 (1997).
    [Crossref]
  6. B. Sheehyet al, “High Harmonic Generation at Long Wavelengths,” Phys. Rev. Lett. 83, 5270 (1999).
    [Crossref]
  7. T. Sekikawaet 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. Salières, 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. Gaardeet 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. Antoineet al, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53, 1725 (1995).
    [Crossref]
  12. Ph. Balcouet 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. Salièreset al, “Studies of the spatial and temporal coherence of high order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83 (1999).
    [Crossref]
  14. M. Belliniet al, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81, 297 (1998).
    [Crossref]
  15. C. Lyngået al, “Studies of the temporal coherence of high-order harmonics,” Phys. Rev. A 60, 4823 (1999).
    [Crossref]

1999 (7)

M. Gisselbrechtet al, “Absolute photoionization cross sections of excited He states in the near-threshold region,” Phys. Rev. Lett. 82, 4607 (1999).
[Crossref]

B. Sheehyet al, “High Harmonic Generation at Long Wavelengths,” Phys. Rev. Lett. 83, 5270 (1999).
[Crossref]

T. Sekikawaet al, “Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase”, Phys. Rev. Lett. 83, 2564 (1999).
[Crossref]

M. B. Gaardeet al, “Spatiotemporal separation of high harmonic radiation into two quantum path components,” Phys. Rev. A 59, 1367 (1999).
[Crossref]

Ph. Balcouet 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. Salièreset al, “Studies of the spatial and temporal coherence of high order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83 (1999).
[Crossref]

C. Lyngået al, “Studies of the temporal coherence of high-order harmonics,” Phys. Rev. A 60, 4823 (1999).
[Crossref]

1998 (1)

M. Belliniet al, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81, 297 (1998).
[Crossref]

1997 (2)

Z. Changet al., “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967 (1997).
[Crossref]

R. Trebinoet al, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277 (1997).
[Crossref]

1995 (3)

For a review, seeA. L’Huillieret al, “High-order harmonics: A coherent source in the XUV range,” J. of Nonl. Opt. Phys. and Mat. 4, 647 (1995).
[Crossref]

Ph. Antoineet al, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53, 1725 (1995).
[Crossref]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747 (1995).
[Crossref] [PubMed]

1993 (1)

C.-G. Wahlströmet al., “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
[Crossref] [PubMed]

Antoine, Ph.

Ph. Antoineet al, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53, 1725 (1995).
[Crossref]

Balcou, Ph.

Ph. Balcouet al, “Quantum-path analysis and phase matching of high-order frequency mixing processes in strong laser fields,” J. Phys. B 32, 2973 (1999).
[Crossref]

Bellini, M.

M. Belliniet al, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81, 297 (1998).
[Crossref]

Chang, Z.

Z. Changet al., “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967 (1997).
[Crossref]

Gaarde, M. B.

M. B. Gaardeet al, “Spatiotemporal separation of high harmonic radiation into two quantum path components,” Phys. Rev. A 59, 1367 (1999).
[Crossref]

Gisselbrecht, M.

M. Gisselbrechtet al, “Absolute photoionization cross sections of excited He states in the near-threshold region,” Phys. Rev. Lett. 82, 4607 (1999).
[Crossref]

Krause, J. L.

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

Kulander, K. C.

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

L’Huillier, A.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747 (1995).
[Crossref] [PubMed]

For a review, seeA. L’Huillieret al, “High-order harmonics: A coherent source in the XUV range,” J. of Nonl. Opt. Phys. and Mat. 4, 647 (1995).
[Crossref]

Lewenstein, M.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747 (1995).
[Crossref] [PubMed]

Lyngå, C.

C. Lyngået al, “Studies of the temporal coherence of high-order harmonics,” Phys. Rev. A 60, 4823 (1999).
[Crossref]

Salières, P.

P. Salièreset al, “Studies of the spatial and temporal coherence of high order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83 (1999).
[Crossref]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747 (1995).
[Crossref] [PubMed]

Schafer, K. J.

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

Sekikawa, T.

T. Sekikawaet al, “Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase”, Phys. Rev. Lett. 83, 2564 (1999).
[Crossref]

Sheehy, B.

B. Sheehyet al, “High Harmonic Generation at Long Wavelengths,” Phys. Rev. Lett. 83, 5270 (1999).
[Crossref]

Trebino, R.

R. Trebinoet al, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277 (1997).
[Crossref]

Wahlström, C.-G.

C.-G. Wahlströmet al., “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
[Crossref] [PubMed]

Adv. At. Mol. Opt. Phys. (1)

P. Salièreset al, “Studies of the spatial and temporal coherence of high order harmonics,” Adv. At. Mol. Opt. Phys. 41, 83 (1999).
[Crossref]

J. of Nonl. Opt. Phys. and Mat. (1)

For a review, seeA. L’Huillieret al, “High-order harmonics: A coherent source in the XUV range,” J. of Nonl. Opt. Phys. and Mat. 4, 647 (1995).
[Crossref]

J. Phys. B (1)

Ph. Balcouet al, “Quantum-path analysis and phase matching of high-order frequency mixing processes in strong laser fields,” J. Phys. B 32, 2973 (1999).
[Crossref]

Phys. Rev. A (5)

Ph. Antoineet al, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53, 1725 (1995).
[Crossref]

C. Lyngået al, “Studies of the temporal coherence of high-order harmonics,” Phys. Rev. A 60, 4823 (1999).
[Crossref]

C.-G. Wahlströmet al., “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
[Crossref] [PubMed]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747 (1995).
[Crossref] [PubMed]

M. B. Gaardeet al, “Spatiotemporal separation of high harmonic radiation into two quantum path components,” Phys. Rev. A 59, 1367 (1999).
[Crossref]

Phys. Rev. Lett. (5)

B. Sheehyet al, “High Harmonic Generation at Long Wavelengths,” Phys. Rev. Lett. 83, 5270 (1999).
[Crossref]

T. Sekikawaet al, “Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase”, Phys. Rev. Lett. 83, 2564 (1999).
[Crossref]

M. Gisselbrechtet al, “Absolute photoionization cross sections of excited He states in the near-threshold region,” Phys. Rev. Lett. 82, 4607 (1999).
[Crossref]

Z. Changet al., “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967 (1997).
[Crossref]

M. Belliniet al, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81, 297 (1998).
[Crossref]

Rev. Sci. Instrum. (1)

R. Trebinoet al, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277 (1997).
[Crossref]

Other (1)

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

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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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