Abstract

We describe theoretically a new technique for quasi-phase-matched generation of high harmonics and attosecond pulses in a gas medium, in a high ionization limit. A corrugated hollow-core fiber modulates the intensity of the fundamental pulse along the direction of propagation, resulting in a periodic modulation of the harmonic emission at wavelengths close to the cutoff. This leads to an increase of the harmonic yield of up to three orders of magnitude. At the same time the highest harmonics merge in a broad band that corresponds to a single attosecond pulse, using 15-fs driving pulses.

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References

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  1. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, H. C. Kapteyn,"Generation of Coherent Soft X Rays at 2.7 nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
    [CrossRef]
  2. C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz,, "Generation of Coherent X-ray Pulses in the Water Window Using 5 fs Laser Pulses," Science 278, 661- 664 (1997).
    [CrossRef]
  3. A. L'Huillier, P. Balcou, and L. Lompre, "Coherence and Resonance Effects in High-Order Harmonic Generation," Phys. Rev. Lett. 68, 166-169 (1992).
    [CrossRef]
  4. A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane and H. Kapteyn, "Phase-Matched Generation of Coherent Soft X-Rays," Science 280, 1412-1415 (1998).
    [CrossRef] [PubMed]
  5. R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane and H. C. Kapteyn, "Shaped-Pulse Optimization of Coherent Emission of High-Harmonic Soft X-Rays," Nature 406, 164-166 (2000).
    [CrossRef] [PubMed]
  6. C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase Matching of High-Order Harmonics in Hollow Waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
    [CrossRef]
  7. I. P. Christov, H. C. Kapteyn and M. M. Murnane, "Dispersion-Controlled Hollow Core Fiber for Phase Matched Harmonic Generation," Opt. Express 3, 360-365 (1998), http://www.opticsexpress.org/oearchive/source/7041.htm
    [CrossRef] [PubMed]
  8. I. P. Christov, "Enhanced Generation of Attosecond Pulses in Dispersion-Controlled Hollow-Core Fiber," Phys. Rev. A 60, 3244-3250 (1999).
    [CrossRef]
  9. P. L. Shkolnikov, A. E. Kaplan, and A. Lago, "Phase-matching Optimization of Large Scale Nonlinear Frequency Upconversion in Neutral and Ionized Gases," J. Opt. Soc. Am. B 13, 412-423 (1996).
    [CrossRef]
  10. J. Peatross, S. Voronov, and I. Prokopovich, "Selective Zoning of High Harmonic Generation Using Counter Propagating Light," Opt. Express 1, 114-125 (1997), http://www.opticsexpress.org/oearchive/source/2247.htm.
    [CrossRef] [PubMed]
  11. H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, "High-Order Harmonic Generation and Quasiphase Matching in Xenon Using Self-Guided Femtosecond Pulses," Phys. Rev. Lett. 81, 1611-1613 (1998).
    [CrossRef]
  12. G. Tempea, M. Geissler, M. Schn�rer, and T. Brabec, "Self-Phase-Matched High Harmonic Generation," Phys. Rev. Lett. 84, 4329-4332 (2000).
    [CrossRef] [PubMed]
  13. I. P. Christov, "Propagation of Ultrashort Pulses in Gaseous Medium: Breakdown of the Quasistatic Approximation," Opt. Express 6, 34-39 (2000), http://www.opticsexpress.org/oearchive/source/18942.htm .
    [CrossRef] [PubMed]
  14. A. Delgarno and A. E. Kingston, "The Refractive Indices and Verdet Constants of the Inert Gases," Proc. R. Soc. A 259, 424-429 (1966).
    [CrossRef]
  15. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, P. B. Corkum, "Theory of High-Harmonic Generation by Low-Frequency Fields," Phys. Rev. A 49, 2117-2132 (1994).
    [CrossRef] [PubMed]
  16. N. B. Delone, and V. P. Krainov, Atoms in Strong Light Fields (Springer, New York, 1984).
  17. I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the 'Single-Cycle' Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
    [CrossRef]
  18. I. P. Christov, M. M. Murnane, H. C. Kapteyn, "Generation and Propagation of Attosecond X-ray Pulses in Gaseous Media," Phys. Rev. A 57, R2285-2288 (1998).
    [CrossRef]
  19. A. de Bohan, Ph. Antoine, D. B. Milosevic, and B. Piraux, "Phase-Dependent Harmonic Emission with Ultrashort Laser Pulses," Phys. Rev. Lett. 81, 1837-1840 (1998).
    [CrossRef]

Other

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, H. C. Kapteyn,"Generation of Coherent Soft X Rays at 2.7 nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz,, "Generation of Coherent X-ray Pulses in the Water Window Using 5 fs Laser Pulses," Science 278, 661- 664 (1997).
[CrossRef]

A. L'Huillier, P. Balcou, and L. Lompre, "Coherence and Resonance Effects in High-Order Harmonic Generation," Phys. Rev. Lett. 68, 166-169 (1992).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane and H. Kapteyn, "Phase-Matched Generation of Coherent Soft X-Rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane and H. C. Kapteyn, "Shaped-Pulse Optimization of Coherent Emission of High-Harmonic Soft X-Rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase Matching of High-Order Harmonics in Hollow Waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

I. P. Christov, H. C. Kapteyn and M. M. Murnane, "Dispersion-Controlled Hollow Core Fiber for Phase Matched Harmonic Generation," Opt. Express 3, 360-365 (1998), http://www.opticsexpress.org/oearchive/source/7041.htm
[CrossRef] [PubMed]

I. P. Christov, "Enhanced Generation of Attosecond Pulses in Dispersion-Controlled Hollow-Core Fiber," Phys. Rev. A 60, 3244-3250 (1999).
[CrossRef]

P. L. Shkolnikov, A. E. Kaplan, and A. Lago, "Phase-matching Optimization of Large Scale Nonlinear Frequency Upconversion in Neutral and Ionized Gases," J. Opt. Soc. Am. B 13, 412-423 (1996).
[CrossRef]

J. Peatross, S. Voronov, and I. Prokopovich, "Selective Zoning of High Harmonic Generation Using Counter Propagating Light," Opt. Express 1, 114-125 (1997), http://www.opticsexpress.org/oearchive/source/2247.htm.
[CrossRef] [PubMed]

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, "High-Order Harmonic Generation and Quasiphase Matching in Xenon Using Self-Guided Femtosecond Pulses," Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

G. Tempea, M. Geissler, M. Schn�rer, and T. Brabec, "Self-Phase-Matched High Harmonic Generation," Phys. Rev. Lett. 84, 4329-4332 (2000).
[CrossRef] [PubMed]

I. P. Christov, "Propagation of Ultrashort Pulses in Gaseous Medium: Breakdown of the Quasistatic Approximation," Opt. Express 6, 34-39 (2000), http://www.opticsexpress.org/oearchive/source/18942.htm .
[CrossRef] [PubMed]

A. Delgarno and A. E. Kingston, "The Refractive Indices and Verdet Constants of the Inert Gases," Proc. R. Soc. A 259, 424-429 (1966).
[CrossRef]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, P. B. Corkum, "Theory of High-Harmonic Generation by Low-Frequency Fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

N. B. Delone, and V. P. Krainov, Atoms in Strong Light Fields (Springer, New York, 1984).

I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the 'Single-Cycle' Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, "Generation and Propagation of Attosecond X-ray Pulses in Gaseous Media," Phys. Rev. A 57, R2285-2288 (1998).
[CrossRef]

A. de Bohan, Ph. Antoine, D. B. Milosevic, and B. Piraux, "Phase-Dependent Harmonic Emission with Ultrashort Laser Pulses," Phys. Rev. Lett. 81, 1837-1840 (1998).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Dependence of the bore radius of a tapered hollow-core waveguide, and of the normalized pulse intensity, as function of the distance: (a,b)-flat fiber; (c,d)-corrugated fiber.

Fig. 2.
Fig. 2.

Time dependence of the laser pulse at the waveguide axis, and ionization probability (red line).

Fig. 3.
Fig. 3.

Energy of 95-th harmonic versus propagation distance for: flat fiber (a); corrugated fiber (b).

Fig. 4.
Fig. 4.

Harmonic spectra for flat fiber (a), and for corrugated fiber (b); at the input- curves (1), at the output-curves (2).

Fig. 5.
Fig. 5.

Output harmonic pulse for flat fiber (a), and for corrugated fiber (b).

Equations (3)

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2 c 2 E z t + Δ E = 4 π c 2 N [ e 2 m P ( E ) E + I p t ( 1 E P ( E ) t ) ] 1 c 2 [ 1 n 2 ( p ) ] 2 E t 2
2 c 2 E h z t + Δ E h = 4 π c 2 N [ e 2 m P ( E ) E h + a ] ,
d ( τ ) = i 0 τ d τ b [ π ε + i ( τ τ b ) ] 1.5 E ( τ b ) exp [ iS ( p s , τ , τ b ) γ ( τ b ) ]

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