Abstract

We describe theoretically the performance of a new design for quasi-phase matched harmonic generation in a gas medium. A hollow core fiber in which thin glass plates are periodically introduced allows good phase control of the fundamental light. The generated x-rays are transmitted through small holes in the plates. An increase of the harmonic yield of up to three orders of magnitude is predicted as a result of the structure. This design can be considered as a phase-locked travelling-wave x-ray laser.

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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. 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]
  6. J. Peatross, S. Voronov, and I. Prokopovich, "Selective Zoning of High Harmonic Generation Using Counter propagating Light," Opt. Express 1, 114-125 (1997), http://epubs.osa.org/oearchive/source/2247.htm .
    [CrossRef] [PubMed]
  7. 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]
  8. J. R. Pierce, "Traveling-Wave Tubes," Bell System Tech. Journal 24, 189-201 (1950).
  9. N. B. Delone, and V. P. Krainov, Atoms in Strong Light Fields (Springer, New York, 1984).
  10. 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]
  11. For clarity throughout this paper we use a fused silica glass (n=1.4533) as a measure of the phase delay due to the positive dispersion introduced.
  12. S. C. Rae and K. Burnett, "Detailed Simulation of Plasma-induced Spectral Blueshifting," Phys. Rev. A 46, 1084-1090 (1992).
    [CrossRef] [PubMed]
  13. 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]
  14. E. A. J. Marcateli and R. A. Schmeltzer, "Hollow Metalic and Dielectric Wave-guides for Long Distance Optical Transmission and Lasers," Bell. Syst. Tech. J. 43, 1783-1809 (1964).

Other (14)

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]

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://epubs.osa.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]

J. R. Pierce, "Traveling-Wave Tubes," Bell System Tech. Journal 24, 189-201 (1950).

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, "Generation and Propagation of Attosecond X-ray Pulses in Gaseous Media," Phys. Rev. A 57, R2285-2288 (1998).
[CrossRef]

For clarity throughout this paper we use a fused silica glass (n=1.4533) as a measure of the phase delay due to the positive dispersion introduced.

S. C. Rae and K. Burnett, "Detailed Simulation of Plasma-induced Spectral Blueshifting," Phys. Rev. A 46, 1084-1090 (1992).
[CrossRef] [PubMed]

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]

E. A. J. Marcateli and R. A. Schmeltzer, "Hollow Metalic and Dielectric Wave-guides for Long Distance Optical Transmission and Lasers," Bell. Syst. Tech. J. 43, 1783-1809 (1964).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of a hollow core fiber with an internal structure for phase control.

Fig. 2.
Fig. 2.

Time dependence of the electric field of a 10 fs laser pulse for different positions along the hollow fiber: (a)- with no phase control, pre-ionized gas; (b)- with a set of glass plates; (c)- with a set of glass plates, pulse-induced ionisation.

Fig. 3.
Fig. 3.

Harmonic energy versus propagation distance for: no-phase control (curve 1, see Fig. 2(a)); 0.3 μm glass plates with holes (curve 3, see Fig. 2(b)); 0.6 μm glass plates with holes; 0.6 μm glass plates with holes, laser induced ionisation (curve 4, see Fig. 2(c)). The inset shows a part of curve 1 near the origin.

Fig. 4.
Fig. 4.

Spatial distribution of the field (solid line) and the ionization probability (dashed line) across the hollow core fiber: (a) with no glass plates; (b) with glass plates with 10 μm holes.

Equations (1)

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( 2 c 2 t z + Δ ) E ( r , z , t ) = 4 π c 2 ( 2 t 2 E q + N e 2 m P ( E ) E + loss ) ,

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