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.

© 1998 Optical Society of America

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  1. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and 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, and 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, and 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).

1998 (3)

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]

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]

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

1997 (4)

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and 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]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[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]

1996 (1)

1992 (2)

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]

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

1964 (1)

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).

1950 (1)

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

Agostini, P.

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]

Backus, S.

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]

Balcou, P.

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]

Breger, P.

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]

Burnett, K.

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

Burnett, N.

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]

Chang, Z.

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]

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

Chiron, A.

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]

Christov, I. P.

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

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

Delone, N. B.

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

Durfee, C.

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]

Herne, C.

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]

Kan, C.

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]

Kaplan, A. E.

Kapteyn, H.

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]

Kapteyn, H. C.

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

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

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

Koppitsch, R.

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]

Krainov, V. P.

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

Krausz, F.

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]

L’Huillier, A.

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]

Lago, A.

Lange, H. R.

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]

Lenzner, M.

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]

Lompre, L.

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]

Marcateli, E. A. J.

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).

Murnane, M.

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]

Murnane, M. M.

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

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

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

Mysyrowicz, A.

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]

Peatross, J.

Pierce, J. R.

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

Prokopovich, I.

Rae, S. C.

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

Ripoche, J.-F.

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]

Rundquist, A.

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]

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

Sartania, S.

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]

Schmeltzer, R. A.

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).

Schnurer, M.

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]

Shkolnikov, P. L.

Spielman, C.

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]

Voronov, S.

Wang, H.

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

Wobrauschek, P.

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]

Bell System Tech. Journal (1)

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

Bell. Syst. Tech. J. (1)

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).

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

Opt. Express (1)

Phys. Rev. A (2)

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

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

Phys. Rev. Lett. (4)

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

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]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of Coherent Soft X Rays at 2.7 nm Using High Harmonics,” Phys. Rev. Lett. 79, 2967–2970 (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]

Science (2)

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]

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]

Other (2)

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

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.

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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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