Abstract

High-order harmonic generation from atomic systems is considered in the crossed fields of a relativistically strong infrared laser and a weak attosecond pulse train of soft x rays. Due to one-photon ionization by the x-ray pulse, the ionized electron obtains a starting momentum that compensates the relativistic drift, which is induced by the laser magnetic field, and allows the electron to efficiently emit harmonic radiation upon recombination with the atomic core in the relativistic regime. This way, short pulses of coherent hard x rays of up to 40keV energy can be generated.

© 2008 Optical Society of America

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References

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  1. P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
    [CrossRef] [PubMed]
  17. A. Bandrauk and N. H. Shon, Phys. Rev. A 66, 031401 (2002).
    [CrossRef]
  18. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, Phys. Rev. Lett. 92, 023003 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  20. K. Ishikawa, Phys. Rev. Lett. 91, 043002 (2003).
    [CrossRef] [PubMed]
  21. Strong APTs of up to 1 keV photon energy can be produced, e.g., via laser pulse interaction with overdense plasmas, see G. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, and F. Krausz, New J. Phys. 8, 19 (2006).
    [CrossRef]
  22. D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403 (2001).
  23. We do not include the Gaussian envelope of the APT in the phase during the saddle point integration, which is justified, as the energy spread of the XUV photons is negligible here: 1/τ≪Δepsi, with the typical energy difference Δepsi~2a.u..

2007 (2)

M. Verschl and C. H. Keitel, Europhys. Lett. 77, 64004 (2007).
[CrossRef]

M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. A 75, 063413 (2007).
[CrossRef]

2006 (6)

Q. Lin, S. Li, and W. Becker, Opt. Lett. 31, 2163 (2006).
[CrossRef] [PubMed]

R. Fischer, M. Lein, and C. H. Keitel, Phys. Rev. Lett. 97, 143901 (2006).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, Science 314, 443 (2006).
[CrossRef] [PubMed]

Y. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 42 (2006).
[CrossRef]

C. Figueira de Morisson Faria, P. Salieres, P. Villain, and M. Lewenstein, Phys. Rev. A 74, 053416 (2006).
[CrossRef]

Strong APTs of up to 1 keV photon energy can be produced, e.g., via laser pulse interaction with overdense plasmas, see G. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, and F. Krausz, New J. Phys. 8, 19 (2006).
[CrossRef]

2005 (1)

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, Nature 433, 596 (2005).
[CrossRef] [PubMed]

2004 (6)

P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
[CrossRef]

C. C. Chirilǎ, N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, Phys. Rev. Lett. 93, 243603 (2004).
[CrossRef]

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

G. Mocken and C. H. Keitel, J. Phys. B 37, L275 (2004).
[CrossRef]

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef] [PubMed]

2003 (1)

K. Ishikawa, Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

2002 (3)

A. Bandrauk and N. H. Shon, Phys. Rev. A 66, 031401 (2002).
[CrossRef]

C. H. Keitel and S. X. Hu, Appl. Phys. Lett. 80, 541 (2002).
[CrossRef]

C. C. Chirilǎ, N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, Phys. Rev. A 66, 063411 (2002).
[CrossRef]

2001 (2)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[CrossRef] [PubMed]

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403 (2001).

2000 (1)

V. D. Taranukhin, Laser Phys. 10, 330 (2000).

Appl. Phys. Lett. (1)

C. H. Keitel and S. X. Hu, Appl. Phys. Lett. 80, 541 (2002).
[CrossRef]

Europhys. Lett. (1)

M. Verschl and C. H. Keitel, Europhys. Lett. 77, 64004 (2007).
[CrossRef]

J. Phys. B (1)

G. Mocken and C. H. Keitel, J. Phys. B 37, L275 (2004).
[CrossRef]

Laser Phys. (1)

V. D. Taranukhin, Laser Phys. 10, 330 (2000).

Nature (2)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature 414, 509 (2001).
[CrossRef] [PubMed]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, Nature 433, 596 (2005).
[CrossRef] [PubMed]

New J. Phys. (1)

Strong APTs of up to 1 keV photon energy can be produced, e.g., via laser pulse interaction with overdense plasmas, see G. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, and F. Krausz, New J. Phys. 8, 19 (2006).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

Y. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 42 (2006).
[CrossRef]

Phys. Rev. A (5)

C. C. Chirilǎ, N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, Phys. Rev. A 66, 063411 (2002).
[CrossRef]

A. Bandrauk and N. H. Shon, Phys. Rev. A 66, 031401 (2002).
[CrossRef]

M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. A 75, 063413 (2007).
[CrossRef]

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403 (2001).

C. Figueira de Morisson Faria, P. Salieres, P. Villain, and M. Lewenstein, Phys. Rev. A 74, 053416 (2006).
[CrossRef]

Phys. Rev. Lett. (6)

K. Ishikawa, Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, Phys. Rev. Lett. 92, 023003 (2004).
[CrossRef] [PubMed]

R. Fischer, M. Lein, and C. H. Keitel, Phys. Rev. Lett. 97, 143901 (2006).
[CrossRef] [PubMed]

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

C. C. Chirilǎ, N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, Phys. Rev. Lett. 93, 243603 (2004).
[CrossRef]

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
[CrossRef]

Science (1)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, Science 314, 443 (2006).
[CrossRef] [PubMed]

Other (1)

We do not include the Gaussian envelope of the APT in the phase during the saddle point integration, which is justified, as the energy spread of the XUV photons is negligible here: 1/τ≪Δepsi, with the typical energy difference Δepsi~2a.u..

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Figures (3)

Fig. 1
Fig. 1

Scheme of the HHG process in the relativistic regime driven by crossed beams of a laser field and an APT; E, k, and k a are the laser polarization, laser propagation, and APT propagation directions.

Fig. 2
Fig. 2

HHG spectra d w n d O via Eq. (3) in a laser field with E 0 = 2.1 a.u. and ω = 0.05 a.u. for I p = 5.29 a.u. ( Ar 7 + ) : (gray) dipole approximation, (red, the lowest curve) Klein–Gordon equation, and (black) additionally assisted by an APT with E 0 a = 0.02 a.u. , frequency Ω = 8.5 a.u. , pulse length τ = 4 a.u. , and a phase delay of 1.2 rad with respect to the laser wave.

Fig. 3
Fig. 3

HHG spectra d w n d O via Eq. (3) in a laser field with E 0 = 2.1 a.u. , ω = 0.05 a.u. , and an APT with E 0 a = 0.02 a.u. , pulse duration τ = 4 a.u. for I p = 5.29 a.u. : (left) for different phase delays 1.50 , 1.35 , 1.20 , 1.05 , and 0.90 rad , respectively, and carrier frequency Ω = 8.5 a.u. , (right) for different frequencies 7, 8.5, and 10 a.u. , respectively, and phase delay 1.2 rad .

Equations (3)

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ε 0 = Ω I p ,
( μ μ + c 2 ) Ψ ( x ) = ( V L + V X + V A I + V H ) Ψ ( x ) ,
M n = i d 4 x d 4 x { Φ ( x ) * V H ( x ) × G L V ( x , x ) x [ E ( x ) + E a ( x ) ] Φ ( x ) } ,

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