Abstract

We demonstrate a technique for multiplicatively increasing the pulse spacing of subfemtosecond pulse trains generated by high-order stimulated Raman scattering, which uses pairs of off-resonant two-photon excitation of a molecular Raman mode to establish strong molecular modulation in the medium. Every laser pair has two single-mode laser beams tuned slightly off two-photon resonance, and the laser pairs have their corresponding carrier frequencies shifted from each other by one half, one third, or one fourth of the selected molecular Raman mode frequency. Theoretical analyses and calculations based on the fundamental vibrational transition of solid hydrogen show that the pulse spacing of the subfemtosecond pulse trains thus generated can readily be doubled, tripled, or even quadrupled.

© 2003 Optical Society of America

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  1. T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  2. P. Corkum, N. Burnett, and M. Ivanov, Opt. Lett. 19, 1870 (1994).
    [CrossRef]
  3. P. Antoine, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
    [CrossRef] [PubMed]
  4. P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
    [CrossRef]
  5. I. Christov, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 78, 1251 (1997).
    [CrossRef]
  6. A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
    [CrossRef] [PubMed]
  7. S. Harris and A. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
    [CrossRef]
  8. A. Sokolov, D. Yavuz, and S. Harris, Opt. Lett. 24, 557 (1999).
    [CrossRef]
  9. F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
    [CrossRef]
  10. A. Sokolov, Opt. Lett. 24, 1248 (1999).
    [CrossRef]
  11. D. Yavuz, D. Walker, G. Yin, and S. Harris, Opt. Lett. 27, 769 (2002).
    [CrossRef]
  12. S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801 (2002).
    [CrossRef]
  13. F. Kien, N. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
    [CrossRef]
  14. S. McCall and E. Hahn, Phys. Rev. Lett. 18, 908 (1967).
    [CrossRef]
  15. K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
    [CrossRef] [PubMed]
  16. A. Allison and A. Dalgarno, At. Data 1, 289 (1970).
    [CrossRef]
  17. G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Dyatomic Molecules (Van Nostrand Reinhold, New York, 1950).

2002 (2)

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801 (2002).
[CrossRef]

D. Yavuz, D. Walker, G. Yin, and S. Harris, Opt. Lett. 27, 769 (2002).
[CrossRef]

2001 (1)

F. Kien, N. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

2000 (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

1999 (3)

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

A. Sokolov, D. Yavuz, and S. Harris, Opt. Lett. 24, 557 (1999).
[CrossRef]

A. Sokolov, Opt. Lett. 24, 1248 (1999).
[CrossRef]

1998 (1)

S. Harris and A. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

1997 (2)

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

I. Christov, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 78, 1251 (1997).
[CrossRef]

1996 (1)

P. Antoine, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

1994 (3)

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
[CrossRef] [PubMed]

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

P. Corkum, N. Burnett, and M. Ivanov, Opt. Lett. 19, 1870 (1994).
[CrossRef]

1970 (1)

A. Allison and A. Dalgarno, At. Data 1, 289 (1970).
[CrossRef]

1967 (1)

S. McCall and E. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

Allison, A.

A. Allison and A. Dalgarno, At. Data 1, 289 (1970).
[CrossRef]

Antoine, P.

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

P. Antoine, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

Brabec, T.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Burnett, N.

Christov, I.

I. Christov, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 78, 1251 (1997).
[CrossRef]

Corkum, P.

Dalgarno, A.

A. Allison and A. Dalgarno, At. Data 1, 289 (1970).
[CrossRef]

Gaarde, M.

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

Gabrys, C.

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

Hahn, E.

S. McCall and E. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

Hakuta, K.

F. Kien, N. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

Harris, S.

Harris, S. E.

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801 (2002).
[CrossRef]

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Dyatomic Molecules (Van Nostrand Reinhold, New York, 1950).

Ivanov, M.

Kaplan, A. E.

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
[CrossRef] [PubMed]

Kapteyn, H.

I. Christov, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 78, 1251 (1997).
[CrossRef]

Katsuragawa, M.

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

Kerr, K.

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

Kien, F.

F. Kien, N. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

Krausz, F.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

L’Huillier, A.

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

P. Antoine, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

Lewenstein, M.

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

P. Antoine, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

Liang, J. Q.

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

McCall, S.

S. McCall and E. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

Milosevic, D.

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

Momose, T.

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

Murnane, M.

I. Christov, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 78, 1251 (1997).
[CrossRef]

Ohtsuki, K.

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

Oka, T.

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

Salieres, P.

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

Shon, N.

F. Kien, N. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

Sokolov, A.

Walker, D.

Walker, D. R.

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801 (2002).
[CrossRef]

Weliky, D.

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

Yavuz, D.

Yavuz, D. D.

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801 (2002).
[CrossRef]

Yin, G.

At. Data (1)

A. Allison and A. Dalgarno, At. Data 1, 289 (1970).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (4)

P. Antoine, D. Milosevic, A. L’Huillier, M. Gaarde, P. Salieres, and M. Lewenstein, Phys. Rev. A 56, 4960 (1997).
[CrossRef]

F. Kien, J. Q. Liang, M. Katsuragawa, K. Ohtsuki, and K. Hakuta, Phys. Rev. A 60, 1562 (1999).
[CrossRef]

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801 (2002).
[CrossRef]

F. Kien, N. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

S. McCall and E. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

K. Kerr, T. Momose, D. Weliky, C. Gabrys, and T. Oka, Phys. Rev. Lett. 72, 3957 (1994).
[CrossRef] [PubMed]

I. Christov, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 78, 1251 (1997).
[CrossRef]

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
[CrossRef] [PubMed]

S. Harris and A. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

P. Antoine, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Other (1)

G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Dyatomic Molecules (Van Nostrand Reinhold, New York, 1950).

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Figures (2)

Fig. 1
Fig. 1

Molecular modulation driven by two pairs of single-mode laser beams. The laser pairs have their carrier frequencies shifted by a proportional fraction of the Raman frequency.

Fig. 2
Fig. 2

Intensity-normalized sub-fs pulse (0.23-fs) trains with various pulse spacings tsp generated by HSRS in solid hydrogen with molecular modulation excited by two single-mode laser pairs slightly off two-photon resonance, with their corresponding carrier frequencies shifted from each other by Δω for (a) Δω=0 cm-1, tsp=8 fs; (b) Δω=1/2×4149.7 cm-1, tsp=16 fs; (c) Δω=1/3×4149.7 cm-1, tsp=24 fs; (d) Δω=1/4×4149.7 cm-1, tsp=32 fs.

Equations (6)

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Eˆξ,t=12qEq exp-iωqτ+Eq* expiωqτ+Eq exp-iωqτ+Eq* expiωqτ,
ωq=ω0+qωb-ωa-δ=ω0+qωm,ωq=ω0+qωb-ωa-δ=ω0+qωm.
Heff=-ABCD-δ,
aq=122juja2ωj-ωa-ωq+uja2ωj-ωa+ωq,bq=122jujb2ωj-ωb-ωq+ujb2ωj-ωb+ωq,dq=122juajujbωj-ωb-ωq+uajujbωj-ωa+ωq.
Eqξ=iNωq0caqρaaEq+bqρbbEq+dq-1ρbaEq-1+dq*ρabEq+1,Eqξ=iNωq0caqρaaEq+bqρbbEq+dq-1ρbaEq-1+dq*ρabEq+1,
ρbb-ρaaτ=-2iBρba-Cρab,ρabτ=iA-D+δρab+Bρbb-ρaa.

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