Abstract

We extend a recent suggestion for the generation of subfemtosecond pulses by molecular modulation [Phys.  Rev.  Lett.  81, 2894 (1998)] to the rotational spectrum of molecular hydrogen H2. When a rotational transition |a|b is strongly driven ρab=0.5 the generation and phase-slip lengths are of the same order and the Raman spectrum has approximately Bessel function sideband amplitudes. Numerical simulation predicts that this spectrum (generated in a 14-cm-long cell at 1-atm pressure of H2) will compress into a train of pulses with 94-fs pulse separation and a pulse length of 0.5  fs.

© 1999 Optical Society of America

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  1. S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
    [CrossRef]
  2. A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994)A. E. Kaplan and P. L. Shkolnikov, J. Opt. Soc. Am. B 13, 347 (1996).
    [CrossRef] [PubMed]
  3. S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993)H. Kawano, Y. Hirakawa, and T. Imasaka, IEEE J. Quantum Electron. 34, 260 (1998).
    [CrossRef]
  4. T. W. Hänsch, Opt. Commun. 80, 71 (1990).
    [CrossRef]
  5. G. Farcas and C. Toth, Phys. Lett. A 168, 447 (1992)S. E. Harris, J. J. Macklin, and T. W. Hänsch, Opt. Commun. 100, 487 (1993)P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996)K. J. Schafer and K. C. Kulander, Phys. Rev. Lett. 78, 638 (1997).
    [CrossRef] [PubMed]
  6. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, Opt. Lett. 19, 1870 (1994).
    [CrossRef]
  7. O. A. Kocharovskaya, Ya. I. Khanin, and V. B. Tsaregradskii, Sov. J. Quantum Electron. 16, 127 (1986).
    [CrossRef]
  8. K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
    [CrossRef]
  9. V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989).
    [CrossRef]
  10. S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
    [CrossRef]
  11. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
    [CrossRef] [PubMed]
  12. S. E. Harris, Phys. Today 50(7), 36 (1997)M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
    [CrossRef]
  13. G. Herzberg, Molecular Spectra and Molecular Structure.?I.?Spectra of Dyatomic Molecules (Van Nostrand Reinhold, New York, 1950).
  14. A. C. Allison and A. Dalgarno, At. Data 1, 289 (1970).
    [CrossRef]
  15. The authors of Ref.??10 had missed this peculiarity and overestimated the coupling constants by a factor of 3.5.
  16. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, Opt. Lett. 19, 737 (1994)A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
    [CrossRef] [PubMed]

1998 (1)

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

1997 (3)

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

S. E. Harris, Phys. Today 50(7), 36 (1997)M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

1996 (1)

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

1994 (3)

1993 (1)

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993)H. Kawano, Y. Hirakawa, and T. Imasaka, IEEE J. Quantum Electron. 34, 260 (1998).
[CrossRef]

1992 (1)

G. Farcas and C. Toth, Phys. Lett. A 168, 447 (1992)S. E. Harris, J. J. Macklin, and T. W. Hänsch, Opt. Commun. 100, 487 (1993)P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996)K. J. Schafer and K. C. Kulander, Phys. Rev. Lett. 78, 638 (1997).
[CrossRef] [PubMed]

1990 (1)

T. W. Hänsch, Opt. Commun. 80, 71 (1990).
[CrossRef]

1986 (1)

O. A. Kocharovskaya, Ya. I. Khanin, and V. B. Tsaregradskii, Sov. J. Quantum Electron. 16, 127 (1986).
[CrossRef]

1970 (1)

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

Allison, A. C.

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

Burnett, N. H.

Butylkin, V. S.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989).
[CrossRef]

Corkum, P. B.

Dalgarno, A.

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

Farcas, G.

G. Farcas and C. Toth, Phys. Lett. A 168, 447 (1992)S. E. Harris, J. J. Macklin, and T. W. Hänsch, Opt. Commun. 100, 487 (1993)P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996)K. J. Schafer and K. C. Kulander, Phys. Rev. Lett. 78, 638 (1997).
[CrossRef] [PubMed]

Goswami, D.

Hakuta, K.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch, Opt. Commun. 80, 71 (1990).
[CrossRef]

Harris, S. E.

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

S. E. Harris, Phys. Today 50(7), 36 (1997)M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Herzberg, G.

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

Hillegas, C. W.

Imasaka, T.

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993)H. Kawano, Y. Hirakawa, and T. Imasaka, IEEE J. Quantum Electron. 34, 260 (1998).
[CrossRef]

Ivanov, M. Y.

Jain, M.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Kaplan, A. E.

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994)A. E. Kaplan and P. L. Shkolnikov, J. Opt. Soc. Am. B 13, 347 (1996).
[CrossRef] [PubMed]

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989).
[CrossRef]

Katsuragawa, M.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
[CrossRef]

Khanin, Ya. I.

O. A. Kocharovskaya, Ya. I. Khanin, and V. B. Tsaregradskii, Sov. J. Quantum Electron. 16, 127 (1986).
[CrossRef]

Khronopulo, Yu. G.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989).
[CrossRef]

Kocharovskaya, O. A.

O. A. Kocharovskaya, Ya. I. Khanin, and V. B. Tsaregradskii, Sov. J. Quantum Electron. 16, 127 (1986).
[CrossRef]

Li, J. Z.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
[CrossRef]

Merriam, A. J.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Sokolov, A. V.

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

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Strickland, D.

Suzuki, M.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
[CrossRef]

Toth, C.

G. Farcas and C. Toth, Phys. Lett. A 168, 447 (1992)S. E. Harris, J. J. Macklin, and T. W. Hänsch, Opt. Commun. 100, 487 (1993)P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996)K. J. Schafer and K. C. Kulander, Phys. Rev. Lett. 78, 638 (1997).
[CrossRef] [PubMed]

Tsaregradskii, V. B.

O. A. Kocharovskaya, Ya. I. Khanin, and V. B. Tsaregradskii, Sov. J. Quantum Electron. 16, 127 (1986).
[CrossRef]

Tull, J. X.

Warren, W. S.

Xia, H.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Yakubovich, E. I.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989).
[CrossRef]

Yin, G. Y.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Yoshikawa, S.

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993)H. Kawano, Y. Hirakawa, and T. Imasaka, IEEE J. Quantum Electron. 34, 260 (1998).
[CrossRef]

At. Data (1)

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

Opt. Commun. (2)

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993)H. Kawano, Y. Hirakawa, and T. Imasaka, IEEE J. Quantum Electron. 34, 260 (1998).
[CrossRef]

T. W. Hänsch, Opt. Commun. 80, 71 (1990).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

G. Farcas and C. Toth, Phys. Lett. A 168, 447 (1992)S. E. Harris, J. J. Macklin, and T. W. Hänsch, Opt. Commun. 100, 487 (1993)P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996)K. J. Schafer and K. C. Kulander, Phys. Rev. Lett. 78, 638 (1997).
[CrossRef] [PubMed]

Phys. Rev. A (1)

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

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

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994)A. E. Kaplan and P. L. Shkolnikov, J. Opt. Soc. Am. B 13, 347 (1996).
[CrossRef] [PubMed]

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, Phys. Rev. Lett. 79, 209 (1997).
[CrossRef]

Phys. Today (1)

S. E. Harris, Phys. Today 50(7), 36 (1997)M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

Sov. J. Quantum Electron. (1)

O. A. Kocharovskaya, Ya. I. Khanin, and V. B. Tsaregradskii, Sov. J. Quantum Electron. 16, 127 (1986).
[CrossRef]

Other (3)

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989).
[CrossRef]

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

The authors of Ref.??10 had missed this peculiarity and overestimated the coupling constants by a factor of 3.5.

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Figures (3)

Fig. 1
Fig. 1

Energy-level schematic for establishing coherence ρab in a molecular system. Laser fields are applied at the frequencies of the q=0 and q=-1 sidebands.

Fig. 2
Fig. 2

Evolution of the ultrashort pulses in the time domain (right) and in the frequency domain (left) through the 14-cm-long H2 cell at 1-atm pressure. The applied laser power densities are 1010 W/cm2, such that ρab=-0.45. Sidebands powers are normalized to those of the incident fields.

Fig. 3
Fig. 3

Instantaneous power density of a signal generated in a 14-cm-long H2 cell at 1  atm and ρab=-0.45, with sideband phases corrected by an external spectral-phase filter.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Heff=-2[ABexp-jωmczCexpjωmczD-2 Δω],
aq=122iμai2ωi-ωa-ωq+μai2ωi-ωa+ωq,bq=122iμaiμbi*ωi-ωa-ωq+μaiμbi*ωi-ωb+ωq,dq=122iμbi2ωi-ωb-ωq+μbi2ωi-ωb+ωq.
|+=cos+θ2expjφ2|a+sinθ2exp-jφ2|b,ρab=½ sinθexpjφ,
Eqz=-jηωqNaqρaaEq+dqρbbEq+bqρabEq-1+bq+1*ρab*Eq+1,
J,vPJ,v2=38π2ϵ0λi3HJJAvv,

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