Abstract

We show how an optimal control approach can be combined with the pump–probe technique for pulse compression by molecular phase modulation in hollow-core fibers to generate single 1-fs pulses in the visible. Varying the intensity and duration of the Gaussian-shaped pump pulse at the input induces optimal rotational response of the molecules. The probe pulse, which scatters off of the resulting time variation of the refractive index, is shaped at the input for optimal compression at the output, including dispersion to all orders.

© 2003 Optical Society of America

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References

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  1. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
    [CrossRef] [PubMed]
  2. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
    [CrossRef]
  3. N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
    [CrossRef]
  4. M. Wittmann, A. Nazarkin, and G. Korn, Opt. Lett. 26, 298 (2001).
    [CrossRef]
  5. M. Wittmann, A. Nazarkin, and G. Korn, Phys. Rev. Lett. 84, 5508 (2000).
    [CrossRef] [PubMed]
  6. R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
    [CrossRef]
  7. V. Kalosha and J. Herrmann, Phys. Rev. Lett. 85, 1226 (2000).
    [CrossRef] [PubMed]
  8. V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2002 (3)

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef]

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
[CrossRef]

2001 (3)

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

G. Yudin and M. Ivanov, Phys. Rev. A 64, 013409 (2001).
[CrossRef]

M. Wittmann, A. Nazarkin, and G. Korn, Opt. Lett. 26, 298 (2001).
[CrossRef]

2000 (4)

F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, Opt. Lett. 25, 575 (2000).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

M. Wittmann, A. Nazarkin, and G. Korn, Phys. Rev. Lett. 84, 5508 (2000).
[CrossRef] [PubMed]

V. Kalosha and J. Herrmann, Phys. Rev. Lett. 85, 1226 (2000).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

1979 (1)

R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Baertschy, M.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Bartels, R. A.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Bullough, R. K.

R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Cheng, Z.

Ciddor, P. E.

Greene, C. H.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Harris, S. E.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Herrmann, J.

V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
[CrossRef]

V. Kalosha and J. Herrmann, Phys. Rev. Lett. 85, 1226 (2000).
[CrossRef] [PubMed]

Ivanov, M.

V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
[CrossRef]

G. Yudin and M. Ivanov, Phys. Rev. A 64, 013409 (2001).
[CrossRef]

Jack, P. M.

R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Kalosha, V.

V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
[CrossRef]

V. Kalosha and J. Herrmann, Phys. Rev. Lett. 85, 1226 (2000).
[CrossRef] [PubMed]

Kapteyn, H. C.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Kitchenside, P. W.

R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Korn, G.

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef]

M. Wittmann, A. Nazarkin, and G. Korn, Opt. Lett. 26, 298 (2001).
[CrossRef]

M. Wittmann, A. Nazarkin, and G. Korn, Phys. Rev. Lett. 84, 5508 (2000).
[CrossRef] [PubMed]

Laude, V.

Murnane, M. M.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Nazarkin, A.

M. Wittmann, A. Nazarkin, and G. Korn, Opt. Lett. 26, 298 (2001).
[CrossRef]

M. Wittmann, A. Nazarkin, and G. Korn, Phys. Rev. Lett. 84, 5508 (2000).
[CrossRef] [PubMed]

Saunders, R.

R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Sokolov, A. V.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Spanner, M.

V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
[CrossRef]

Spielmann, Ch.

Tournois, P.

Verluise, F.

Wagner, N.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Walker, D. R.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Weinacht, T. C.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

Weiner, A. M.

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

Wittmann, M.

M. Wittmann, A. Nazarkin, and G. Korn, Opt. Lett. 26, 298 (2001).
[CrossRef]

M. Wittmann, A. Nazarkin, and G. Korn, Phys. Rev. Lett. 84, 5508 (2000).
[CrossRef] [PubMed]

Yavuz, D. D.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Yin, G. Y.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Yudin, G.

G. Yudin and M. Ivanov, Phys. Rev. A 64, 013409 (2001).
[CrossRef]

Zhavoronkov, N.

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef]

Appl. Opt. (1)

Opt. Lett. (2)

Phys. Rev. A (1)

G. Yudin and M. Ivanov, Phys. Rev. A 64, 013409 (2001).
[CrossRef]

Phys. Rev. Lett. (7)

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef]

M. Wittmann, A. Nazarkin, and G. Korn, Phys. Rev. Lett. 84, 5508 (2000).
[CrossRef] [PubMed]

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef]

V. Kalosha and J. Herrmann, Phys. Rev. Lett. 85, 1226 (2000).
[CrossRef] [PubMed]

V. Kalosha, M. Spanner, J. Herrmann, and M. Ivanov, Phys. Rev. Lett. 88, 103901 (2002).
[CrossRef]

Phys. Scr. (1)

R. K. Bullough, P. M. Jack, P. W. Kitchenside, and R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Prog. Quantum Electron. (1)

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

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Figures (3)

Fig. 1
Fig. 1

Propagation of the optimized pump pulse, στ=60 fs, for intensity 6.5×1013 W/cm2. (a) Alignment at the input of the fiber versus pump duration for 8×1013 W/cm2. (b) Pump pulse (solid curve) and alignment (dashed curve) at the input of the fiber for στ=60 fs versus time. (c) Same at the fiber output. (d) Alignment recurrence at the input and output of the fiber used to compress the probe.

Fig. 2
Fig. 2

Compression of an 800-nm probe pulse. (a) Amplitude (thick curve) and instantaneous frequency (thin curve) of the probe at the fiber input. (b) Optimized spectrum (thick curve) of the probe in (a) and spectrum of an alternate probe (thin curve; see text) at the fiber input. (c) Compressed probe (thick curve, envelope; thin curve, field) and (d) spectrum after propagation through the medium and through the CaF2 window.

Fig. 3
Fig. 3

Same as Fig. 2 but for a probe optimized for 400 nm at the input of the fiber.

Equations (6)

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Esx+1cEst=-2πcPst.
Ps=Pθ+PK+Pfe,
Pθ=Nαω+Δαωcos2 θx,tEsω,
itΨθ,x,t=Jˆ22I-ΔαEs2x,t4cos2θΨθ,x,t
Pfe=-NWx,t/ω2Esω,
Pw=Pθ+Pfe, Pθ=Nαω+Δαωcos2θx,τ-τdEwω, Pfe=-NWx/ω2Ewω.

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