Abstract

We compare the results of the propagation of strong ultrashort laser pulse in gas medium where the atomic ionization is calculated in quasi-static approximation, and by using ab initio solution of the Schroedinger equation. Our models reveal significant difference between the predictions of the two models which may have an impact on the phase matched high-harmonic and attosecond pulse generation. A novel equation that avoids the concept of ionisation rate is introduced, which can be used to accurately model the generation and propagation of attosecond-duration pulses.

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References

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  1. S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, "High-Power Ultrafast Lasers," Rev.Sci.Instrum. 69, 1207-1223 (1998).
    [CrossRef]
  2. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, . G. Tempea, C. Spielmann, and F.Krausz, "Toward a Terawatt-Scale Sub-10-fs Laser Technology," IEEE Sel. Topics in Quantum Electron. 4, 414-420 (1998).
    [CrossRef]
  3. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, H. C. Kapteyn,"Generation of Coherent Soft X Rays at 2.7 nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
    [CrossRef]
  4. 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]
  5. I. P. Christov, "Enhanced Generation of Attosecond Pulses in Dispersion Controlled Hollow-Core Fiber," Phys. Rev. A 60, 3244-3250 (1999).
    [CrossRef]
  6. V. P. Krainov, "Ionization Rates and Energy Angular Distributions at the Barrier Suppression Ionization of Complex Atoms and Atomic Ions," J. Opt. Soc. Amer. B 14, 425-431 (1997).
    [CrossRef]
  7. M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, "Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics." Phys. Rev. Lett. 83, 2930-2933 (1999).
    [CrossRef]
  8. I. P. Christov, J. Peatross, J. Zhou, A. Rundquist, M. M. Murnane, and H. C. Kapteyn, "Nonadiabatic Effects in High-Harmonic Generation with Ultrashort Pulses," Phys. Rev. Lett. 77, 1743-1746 (1996).
    [CrossRef] [PubMed]
  9. I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the 'Single-Cycle' Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
    [CrossRef]
  10. S. C. Rae and K. Burnett, "Detailed Simulations of Plasma-Induced Blueshifting," Phys. Rev. A 46, 1084-1090 (1992).
    [CrossRef] [PubMed]
  11. A. Delgarno and A. E. Kingston, "The Refractive Indices and Verdet Constants of the Inert Gases," Proc. R. Soc. A 259, 424-429 (1966).
    [CrossRef]
  12. I. P. Christov, M. M. Murnane, H. C. Kapteyn, "Generation and Propagation of Attosecond X-ray Pulses in Gaseous Media," Phys. Rev. A 57, R2285-2288 (1998).
    [CrossRef]
  13. J. H. Eberly, J. Javanainen, and K. Rzazewski, "Above-Threshold Ionization," Phys. Rep. 204, 331-383 (1991).
    [CrossRef]
  14. I. P. Christov, "Phase-Dependent Loss Due to Nonadiabatic Ionization by sub-10 fs Pulses," Opt. Lett. 24, 1425- 1427 (1999).
    [CrossRef]

Other (14)

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, "High-Power Ultrafast Lasers," Rev.Sci.Instrum. 69, 1207-1223 (1998).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, . G. Tempea, C. Spielmann, and F.Krausz, "Toward a Terawatt-Scale Sub-10-fs Laser Technology," IEEE Sel. Topics in Quantum Electron. 4, 414-420 (1998).
[CrossRef]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, 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, "Enhanced Generation of Attosecond Pulses in Dispersion Controlled Hollow-Core Fiber," Phys. Rev. A 60, 3244-3250 (1999).
[CrossRef]

V. P. Krainov, "Ionization Rates and Energy Angular Distributions at the Barrier Suppression Ionization of Complex Atoms and Atomic Ions," J. Opt. Soc. Amer. B 14, 425-431 (1997).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, "Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics." Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

I. P. Christov, J. Peatross, J. Zhou, A. Rundquist, M. M. Murnane, and H. C. Kapteyn, "Nonadiabatic Effects in High-Harmonic Generation with Ultrashort Pulses," Phys. Rev. Lett. 77, 1743-1746 (1996).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the 'Single-Cycle' Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

S. C. Rae and K. Burnett, "Detailed Simulations of Plasma-Induced Blueshifting," Phys. Rev. A 46, 1084-1090 (1992).
[CrossRef] [PubMed]

A. Delgarno and A. E. Kingston, "The Refractive Indices and Verdet Constants of the Inert Gases," Proc. R. Soc. A 259, 424-429 (1966).
[CrossRef]

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

J. H. Eberly, J. Javanainen, and K. Rzazewski, "Above-Threshold Ionization," Phys. Rep. 204, 331-383 (1991).
[CrossRef]

I. P. Christov, "Phase-Dependent Loss Due to Nonadiabatic Ionization by sub-10 fs Pulses," Opt. Lett. 24, 1425- 1427 (1999).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Time dependence of the ionization (a) and the ionization “rate” (b) for a hydrogen atom. Solid line-numerical results; dashed line-quasistatic approximation.

Fig. 2.
Fig. 2.

Time dependence of the field (a,d), the envelope (b,e), and the time averaged envelope (c,f) of 5 fs pulse at the output of the gas medium. (a-c)-with the loss term only; (d-f)-with all terms. Solid line-numerical results; dashed line-quasistatic approximation.

Fig. 3.
Fig. 3.

Time dependence of the field (a), the envelope (b), and the time averaged envelope (c) of 10 fs pulse at the output of the gas medium, with all terms in Eq.1. Solid line-numerical results; dashed line-quasistatic approximation.

Fig. 4.
Fig. 4.

Dependence of the maximum field amplitude (a) and of the final ionization (b) on the absolute phase of the laser pulse. Solid line-numerical results; dashed line-quasistatic approximation.

Equations (3)

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2 c 2 E z t + Δ E = 4 π c 2 N [ e 2 m P ( E ) E + I p t ( 1 E P ( E ) t ) ]
1 c 2 [ 1 n 2 ( p ) ] 2 E t 2 ,
i t ψ ( r , t ) = [ 2 2 m 2 e 2 r + α e r · E ( t ) ] ψ ( r , t ) ,

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