Abstract

We numerically simulate the propagation of high-intensity laser pulses in helium to investigate the role of nonlinear effects in gas-cell high-harmonics experiments. An aperture located before the focusing lens is also included in the simulation. Numerical results for the radial fluence profile as a function of axial position, as well as for the spectral shift and ionization levels, agree with experimental observations. The simulations confirm that a significant Kerr effect is not required to generate the observed double focus in the fluence. The beam simulation also permits an investigation of high-harmonic phase matching. Most of the harmonic energy is seen to come from the forward portion of the laser pulse, whereas the latter portion gives rise to the incidental double laser focusing. Good phase matching for the harmonics arises in large measure from a balance between the linear phase delay of the neutral atoms and the Gouy shift, which is elongated and nearly linearized when the aperture is partially closed on the beam.

© 2008 Optical Society of America

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References

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  1. J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, "Direct observation of laser filamentation in high-order harmonic generation," Opt. Lett. 31, 3471-3473 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, "Measurement of the Kerr constant of He, A, O2, H2, and D2," Nuovo Cimento 5D, 328-338 (1985).
    [CrossRef]
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  8. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Theberge, N. Akozbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
    [CrossRef]
  9. H. T. Kim, I. J. Kim, V. Tosa, Y. S. Lee, and C. H. Nam, "High brightness harmonic generation at 13 nm using self-guided and chirped femtosecond laser pulses," Appl. Phys. B 78, 863-867 (2004).
    [CrossRef]
  10. V. Tosa, E. Takahashi, Y. Nabekawa, and K. Midorikawa, "Generation of high-order harmonics in a self-guided beam," Phys. Rev. A 67, 063817 (2003).
    [CrossRef]
  11. M. Lewenstein, P. Salieres, and A. L’Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 62, 4747-4754 (1995).
    [CrossRef]
  12. B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data and Nuclear Tables, (Academic, San Diego, 1993) Vol. 54; see http://henke.lbl.gov/optical constants/.
  13. J. Sutherland, E. Christensen, N. Powers, S. Rhynard, P. Painter, and J. Peatross, "High harmonic generation in a semi-infinite gas cell," Opt. Express 12, 4430-4436 (2004).
    [CrossRef] [PubMed]
  14. S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, "High order harmonic generation optimization with an apertured laser beam," Eur. Phys. J. D 21, 353-359 (2002).
    [CrossRef]

2007 (3)

2006 (1)

2005 (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Theberge, N. Akozbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

2004 (2)

H. T. Kim, I. J. Kim, V. Tosa, Y. S. Lee, and C. H. Nam, "High brightness harmonic generation at 13 nm using self-guided and chirped femtosecond laser pulses," Appl. Phys. B 78, 863-867 (2004).
[CrossRef]

J. Sutherland, E. Christensen, N. Powers, S. Rhynard, P. Painter, and J. Peatross, "High harmonic generation in a semi-infinite gas cell," Opt. Express 12, 4430-4436 (2004).
[CrossRef] [PubMed]

2003 (1)

V. Tosa, E. Takahashi, Y. Nabekawa, and K. Midorikawa, "Generation of high-order harmonics in a self-guided beam," Phys. Rev. A 67, 063817 (2003).
[CrossRef]

2002 (1)

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, "High order harmonic generation optimization with an apertured laser beam," Eur. Phys. J. D 21, 353-359 (2002).
[CrossRef]

1999 (1)

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, "Numerical simulations of the nonlinear propagation of femtosecond optical pulses in gases," Eur. Phys. J. D 6, 383-396 (1999).
[CrossRef]

1995 (1)

M. Lewenstein, P. Salieres, and A. L’Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 62, 4747-4754 (1995).
[CrossRef]

1986 (1)

M. Ammosov, N. Delone, and V. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64, 1191-1194 (1986).

1985 (1)

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, "Measurement of the Kerr constant of He, A, O2, H2, and D2," Nuovo Cimento 5D, 328-338 (1985).
[CrossRef]

Appl. Phys. B (1)

H. T. Kim, I. J. Kim, V. Tosa, Y. S. Lee, and C. H. Nam, "High brightness harmonic generation at 13 nm using self-guided and chirped femtosecond laser pulses," Appl. Phys. B 78, 863-867 (2004).
[CrossRef]

Can. J. Phys. (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Theberge, N. Akozbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Eur. Phys. J. D (2)

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, "High order harmonic generation optimization with an apertured laser beam," Eur. Phys. J. D 21, 353-359 (2002).
[CrossRef]

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, "Numerical simulations of the nonlinear propagation of femtosecond optical pulses in gases," Eur. Phys. J. D 6, 383-396 (1999).
[CrossRef]

Nuovo Cimento (1)

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, "Measurement of the Kerr constant of He, A, O2, H2, and D2," Nuovo Cimento 5D, 328-338 (1985).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (2)

V. Tosa, E. Takahashi, Y. Nabekawa, and K. Midorikawa, "Generation of high-order harmonics in a self-guided beam," Phys. Rev. A 67, 063817 (2003).
[CrossRef]

M. Lewenstein, P. Salieres, and A. L’Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 62, 4747-4754 (1995).
[CrossRef]

Sov. Phys. JETP (1)

M. Ammosov, N. Delone, and V. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64, 1191-1194 (1986).

Other (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data and Nuclear Tables, (Academic, San Diego, 1993) Vol. 54; see http://henke.lbl.gov/optical constants/.

Supplementary Material (2)

» Media 1: MOV (4869 KB)     
» Media 2: MOV (4298 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Movie of the (a) pulse intensity (dark red indicates the peak intensity of 5.7×1014 W/cm2), (b) free-electron density (dark red indicates the peak free-electron density of 5.3×1022 electrons/m3, equivalent to 2.1% ionization), and (c) fluence as the pulse propagates 10 cm through the focus. Each frame shows a snapshot of the pulse at locations 1 mm apart along the direction of travel. The contour lines in frame (b) indicate pulse intensity, with lines representing a 20% change in intensity. (4.7 MB) [Media 1]

Fig. 2.
Fig. 2.

(a) The on-axis fluence from the experiment (dots) and simulation (line), and the calculated peak pulse intensity as a function of axial position in the focus. (b) FWHM values for the fluence along the propagation axis given by simulation (line) and by experiment (dots). The propagation axis location is given as a distance from the focusing optic (f=100 cm).

Fig. 3.
Fig. 3.

Movie of coherence lengths of the 75th harmonic for each point on the pulse for (a) conventional and (b) intrinsic intensity-dependent phase. Coherence lengths have been capped at a reabsorption limit of 2 cm (dark red). (c) Movie of the fifth power of the laser intensity multiplied by the square of the coherence length (including both conventional and intrinsic phases) at each point on the pulse. The white contour lines indicate laser intensity. The dark red color in (c) indicates strong harmonic generation in arbitrary units. (4.2 MB) [Media 2]

Fig. 4.
Fig. 4.

(a) The calculated (solid line) and measured (dots) overall emission for the 75th harmonic with an aperture in the beam. Also plotted is calculated overall emission for the same harmonic with an unapertured pulse (dashed line). (b) Beam phase due to the Gouy shift for an apertured (solid line) and an unapertured (dashed line) beam.

Equations (1)

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2 ik 0 c ω 0 E η + ρ 2 E + 2 n 0 Δ n E = 0 ,

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