Abstract

The normal-incidence reflectivity of a plasma generated on a solid surface by a very intense laser field is studied. We demonstrate that the reflected field has the form of trains of subfemtosecond pulses under suitable conditions. Particle-in-cell computations are presented and compared with a naïve moving-mirror model. The physical origin of this behavior is discussed in terms of the relativistic motion of the electron plasma.

[Optical Society of America ]

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References

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  1. G. Farkas and C. Toth , Phys. Lett. A PYLAAG 168 , 447 ( 1992
    [CrossRef]
  2. S. E. Harris , J. J. Macklin , and T. W. Hansch , Opt. Commun. OPCOB8 100 , 487 ( 1993
    [CrossRef]
  3. Ph. Antoine , A. L Huillier , and M. Lewenstein , Phys. Rev. Lett. PRLTAO 77 , 1234 ( 1996
    [CrossRef] [PubMed]
  4. K. J. Schafer and K. C. Kulander , Phys. Rev. Lett. PRLTAO 78 , 638 ( 1997
    [CrossRef]
  5. For early work with CO 2 lasers, see R. L. Carman , D. W. Forslund , and J. M. Kindel , Phys. Rev. Lett. PRLTAO 46 , 29 ( 1981
    [CrossRef]
  6. S. Kohlweyer , G. D. Tsakiris , C. G. Wahlstro m , C. Tillman , and I. Mercer , Opt. Commun. OPCOB8 117 , 431 ( 1995
    [CrossRef]
  7. D. von der Linde , T. Engers , G. Jenke , P. Agostini , G. Grillon , E. Nibbering , A. Mysyrowicz , and A. Antonetti , Phys. Rev. A PLRAAN 52 , R25 ( 1995
    [CrossRef]
  8. P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
    [CrossRef] [PubMed]
  9. P. Gibbon , Phys. Rev. Lett. PRLTAO 76 , 50 ( 1996
    [CrossRef] [PubMed]
  10. A. Pukhov and J. Meyer-ter-Vehn , Phys. Rev. Lett. PRLTAO 76 , 3975 ( 1996
    [CrossRef] [PubMed]
  11. S. V. Bulanov , N. M. Naumova , and F. Pegoraro , Phys. Plasmas PHPAEN 1 , 745 ( 1994
    [CrossRef]
  12. R. Lichters , J. Meyer-ter-Vehn , and A. Pukhov , Phys. Plasmas PHPAEN 3 , 3425 ( 1996
    [CrossRef]
  13. D. von der Linde and K. Rza z ewski , Appl. Phys. B: Photophys. Laser Chem. APPCDL 63 , 499 ( 1996
    [CrossRef]
  14. J. M. Dawson , Rev. Mod. Phys. RMPHAT 55 , 403 ( 1983
    [CrossRef]

Angor, A. E

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Bekarezos, M

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Bulanov, S. V

S. V. Bulanov , N. M. Naumova , and F. Pegoraro , Phys. Plasmas PHPAEN 1 , 745 ( 1994
[CrossRef]

Danzos, C. N

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Dyson, A

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Fews, A. P

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Kindel, J. M

For early work with CO 2 lasers, see R. L. Carman , D. W. Forslund , and J. M. Kindel , Phys. Rev. Lett. PRLTAO 46 , 29 ( 1981
[CrossRef]

Lee, P

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Lichters, R

R. Lichters , J. Meyer-ter-Vehn , and A. Pukhov , Phys. Plasmas PHPAEN 3 , 3425 ( 1996
[CrossRef]

Loukakos, P

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Meyer-ter-Vehn, J

A. Pukhov and J. Meyer-ter-Vehn , Phys. Rev. Lett. PRLTAO 76 , 3975 ( 1996
[CrossRef] [PubMed]

Moustaizis, S

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Naumova, N. M

S. V. Bulanov , N. M. Naumova , and F. Pegoraro , Phys. Plasmas PHPAEN 1 , 745 ( 1994
[CrossRef]

Pegoraro, F

S. V. Bulanov , N. M. Naumova , and F. Pegoraro , Phys. Plasmas PHPAEN 1 , 745 ( 1994
[CrossRef]

Pukhov, A

A. Pukhov and J. Meyer-ter-Vehn , Phys. Rev. Lett. PRLTAO 76 , 3975 ( 1996
[CrossRef] [PubMed]

Wajsh, F. N

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

Other (14)

G. Farkas and C. Toth , Phys. Lett. A PYLAAG 168 , 447 ( 1992
[CrossRef]

S. E. Harris , J. J. Macklin , and T. W. Hansch , Opt. Commun. OPCOB8 100 , 487 ( 1993
[CrossRef]

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

K. J. Schafer and K. C. Kulander , Phys. Rev. Lett. PRLTAO 78 , 638 ( 1997
[CrossRef]

For early work with CO 2 lasers, see R. L. Carman , D. W. Forslund , and J. M. Kindel , Phys. Rev. Lett. PRLTAO 46 , 29 ( 1981
[CrossRef]

S. Kohlweyer , G. D. Tsakiris , C. G. Wahlstro m , C. Tillman , and I. Mercer , Opt. Commun. OPCOB8 117 , 431 ( 1995
[CrossRef]

D. von der Linde , T. Engers , G. Jenke , P. Agostini , G. Grillon , E. Nibbering , A. Mysyrowicz , and A. Antonetti , Phys. Rev. A PLRAAN 52 , R25 ( 1995
[CrossRef]

P. A. Norreys , M. Zepf , S. Moustaizis , A. P. Fews , J. Zhang , P. Lee , M. Bekarezos , C. N. Danzos , A. Dyson , P. Gibbon , P. Loukakos , D. Neely , F. N. Wajsh , J. S. Wark , and A. E. Angor , Phys. Rev. Lett. PRLTAO 76 , 1832 ( 1996
[CrossRef] [PubMed]

P. Gibbon , Phys. Rev. Lett. PRLTAO 76 , 50 ( 1996
[CrossRef] [PubMed]

A. Pukhov and J. Meyer-ter-Vehn , Phys. Rev. Lett. PRLTAO 76 , 3975 ( 1996
[CrossRef] [PubMed]

S. V. Bulanov , N. M. Naumova , and F. Pegoraro , Phys. Plasmas PHPAEN 1 , 745 ( 1994
[CrossRef]

R. Lichters , J. Meyer-ter-Vehn , and A. Pukhov , Phys. Plasmas PHPAEN 3 , 3425 ( 1996
[CrossRef]

D. von der Linde and K. Rza z ewski , Appl. Phys. B: Photophys. Laser Chem. APPCDL 63 , 499 ( 1996
[CrossRef]

J. M. Dawson , Rev. Mod. Phys. RMPHAT 55 , 403 ( 1983
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of the geometry of the laser–plasma interaction studied. The laser beam is a linearly polarized plane wave that shines a thin foil. Only the normal incidence case is studied.

Fig. 2
Fig. 2

Numerical PIC simulation for a feasible set of laser parameters, ωL=0.057 a.u., E0=25 a.u., and for an overcritical plasma density, ωP=4ωL. (a) Time-dependent intensity profile, or more precisely, the time dependence of the electric-field amplitude square, Ey2(t), in the far-field region, at a distance R of the thin film. Intensity is rescaled by (R/A)2 to account for the distance and for the thin-film area. (b) Time evolution of the electronic plasma-cloud density ρ2(x, t), along the x axis, for these parameters.

Fig. 3
Fig. 3

Numerical PIC simulation for laser frequency ωL=0.228 a.u. and amplitude E0=55 a.u. (intensity 1020 W/cm2) and for a critical density, ωP=ωL. The slab is now one wavelength 200 nm thick. Only the time evolution of the electronic plasma-cloud density ρ2(x, t), along the x axis, is shown. Clearly the oscillation of the electrons is not regular. The time-dependent intensity profile does not show narrow peaks for these parameters.

Fig. 4
Fig. 4

Numerical PIC simulation for laser frequency ωL=0.228 a.u., amplitude E0=55 a.u. (intensity 1020 W/cm2),and critical density ωP=ωL, the same parameters as in the previous figure. Now the thickness of the slab has been reduced to λ/10, 20 nm. This reduction is enough for the reappearance of the train of short peaks. (a) Time-dependent intensity profile. (b) Time evolution of the electronic plasma-cloud density ρ2(x, t), along the x axis. Now the regular sequence of peaks last longer than in Fig. 2 because of the short frequency of the laser, but eventually all electrons leave the solid vicinity.

Fig. 5
Fig. 5

Time profile for the reflected intensity ER2(t) depicted for an incident pulse with a sin2 envelope and with a total duration of 50 cycles. The incident amplitude peak is E0=55 a.u. (intensity of 1×1020 W/cm2). The electron density for these drawings is exactly equal to the critical density, ωP=ωL. (a) ωL=0.057 a.u., a result that is not realistic. (b) ωL=0.228 a.u., which agrees with PIC simulation.

Fig. 6
Fig. 6

Motion of one selected electron in the plasma for the same parameters as Fig. 4, ωP=ωL=0.228 a.u. and E0=55 a.u., extracted from the PIC simulation. Only one electron trajectory is selected that shows what can be called a typical trajectory. (a) Longitudinal coordinate as a function of time. (b) Longitudinal velocity, vx, as a function of its transversal velocity, vy.

Fig. 7
Fig. 7

Electron dynamics calculated from the Lorentz force as indicated in Eq. (3). The figure shows the longitudinal velocity, vx, as a function of the transversal velocity, vy, for the same parameters as in Fig. 6. The similarity with Fig. 6(b) is remarkable, and this is the reason of the validity of the moving-mirror result for these parameters. Observe the proximity of the speed of light limit, c=137 a.u., indicating the necessity of a relativistic description of the dynamics.

Fig. 8
Fig. 8

Longitudinal electric field Ex(x, t) at each point of the longitudinal coordinate calculated with the PIC code for an incident amplitude E0=55 a.u., frequency ωL=0.228 a.u., and critical density ωP=ωL. (a) Spatio-temporal profile for one cycle. (b) Cut at a convenient value of the x coordinate.

Fig. 9
Fig. 9

Harmonic spectrum of the reflected far field computed in the PIC simulation for laser frequency ωL=0.228 a.u., amplitude E0=55 a.u. (intensity 1020 W/cm2), critical density ωP=ωL, and slab thickness equal to λ/10, 20 nm, which are the same parameters as in Fig. 4, where a nice train of short pulses appeared. (a) Intensity spectrum, (b) phases of the harmonics.

Equations (7)

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Ey(x, t)=E0f(t-x/c)cos[ωL(t-x/c)],
Bz(x, t)=B0f(t-x/c)cos[ωL(t-x/c)],
En(x, t)AcRqnex×{ex+βn}×β˙n(1+βnex)ret,
dpdt=qE(r, t)+qcvB(r, t)-mωP2x,
duxdt=+qγmcuyBz(x, t)-ωP2x,
duydt=qmEy(x, t)-qγmcuxBz(x, t).
ER[t-sx(t)/c]+E0 cos{ωL[t+sx(t)/c]}=0.

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