Abstract

We studied theoretically the influence of relativistic effects on the energy distribution of electrons in the tunneling ionization of atoms by a field of linearly polarized super-intense laser radiation. It was shown that the energy distribution of ejected electrons is determined by relativistic law though the electron kinetic energy can be less than its rest energy. The relativistic probability of ionization along the field strength decreases exponentially with the electron kinetic energy, but more quickly than in the non-relativistic case.

© 1998 Optical Society of America

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References

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  1. N.B. Delone and V.P. Krainov, Atoms in Strong Light Fields (Springer, Berlin-Heidelberg1985).
    [Crossref]
  2. N.B. Delone and V.P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation”, J. Opt. Soc. Am. B 8, 1207–1211 (1991).
    [Crossref]
  3. N.B. Delone and V.P. Krainov, Multiphoton Processes in Atoms (Springer, Berlin-Heidelberg1994).
    [Crossref]
  4. H.R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes”, Prog. Quantum Electron. 16, 1–71 (1992).
    [Crossref]
  5. V.P. Krainov and S.P. Roshchupkin, “Relativistic effects in the angular distribution of ejected electronds in tunneling ionization of atoms by strong electromagnetic field”, J. Opt. Soc. Am. B 9, 1231–1233 (1992).
    [Crossref]
  6. V.P. Krainov and B. Shokri, “Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field”, Laser Phys. 5, 793–796 (1995).
  7. L.D. Landau and E.M. Lifshitz, Field Theory (Oxford, Pergamon1977).
  8. M.V. Ammosov, N.B. Delone, and V.P. Krainov, “Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field”, Sov. Phys. JETP 64, 1191–1194 (1986).
  9. P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit”, Phys. Rev. Lett. 62, 1259–1262 (1989).
    [Crossref] [PubMed]
  10. B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

1997 (1)

B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

1995 (1)

V.P. Krainov and B. Shokri, “Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field”, Laser Phys. 5, 793–796 (1995).

1992 (2)

H.R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes”, Prog. Quantum Electron. 16, 1–71 (1992).
[Crossref]

V.P. Krainov and S.P. Roshchupkin, “Relativistic effects in the angular distribution of ejected electronds in tunneling ionization of atoms by strong electromagnetic field”, J. Opt. Soc. Am. B 9, 1231–1233 (1992).
[Crossref]

1991 (1)

1989 (1)

P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit”, Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

1986 (1)

M.V. Ammosov, N.B. Delone, and V.P. Krainov, “Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field”, Sov. Phys. JETP 64, 1191–1194 (1986).

Ammosov, M.V.

M.V. Ammosov, N.B. Delone, and V.P. Krainov, “Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field”, Sov. Phys. JETP 64, 1191–1194 (1986).

Brunel, F.

P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit”, Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Buerke, B.

B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

Burnett, N.H.

P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit”, Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Corkum, P.B.

P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit”, Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Delone, N.B.

N.B. Delone and V.P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation”, J. Opt. Soc. Am. B 8, 1207–1211 (1991).
[Crossref]

M.V. Ammosov, N.B. Delone, and V.P. Krainov, “Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field”, Sov. Phys. JETP 64, 1191–1194 (1986).

N.B. Delone and V.P. Krainov, Atoms in Strong Light Fields (Springer, Berlin-Heidelberg1985).
[Crossref]

N.B. Delone and V.P. Krainov, Multiphoton Processes in Atoms (Springer, Berlin-Heidelberg1994).
[Crossref]

Knauer, J.P.

B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

Krainov, V.P.

V.P. Krainov and B. Shokri, “Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field”, Laser Phys. 5, 793–796 (1995).

V.P. Krainov and S.P. Roshchupkin, “Relativistic effects in the angular distribution of ejected electronds in tunneling ionization of atoms by strong electromagnetic field”, J. Opt. Soc. Am. B 9, 1231–1233 (1992).
[Crossref]

N.B. Delone and V.P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation”, J. Opt. Soc. Am. B 8, 1207–1211 (1991).
[Crossref]

M.V. Ammosov, N.B. Delone, and V.P. Krainov, “Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field”, Sov. Phys. JETP 64, 1191–1194 (1986).

N.B. Delone and V.P. Krainov, Atoms in Strong Light Fields (Springer, Berlin-Heidelberg1985).
[Crossref]

N.B. Delone and V.P. Krainov, Multiphoton Processes in Atoms (Springer, Berlin-Heidelberg1994).
[Crossref]

Landau, L.D.

L.D. Landau and E.M. Lifshitz, Field Theory (Oxford, Pergamon1977).

Lifshitz, E.M.

L.D. Landau and E.M. Lifshitz, Field Theory (Oxford, Pergamon1977).

McNaught, S.J.

B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

Meyerhofer, D.D.

B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

Reiss, H.R.

H.R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes”, Prog. Quantum Electron. 16, 1–71 (1992).
[Crossref]

Roshchupkin, S.P.

Shokri, B.

V.P. Krainov and B. Shokri, “Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field”, Laser Phys. 5, 793–796 (1995).

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

V.P. Krainov and B. Shokri, “Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field”, Laser Phys. 5, 793–796 (1995).

OSA Technical Digest Series (1)

B. Buerke, J.P. Knauer, S.J. McNaught, and D.D. Meyerhofer, “Precision tests of laser-tunneling ionization models”: in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75–76 (1997).

Phys. Rev. Lett. (1)

P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit”, Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Prog. Quantum Electron. (1)

H.R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes”, Prog. Quantum Electron. 16, 1–71 (1992).
[Crossref]

Sov. Phys. JETP (1)

M.V. Ammosov, N.B. Delone, and V.P. Krainov, “Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field”, Sov. Phys. JETP 64, 1191–1194 (1986).

Other (3)

L.D. Landau and E.M. Lifshitz, Field Theory (Oxford, Pergamon1977).

N.B. Delone and V.P. Krainov, Atoms in Strong Light Fields (Springer, Berlin-Heidelberg1985).
[Crossref]

N.B. Delone and V.P. Krainov, Multiphoton Processes in Atoms (Springer, Berlin-Heidelberg1994).
[Crossref]

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Equations (9)

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ω if exp { 2 Im 0 t 0 [ E f ( t ) + E i ] dt } .
γ = ω 2 E i F 1 .
E f ( t ) = 1 2 p 0 2 c 2 + c 4 c 2 + p 2 c 2 + c 4 2 p 0 2 c 2 + c 4 .
2 F sin ωt ω = ( 1 + c 4 p 0 2 c 2 + c 4 ) ( p p 0 ) + c 2 3 ( p 0 2 c 2 + c 4 ) ( p 3 p 0 3 ) .
E e = p 0 2 c 2 + c 4 c 2 < c 2
ω if = ω 0 exp [ 2 E e γ 3 3 ω E e 2 γ ω c 2 ] .
Δ E e ( non rel ) ~ 3 ω 2 γ 3 .
E e > γ 2 c 2
Δ E e ( rel ) ~ c γ ω .

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