Abstract

Electromagnetic plasma computer simulations are used to analyze the frequency shifts caused by the ionization of atmospheric-density noble gases during interaction with intense femtosecond laser pulses; the results are presented and compared with experimental data. The simulations trace the temporal evolution of plasma growth during the femtosecond ionizing pulse and calculate the resulting self-induced blue shift of the ionizing pulse spectrum. Variations with pulse intensity, gas pressure, and gas species are calculated. The relative contributions of strong-field ionization and electron-impact ionization on the frequency shifts are discussed. The simulations provide qualitative explanations of most of the features observed experimentally in the blue-shifted spectra. The technique of spectral blue shifting intense femtosecond laser pulses provides a new diagnostic tool for studying strong-field ionization and laser-induced breakdown in dense plasmas.

© 1992 Optical Society of America

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  1. W. M. Wood, G. Focht, and M. C. Downer, Opt. Lett. 13, 984 (1988).
    [CrossRef] [PubMed]
  2. M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
    [CrossRef]
  3. W. M. Wood, C. W. Siders, and M. C. Downer, Phys. Rev. Lett. 67, 3523 (1991).
    [CrossRef] [PubMed]
  4. E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972)
    [CrossRef]
  5. N. Bloembergen, Opt. Commun. 8, 285 (1973).
    [CrossRef]
  6. E. Yablonovitch, Phys. Rev. Lett. 31, 877 (1973).
    [CrossRef]
  7. E. Yablonovitch, Phys. Rev. Lett. 32, 1101 (1974).
    [CrossRef]
  8. E. Yablonovitch, Phys. Rev. A 10, 1888 (1974).
    [CrossRef]
  9. S. C. Wilks, J. M. Dawson, and M. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
    [CrossRef] [PubMed]
  10. V. B. Gildenburg, A. V. Kim, and A. M. Sergeev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 91 (1990) [JETP Lett. 51, 104 (1990)].
  11. E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
    [CrossRef] [PubMed]
  12. M. C. Downer, W. M. Wood, and J. I. Trisnadi, Phys. Rev. Lett. 65, 2832 (1990).
    [CrossRef]
  13. R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
    [CrossRef] [PubMed]
  14. C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
    [CrossRef]
  15. M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1986)].
  16. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].
  17. S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
    [CrossRef] [PubMed]
  18. S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, J. Opt. Soc. Am. B 8, 858 (1991).
    [CrossRef]
  19. W. M. Wood, “Femtosecond time-resolved study of plasma generation and dynamics by blue shifting of high-intensity laser pulses,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1991).
  20. B. M. Penetrante and J. N. Bardsley, Phys. Rev. A 43, 4100 (1991).
    [CrossRef]
  21. W. Lotz, Z. Phys 206, 205 (1967);Z. Phys 216, 241 (1968).
    [CrossRef]
  22. H. Tawara and T. Kato, At. Data Nucl. Data Tables 36, 167 (1987).
    [CrossRef]
  23. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).

1991 (3)

W. M. Wood, C. W. Siders, and M. C. Downer, Phys. Rev. Lett. 67, 3523 (1991).
[CrossRef] [PubMed]

B. M. Penetrante and J. N. Bardsley, Phys. Rev. A 43, 4100 (1991).
[CrossRef]

S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, J. Opt. Soc. Am. B 8, 858 (1991).
[CrossRef]

1990 (3)

M. C. Downer, W. M. Wood, and J. I. Trisnadi, Phys. Rev. Lett. 65, 2832 (1990).
[CrossRef]

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

V. B. Gildenburg, A. V. Kim, and A. M. Sergeev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 91 (1990) [JETP Lett. 51, 104 (1990)].

1989 (1)

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

1988 (3)

S. C. Wilks, J. M. Dawson, and M. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
[CrossRef] [PubMed]

W. M. Wood, G. Focht, and M. C. Downer, Opt. Lett. 13, 984 (1988).
[CrossRef] [PubMed]

1987 (2)

H. Tawara and T. Kato, At. Data Nucl. Data Tables 36, 167 (1987).
[CrossRef]

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1986)].

1974 (2)

E. Yablonovitch, Phys. Rev. Lett. 32, 1101 (1974).
[CrossRef]

E. Yablonovitch, Phys. Rev. A 10, 1888 (1974).
[CrossRef]

1973 (2)

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 31, 877 (1973).
[CrossRef]

1972 (1)

E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972)
[CrossRef]

1967 (1)

W. Lotz, Z. Phys 206, 205 (1967);Z. Phys 216, 241 (1968).
[CrossRef]

1964 (1)

L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1986)].

Augst, S.

S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, J. Opt. Soc. Am. B 8, 858 (1991).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

Bardsley, J. N.

B. M. Penetrante and J. N. Bardsley, Phys. Rev. A 43, 4100 (1991).
[CrossRef]

Birdsall, C. K.

C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).

Bloembergen, N.

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972)
[CrossRef]

Bucksbaum, P. H.

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

Chin, S. L.

S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, J. Opt. Soc. Am. B 8, 858 (1991).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

Clayton, C. E.

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

Darak, S.

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

Dawson, J. M.

S. C. Wilks, J. M. Dawson, and M. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef] [PubMed]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1986)].

Downer, M. C.

W. M. Wood, C. W. Siders, and M. C. Downer, Phys. Rev. Lett. 67, 3523 (1991).
[CrossRef] [PubMed]

M. C. Downer, W. M. Wood, and J. I. Trisnadi, Phys. Rev. Lett. 65, 2832 (1990).
[CrossRef]

W. M. Wood, G. Focht, and M. C. Downer, Opt. Lett. 13, 984 (1988).
[CrossRef] [PubMed]

M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
[CrossRef]

Eberly, J. H.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

Focht, G.

W. M. Wood, G. Focht, and M. C. Downer, Opt. Lett. 13, 984 (1988).
[CrossRef] [PubMed]

M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
[CrossRef]

Freeman, R. R.

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

Geusic, M. E.

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

Gildenburg, V. B.

V. B. Gildenburg, A. V. Kim, and A. M. Sergeev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 91 (1990) [JETP Lett. 51, 104 (1990)].

Hopkins, D. B.

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

Joshi, C. J.

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

Kato, T.

H. Tawara and T. Kato, At. Data Nucl. Data Tables 36, 167 (1987).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].

Kim, A. V.

V. B. Gildenburg, A. V. Kim, and A. M. Sergeev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 91 (1990) [JETP Lett. 51, 104 (1990)].

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1986)].

Langdon, A. B.

C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).

Lotz, W.

W. Lotz, Z. Phys 206, 205 (1967);Z. Phys 216, 241 (1968).
[CrossRef]

Marsh, K.

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

Meyerhofer, D. D.

S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, J. Opt. Soc. Am. B 8, 858 (1991).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

Milberg, H.

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

Mori, M. B.

S. C. Wilks, J. M. Dawson, and M. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef] [PubMed]

Penetrante, B. M.

B. M. Penetrante and J. N. Bardsley, Phys. Rev. A 43, 4100 (1991).
[CrossRef]

Reitze, D. H.

M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
[CrossRef]

Schumacher, D.

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

Sergeev, A. M.

V. B. Gildenburg, A. V. Kim, and A. M. Sergeev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 91 (1990) [JETP Lett. 51, 104 (1990)].

Sessler, A.

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

Siders, C. W.

W. M. Wood, C. W. Siders, and M. C. Downer, Phys. Rev. Lett. 67, 3523 (1991).
[CrossRef] [PubMed]

Strickland, D.

S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, J. Opt. Soc. Am. B 8, 858 (1991).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

Tawara, H.

H. Tawara and T. Kato, At. Data Nucl. Data Tables 36, 167 (1987).
[CrossRef]

Trisnadi, J. I.

M. C. Downer, W. M. Wood, and J. I. Trisnadi, Phys. Rev. Lett. 65, 2832 (1990).
[CrossRef]

Whittum, D.

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

Wilks, S. C.

S. C. Wilks, J. M. Dawson, and M. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef] [PubMed]

Wood, W. M.

W. M. Wood, C. W. Siders, and M. C. Downer, Phys. Rev. Lett. 67, 3523 (1991).
[CrossRef] [PubMed]

M. C. Downer, W. M. Wood, and J. I. Trisnadi, Phys. Rev. Lett. 65, 2832 (1990).
[CrossRef]

W. M. Wood, G. Focht, and M. C. Downer, Opt. Lett. 13, 984 (1988).
[CrossRef] [PubMed]

M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
[CrossRef]

W. M. Wood, “Femtosecond time-resolved study of plasma generation and dynamics by blue shifting of high-intensity laser pulses,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1991).

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 32, 1101 (1974).
[CrossRef]

E. Yablonovitch, Phys. Rev. A 10, 1888 (1974).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 31, 877 (1973).
[CrossRef]

E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972)
[CrossRef]

Zhang, T. R.

M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
[CrossRef]

At. Data Nucl. Data Tables (1)

H. Tawara and T. Kato, At. Data Nucl. Data Tables 36, 167 (1987).
[CrossRef]

IEEE. Trans. Plasma Sci. (1)

C. J. Joshi, C. E. Clayton, K. Marsh, D. B. Hopkins, A. Sessler, and D. Whittum, IEEE. Trans. Plasma Sci. 18, 814 (1990).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

E. Yablonovitch, Phys. Rev. A 10, 1888 (1974).
[CrossRef]

B. M. Penetrante and J. N. Bardsley, Phys. Rev. A 43, 4100 (1991).
[CrossRef]

Phys. Rev. Lett. (9)

E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
[CrossRef] [PubMed]

M. C. Downer, W. M. Wood, and J. I. Trisnadi, Phys. Rev. Lett. 65, 2832 (1990).
[CrossRef]

R. R. Freeman, P. H. Bucksbaum, H. Milberg, S. Darak, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987).
[CrossRef] [PubMed]

S. C. Wilks, J. M. Dawson, and M. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 31, 877 (1973).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 32, 1101 (1974).
[CrossRef]

W. M. Wood, C. W. Siders, and M. C. Downer, Phys. Rev. Lett. 67, 3523 (1991).
[CrossRef] [PubMed]

E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972)
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[CrossRef] [PubMed]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. B. Gildenburg, A. V. Kim, and A. M. Sergeev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 91 (1990) [JETP Lett. 51, 104 (1990)].

Z. Phys (1)

W. Lotz, Z. Phys 206, 205 (1967);Z. Phys 216, 241 (1968).
[CrossRef]

Zh. Eksp. Teor. Fiz. (2)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191 (1986)].

L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].

Other (3)

W. M. Wood, “Femtosecond time-resolved study of plasma generation and dynamics by blue shifting of high-intensity laser pulses,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1991).

M. C. Downer, G. Focht, D. H. Reitze, W. M. Wood, and T. R. Zhang, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, and S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), pp. 128–131.
[CrossRef]

C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).

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Figures (11)

Fig. 1
Fig. 1

Calculated spectra for a 100-fs laser pulse with an original wavelength of 620 nm. The laser is propagated through a spatially uniform plasma with an interaction length of 10 μm and an ionization rate of 2.805 × 1033 cm−3 s−1. The dotted curve is the incident spectrum; the solid curve is the transmitted spectrum.

Fig. 2
Fig. 2

Measured spectra after shifting through 5 atm (3.8 kTorr) of He and Ar gases with a peak laser intensity of 1016 W/cm2.

Fig. 3
Fig. 3

Measured spectra after interaction with 5 atm of Kr as a function of pulse energy. Pulse energy is increasing toward the bottom of the figure in steps of (×100.2). The center of the original spectrum is indicated by a vertical line at 620 nm.

Fig. 4
Fig. 4

Measured spectra after interaction of 0.25-mJ pulses in 5 atm of each of the noble gases studied. The center of original pulse spectrum is indicated by a vertical dashed line at 620 nm.

Fig. 5
Fig. 5

Measured spectra after interaction of 0.25-mJ pulses with Ar gas as a function of gas pressure. Pressure is increasing toward the bottom of the figure. The center of original pulse spectrum is indicated by a vertical dashed line at 620 nm.

Fig. 6
Fig. 6

Evolution of the degree of ionization in 5 atm of the noble gases with a peak laser intensity of 1016 W/cm2, calculated using (a) Keldysh and (b) Ammosov et al. rates for strong-field ionization. The solid curves are calculations that include collisional ionization; the dashed curves are without collisional ionization. The time profile of the laser pulse is shown by the dotted curves.

Fig. 7
Fig. 7

Spectra for ionization of 5 atm of Xe by 100-fs pulse of peak intensity 1016 W/cm2, calculated using Keldysh and Ammosov et al. rates for strong-field ionization. The laser-plasma interaction length is 10 μm. The dotted curves shows the original spectra; the solid curves are the shifted spectra including collisional ionization; the dashed curves are without collisional ionization.

Fig. 8
Fig. 8

Spectra for ionization of 5 atm of He, Ne, Ar, and Kr by a 100-fs pulse of peak intensity 1016 W/cm2, calculated with the Ammosov et al. rates used for field ionization. The laser–plasma interaction length is 10 μm. The dotted curves shows the original spectra; the solid curves are the shifted spectra including collisional ionization; the dashed curves are without collisional ionization.

Fig. 9
Fig. 9

Calculated evolution of the degree of ionization in 5 atm of Ar for various peak laser intensities. The time profile of the laser pulse is shown by the dotted curve.

Fig. 10
Fig. 10

Calculated spectra in 5 atm of Ar for various peak laser intensities. The dotted curve shows the original spectrum.

Fig. 11
Fig. 11

Calculated spectra for ionization of Ar at various pressures with a peak laser intensity of 1016 W/cm2. The dotted curve shows the original spectrum.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

Δ ω = ω 0 c L n ( x , t ) t d x ,
n 2 = 1 ω p 2 ( ω 0 2 + γ 2 ) ,
E t = c × B 4 π J , B t = c × E .
N 0 t = W 1 N 0 N j t = W j N j 1 W j + 1 N j , N z max t = W z max N z max 1 , n e = j = 1 z max j N j ,
J y t = e 2 m n e E y .
W = A ω [ U i ( 0 ) h ω ] 3 / 2 [ γ ( 1 + γ 2 ) 1 / 2 ] 5 / 2 S [ γ , U i ( ω ) h ω ] × exp { 2 U i ( ω ) h ω [ sinh 1 γ γ ( 1 + γ 2 ) 1 / 2 1 + 2 γ 2 ] } ,
γ = ω [ 2 m U i ( 0 ) ] 1 / 2 e E ,
U i ( ω ) = U i ( 0 ) ( 1 + 1 2 γ 2 ) , S [ γ , U i ( ω ) h ω ] = m = 0 ( exp { [ 2 U i ( ω ) h ω + 1 U i ( ω ) h ω + m ] [ sinh 1 γ γ ( 1 + γ 2 ) 1 / 2 ] } ) × Φ ( { 2 γ ( 1 + γ 2 ) 1 / 2 [ U i ( ω ) h ω + 1 U i ( ω ) h ω + m ] } 1 / 2 ) , Φ ( x ) = 0 x exp ( t 2 x 2 ) d t .
W = 1.61 ω au Z 2 n eff 4.5 ( 1.87 Z 3 n eff 4 E au E ) 2 n eff 1.5 × exp ( 2 3 Z 3 n eff 3 E au E ) ,
n eff = Z ( U i / U H ) 1 / 2 ,
σ i i + 1 = j = 1 a i j q i j E e P i j ln E e P i j { 1 b i j exp [ c i j ( E e P i j 1 ) ] } .
E y = B z = E 0 sin ( ω 0 t ) exp ( t 2 / t pulse 2 ) ,
E y R ( t + Δ t , x + Δ x ) = E y R ( t , x ) π Δ t [ J y ( t + Δ t 2 , x ) + J y ( t + Δ t 2 , x + Δ x ) ] , E y L ( t + Δ t , x ) = E y L ( t , x + Δ x ) π Δ t [ J y ( t + Δ t 2 , x ) + J y ( t + Δ t 2 , x + Δ x ) ] .
E y R ( t , x = 0 ) = E 0 sin ( ω 0 t ) exp ( t 2 / t pulse 2 ) , E y L ( t , x = L ) = 0 .
J y ( t + Δ t 2 , x ) J y ( t Δ t 2 , x ) = Δ t e 2 m n e ( t , x ) [ E y R ( t , x ) + E y L ( t , x ) ] .
Δ λ = e 2 L λ 0 3 2 π m c c 3 d n e d t .

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