Abstract

An intense ultrafast laser pulse propagating through a plasma undergoes self-focusing and self-phase-modulation as a result of relativistic mass nonlinearity. The inclusion of a quartic (r4) term in the expansion of the eikonal in the radial coordinate r allows the modification of the shape of the radial intensity profile. The front of the pulse, under the combined effects of time-dependent self-focusing and frequency downshifting, acquires a severely distorted temporal shape. The radial profile for Iλμ2<2.8×1018 W/cm2, where I is the axial laser intensity and λμ is the laser wavelength in micrometers, is transformed from a Gaussian to a super-Gaussian because of the faster convergence of the marginal rays than the paraxial rays. In the opposite case of Iλμ2>2.8×1018W/cm2 when nonlinear plasma permittivity approaches saturation, the radial profile in the axial region becomes broader than the Gaussian.

© 2001 Optical Society of America

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  1. M. Honda, J. Meyer-ter-Vehn, A. Pukhov, “Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic current in plasma,” Phys. Plasmas 7, 1302–1308 (2000).
    [CrossRef]
  2. G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
    [CrossRef]
  3. S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
    [CrossRef]
  4. G. D. Tsakiris, C. Gahn, V. K. Tripathi, “Laser induced electron acceleration in the presence of static electric and magnetic fields in a plasma,” Phys. Plasmas 7, 3017–3030 (2000).
    [CrossRef]
  5. C. S. Liu, V. K. Tripathi, Interaction of Electromagnetic Waves with Electron Beams and Plasmas (World Scientific, Singapore, 1994), Chap. 4.
  6. P. Sprangle, E. Esarey, J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211–4232 (1996).
    [CrossRef]
  7. A. Couairon, L. Berge, “Modeling the filamentation of ultra-short pulses in ionizing media,” Phys. Plasmas 7, 193–209 (2000).
    [CrossRef]
  8. J. Parashar, H. D. Pandey, V. K. Tripathi, “Two-dimensional effects in a tunnel ionized plasma,” Phys. Plasmas 4, 3040–3043 (1997).
    [CrossRef]
  9. P. B. Corkum, C. Rolland, T. Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
    [CrossRef] [PubMed]
  10. A. Ting, K. Krushelnick, H. R. Burris, A. Fisher, C. Manka, C. J. Moore, “Backscattered supercontinuum emission from high-intensity laser–plasma interactions,” Opt. Lett. 21, 1096–1098 (1996).
    [CrossRef] [PubMed]
  11. L. V. Keldysh, “Ionization in the field of a strong electromagnetic waves,” JETP 20, 1307–1314 (1965).
  12. See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
    [CrossRef]
  13. V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
    [CrossRef]
  14. S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 93, 609–636 (1968).
    [CrossRef]
  15. R. Fedosejevs, X. F. Wang, G. D. Tsakiris, “Onset of relativistic self-focusing in high density gas jet targets,” Phys. Rev. E 56, 4615–4639 (1997).
    [CrossRef]
  16. P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
    [CrossRef]
  17. C. S. Liu, V. K. Tripathi, “Laser frequency upshift, self-defocusing, and ring formation in tunnel ionizing gases and plasmas,” Phys. Plasmas 7, 4360–4363 (2000).
    [CrossRef]

2000 (4)

M. Honda, J. Meyer-ter-Vehn, A. Pukhov, “Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic current in plasma,” Phys. Plasmas 7, 1302–1308 (2000).
[CrossRef]

G. D. Tsakiris, C. Gahn, V. K. Tripathi, “Laser induced electron acceleration in the presence of static electric and magnetic fields in a plasma,” Phys. Plasmas 7, 3017–3030 (2000).
[CrossRef]

A. Couairon, L. Berge, “Modeling the filamentation of ultra-short pulses in ionizing media,” Phys. Plasmas 7, 193–209 (2000).
[CrossRef]

C. S. Liu, V. K. Tripathi, “Laser frequency upshift, self-defocusing, and ring formation in tunnel ionizing gases and plasmas,” Phys. Plasmas 7, 4360–4363 (2000).
[CrossRef]

1999 (2)

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

1997 (3)

J. Parashar, H. D. Pandey, V. K. Tripathi, “Two-dimensional effects in a tunnel ionized plasma,” Phys. Plasmas 4, 3040–3043 (1997).
[CrossRef]

R. Fedosejevs, X. F. Wang, G. D. Tsakiris, “Onset of relativistic self-focusing in high density gas jet targets,” Phys. Rev. E 56, 4615–4639 (1997).
[CrossRef]

See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
[CrossRef]

1996 (2)

A. Ting, K. Krushelnick, H. R. Burris, A. Fisher, C. Manka, C. J. Moore, “Backscattered supercontinuum emission from high-intensity laser–plasma interactions,” Opt. Lett. 21, 1096–1098 (1996).
[CrossRef] [PubMed]

P. Sprangle, E. Esarey, J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211–4232 (1996).
[CrossRef]

1993 (1)

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

1986 (1)

P. B. Corkum, C. Rolland, T. Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[CrossRef] [PubMed]

1968 (1)

S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 93, 609–636 (1968).
[CrossRef]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic waves,” JETP 20, 1307–1314 (1965).

1089 (1)

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 93, 609–636 (1968).
[CrossRef]

Amiranoff, F.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Berge, L.

A. Couairon, L. Berge, “Modeling the filamentation of ultra-short pulses in ionizing media,” Phys. Plasmas 7, 193–209 (2000).
[CrossRef]

Burris, H. R.

Chen, S. Y.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Chessa, P.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Corkum, P. B.

P. B. Corkum, C. Rolland, T. Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[CrossRef] [PubMed]

Couairon, A.

A. Couairon, L. Berge, “Modeling the filamentation of ultra-short pulses in ionizing media,” Phys. Plasmas 7, 193–209 (2000).
[CrossRef]

Dawson, J. M.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
[CrossRef]

De Wispelaere, E.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Dorchies, F.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Esarey, E.

See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
[CrossRef]

P. Sprangle, E. Esarey, J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211–4232 (1996).
[CrossRef]

Fedosejevs, R.

R. Fedosejevs, X. F. Wang, G. D. Tsakiris, “Onset of relativistic self-focusing in high density gas jet targets,” Phys. Rev. E 56, 4615–4639 (1997).
[CrossRef]

Fisher, A.

Gahn, C.

G. D. Tsakiris, C. Gahn, V. K. Tripathi, “Laser induced electron acceleration in the presence of static electric and magnetic fields in a plasma,” Phys. Plasmas 7, 3017–3030 (2000).
[CrossRef]

Gildenburg, V. B.

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

Hamoniaux, G.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Honda, M.

M. Honda, J. Meyer-ter-Vehn, A. Pukhov, “Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic current in plasma,” Phys. Plasmas 7, 1302–1308 (2000).
[CrossRef]

Jones, M. E.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
[CrossRef]

Katsouleas, T.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic waves,” JETP 20, 1307–1314 (1965).

Khokhlov, R. V.

S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 93, 609–636 (1968).
[CrossRef]

Kim, A. V.

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

Krall, J.

See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
[CrossRef]

P. Sprangle, E. Esarey, J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211–4232 (1996).
[CrossRef]

Krupnov, V. A.

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

Krushelnick, K.

Liu, C. S.

C. S. Liu, V. K. Tripathi, “Laser frequency upshift, self-defocusing, and ring formation in tunnel ionizing gases and plasmas,” Phys. Plasmas 7, 4360–4363 (2000).
[CrossRef]

C. S. Liu, V. K. Tripathi, Interaction of Electromagnetic Waves with Electron Beams and Plasmas (World Scientific, Singapore, 1994), Chap. 4.

Maksimchuk, A.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Malka, V.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Manka, C.

Marquès, J. R.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Meyer-ter-Vehn, J.

M. Honda, J. Meyer-ter-Vehn, A. Pukhov, “Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic current in plasma,” Phys. Plasmas 7, 1302–1308 (2000).
[CrossRef]

Moore, C. J.

Mora, P.

P. Chessa, E. De Wispelaere, F. Dorchies, V. Malka, J. R. Marquès, G. Hamoniaux, P. Mora, F. Amiranoff, “Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas,” Phys. Rev. Lett. 82, 552–555 (1999).
[CrossRef]

Mori, W. B.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
[CrossRef]

Mourou, G.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Novikov, V. N.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Pandey, H. D.

J. Parashar, H. D. Pandey, V. K. Tripathi, “Two-dimensional effects in a tunnel ionized plasma,” Phys. Plasmas 4, 3040–3043 (1997).
[CrossRef]

Parashar, J.

J. Parashar, H. D. Pandey, V. K. Tripathi, “Two-dimensional effects in a tunnel ionized plasma,” Phys. Plasmas 4, 3040–3043 (1997).
[CrossRef]

Pukhov, A.

M. Honda, J. Meyer-ter-Vehn, A. Pukhov, “Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic current in plasma,” Phys. Plasmas 7, 1302–1308 (2000).
[CrossRef]

Rao, T.

P. B. Corkum, C. Rolland, T. Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[CrossRef] [PubMed]

Rolland, C.

P. B. Corkum, C. Rolland, T. Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[CrossRef] [PubMed]

Semenov, V. E.

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

Sergeev, A. M.

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

Serkisov, G. S.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Sprangle, P.

See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
[CrossRef]

P. Sprangle, E. Esarey, J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211–4232 (1996).
[CrossRef]

Sukhorukov, A. P.

S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 93, 609–636 (1968).
[CrossRef]

Tikhonchuk, V. T.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Ting, A.

See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
[CrossRef]

A. Ting, K. Krushelnick, H. R. Burris, A. Fisher, C. Manka, C. J. Moore, “Backscattered supercontinuum emission from high-intensity laser–plasma interactions,” Opt. Lett. 21, 1096–1098 (1996).
[CrossRef] [PubMed]

Tripathi, V. K.

G. D. Tsakiris, C. Gahn, V. K. Tripathi, “Laser induced electron acceleration in the presence of static electric and magnetic fields in a plasma,” Phys. Plasmas 7, 3017–3030 (2000).
[CrossRef]

C. S. Liu, V. K. Tripathi, “Laser frequency upshift, self-defocusing, and ring formation in tunnel ionizing gases and plasmas,” Phys. Plasmas 7, 4360–4363 (2000).
[CrossRef]

J. Parashar, H. D. Pandey, V. K. Tripathi, “Two-dimensional effects in a tunnel ionized plasma,” Phys. Plasmas 4, 3040–3043 (1997).
[CrossRef]

C. S. Liu, V. K. Tripathi, Interaction of Electromagnetic Waves with Electron Beams and Plasmas (World Scientific, Singapore, 1994), Chap. 4.

Tsakiris, G. D.

G. D. Tsakiris, C. Gahn, V. K. Tripathi, “Laser induced electron acceleration in the presence of static electric and magnetic fields in a plasma,” Phys. Plasmas 7, 3017–3030 (2000).
[CrossRef]

R. Fedosejevs, X. F. Wang, G. D. Tsakiris, “Onset of relativistic self-focusing in high density gas jet targets,” Phys. Rev. E 56, 4615–4639 (1997).
[CrossRef]

Umstadter, D.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Wagner, R.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Wang, X. F.

R. Fedosejevs, X. F. Wang, G. D. Tsakiris, “Onset of relativistic self-focusing in high density gas jet targets,” Phys. Rev. E 56, 4615–4639 (1997).
[CrossRef]

Wilks, S. C.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1089).
[CrossRef]

Yu, V.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Yu Bychenkov, V.

G. S. Serkisov, V. Yu, V. Yu Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S. Y. Chen, R. Wagner, G. Mourou, D. Umstadter, “Self-focusing, channel formation, and high energy ion generation in interaction of an intense short laser pulse with He jet,” Phys. Rev. E 59, 7042–7054 (1999).
[CrossRef]

Zharova, N. A.

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

See E. Esarey, P. Sprangle, J. Krall, A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997) and references therein.
[CrossRef]

IEEE Trans. Plasma Sci. (1)

V. B. Gildenburg, A. V. Kim, V. A. Krupnov, V. E. Semenov, A. M. Sergeev, N. A. Zharova, “Adiabatic frequency up-conversion of a powerful electromagnetic pulse producing gas ionization,” IEEE Trans. Plasma Sci. 21, 34–44 (1993).
[CrossRef]

JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic waves,” JETP 20, 1307–1314 (1965).

Opt. Lett. (1)

Phys. Plasmas (5)

A. Couairon, L. Berge, “Modeling the filamentation of ultra-short pulses in ionizing media,” Phys. Plasmas 7, 193–209 (2000).
[CrossRef]

J. Parashar, H. D. Pandey, V. K. Tripathi, “Two-dimensional effects in a tunnel ionized plasma,” Phys. Plasmas 4, 3040–3043 (1997).
[CrossRef]

M. Honda, J. Meyer-ter-Vehn, A. Pukhov, “Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic current in plasma,” Phys. Plasmas 7, 1302–1308 (2000).
[CrossRef]

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Other (1)

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Figures (4)

Fig. 1
Fig. 1

Beam-width parameter f plotted as a function of the distance of propagation normalized to the Rayleigh length at T(t-z/c)/τ=0, 1, 2, 3, where τ is the pulse rise time. The parameters are r0ωp/c=5, ω0τ=40, and v0/c=1.

Fig. 2
Fig. 2

Normalized frequency of the laser plotted as a function of the retarded time T(t-z/c)/τ at z/Rd=1. The other parameters are the same as those for Fig. 1.

Fig. 3
Fig. 3

Normalized axial intensity |E|r=02/E002 plotted as a function of the retarded time T at z=0, Rd. The other parameters are the same as those for Fig. 1.

Fig. 4
Fig. 4

Radial intensity profile at z=0 and at z=Rd for (t-z/c)/τ=1.5. The other parameters are the same as those for Fig. 1.

Equations (28)

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Γj=(π/2)1/2(Ij/)(|E|/Ej)1/2exp(-Ej/|E|),
j=1, 2, ,
0I2πrdr
E=E0(xˆ+iyˆ)exp(iω0t),
E02=E002exp(-r2/r02)g(t),
v=eEmiωγ,γ=1+e2|A|2m2ω2c21/2,
2E-1c22Et2=ωp2γc2E,
ω2=ωp2γ0+k2c2,
2ikAz+2iωc2At+2A+ikzA+1c2ωtA
=1c2ωp2γ-ωp2γ0A,
ω2t+vgω2z=-ωp2γ03e22mc2t|A|2ω2.
2iωcFz+2F=ωp2c21γ-1γ0F,
ω2z=ωp2γ03e22mω02c2t|F|2(ω/ω0)3,
-2ωcSzF0+2F0r2+1rF0r-Sr2F0
=1c2ωp2γ-ωp2γ0F0,
ωcF02z+2Sr2+1rSrF02+SrF02r=0.
ωcF02z+4S2r02F02+2S2r02rF02r=0.
S2=ωr022c1ffz,
F02=E002f 2exp-r2r02 f 2g(t),
ξ=z/Rd,Ω=ω/ω0,Rd=(ω0/c)r02,v0/c=eE00/mω0c,
S0/ξ=-1/(f 2Ω),S2=(Ω/2f)f/ξ,
2fξ2+1ΩΩξfξ=1Ω2f 3-r02ωp2c2Ω4v02g(t)2c2γ03 f 3,
Ωξ=r02ωp2c2Ωv024c2γ03ω0tg(t)f 2Ω3.
S=S0+S2r2/r02+S4r4/r04
F02=1+a2r2r02 f 2+a4r4r04 f 4  E002f 2exp(-r2/r02 f 2),
ξ(S4 f 4)=ωp2r0216c2v02c2γ03f 2Ω3×1-3v02g(t)2γ02c2f 2Ω2-2a2+2a4+14Ωf 2(-14a2a4+4a23-4a4+2a22),
a2ξ=-32S4f 2/Ω,a4ξ=-16S4 f 2(3a2-1),
2fξ2+1ΩΩξfξ=1Ω2f 3-r02ωp22c2v02(1-a2)g(t)γ03c2f 3Ω4+8a4-2a2-3a22Ω2f 3.

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