Abstract

It is known that a high-power laser propagating through an underdense plasma can acquire a minimum spot size due to relativistic self-focusing. Beyond the focus, the nonlinear refraction starts weakening, and the spot size of the laser increases, showing periodic self-focusing/ defocusing behavior with the distance of propagation. To overcome the defocusing, we propose the introduction of a localized upward plasma density ramp. In the presence of an upward ramp of plasma density, the laser beam obtains a minimum spot size and maintains it with only a mild ripple. For suitable parameters of the laser and the plasma, we have deduced conditions for the self-focusing. This kind of plasma density ramp may be observed in a gas-jet plasma experiment and resembles a plasma lens.

© 2007 Optical Society of America

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  1. K. A. Brueckner and S. Jorna, 'Laser-driven fusion,' Rev. Mod. Phys. 46, 325-367 (1974).
    [CrossRef]
  2. P. Sprangle, E. Esarey, and J. Krall, 'Laser driven electron acceleration in vacuum, gases, and plasmas,' Phys. Plasmas 3, 2183-2190 (1996).
    [CrossRef]
  3. A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
    [CrossRef] [PubMed]
  4. D. Umstadter, 'Review of physics and applications of relativistic plasmas driven by ultra-intense lasers,' Phys. Plasmas 8, 1774-1785 (2001).
    [CrossRef]
  5. D. N. Gupta, M. S. Hur, and H. Suk, 'Energy exchange during stimulated Raman scattering of a relativistic laser in a plasma,' J. Appl. Phys. 100, 103101 (2006).
    [CrossRef]
  6. D. N. Gupta and H. Suk, 'Frequency chirp for resonance-enhanced electron energy during laser acceleration,' Phys. Plasmas 13, 044507 (2006).
    [CrossRef]
  7. H. Hora, 'Theory of relativistic self-focusing of laser radiation in plasmas,' J. Opt. Soc. Am. 65, 882-886 (1975).
    [CrossRef]
  8. H. Hora, 'The transient electrodynamic forces at laser-plasma interaction,' Phys. Fluids 28, 3705-3706 (1985).
    [CrossRef]
  9. X. L. Chen and R. N. Sudan, 'Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma,' Phys. Rev. Lett. 70, 2082-2085 (1993).
    [CrossRef] [PubMed]
  10. C. S. Liu and V. K. Tripathi, Interaction of Electromagnetic Waves and Electron Beams with Plasmas (World Scientific, 1994).
    [CrossRef]
  11. W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
    [CrossRef]
  12. P. Chessa, P. Mora, and Thomas M. Antonsen, Jr., 'Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma,' Phys. Plasmas 5, 3451-3458 (1998).
    [CrossRef]
  13. J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
    [CrossRef]
  14. P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
    [CrossRef]
  15. D. N. Gupta and A. K. Sharma, 'Transient self-focusing of an intense short pulse laser in magnetized plasma,' Phys. Scr. 66, 262-264 (2002).
    [CrossRef]
  16. R. Fedosejevs, X. F. Wang, and G. D. Tsakiris, 'Onset of relativistic self-focusing in high density gas jet targets,' Phys. Rev. E 56, 4615-4639 (1997).
    [CrossRef]
  17. G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
    [CrossRef]
  18. H. Hora, Physics of Laser Driven Plasmas (Wiley, 1981).
  19. T. Hauser, W. Scheid, and H. Hora, 'Analytical calculation of relativistic self-focusing length in the WKB approximation,' J. Opt. Soc. Am. B 5, 2029-2034 (1988).
    [CrossRef]
  20. F. Osman, R. Castillo, and H. Hora, 'Numerical programming of self-focusing at laser-plasma interaction,' Laser Part. Beams 18, 59-72 (2000).
    [CrossRef]
  21. E. Esarey, P. Sprangle, and J. Krall, 'Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,' IEEE J. Quantum Electron. 33, 1879-1914 (1997).
    [CrossRef]
  22. B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
    [CrossRef]
  23. C. S. Liu and V. K. Tripathi, 'Relativistic laser guiding in an azimuthal magnetic field in a plasma,' Phys. Plasmas 8, 285-288 (2001).
    [CrossRef]
  24. H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
    [CrossRef] [PubMed]
  25. C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
    [CrossRef]
  26. A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
    [CrossRef]
  27. A. Upadhyay, V. K. Tripathi, and H. C. Pant, 'Pulse front sharpening of a laser beam in plasma,' Phys. Scr. 63, 326-328 (2001).
    [CrossRef]
  28. G. Mourou, T. Tajima, and S. V. Bulanov, 'Optics in the relativistic regime,' Rev. Mod. Phys. 78, 309-371 (2006).
    [CrossRef]
  29. D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
    [CrossRef]
  30. T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
    [CrossRef] [PubMed]
  31. V. K. Tripathi, T. Taguchi, and C. S. Liu, 'Plasma channel charging by an intense short pulse laser and ion Coulomb explosion,' Phys. Plasmas 12, 043106 (2005).
    [CrossRef]
  32. M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, 'Self-focusing of lasers in plasmas and semiconductors,' in Progress in Optics, Vol. XIII, E.Wolf, ed. (North-Holland, 1976), pp. 169-333.
    [CrossRef]
  33. M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974).
  34. C. G. Durfee III and H. M. Milchberg, 'Light pipe for high intensity laser pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
    [CrossRef] [PubMed]
  35. M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
    [CrossRef]

2006 (3)

G. Mourou, T. Tajima, and S. V. Bulanov, 'Optics in the relativistic regime,' Rev. Mod. Phys. 78, 309-371 (2006).
[CrossRef]

D. N. Gupta, M. S. Hur, and H. Suk, 'Energy exchange during stimulated Raman scattering of a relativistic laser in a plasma,' J. Appl. Phys. 100, 103101 (2006).
[CrossRef]

D. N. Gupta and H. Suk, 'Frequency chirp for resonance-enhanced electron energy during laser acceleration,' Phys. Plasmas 13, 044507 (2006).
[CrossRef]

2005 (3)

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

V. K. Tripathi, T. Taguchi, and C. S. Liu, 'Plasma channel charging by an intense short pulse laser and ion Coulomb explosion,' Phys. Plasmas 12, 043106 (2005).
[CrossRef]

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

2004 (1)

P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
[CrossRef]

2002 (3)

D. N. Gupta and A. K. Sharma, 'Transient self-focusing of an intense short pulse laser in magnetized plasma,' Phys. Scr. 66, 262-264 (2002).
[CrossRef]

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
[CrossRef]

2001 (5)

A. Upadhyay, V. K. Tripathi, and H. C. Pant, 'Pulse front sharpening of a laser beam in plasma,' Phys. Scr. 63, 326-328 (2001).
[CrossRef]

C. S. Liu and V. K. Tripathi, 'Relativistic laser guiding in an azimuthal magnetic field in a plasma,' Phys. Plasmas 8, 285-288 (2001).
[CrossRef]

H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
[CrossRef] [PubMed]

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

D. Umstadter, 'Review of physics and applications of relativistic plasmas driven by ultra-intense lasers,' Phys. Plasmas 8, 1774-1785 (2001).
[CrossRef]

2000 (2)

B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
[CrossRef]

F. Osman, R. Castillo, and H. Hora, 'Numerical programming of self-focusing at laser-plasma interaction,' Laser Part. Beams 18, 59-72 (2000).
[CrossRef]

1999 (1)

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

1998 (3)

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

P. Chessa, P. Mora, and Thomas M. Antonsen, Jr., 'Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma,' Phys. Plasmas 5, 3451-3458 (1998).
[CrossRef]

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

1997 (2)

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

E. Esarey, P. Sprangle, and J. Krall, 'Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,' IEEE J. Quantum Electron. 33, 1879-1914 (1997).
[CrossRef]

1996 (1)

P. Sprangle, E. Esarey, and J. Krall, 'Laser driven electron acceleration in vacuum, gases, and plasmas,' Phys. Plasmas 3, 2183-2190 (1996).
[CrossRef]

1993 (2)

C. G. Durfee III and H. M. Milchberg, 'Light pipe for high intensity laser pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

X. L. Chen and R. N. Sudan, 'Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma,' Phys. Rev. Lett. 70, 2082-2085 (1993).
[CrossRef] [PubMed]

1988 (1)

1985 (1)

H. Hora, 'The transient electrodynamic forces at laser-plasma interaction,' Phys. Fluids 28, 3705-3706 (1985).
[CrossRef]

1975 (1)

1974 (1)

K. A. Brueckner and S. Jorna, 'Laser-driven fusion,' Rev. Mod. Phys. 46, 325-367 (1974).
[CrossRef]

1966 (1)

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Amiranoff, F.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

Antonsen, T. M.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

Antonsen, Thomas M.

P. Chessa, P. Mora, and Thomas M. Antonsen, Jr., 'Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma,' Phys. Plasmas 5, 3451-3458 (1998).
[CrossRef]

Barov, N.

H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
[CrossRef] [PubMed]

Brueckner, K. A.

K. A. Brueckner and S. Jorna, 'Laser-driven fusion,' Rev. Mod. Phys. 46, 325-367 (1974).
[CrossRef]

Bulanov, S. V.

G. Mourou, T. Tajima, and S. V. Bulanov, 'Optics in the relativistic regime,' Rev. Mod. Phys. 78, 309-371 (2006).
[CrossRef]

Bychenkov, V. Yu.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Castillo, R.

F. Osman, R. Castillo, and H. Hora, 'Numerical programming of self-focusing at laser-plasma interaction,' Laser Part. Beams 18, 59-72 (2000).
[CrossRef]

Chang, C. L.

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

Chattopadhyay, S.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Chen, S. Y.

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

Chen, S.-Y.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Chen, X. L.

X. L. Chen and R. N. Sudan, 'Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma,' Phys. Rev. Lett. 70, 2082-2085 (1993).
[CrossRef] [PubMed]

Chessa, P.

P. Chessa, P. Mora, and Thomas M. Antonsen, Jr., 'Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma,' Phys. Plasmas 5, 3451-3458 (1998).
[CrossRef]

Chien, T. Y.

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

Close, D. H.

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Das, A.

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

David, P. G.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

Duda, B. J.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

Durfee, C. G.

C. G. Durfee III and H. M. Milchberg, 'Light pipe for high intensity laser pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

Esarey, E.

H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
[CrossRef] [PubMed]

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

E. Esarey, P. Sprangle, and J. Krall, 'Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,' IEEE J. Quantum Electron. 33, 1879-1914 (1997).
[CrossRef]

P. Sprangle, E. Esarey, and J. Krall, 'Laser driven electron acceleration in vacuum, gases, and plasmas,' Phys. Plasmas 3, 2183-2190 (1996).
[CrossRef]

Faure, J.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

Fedosejevs, R.

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

Feit, M. D.

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974).

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, 'Self-focusing of lasers in plasmas and semiconductors,' in Progress in Optics, Vol. XIII, E.Wolf, ed. (North-Holland, 1976), pp. 169-333.
[CrossRef]

Giuliano, C. R.

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Guo, K. Z.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Gupta, D. N.

D. N. Gupta, M. S. Hur, and H. Suk, 'Energy exchange during stimulated Raman scattering of a relativistic laser in a plasma,' J. Appl. Phys. 100, 103101 (2006).
[CrossRef]

D. N. Gupta and H. Suk, 'Frequency chirp for resonance-enhanced electron energy during laser acceleration,' Phys. Plasmas 13, 044507 (2006).
[CrossRef]

D. N. Gupta and A. K. Sharma, 'Transient self-focusing of an intense short pulse laser in magnetized plasma,' Phys. Scr. 66, 262-264 (2002).
[CrossRef]

Hafizi, B.

B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
[CrossRef]

Hauser, T.

Hellwarth, R. W.

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Hemker, R. G.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

Hess, L. D.

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Hora, H.

F. Osman, R. Castillo, and H. Hora, 'Numerical programming of self-focusing at laser-plasma interaction,' Laser Part. Beams 18, 59-72 (2000).
[CrossRef]

T. Hauser, W. Scheid, and H. Hora, 'Analytical calculation of relativistic self-focusing length in the WKB approximation,' J. Opt. Soc. Am. B 5, 2029-2034 (1988).
[CrossRef]

H. Hora, 'The transient electrodynamic forces at laser-plasma interaction,' Phys. Fluids 28, 3705-3706 (1985).
[CrossRef]

H. Hora, 'Theory of relativistic self-focusing of laser radiation in plasmas,' J. Opt. Soc. Am. 65, 882-886 (1975).
[CrossRef]

H. Hora, Physics of Laser Driven Plasmas (Wiley, 1981).

Hubbard, R. F.

B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
[CrossRef]

Hur, M. S.

D. N. Gupta, M. S. Hur, and H. Suk, 'Energy exchange during stimulated Raman scattering of a relativistic laser in a plasma,' J. Appl. Phys. 100, 103101 (2006).
[CrossRef]

Jha, P.

P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
[CrossRef]

Jorna, S.

K. A. Brueckner and S. Jorna, 'Laser-driven fusion,' Rev. Mod. Phys. 46, 325-367 (1974).
[CrossRef]

Katsouleas, T.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

Kaw, P. K.

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

Komashko, A. M.

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

Krall, J.

E. Esarey, P. Sprangle, and J. Krall, 'Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,' IEEE J. Quantum Electron. 33, 1879-1914 (1997).
[CrossRef]

P. Sprangle, E. Esarey, and J. Krall, 'Laser driven electron acceleration in vacuum, gases, and plasmas,' Phys. Plasmas 3, 2183-2190 (1996).
[CrossRef]

Kumar, G. R.

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

Lee, C. H.

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

Lee, P. B.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Leemans, W. B.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Lin, J. Y.

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

Liu, C. S.

V. K. Tripathi, T. Taguchi, and C. S. Liu, 'Plasma channel charging by an intense short pulse laser and ion Coulomb explosion,' Phys. Plasmas 12, 043106 (2005).
[CrossRef]

C. S. Liu and V. K. Tripathi, 'Relativistic laser guiding in an azimuthal magnetic field in a plasma,' Phys. Plasmas 8, 285-288 (2001).
[CrossRef]

C. S. Liu and V. K. Tripathi, Interaction of Electromagnetic Waves and Electron Beams with Plasmas (World Scientific, 1994).
[CrossRef]

Maksimchuk, A.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Malka, V.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

Marques, J. R.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

McClung, F. J.

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Milchberg, H. M.

C. G. Durfee III and H. M. Milchberg, 'Light pipe for high intensity laser pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

Mora, P.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

P. Chessa, P. Mora, and Thomas M. Antonsen, Jr., 'Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma,' Phys. Plasmas 5, 3451-3458 (1998).
[CrossRef]

Mori, W. B.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

Mourou, G.

G. Mourou, T. Tajima, and S. V. Bulanov, 'Optics in the relativistic regime,' Rev. Mod. Phys. 78, 309-371 (2006).
[CrossRef]

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Musher, S. L.

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

Novikov, V. N.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Osman, F.

F. Osman, R. Castillo, and H. Hora, 'Numerical programming of self-focusing at laser-plasma interaction,' Laser Part. Beams 18, 59-72 (2000).
[CrossRef]

Pant, H. C.

A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
[CrossRef]

A. Upadhyay, V. K. Tripathi, and H. C. Pant, 'Pulse front sharpening of a laser beam in plasma,' Phys. Scr. 63, 326-328 (2001).
[CrossRef]

Raj, G.

P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
[CrossRef]

Ren, C.

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

Resenzweig, J. B.

H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
[CrossRef] [PubMed]

Rousse, A.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

Rubenchik, A. M.

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

Sandhu, A. S.

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

Sarkisov, G. S.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Scheid, W.

Schroeder, C. B.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Sengupta, S.

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

Shadwick, B. A.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Sharma, A. K.

A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
[CrossRef]

D. N. Gupta and A. K. Sharma, 'Transient self-focusing of an intense short pulse laser in magnetized plasma,' Phys. Scr. 66, 262-264 (2002).
[CrossRef]

Sodha, M. S.

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, 'Self-focusing of lasers in plasmas and semiconductors,' in Progress in Optics, Vol. XIII, E.Wolf, ed. (North-Holland, 1976), pp. 169-333.
[CrossRef]

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974).

Sprangle, P.

B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
[CrossRef]

E. Esarey, P. Sprangle, and J. Krall, 'Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,' IEEE J. Quantum Electron. 33, 1879-1914 (1997).
[CrossRef]

P. Sprangle, E. Esarey, and J. Krall, 'Laser driven electron acceleration in vacuum, gases, and plasmas,' Phys. Plasmas 3, 2183-2190 (1996).
[CrossRef]

Sudan, R. N.

X. L. Chen and R. N. Sudan, 'Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma,' Phys. Rev. Lett. 70, 2082-2085 (1993).
[CrossRef] [PubMed]

Suk, H.

D. N. Gupta, M. S. Hur, and H. Suk, 'Energy exchange during stimulated Raman scattering of a relativistic laser in a plasma,' J. Appl. Phys. 100, 103101 (2006).
[CrossRef]

D. N. Gupta and H. Suk, 'Frequency chirp for resonance-enhanced electron energy during laser acceleration,' Phys. Plasmas 13, 044507 (2006).
[CrossRef]

H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
[CrossRef] [PubMed]

Ta Phuoc, K.

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

Taguchi, T.

V. K. Tripathi, T. Taguchi, and C. S. Liu, 'Plasma channel charging by an intense short pulse laser and ion Coulomb explosion,' Phys. Plasmas 12, 043106 (2005).
[CrossRef]

Tajima, T.

G. Mourou, T. Tajima, and S. V. Bulanov, 'Optics in the relativistic regime,' Rev. Mod. Phys. 78, 309-371 (2006).
[CrossRef]

Tikhonchuk, V. T.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Ting, A.

B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
[CrossRef]

Tripathi, V. K.

V. K. Tripathi, T. Taguchi, and C. S. Liu, 'Plasma channel charging by an intense short pulse laser and ion Coulomb explosion,' Phys. Plasmas 12, 043106 (2005).
[CrossRef]

A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
[CrossRef]

A. Upadhyay, V. K. Tripathi, and H. C. Pant, 'Pulse front sharpening of a laser beam in plasma,' Phys. Scr. 63, 326-328 (2001).
[CrossRef]

C. S. Liu and V. K. Tripathi, 'Relativistic laser guiding in an azimuthal magnetic field in a plasma,' Phys. Plasmas 8, 285-288 (2001).
[CrossRef]

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, 'Self-focusing of lasers in plasmas and semiconductors,' in Progress in Optics, Vol. XIII, E.Wolf, ed. (North-Holland, 1976), pp. 169-333.
[CrossRef]

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974).

C. S. Liu and V. K. Tripathi, Interaction of Electromagnetic Waves and Electron Beams with Plasmas (World Scientific, 1994).
[CrossRef]

Tsakiris, G. D.

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

Turitsyn, S. K.

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

Umstadter, D.

D. Umstadter, 'Review of physics and applications of relativistic plasmas driven by ultra-intense lasers,' Phys. Plasmas 8, 1774-1785 (2001).
[CrossRef]

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Upadhyay, A.

A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
[CrossRef]

A. Upadhyay, V. K. Tripathi, and H. C. Pant, 'Pulse front sharpening of a laser beam in plasma,' Phys. Scr. 63, 326-328 (2001).
[CrossRef]

Upadhyaya, A. K.

P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
[CrossRef]

Volfbeyn, P.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

Wadhwani, N.

P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
[CrossRef]

Wagner, R.

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

Wagner, W. G.

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

Wang, J.

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

Wang, X. F.

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

Wurtele, J. S.

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. Esarey, P. Sprangle, and J. Krall, 'Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,' IEEE J. Quantum Electron. 33, 1879-1914 (1997).
[CrossRef]

D. H. Close, C. R. Giuliano, R. W. Hellwarth, L. D. Hess, F. J. McClung, and W. G. Wagner, 'The self-focusing of light of different polarizations,' IEEE J. Quantum Electron. 2, 553-557 (1966).
[CrossRef]

J. Appl. Phys. (1)

D. N. Gupta, M. S. Hur, and H. Suk, 'Energy exchange during stimulated Raman scattering of a relativistic laser in a plasma,' J. Appl. Phys. 100, 103101 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Plasma Phys. (1)

A. Upadhyay, V. K. Tripathi, A. K. Sharma, and H. C. Pant, 'Asymmetric self-focusing of a laser pulse in plasma,' J. Plasma Phys. 68, 75-80 (2002).
[CrossRef]

Laser Part. Beams (1)

F. Osman, R. Castillo, and H. Hora, 'Numerical programming of self-focusing at laser-plasma interaction,' Laser Part. Beams 18, 59-72 (2000).
[CrossRef]

Phys. Fluids (1)

H. Hora, 'The transient electrodynamic forces at laser-plasma interaction,' Phys. Fluids 28, 3705-3706 (1985).
[CrossRef]

Phys. Plasmas (9)

V. K. Tripathi, T. Taguchi, and C. S. Liu, 'Plasma channel charging by an intense short pulse laser and ion Coulomb explosion,' Phys. Plasmas 12, 043106 (2005).
[CrossRef]

C. S. Liu and V. K. Tripathi, 'Relativistic laser guiding in an azimuthal magnetic field in a plasma,' Phys. Plasmas 8, 285-288 (2001).
[CrossRef]

D. N. Gupta and H. Suk, 'Frequency chirp for resonance-enhanced electron energy during laser acceleration,' Phys. Plasmas 13, 044507 (2006).
[CrossRef]

D. Umstadter, 'Review of physics and applications of relativistic plasmas driven by ultra-intense lasers,' Phys. Plasmas 8, 1774-1785 (2001).
[CrossRef]

W. B. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, 'Laser-driven plasma-based accelerators: wake field excitation, channel guiding, and laser triggered particle injection,' Phys. Plasmas 5, 1615-1632 (1998).
[CrossRef]

P. Chessa, P. Mora, and Thomas M. Antonsen, Jr., 'Numerical simulation of short laser pulse relativistic self-focusing in underdense plasma,' Phys. Plasmas 5, 3451-3458 (1998).
[CrossRef]

J. Faure, V. Malka, J. R. Marques, P. G. David, F. Amiranoff, K. Ta Phuoc, and A. Rousse, 'Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas,' Phys. Plasmas 9, 756-759 (2002).
[CrossRef]

P. Jha, N. Wadhwani, G. Raj, and A. K. Upadhyaya, 'Relativistic and ponderomotive effects on laser plasma interaction dynamics,' Phys. Plasmas 11, 1834-1839 (2004).
[CrossRef]

P. Sprangle, E. Esarey, and J. Krall, 'Laser driven electron acceleration in vacuum, gases, and plasmas,' Phys. Plasmas 3, 2183-2190 (1996).
[CrossRef]

Phys. Rev. E (5)

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

G. S. Sarkisov, V. Yu. Bychenkov, V. N. Novikov, V. T. Tikhonchuk, A. Maksimchuk, S.-Y. Chen, R. Wagner, G. Mourou, and D. Umstadter, 'Self-focusing, channel formation, and high-energy ion generation in interaction of an intense short laser pulse with a He jet,' Phys. Rev. E 59, 7042-7054 (1999).
[CrossRef]

B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, 'Relativistic focusing and ponderomotive channeling of intense laser beams,' Phys. Rev. E 62, 4120-4125 (2000).
[CrossRef]

C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, 'Compressing and focusing a short laser pulse by a thin plasma lens,' Phys. Rev. E 63, 026411 (2001).
[CrossRef]

M. D. Feit, A. M. Komashko, S. L. Musher, A. M. Rubenchik, and S. K. Turitsyn, 'Electron cavitation and relativistic self-focusing in underdense plasma,' Phys. Rev. E 57, 7122-7125 (1998).
[CrossRef]

Phys. Rev. Lett. (5)

C. G. Durfee III and H. M. Milchberg, 'Light pipe for high intensity laser pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

X. L. Chen and R. N. Sudan, 'Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma,' Phys. Rev. Lett. 70, 2082-2085 (1993).
[CrossRef] [PubMed]

T. Y. Chien, C. L. Chang, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, 'Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp,' Phys. Rev. Lett. 94, 115003 (2005).
[CrossRef] [PubMed]

H. Suk, N. Barov, J. B. Resenzweig, and E. Esarey, 'Plasma electron trapping and acceleration in a plasma wake field using a density transition,' Phys. Rev. Lett. 86, 1011-1014 (2001).
[CrossRef] [PubMed]

A. S. Sandhu, G. R. Kumar, S. Sengupta, A. Das, and P. K. Kaw, 'Laser-pulse-induced second-harmonic and hard x-ray emission: role of plasma-wave breaking,' Phys. Rev. Lett. 95, 025005 (2005).
[CrossRef] [PubMed]

Phys. Scr. (2)

D. N. Gupta and A. K. Sharma, 'Transient self-focusing of an intense short pulse laser in magnetized plasma,' Phys. Scr. 66, 262-264 (2002).
[CrossRef]

A. Upadhyay, V. K. Tripathi, and H. C. Pant, 'Pulse front sharpening of a laser beam in plasma,' Phys. Scr. 63, 326-328 (2001).
[CrossRef]

Rev. Mod. Phys. (2)

G. Mourou, T. Tajima, and S. V. Bulanov, 'Optics in the relativistic regime,' Rev. Mod. Phys. 78, 309-371 (2006).
[CrossRef]

K. A. Brueckner and S. Jorna, 'Laser-driven fusion,' Rev. Mod. Phys. 46, 325-367 (1974).
[CrossRef]

Other (4)

H. Hora, Physics of Laser Driven Plasmas (Wiley, 1981).

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, 'Self-focusing of lasers in plasmas and semiconductors,' in Progress in Optics, Vol. XIII, E.Wolf, ed. (North-Holland, 1976), pp. 169-333.
[CrossRef]

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974).

C. S. Liu and V. K. Tripathi, Interaction of Electromagnetic Waves and Electron Beams with Plasmas (World Scientific, 1994).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Plasma density ( ω p ω 0 ) variation with normalized distance ( ξ ) . The normalized parameters are d = 10 and ω p 0 ω 0 = 0.2 .

Fig. 2
Fig. 2

Beam-width parameter ( f ) with the normalized propagation distance ( ξ ) with a plasma density ramp (gray curve) and without a plasma density ramp (black curve). The used numerical parameters are given in the text.

Equations (9)

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E L = x ̂ E 0 ( r , z , t ) exp [ i ( ω 0 t k 0 z ) ] ,
n 1 = n ( z ) [ 1 + 1 m ω p 2 ( z ) { m c 2 2 ( 1 + a 2 2 ) 1 2 } ] .
n 1 = n ( z ) [ 1 c 2 ω p 2 ( z ) r 0 2 f 2 a 2 ( 1 + a 2 2 ) 1 2 + c 2 ω p 2 ( z ) r 2 r 0 4 f 4 a 2 ( 1 + a 2 4 ) ( 1 + a 2 2 ) 3 2 ] .
ϵ = ϵ 0 + Φ r 2 ,
Φ = ω p 2 ( z ) 4 ω 0 2 a 0 2 f 4 ( 1 + a 0 2 2 f 2 ) 3 2 [ 1 + c 2 r 0 2 ω p 2 ( z ) f 2 8 + a 0 2 f 2 ( 1 + a 0 2 2 f 2 ) 1 2 ] ,
ϵ 0 = 1 ω p 2 ( z ) ω 0 2 ( 1 + a 0 2 2 f 2 ) 1 2 ,
2 E + ω 0 2 c 2 ϵ E = 0 .
k 0 2 A + 2 i k 0 A 2 A = ω 0 2 c 2 ϵ A .
2 f ξ 2 = 1 f 3 1 2 ( ϵ 0 ξ ) f ξ R d 0 2 f r 0 2 ( 1 ϵ 0 1 ) Φ ,

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