Abstract

An overdense plasma layer irradiated by intense light can exhibit dramatic nonlinear-optical effects due to a relativistic mass-effect of free electrons: highly-multiple hysteresises of reflection and transition, and emergence of immobile waves of large amplitude. Those are trapped quasi-soliton spikes sustained by a weak pumping having a tiny fraction of their peak intensity once they have been excited first by higher power pumping. The phenomenon persists even in the layers with ”soft”, wash-out boundaries, as well as in a semi-infinite plasma with low absorption.

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  1. A. E. Kaplan, “Hysteresis reflection and refraction by nonlinear boundary - a new class of effects in nonlinear optics,” JETP Lett.24, 114–119 (1976).
  2. A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Physics JETP45, 896–905 (1977).
  3. P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
    [CrossRef]
  4. P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
    [CrossRef]
  5. P. W. Smith and W. J. Tomlinson, “Nonlinear optical interfaces – switching behavior,” IEEE JQE20, 30–36 (1984).
    [CrossRef]
  6. S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
    [CrossRef]
  7. A. I. Akhiezer and R. V. Polovin, “Theory of wave motion of an electron plasma” Sov. Phys. JETP-USSR, 3, 696–705 (1956).
  8. C. Max and F. Perkins, “Strong electromagnetic waves in overdense plasmas” Phys. Rev. Lett., 27, 1342–1345 (1971).
    [CrossRef]
  9. J. H. Marburger and R. F. Tooper, “Nonlinear optical standing waves in overdense plasmas, ” Phys. Rev. Lett., 35, 1001–1004 (1975).
    [CrossRef]
  10. S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
    [CrossRef]
  11. T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
    [CrossRef]
  12. M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
    [CrossRef]
  13. T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
    [CrossRef]
  14. G. Lehmann, E. W. Laedke, and K. H. Spatchek, “Two-dimensional dynamics of relativistic solitons in cold plasmas,” Phys. Plasma15, 072307 (2008) and references therein
    [CrossRef]
  15. G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys.78, 309–371 (2006), and references therein.
    [CrossRef]
  16. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58, 160–163 (1987).
    [CrossRef] [PubMed]
  17. J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in periodic structure,” Opt. Lett.13, 132–133 (1988).
    [CrossRef] [PubMed]
  18. D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62, 1746 (1989).
    [CrossRef] [PubMed]
  19. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
    [CrossRef] [PubMed]
  20. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
    [CrossRef] [PubMed]
  21. O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
    [CrossRef]
  22. H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate four-wave mixing”, Appl. Phys. Lett.,36, 613–614 (1980).
    [CrossRef]
  23. A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quant. Electr., QE-21: 1529–1537 (1985).
    [CrossRef]
  24. D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
    [CrossRef] [PubMed]
  25. A. E. Kaplan and Y. J. Ding, “Hysteretic and multiphoton optical resonances of a single cyclotron electron,” IEEE JQE24, 1470–1482 (1988), and references therein.
    [CrossRef]
  26. A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
    [CrossRef]
  27. A. E. Kaplan, “Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron,” Phys. Rev. Lett.48, 138–141 (1982).
    [CrossRef]
  28. G. Gabrielse, H. Dehmelt, and W. Kells, “Observation of a relativistic bistable hysteresis in the cyclotron motion of a single electron,” Phys. Rev. Lett.54, 537–539 (1985).
    [CrossRef] [PubMed]
  29. A. E. Kaplan, “Relativistic nonlinear optics of a single cyclotron electron,” Phys. Rev. Lett.56: 456–459 (1986).
    [CrossRef] [PubMed]
  30. A. E. Kaplan and P. L. Shkolnikov, “Lasetron: a proposed source of powerful nuclear-time-scale electromagnetic bursts,” Phys. Rev. Lett.88, 074801(1–4), (2002).
    [CrossRef] [PubMed]
  31. R. J. Noble, “Plasma wave generation in the beat-wave accelerator,” Phys. Rev. A32, 460–471 (1985).
    [CrossRef] [PubMed]
  32. A. B. Shvartsburg, “Resonant Joule phenomena in a magnetoplasma”, Phys. Reports, 125, 187–252 (1985)
    [CrossRef]
  33. B. M. Ashkinadze and V. I. Yudson, “Hysteretic microwave cyclotron-like resonance in a laterally confined two-dimensional electron gas,” Phys. Rev. Lett.83, 812–815 (1999).
    [CrossRef]
  34. G. Shvets, “Beat-wave excitation of plasma waves based on relativistic bistability,” Phys. Rev. Lett.93, 195004 (2004).
    [CrossRef] [PubMed]
  35. B.Ya. Zeldovich, “Nonlinear optical effects and the conservation laws,” Brief Comm. Physics, Lebedev Inst. (FIAN), Moscow2(5), 20–25 (1970).
  36. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabri-Perot interferometer,” Phys. Rev. Lett.36, 1135–1138 (1976).
    [CrossRef]
  37. This suggests an explanation of a hysteresis lacking in [5]: an artificial nonlinearity used there was due to small dielectric particles suspended in a liquid and had large dissipation because of strong light scattering, vsthe experiments [3,4,6] with nearly transparent fluids.
  38. A. E. Kaplan, “Gradient marker” – a universal wave pattern in inhomogeneous continuum”, Phys. Rev. Lett.,109, 153901(1–5) (2012)
    [CrossRef]
  39. G. A. Askaryan, “Effects of the gradient of a strong electromagnetic beam on electrons and atoms” Sov. Phys., JETP-USSR, 15, 1088–1090 (1962).
  40. V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids” JETP Lett.3, 307–310 (1966).

2012 (1)

A. E. Kaplan, “Gradient marker” – a universal wave pattern in inhomogeneous continuum”, Phys. Rev. Lett.,109, 153901(1–5) (2012)
[CrossRef]

2008 (1)

G. Lehmann, E. W. Laedke, and K. H. Spatchek, “Two-dimensional dynamics of relativistic solitons in cold plasmas,” Phys. Plasma15, 072307 (2008) and references therein
[CrossRef]

2007 (1)

A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
[CrossRef]

2006 (1)

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys.78, 309–371 (2006), and references therein.
[CrossRef]

2004 (1)

G. Shvets, “Beat-wave excitation of plasma waves based on relativistic bistability,” Phys. Rev. Lett.93, 195004 (2004).
[CrossRef] [PubMed]

2003 (1)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

2002 (2)

A. E. Kaplan and P. L. Shkolnikov, “Lasetron: a proposed source of powerful nuclear-time-scale electromagnetic bursts,” Phys. Rev. Lett.88, 074801(1–4), (2002).
[CrossRef] [PubMed]

T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
[CrossRef]

2001 (1)

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

1999 (2)

B. M. Ashkinadze and V. I. Yudson, “Hysteretic microwave cyclotron-like resonance in a laterally confined two-dimensional electron gas,” Phys. Rev. Lett.83, 812–815 (1999).
[CrossRef]

O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
[CrossRef]

1998 (1)

T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
[CrossRef]

1996 (1)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

1992 (1)

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

1990 (1)

D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
[CrossRef] [PubMed]

1989 (2)

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62, 1746 (1989).
[CrossRef] [PubMed]

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

1988 (2)

J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in periodic structure,” Opt. Lett.13, 132–133 (1988).
[CrossRef] [PubMed]

A. E. Kaplan and Y. J. Ding, “Hysteretic and multiphoton optical resonances of a single cyclotron electron,” IEEE JQE24, 1470–1482 (1988), and references therein.
[CrossRef]

1987 (1)

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58, 160–163 (1987).
[CrossRef] [PubMed]

1986 (1)

A. E. Kaplan, “Relativistic nonlinear optics of a single cyclotron electron,” Phys. Rev. Lett.56: 456–459 (1986).
[CrossRef] [PubMed]

1985 (4)

R. J. Noble, “Plasma wave generation in the beat-wave accelerator,” Phys. Rev. A32, 460–471 (1985).
[CrossRef] [PubMed]

A. B. Shvartsburg, “Resonant Joule phenomena in a magnetoplasma”, Phys. Reports, 125, 187–252 (1985)
[CrossRef]

A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quant. Electr., QE-21: 1529–1537 (1985).
[CrossRef]

G. Gabrielse, H. Dehmelt, and W. Kells, “Observation of a relativistic bistable hysteresis in the cyclotron motion of a single electron,” Phys. Rev. Lett.54, 537–539 (1985).
[CrossRef] [PubMed]

1984 (1)

P. W. Smith and W. J. Tomlinson, “Nonlinear optical interfaces – switching behavior,” IEEE JQE20, 30–36 (1984).
[CrossRef]

1982 (1)

A. E. Kaplan, “Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron,” Phys. Rev. Lett.48, 138–141 (1982).
[CrossRef]

1981 (1)

P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
[CrossRef]

1980 (1)

H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate four-wave mixing”, Appl. Phys. Lett.,36, 613–614 (1980).
[CrossRef]

1979 (1)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
[CrossRef]

1977 (1)

A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Physics JETP45, 896–905 (1977).

1976 (2)

A. E. Kaplan, “Hysteresis reflection and refraction by nonlinear boundary - a new class of effects in nonlinear optics,” JETP Lett.24, 114–119 (1976).

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabri-Perot interferometer,” Phys. Rev. Lett.36, 1135–1138 (1976).
[CrossRef]

1975 (1)

J. H. Marburger and R. F. Tooper, “Nonlinear optical standing waves in overdense plasmas, ” Phys. Rev. Lett., 35, 1001–1004 (1975).
[CrossRef]

1971 (1)

C. Max and F. Perkins, “Strong electromagnetic waves in overdense plasmas” Phys. Rev. Lett., 27, 1342–1345 (1971).
[CrossRef]

1970 (1)

B.Ya. Zeldovich, “Nonlinear optical effects and the conservation laws,” Brief Comm. Physics, Lebedev Inst. (FIAN), Moscow2(5), 20–25 (1970).

1966 (1)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids” JETP Lett.3, 307–310 (1966).

1962 (1)

G. A. Askaryan, “Effects of the gradient of a strong electromagnetic beam on electrons and atoms” Sov. Phys., JETP-USSR, 15, 1088–1090 (1962).

1956 (1)

A. I. Akhiezer and R. V. Polovin, “Theory of wave motion of an electron plasma” Sov. Phys. JETP-USSR, 3, 696–705 (1956).

Aitchison, J. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

Akhiezer, A. I.

A. I. Akhiezer and R. V. Polovin, “Theory of wave motion of an electron plasma” Sov. Phys. JETP-USSR, 3, 696–705 (1956).

Anderson, D.

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

Ashkinadze, B. M.

B. M. Ashkinadze and V. I. Yudson, “Hysteretic microwave cyclotron-like resonance in a laterally confined two-dimensional electron gas,” Phys. Rev. Lett.83, 812–815 (1999).
[CrossRef]

Askaryan, G. A.

G. A. Askaryan, “Effects of the gradient of a strong electromagnetic beam on electrons and atoms” Sov. Phys., JETP-USSR, 15, 1088–1090 (1962).

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids” JETP Lett.3, 307–310 (1966).

Boyd, R. W.

D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
[CrossRef] [PubMed]

Bulanov, S. V.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys.78, 309–371 (2006), and references therein.
[CrossRef]

T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
[CrossRef]

T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
[CrossRef]

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

Cattani, F.

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

Chen, W.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58, 160–163 (1987).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62, 1746 (1989).
[CrossRef] [PubMed]

De Nicola, S.

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

Dehmelt, H.

G. Gabrielse, H. Dehmelt, and W. Kells, “Observation of a relativistic bistable hysteresis in the cyclotron motion of a single electron,” Phys. Rev. Lett.54, 537–539 (1985).
[CrossRef] [PubMed]

Ding, Y. J.

A. E. Kaplan and Y. J. Ding, “Hysteretic and multiphoton optical resonances of a single cyclotron electron,” IEEE JQE24, 1470–1482 (1988), and references therein.
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

Eremin, V. I.

A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
[CrossRef]

Esirkepov, T.

T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
[CrossRef]

Esirkepov, T. Z.

T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
[CrossRef]

Gabrielse, G.

G. Gabrielse, H. Dehmelt, and W. Kells, “Observation of a relativistic bistable hysteresis in the cyclotron motion of a single electron,” Phys. Rev. Lett.54, 537–539 (1985).
[CrossRef] [PubMed]

Gaeta, A. L.

D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
[CrossRef] [PubMed]

Gauthier, D. J.

D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
[CrossRef] [PubMed]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabri-Perot interferometer,” Phys. Rev. Lett.36, 1135–1138 (1976).
[CrossRef]

Hermann, J. P.

P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
[CrossRef]

Inovenkov, I. N.

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62, 1746 (1989).
[CrossRef] [PubMed]

Kamenets, F. F.

T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, “Gradient marker” – a universal wave pattern in inhomogeneous continuum”, Phys. Rev. Lett.,109, 153901(1–5) (2012)
[CrossRef]

A. E. Kaplan and P. L. Shkolnikov, “Lasetron: a proposed source of powerful nuclear-time-scale electromagnetic bursts,” Phys. Rev. Lett.88, 074801(1–4), (2002).
[CrossRef] [PubMed]

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

A. E. Kaplan and Y. J. Ding, “Hysteretic and multiphoton optical resonances of a single cyclotron electron,” IEEE JQE24, 1470–1482 (1988), and references therein.
[CrossRef]

A. E. Kaplan, “Relativistic nonlinear optics of a single cyclotron electron,” Phys. Rev. Lett.56: 456–459 (1986).
[CrossRef] [PubMed]

A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quant. Electr., QE-21: 1529–1537 (1985).
[CrossRef]

A. E. Kaplan, “Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron,” Phys. Rev. Lett.48, 138–141 (1982).
[CrossRef]

A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Physics JETP45, 896–905 (1977).

A. E. Kaplan, “Hysteresis reflection and refraction by nonlinear boundary - a new class of effects in nonlinear optics,” JETP Lett.24, 114–119 (1976).

Kells, W.

G. Gabrielse, H. Dehmelt, and W. Kells, “Observation of a relativistic bistable hysteresis in the cyclotron motion of a single electron,” Phys. Rev. Lett.54, 537–539 (1985).
[CrossRef] [PubMed]

Kim, A.

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

Kim, A. V.

A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
[CrossRef]

Kirsanov, V. I.

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

Korzhimanov, A. V.

A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
[CrossRef]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

Laedke, E. W.

G. Lehmann, E. W. Laedke, and K. H. Spatchek, “Two-dimensional dynamics of relativistic solitons in cold plasmas,” Phys. Plasma15, 072307 (2008) and references therein
[CrossRef]

Law, C. T.

A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quant. Electr., QE-21: 1529–1537 (1985).
[CrossRef]

Lehmann, G.

G. Lehmann, E. W. Laedke, and K. H. Spatchek, “Two-dimensional dynamics of relativistic solitons in cold plasmas,” Phys. Plasma15, 072307 (2008) and references therein
[CrossRef]

Lisak, M.

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

Malcut, M. S.

D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
[CrossRef] [PubMed]

Maloney, P. J.

P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
[CrossRef]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

Marburger, J. H.

H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate four-wave mixing”, Appl. Phys. Lett.,36, 613–614 (1980).
[CrossRef]

J. H. Marburger and R. F. Tooper, “Nonlinear optical standing waves in overdense plasmas, ” Phys. Rev. Lett., 35, 1001–1004 (1975).
[CrossRef]

Martellucci, S.

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

Max, C.

C. Max and F. Perkins, “Strong electromagnetic waves in overdense plasmas” Phys. Rev. Lett., 27, 1342–1345 (1971).
[CrossRef]

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabri-Perot interferometer,” Phys. Rev. Lett.36, 1135–1138 (1976).
[CrossRef]

Meystre, P.

O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
[CrossRef]

Mills, D. L.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58, 160–163 (1987).
[CrossRef] [PubMed]

Morandotti, R.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

Mormile, P.

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

Mourou, G. A.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys.78, 309–371 (2006), and references therein.
[CrossRef]

Naumova, N. M.

T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
[CrossRef]

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

Nishihara, K.

T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
[CrossRef]

Noble, R. J.

R. J. Noble, “Plasma wave generation in the beat-wave accelerator,” Phys. Rev. A32, 460–471 (1985).
[CrossRef] [PubMed]

Pegoraro, F.

T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
[CrossRef]

Perkins, F.

C. Max and F. Perkins, “Strong electromagnetic waves in overdense plasmas” Phys. Rev. Lett., 27, 1342–1345 (1971).
[CrossRef]

Pierattini, G.

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

Polovin, R. V.

A. I. Akhiezer and R. V. Polovin, “Theory of wave motion of an electron plasma” Sov. Phys. JETP-USSR, 3, 696–705 (1956).

Potting, S.

O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
[CrossRef]

Quartieri, J.

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

Sakharov, A. S.

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

Shkolnikov, P. L.

A. E. Kaplan and P. L. Shkolnikov, “Lasetron: a proposed source of powerful nuclear-time-scale electromagnetic bursts,” Phys. Rev. Lett.88, 074801(1–4), (2002).
[CrossRef] [PubMed]

Shvartsburg, A. B.

A. B. Shvartsburg, “Resonant Joule phenomena in a magnetoplasma”, Phys. Reports, 125, 187–252 (1985)
[CrossRef]

Shvets, G.

G. Shvets, “Beat-wave excitation of plasma waves based on relativistic bistability,” Phys. Rev. Lett.93, 195004 (2004).
[CrossRef] [PubMed]

Silberberg, Y.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in periodic structure,” Opt. Lett.13, 132–133 (1988).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

Smith, P. W.

P. W. Smith and W. J. Tomlinson, “Nonlinear optical interfaces – switching behavior,” IEEE JQE20, 30–36 (1984).
[CrossRef]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
[CrossRef]

Spatchek, K. H.

G. Lehmann, E. W. Laedke, and K. H. Spatchek, “Two-dimensional dynamics of relativistic solitons in cold plasmas,” Phys. Plasma15, 072307 (2008) and references therein
[CrossRef]

Tajima, T.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys.78, 309–371 (2006), and references therein.
[CrossRef]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids” JETP Lett.3, 307–310 (1966).

Tomlinson, W. J.

P. W. Smith and W. J. Tomlinson, “Nonlinear optical interfaces – switching behavior,” IEEE JQE20, 30–36 (1984).
[CrossRef]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
[CrossRef]

Tooper, R. F.

J. H. Marburger and R. F. Tooper, “Nonlinear optical standing waves in overdense plasmas, ” Phys. Rev. Lett., 35, 1001–1004 (1975).
[CrossRef]

Tushentsov, M.

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

Tushentsov, M. R.

A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
[CrossRef]

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabri-Perot interferometer,” Phys. Rev. Lett.36, 1135–1138 (1976).
[CrossRef]

Winful, H. G.

J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in periodic structure,” Opt. Lett.13, 132–133 (1988).
[CrossRef] [PubMed]

H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate four-wave mixing”, Appl. Phys. Lett.,36, 613–614 (1980).
[CrossRef]

Wright, E. M.

O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
[CrossRef]

Yudson, V. I.

B. M. Ashkinadze and V. I. Yudson, “Hysteretic microwave cyclotron-like resonance in a laterally confined two-dimensional electron gas,” Phys. Rev. Lett.83, 812–815 (1999).
[CrossRef]

Zeldovich, B.Ya.

B.Ya. Zeldovich, “Nonlinear optical effects and the conservation laws,” Brief Comm. Physics, Lebedev Inst. (FIAN), Moscow2(5), 20–25 (1970).

Zobay, O.

O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
[CrossRef]

Appl. Phys. B (1)

S. De Nicola, A. E. Kaplan, S. Martellucci, P. Mormile, G. Pierattini, and J. Quartieri, “Stable hysteretic reflection of light at a nonlinear interface,” Appl. Phys. B49, 441–444 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a non-linear interface,” Appl. Phys. Lett.35, 846–848 (1979).
[CrossRef]

Appl. Phys. Lett., (1)

H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate four-wave mixing”, Appl. Phys. Lett.,36, 613–614 (1980).
[CrossRef]

Brief Comm. Physics, Lebedev Inst. (FIAN), Moscow (1)

B.Ya. Zeldovich, “Nonlinear optical effects and the conservation laws,” Brief Comm. Physics, Lebedev Inst. (FIAN), Moscow2(5), 20–25 (1970).

IEEE J. Quant. Electr. (1)

A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quant. Electr., QE-21: 1529–1537 (1985).
[CrossRef]

IEEE JQE (3)

A. E. Kaplan and Y. J. Ding, “Hysteretic and multiphoton optical resonances of a single cyclotron electron,” IEEE JQE24, 1470–1482 (1988), and references therein.
[CrossRef]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, “Experimental studies of a non-linear interface,” IEEE JQE17, 340–348 (1981).
[CrossRef]

P. W. Smith and W. J. Tomlinson, “Nonlinear optical interfaces – switching behavior,” IEEE JQE20, 30–36 (1984).
[CrossRef]

J. Expr. Theor. Phys. (1)

A. V. Korzhimanov, V. I. Eremin, A. V. Kim, and M. R. Tushentsov, “Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma,” J. Expr. Theor. Phys., 105, 675–686 (2007)
[CrossRef]

JETP Lett. (3)

A. E. Kaplan, “Hysteresis reflection and refraction by nonlinear boundary - a new class of effects in nonlinear optics,” JETP Lett.24, 114–119 (1976).

T. Z. Esirkepov, F. F. Kamenets, S. V. Bulanov, and N. M. Naumova, “Low-frequency relativistic electromagnetic solitons in collisionless plasmas,” JETP Lett.68, 36–41 (1998).
[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids” JETP Lett.3, 307–310 (1966).

Opt. Lett. (1)

Phys. Fluids B (1)

S. V. Bulanov, I. N. Inovenkov, V. I. Kirsanov, N. M. Naumova, and A. S. Sakharov, “Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma,” Phys. Fluids B4, 1935–1942 (1992).
[CrossRef]

Phys. Plasma (1)

G. Lehmann, E. W. Laedke, and K. H. Spatchek, “Two-dimensional dynamics of relativistic solitons in cold plasmas,” Phys. Plasma15, 072307 (2008) and references therein
[CrossRef]

Phys. Reports (1)

A. B. Shvartsburg, “Resonant Joule phenomena in a magnetoplasma”, Phys. Reports, 125, 187–252 (1985)
[CrossRef]

Phys. Rev. A (2)

O. Zobay, S. Potting, P. Meystre, and E. M. Wright, “Creation of gap solitons in Bose-Einstein condensates,” Phys. Rev. A59, 643–648 (1999).
[CrossRef]

R. J. Noble, “Plasma wave generation in the beat-wave accelerator,” Phys. Rev. A32, 460–471 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett (2)

C. Max and F. Perkins, “Strong electromagnetic waves in overdense plasmas” Phys. Rev. Lett., 27, 1342–1345 (1971).
[CrossRef]

J. H. Marburger and R. F. Tooper, “Nonlinear optical standing waves in overdense plasmas, ” Phys. Rev. Lett., 35, 1001–1004 (1975).
[CrossRef]

Phys. Rev. Lett. (14)

M. Tushentsov, A. Kim, F. Cattani, D. Anderson, and M. Lisak, “Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions,” Phys. Rev. Lett.87, 275002 (2001).
[CrossRef]

T. Esirkepov, K. Nishihara, S. V. Bulanov, and F. Pegoraro, “Three-dimensional relativistic electromagnetic subcycle solitons,” Phys. Rev. Lett.89, 275002 (2002).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62, 1746 (1989).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett.76, 1627–1630 (1996).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90, 053902 (2003).
[CrossRef] [PubMed]

B. M. Ashkinadze and V. I. Yudson, “Hysteretic microwave cyclotron-like resonance in a laterally confined two-dimensional electron gas,” Phys. Rev. Lett.83, 812–815 (1999).
[CrossRef]

G. Shvets, “Beat-wave excitation of plasma waves based on relativistic bistability,” Phys. Rev. Lett.93, 195004 (2004).
[CrossRef] [PubMed]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabri-Perot interferometer,” Phys. Rev. Lett.36, 1135–1138 (1976).
[CrossRef]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58, 160–163 (1987).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcut, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams”, Phys. Rev. Lett.64, 1721–1724 (1990)
[CrossRef] [PubMed]

A. E. Kaplan, “Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron,” Phys. Rev. Lett.48, 138–141 (1982).
[CrossRef]

G. Gabrielse, H. Dehmelt, and W. Kells, “Observation of a relativistic bistable hysteresis in the cyclotron motion of a single electron,” Phys. Rev. Lett.54, 537–539 (1985).
[CrossRef] [PubMed]

A. E. Kaplan, “Relativistic nonlinear optics of a single cyclotron electron,” Phys. Rev. Lett.56: 456–459 (1986).
[CrossRef] [PubMed]

A. E. Kaplan and P. L. Shkolnikov, “Lasetron: a proposed source of powerful nuclear-time-scale electromagnetic bursts,” Phys. Rev. Lett.88, 074801(1–4), (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett., (1)

A. E. Kaplan, “Gradient marker” – a universal wave pattern in inhomogeneous continuum”, Phys. Rev. Lett.,109, 153901(1–5) (2012)
[CrossRef]

Rev. Mod. Phys. (1)

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys.78, 309–371 (2006), and references therein.
[CrossRef]

Sov. Phys. JETP-USSR (1)

A. I. Akhiezer and R. V. Polovin, “Theory of wave motion of an electron plasma” Sov. Phys. JETP-USSR, 3, 696–705 (1956).

Sov. Phys., JETP-USSR (1)

G. A. Askaryan, “Effects of the gradient of a strong electromagnetic beam on electrons and atoms” Sov. Phys., JETP-USSR, 15, 1088–1090 (1962).

Sov. Physics JETP (1)

A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Physics JETP45, 896–905 (1977).

Other (1)

This suggests an explanation of a hysteresis lacking in [5]: an artificial nonlinearity used there was due to small dielectric particles suspended in a liquid and had large dissipation because of strong light scattering, vsthe experiments [3,4,6] with nearly transparent fluids.

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Figures (3)

Fig. 1
Fig. 1

Hysteretic transmission of light through a plasma layer of thickness L. FT and NTR are full transparency and near total reflection limits. Points 1, 2, 3 mark a linear evanescent wave, 1-st, and 2-nd upper stable states respectively, and 4 – a QS sustained by a very low pumping. Arrows indicate direction of jumps within the lowest hysteretic loop. Inset: spatial amplitude profiles of waves corresponding to points 1–4 in the main plot.

Fig. 2
Fig. 2

Hysteretic transmission and reflection of light and multi-self-induced resonances at a plasma layer formed by a homogeneous, L-thick sub-layer, having plasma density ρ0, and two S-thick shoulders, with the plasma density, ρ, tapered smoothly to zero. FT marks full transparency. Inset: a spatial profile of normalized plasma density ρ(z)/ρ0.

Fig. 3
Fig. 3

Hysteretic absorption of light in a semi-infinite plasma layer with absorption α = 10−3. FA is a full absorption limit. Points 1, 2, 3 mark a linear evanescent wave, 1-st, and 2-nd upper stable states respectively. Arrows – the same as in Fig. 1. Inset: intensity profile; points and verticals 1–3 indicate locations of the plasma boundary for the respective points in the main plot; ◃’s show direction into plasma layer.

Equations (28)

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[ 2 2 / ( v t ) 2 ] ψ = k 0 2 f ( | ψ | 2 ) ψ ; f ( 0 ) = 1 .
2 + k 2 ε ( u 2 ) = 0 ; ε p l = 1 ω p l 2 ( u 2 ) / ω 2
ε r l = 1 [ ν 2 γ ( u 2 ) ] 1 with ν = ω / ( ω p l ) 0
+ ε ( ζ , u 2 ) = 0 ,
= u ( ζ ) exp [ i ϕ ( ζ ) ] .
P u 2 ϕ = inv .
u + u [ ε ( ζ , u 2 ) P 2 / u 4 ] = 0 ,
u 2 / 2 + U ( u 2 ) = W = inv , with U = 1 2 [ 0 u 2 ε ( u 2 ) d ( u 2 ) + P 2 / u 2 ] ,
U ( u 2 ) = ( u 2 + P 2 / u 2 ) / 2 [ γ ( u 2 ) 1 ] / ν 2 .
ζ = { 2 [ W U ( u 2 ) ] } 1 / 2 d u .
in , rfl = [ u ± ε in 1 / 2 ( P / u i u ) ] / 2 ;
trv = u trv exp ( i ϕ ζ ) , ϕ = ± ε ( u trv 2 ) ,
u 2 = 8 δ / cosh 2 [ ( ζ ζ p k ) 2 δ ]
u sol 2 = 4 ( 1 ν 2 ) / ν 4 ,
ε ( u pk 2 ) = ( 1 ν 2 ) / ( 2 ν 2 ) 0 .
u 2 u sol 2 cos 2 ( ζ ζ pk ) at u 2 > 1 .
P = u ex 2 u 2 u pk 2 8 δ + P / 2 δ
Λ / λ ln ( 16 δ / P ) / ( 2 π 2 δ )
u pk 2 / P 1 + ( 1 + P ) 2 , and Λ λ / 2 ,
Q = ( u in ) pk 2 ( u in ) min 2 exp ( 2 π L 2 δ / N λ ) 128 δ 1
1 ( u ex 2 ) min 1 4 ( u in 4 4 δ 2 ) + 1 u in 2
ε ( ζ , u 2 ) = 1 ρ ( ζ ) [ ρ 0 ν 2 γ ( u 2 ) ] 1
ρ ( z ) / ρ 0 = cos 2 [ π ( | z | L / 2 ) / 2 S ] at L / 2 < | z | L / 2 + S
ν 2 ν 2 ( 1 + i α ) ; with α = ( ω τ ) 1
α < α cr e δ if δ 1
u in 2 2 δ
u min 2 / u max 2 α / δ ; i . e . u min 2 8 α
L spc k 1 2 / δ [ 1 + ln ( δ / α ) ] if α δ 1

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