Abstract

A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in nonlinear Kerr media, and an extended phase-space evolution equation is derived along with invariant quantities. The formalism is additionally used to analyze the modulational instability.

© 2013 Optical Society of America

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  1. M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
    [CrossRef]
  2. H.-W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147–211 (1995).
    [CrossRef]
  3. W. P. Schleich, Quantum Optics in Phase Space (Wiley, 2011).
  4. P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
    [CrossRef]
  5. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [CrossRef]
  6. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
    [CrossRef]
  7. P. K. Shukla and B. Eliasson, “Nonlinear aspects of quantum plasma physics,” Phys. Usp. 53, 51–76 (2010).
    [CrossRef]
  8. M. Marklund and G. Brodin, “Dynamics of spin-1/2 quantum plasmas,” Phys. Rev. Lett. 98, 025001 (2007).
    [CrossRef]
  9. G. Brodin and M. Marklund, “Spin magnetohydrodynamics,” New J. Phys. 9, 277 (2007).
    [CrossRef]
  10. S. M. Mahajan and F. A. Asenjo, “Vortical dynamics of spinning quantum plasmas: helicity conservation,” Phys. Rev. Lett. 107, 195003 (2011).
    [CrossRef]
  11. G. Brodin and M. Marklund, “On the possibility of metamaterial properties in spin plasmas,” New J. Phys. 10, 115031 (2008).
    [CrossRef]
  12. M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E 76, 067401 (2007).
    [CrossRef]
  13. S. Braun, F. A. Asenjo, and S. M. Mahajan, “Spin gradient driven light amplification in a quantum plasmas,” Phys. Rev. Lett.109, 175003 (2012).
    [CrossRef]
  14. J. Lundin and G. Brodin, “A linearized kinetic theory of spin-1/2 particles in magnetized plasmas,” Phys. Rev. E 82, 056407 (2010).
    [CrossRef]
  15. C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation (Springer Verlag, 1999), pp. 3–7.
  16. A. Scott, Nonlinear Science (Oxford University, 2003), pp. 88–92.
  17. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [CrossRef]
  18. P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
    [CrossRef]
  19. M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78, 591–640 (2006).
    [CrossRef]
  20. G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
    [CrossRef]
  21. A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer Verlag, 2002).
  22. L. Stenflo and M. Marklund, “Rogue waves in the atmosphere,” J. Plasma Phys. 76, 293–295 (2010).
    [CrossRef]
  23. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982), pp. 237–242, 511–514.
  24. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
    [CrossRef]
  25. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007), pp. 180–191.
  26. J. D. Jackson, Classical Electrodynamics (Wiley, 1999), pp. 299–302.
  27. M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), pp. 31–33.
  28. J. Zamanian, M. Marklund, and G. Brodin, “Scalar quantum kinetic theory for spin-1/2 particles: mean field theory,” New J. Phys. 12, 043019 (2010).
    [CrossRef]
  29. A. Luis, “Scalar Wigner function for vectorial fields and spatial-angular Stokes parameters,” Opt. Commun. 246, 437–443 (2005).
    [CrossRef]
  30. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
    [CrossRef]
  31. D. Dragoman, “Wigner distribution function in nonlinear optics,” Appl. Opt. 35, 4142–4146 (1996).
    [CrossRef]
  32. T. Hansson, M. Lisak, and D. Anderson, “Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media,” Phys. Rev. Lett. 108, 063901 (2012).
    [CrossRef]
  33. L. Silva and J. T. Mendonca, “Photon kinetic theory of self-phase modulation,” Opt. Commun. 196, 285–291 (2001).
    [CrossRef]
  34. J. T. Mendonca, Theory of Photon Acceleration (Institute of Physics, 2001), pp. 67–96.
  35. M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).
  36. S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
    [CrossRef]
  37. V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
    [CrossRef]

2012

T. Hansson, M. Lisak, and D. Anderson, “Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media,” Phys. Rev. Lett. 108, 063901 (2012).
[CrossRef]

2011

S. M. Mahajan and F. A. Asenjo, “Vortical dynamics of spinning quantum plasmas: helicity conservation,” Phys. Rev. Lett. 107, 195003 (2011).
[CrossRef]

2010

P. K. Shukla and B. Eliasson, “Nonlinear aspects of quantum plasma physics,” Phys. Usp. 53, 51–76 (2010).
[CrossRef]

J. Lundin and G. Brodin, “A linearized kinetic theory of spin-1/2 particles in magnetized plasmas,” Phys. Rev. E 82, 056407 (2010).
[CrossRef]

L. Stenflo and M. Marklund, “Rogue waves in the atmosphere,” J. Plasma Phys. 76, 293–295 (2010).
[CrossRef]

J. Zamanian, M. Marklund, and G. Brodin, “Scalar quantum kinetic theory for spin-1/2 particles: mean field theory,” New J. Phys. 12, 043019 (2010).
[CrossRef]

2008

G. Brodin and M. Marklund, “On the possibility of metamaterial properties in spin plasmas,” New J. Phys. 10, 115031 (2008).
[CrossRef]

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

2007

M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E 76, 067401 (2007).
[CrossRef]

M. Marklund and G. Brodin, “Dynamics of spin-1/2 quantum plasmas,” Phys. Rev. Lett. 98, 025001 (2007).
[CrossRef]

G. Brodin and M. Marklund, “Spin magnetohydrodynamics,” New J. Phys. 9, 277 (2007).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

2006

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78, 591–640 (2006).
[CrossRef]

2005

A. Luis, “Scalar Wigner function for vectorial fields and spatial-angular Stokes parameters,” Opt. Commun. 246, 437–443 (2005).
[CrossRef]

2004

2003

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

2002

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

2001

L. Silva and J. T. Mendonca, “Photon kinetic theory of self-phase modulation,” Opt. Commun. 196, 285–291 (2001).
[CrossRef]

1996

D. Dragoman, “Wigner distribution function in nonlinear optics,” Appl. Opt. 35, 4142–4146 (1996).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef]

1995

H.-W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147–211 (1995).
[CrossRef]

1989

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
[CrossRef]

1988

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
[CrossRef]

1984

M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
[CrossRef]

1932

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007), pp. 180–191.

Anderson, D.

T. Hansson, M. Lisak, and D. Anderson, “Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media,” Phys. Rev. Lett. 108, 063901 (2012).
[CrossRef]

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Asenjo, F. A.

S. M. Mahajan and F. A. Asenjo, “Vortical dynamics of spinning quantum plasmas: helicity conservation,” Phys. Rev. Lett. 107, 195003 (2011).
[CrossRef]

S. Braun, F. A. Asenjo, and S. M. Mahajan, “Spin gradient driven light amplification in a quantum plasmas,” Phys. Rev. Lett.109, 175003 (2012).
[CrossRef]

Auffeves, A.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Barnett, S.

Bertet, P.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), pp. 31–33.

Braun, S.

S. Braun, F. A. Asenjo, and S. M. Mahajan, “Spin gradient driven light amplification in a quantum plasmas,” Phys. Rev. Lett.109, 175003 (2012).
[CrossRef]

Brodin, G.

J. Zamanian, M. Marklund, and G. Brodin, “Scalar quantum kinetic theory for spin-1/2 particles: mean field theory,” New J. Phys. 12, 043019 (2010).
[CrossRef]

J. Lundin and G. Brodin, “A linearized kinetic theory of spin-1/2 particles in magnetized plasmas,” Phys. Rev. E 82, 056407 (2010).
[CrossRef]

G. Brodin and M. Marklund, “On the possibility of metamaterial properties in spin plasmas,” New J. Phys. 10, 115031 (2008).
[CrossRef]

M. Marklund and G. Brodin, “Dynamics of spin-1/2 quantum plasmas,” Phys. Rev. Lett. 98, 025001 (2007).
[CrossRef]

G. Brodin and M. Marklund, “Spin magnetohydrodynamics,” New J. Phys. 9, 277 (2007).
[CrossRef]

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

Brune, M.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Courtial, J.

Dodd, R. K.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982), pp. 237–242, 511–514.

Dragoman, D.

Eilbeck, J. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982), pp. 237–242, 511–514.

Eliasson, B.

P. K. Shukla and B. Eliasson, “Nonlinear aspects of quantum plasma physics,” Phys. Usp. 53, 51–76 (2010).
[CrossRef]

M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E 76, 067401 (2007).
[CrossRef]

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef]

Fedele, R.

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Franke-Arnold, S.

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef]

Gibbon, J. D.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982), pp. 237–242, 511–514.

Gibson, G.

Hall, B.

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Hansson, T.

T. Hansson, M. Lisak, and D. Anderson, “Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media,” Phys. Rev. Lett. 108, 063901 (2012).
[CrossRef]

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

Haroche, S.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Hasegawa, A.

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer Verlag, 2002).

Heckenberg, N. R.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef]

Helczynski-Wolf, L.

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

Hillery, M.

M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), pp. 299–302.

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Johannisson, P.

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Kourakis, I.

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

Lee, H.-W.

H.-W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147–211 (1995).
[CrossRef]

Lisak, M.

T. Hansson, M. Lisak, and D. Anderson, “Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media,” Phys. Rev. Lett. 108, 063901 (2012).
[CrossRef]

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Luis, A.

A. Luis, “Scalar Wigner function for vectorial fields and spatial-angular Stokes parameters,” Opt. Commun. 246, 437–443 (2005).
[CrossRef]

Lundin, J.

J. Lundin and G. Brodin, “A linearized kinetic theory of spin-1/2 particles in magnetized plasmas,” Phys. Rev. E 82, 056407 (2010).
[CrossRef]

Mahajan, S. M.

S. M. Mahajan and F. A. Asenjo, “Vortical dynamics of spinning quantum plasmas: helicity conservation,” Phys. Rev. Lett. 107, 195003 (2011).
[CrossRef]

S. Braun, F. A. Asenjo, and S. M. Mahajan, “Spin gradient driven light amplification in a quantum plasmas,” Phys. Rev. Lett.109, 175003 (2012).
[CrossRef]

Maioli, P.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Marklund, M.

L. Stenflo and M. Marklund, “Rogue waves in the atmosphere,” J. Plasma Phys. 76, 293–295 (2010).
[CrossRef]

J. Zamanian, M. Marklund, and G. Brodin, “Scalar quantum kinetic theory for spin-1/2 particles: mean field theory,” New J. Phys. 12, 043019 (2010).
[CrossRef]

G. Brodin and M. Marklund, “On the possibility of metamaterial properties in spin plasmas,” New J. Phys. 10, 115031 (2008).
[CrossRef]

M. Marklund and G. Brodin, “Dynamics of spin-1/2 quantum plasmas,” Phys. Rev. Lett. 98, 025001 (2007).
[CrossRef]

M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E 76, 067401 (2007).
[CrossRef]

G. Brodin and M. Marklund, “Spin magnetohydrodynamics,” New J. Phys. 9, 277 (2007).
[CrossRef]

M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78, 591–640 (2006).
[CrossRef]

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

Matsumoto, M.

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer Verlag, 2002).

Mendonca, J. T.

L. Silva and J. T. Mendonca, “Photon kinetic theory of self-phase modulation,” Opt. Commun. 196, 285–291 (2001).
[CrossRef]

J. T. Mendonca, Theory of Photon Acceleration (Institute of Physics, 2001), pp. 67–96.

Meunier, T.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Morris, H. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982), pp. 237–242, 511–514.

O’Connell, R. F.

M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
[CrossRef]

Osnaghi, S.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Österberg, U.

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

Padgett, M.

Pas’ko, V.

Raimond, J. M.

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef]

Schleich, W. P.

W. P. Schleich, Quantum Optics in Phase Space (Wiley, 2011).

Scott, A.

A. Scott, Nonlinear Science (Oxford University, 2003), pp. 88–92.

Scully, M. O.

M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
[CrossRef]

Semenov, V.

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

Semenov, V. E.

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Shukla, P. K.

P. K. Shukla and B. Eliasson, “Nonlinear aspects of quantum plasma physics,” Phys. Usp. 53, 51–76 (2010).
[CrossRef]

M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E 76, 067401 (2007).
[CrossRef]

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78, 591–640 (2006).
[CrossRef]

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Silva, L.

L. Silva and J. T. Mendonca, “Photon kinetic theory of self-phase modulation,” Opt. Commun. 196, 285–291 (2001).
[CrossRef]

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Stegeman, G. I.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
[CrossRef]

Stenflo, L.

L. Stenflo and M. Marklund, “Rogue waves in the atmosphere,” J. Plasma Phys. 76, 293–295 (2010).
[CrossRef]

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

Sulem, C.

C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation (Springer Verlag, 1999), pp. 3–7.

Sulem, P.-L.

C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation (Springer Verlag, 1999), pp. 3–7.

Trillo, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
[CrossRef]

Vasnetsov, M.

Wabnitz, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
[CrossRef]

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
[CrossRef]

Wigner, E.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Wigner, E. P.

M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), pp. 31–33.

Wright, E. M.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
[CrossRef]

Zamanian, J.

J. Zamanian, M. Marklund, and G. Brodin, “Scalar quantum kinetic theory for spin-1/2 particles: mean field theory,” New J. Phys. 12, 043019 (2010).
[CrossRef]

Appl. Opt.

J. Phys. A

V. Semenov, M. Lisak, D. Anderson, T. Hansson, L. Helczynski-Wolf, and U. Österberg, “Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media,” J. Phys. A 41, 335207 (2008).
[CrossRef]

J. Plasma Phys.

L. Stenflo and M. Marklund, “Rogue waves in the atmosphere,” J. Plasma Phys. 76, 293–295 (2010).
[CrossRef]

Nature

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

New J. Phys.

G. Brodin and M. Marklund, “Spin magnetohydrodynamics,” New J. Phys. 9, 277 (2007).
[CrossRef]

G. Brodin and M. Marklund, “On the possibility of metamaterial properties in spin plasmas,” New J. Phys. 10, 115031 (2008).
[CrossRef]

J. Zamanian, M. Marklund, and G. Brodin, “Scalar quantum kinetic theory for spin-1/2 particles: mean field theory,” New J. Phys. 12, 043019 (2010).
[CrossRef]

Opt. Commun.

A. Luis, “Scalar Wigner function for vectorial fields and spatial-angular Stokes parameters,” Opt. Commun. 246, 437–443 (2005).
[CrossRef]

L. Silva and J. T. Mendonca, “Photon kinetic theory of self-phase modulation,” Opt. Commun. 196, 285–291 (2001).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarized soliton instability and branching in birefringent fibers,” Opt. Commun. 70, 166–172 (1989).
[CrossRef]

Opt. Express

Phys. Lett. A

G. Brodin, L. Stenflo, D. Anderson, M. Lisak, M. Marklund, and P. Johannisson, “Light bullets and optical collapse in vacuum,” Phys. Lett. A 306, 206–210 (2003).
[CrossRef]

Phys. Rep.

M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).
[CrossRef]

H.-W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147–211 (1995).
[CrossRef]

Phys. Rev.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Phys. Rev. A

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef]

Phys. Rev. E

M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E 76, 067401 (2007).
[CrossRef]

J. Lundin and G. Brodin, “A linearized kinetic theory of spin-1/2 particles in magnetized plasmas,” Phys. Rev. E 82, 056407 (2010).
[CrossRef]

Phys. Rev. Lett.

S. M. Mahajan and F. A. Asenjo, “Vortical dynamics of spinning quantum plasmas: helicity conservation,” Phys. Rev. Lett. 107, 195003 (2011).
[CrossRef]

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97, 094501 (2006).
[CrossRef]

M. Marklund and G. Brodin, “Dynamics of spin-1/2 quantum plasmas,” Phys. Rev. Lett. 98, 025001 (2007).
[CrossRef]

P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the Wigner-function of a one-photon Fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[CrossRef]

T. Hansson, M. Lisak, and D. Anderson, “Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media,” Phys. Rev. Lett. 108, 063901 (2012).
[CrossRef]

Phys. Scr.

M. Lisak, B. Hall, D. Anderson, R. Fedele, V. E. Semenov, P. K. Shukla, and A. Hasegawa, “Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method,” Phys. Scr. 98, 12–17 (2002).

Phys. Usp.

P. K. Shukla and B. Eliasson, “Nonlinear aspects of quantum plasma physics,” Phys. Usp. 53, 51–76 (2010).
[CrossRef]

Rev. Mod. Phys.

M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78, 591–640 (2006).
[CrossRef]

Other

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer Verlag, 2002).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007), pp. 180–191.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), pp. 299–302.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), pp. 31–33.

C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation (Springer Verlag, 1999), pp. 3–7.

A. Scott, Nonlinear Science (Oxford University, 2003), pp. 88–92.

S. Braun, F. A. Asenjo, and S. M. Mahajan, “Spin gradient driven light amplification in a quantum plasmas,” Phys. Rev. Lett.109, 175003 (2012).
[CrossRef]

J. T. Mendonca, Theory of Photon Acceleration (Institute of Physics, 2001), pp. 67–96.

W. P. Schleich, Quantum Optics in Phase Space (Wiley, 2011).

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982), pp. 237–242, 511–514.

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Equations (33)

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i(ψ+z+1vg+ψ+x)+α22ψ+x2=β+2ψ++κ2ψ+γ[(1ν)|ψ+|2+(1+ν)|ψ|2]ψ+,
i(ψz+1vgψx)+α22ψx2=β2ψ+κ2ψ++γ[(1ν)|ψ|2+(1+ν)|ψ+|2]ψ,
L=n=+,{i2[(ψn*z+1vgnψn*x)ψnψn*(ψnz+1vgnψnx)]+α2|ψnx|2+βn2|ψn|2+γ2(1ν)|ψn|4}+κ2(ψ+*ψ+ψ*ψ+)+γ(1+ν)|ψ+|2|ψ|2.
Wmn(x,p,z)=12πΓmn(x+ξ/2,xξ/2,z)eipξdξ,
Sj(x)=tr(Γmn(x1,x2)σj)|x1=x2=x
Sj(x)=tr(Wmnσj)dp
S0(x)=|ψ+|2(x)+|ψ|2(x),
S1(x)=2ψ+ψcos(δ)(x),
S2(x)=2ψ+ψsin(δ)(x),
S3(x)=|ψ+|2(x)|ψ|2(x),
W(x,p,z,s^)=m,n12[(1,s^)j·σj]mnWmn.
|ψ+|2=W(x,p,z,z^)dp
|ψ|2=W(x,p,z,z^)dp,
2W(x,p,z,x^)dp=|ψ+|2+|ψ|2+2ψ+ψcos(δ),
Wz+12[(1vg++1vg)+(1vg+1vg)[z^·s^+(s^·z^)(1s^·s^)]+2αp]Wx+[p(1vg+1vg)(s^×z^)s^×(κx^+Δβ2z^)]·s^W+2γν(|ψ+|2|ψ|2)[(s^×z^)·s^]cos(12xp)W2γ[(|ψ+|2+|ψ|2)ν(|ψ+|2|ψ|2)[z^·s^+(s^·z^)(1s^·s^)]]sin(12xp)W=0,
I0=|ψ+|2+|ψ|2=2W(x,p,z,0)dp=2(1s^·s^)Wdp
I3=|ψ+|2|ψ|2=2z^·s^Wdp.
E=(1s^·s^)Wdpdx=const.
M=p(1s^·s^)Wdpdx=const.
H=[αp2(1s^·s^)Wdp+Δβ2z^·s^Wdp+(1vg+1vg)pz^·s^Wdp+2γ((1s^·s^)Wdp)2+κx^·s^Wdp2γν(z^·s^Wdp)2]dx=const.
dWdζ=0
ddζz+χ^·s^+fpxfxp,
f=12(1vg++1vg)p+12αp2+γI0+[12(1vg+1vg)pγνI3][z^·s^+(s^·z^)(1s^·s^)]
χ^=s^×{κx^+[Δβ2p(1vg+1vg)2γνI3]z^}.
Wz+s^·(χ^W)+x(fpW)p(fxW)=0,
12γ(Δ(1s^·s^)W0η¯νΔ(1s^·s^)W0η4κ2/η¯)4γ2ν[Δ(1s^·s^)W0η¯Δ(1s^·s^)W0η4κ2/η¯Δz^·s^W0η¯Δz^·s^W0η4κ2/η¯]+2κγνΣx^·s^W0η24κ2¯(2γΔ(1s^·s^)W0η¯1)i4κγ2νΔy^·s^W0η24κ2¯Δz^·s^W0η¯=0,
W=I0(1sx)δ(p),
12γ(1ν)Δ(1s^·s^)W0η¯4γ2ν[(Δ(1s^·s^)W0η¯)2(Δz^·s^W0η¯)2]=0.
W0=12[(|ψ+|2+|ψ|2)+sx(ψ*ψ++ψ+*ψ)+isy(ψ*ψ+ψ+*ψ)+sz(|ψ+|2|ψ|2)]δ(p),
(1s^·s^)W0=12I0δ(p),z^·s^W0=12I3δ(p),
ω=kvg±|αk|2k2+2γα(1ν)I0±2γα(1+ν)2I024νI32.
Ω=|αk|22γα[(1+ν)2I024νI32(1ν)I0]k2.
Ω=|αk|22γα[(1ν)I0+(1+ν)2I024νI32]k2,

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