Abstract

Spectral incoherent solitons (SIS) refer to an incoherent solitonic structure that only can be identified in the frequency domain and which is sustained by noninstantaneous Raman-like nonlinearities. We provide a generalized formulation of SIS by considering the generalized nonlinear Schrödinger equation. We show that nonlinear dispersive effects (e.g., self-steepening) dramatically affect the structure of SIS, in particular by significantly decelerating their spectral velocity in frequency space. The wave turbulence description of the problem reveals an underlying self-organization process: the soliton trajectory in frequency space is selected in such a way that it allows the system to self-organize into a stationary SIS state.

© 2014 Optical Society of America

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  1. A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).
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  5. Y. Silberberg, Y. Lahini, Y. Bromberg, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
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  6. P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
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  7. C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
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    [CrossRef]
  9. E. Turitsyna, S. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. Podivilov, D. Churkin, G. Falkovich, and S. Turitsyn, Nat. Photonics 7, 783 (2013).
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  16. S. Derevyanko and E. Small, Phys. Rev. A 85, 053816 (2012).
    [CrossRef]
  17. P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
    [CrossRef]
  18. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef]
  19. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef]
  20. B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
    [CrossRef]
  21. C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, Nat. Photonics 2, 371 (2008).
    [CrossRef]
  22. A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
    [CrossRef]
  23. C. Michel, B. Kibler, J. Garnier, and A. Picozzi, Phys. Rev. A 86, 041801(R) (2012).
    [CrossRef]
  24. J. Garnier and A. Picozzi, Phys. Rev. A 81, 033831 (2010).
    [CrossRef]
  25. C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
    [CrossRef]
  26. B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
    [CrossRef]
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    [CrossRef]
  29. J. Travers, M. Frosz, and J. Dudley, “Nonlinear fibre optics overview,” in Supercontinuum Generation in Optical Fibers, J. Dudley and J. R. Taylor, eds. (Cambridge University, 2010), p. 32.
  30. J. Laegsgaard, Opt. Express 15, 16110 (2007).
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  31. A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
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  32. A. A. Voronin, A. M. Zheltikov, and M. Aleksei, Opt. Lett. 33, 1723 (2008).
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  33. M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, Opt. Express 21, 31239 (2013).
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  34. S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
    [CrossRef]
  35. C. Montes, Phys. Rev. A 20, 1081 (1979).
    [CrossRef]

2013 (4)

E. Turitsyna, S. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. Podivilov, D. Churkin, G. Falkovich, and S. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, Phys. Rev. Lett. 111, 113902 (2013).
[CrossRef]

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, Opt. Express 21, 31239 (2013).
[CrossRef]

2012 (5)

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

C. Michel, B. Kibler, J. Garnier, and A. Picozzi, Phys. Rev. A 86, 041801(R) (2012).
[CrossRef]

M. Erkintalo, M. Surakka, J. Turunen, A. T. Friberg, and G. Genty, Opt. Lett. 37, 169 (2012).
[CrossRef]

S. Derevyanko and E. Small, Phys. Rev. A 85, 053816 (2012).
[CrossRef]

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

2011 (4)

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
[CrossRef]

2010 (4)

J. Garnier and A. Picozzi, Phys. Rev. A 81, 033831 (2010).
[CrossRef]

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

A. Piskarskas, V. Pyragaite, and A. Stabinis, Phys. Rev. A 82, 053817 (2010).
[CrossRef]

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

2009 (2)

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

Y. Silberberg, Y. Lahini, Y. Bromberg, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

2008 (5)

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, J. Opt. Soc. Am. B 25, 1780 (2008).
[CrossRef]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, Nat. Photonics 2, 371 (2008).
[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

A. A. Voronin, A. M. Zheltikov, and M. Aleksei, Opt. Lett. 33, 1723 (2008).
[CrossRef]

2007 (2)

2000 (1)

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

1997 (1)

A. Schwache and F. Mitschke, Phys. Rev. E 55, 7720 (1997).
[CrossRef]

1996 (1)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef]

1995 (1)

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
[CrossRef]

1989 (1)

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

1979 (1)

C. Montes, Phys. Rev. A 20, 1081 (1979).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

Aleksei, M.

Anderson, D.

Angelani, L.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Aschieri, P.

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

Babin, S.

E. Turitsyna, S. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. Podivilov, D. Churkin, G. Falkovich, and S. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

S. Babin, D. Churkin, A. Ismagulov, S. Kablukov, and E. Podivilov, J. Opt. Soc. Am. B 24, 1729 (2007).
[CrossRef]

Barviau, B.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

Biancalana, F.

Blow, K. J.

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Bortolozzo, U.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Bromberg, Y.

Y. Silberberg, Y. Lahini, Y. Bromberg, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

Chen, Z.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef]

Christodoulides, D.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).

Christodoulides, D. N.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Churkin, D.

E. Turitsyna, S. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. Podivilov, D. Churkin, G. Falkovich, and S. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

S. Babin, D. Churkin, A. Ismagulov, S. Kablukov, and E. Podivilov, J. Opt. Soc. Am. B 24, 1729 (2007).
[CrossRef]

Cohen, O.

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, Nat. Photonics 2, 371 (2008).
[CrossRef]

Conforti, M.

Conti, C.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Derevyanko, S.

S. Derevyanko and E. Small, Phys. Rev. A 85, 053816 (2012).
[CrossRef]

Doya, V.

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

Dudley, J.

J. Travers, M. Frosz, and J. Dudley, “Nonlinear fibre optics overview,” in Supercontinuum Generation in Optical Fibers, J. Dudley and J. R. Taylor, eds. (Cambridge University, 2010), p. 32.

Erkintalo, M.

Faccio, D.

Falkovich, G.

E. Turitsyna, S. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. Podivilov, D. Churkin, G. Falkovich, and S. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

Fischer, B.

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

Fratalocchi, A.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Friberg, A. T.

Frosz, M.

J. Travers, M. Frosz, and J. Dudley, “Nonlinear fibre optics overview,” in Supercontinuum Generation in Optical Fibers, J. Dudley and J. R. Taylor, eds. (Cambridge University, 2010), p. 32.

Garnier, J.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, Phys. Rev. Lett. 111, 113902 (2013).
[CrossRef]

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

C. Michel, B. Kibler, J. Garnier, and A. Picozzi, Phys. Rev. A 86, 041801(R) (2012).
[CrossRef]

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
[CrossRef]

J. Garnier and A. Picozzi, Phys. Rev. A 81, 033831 (2010).
[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).

Gat, O.

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

Genty, G.

Hansson, T.

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, J. Opt. Soc. Am. B 25, 1780 (2008).
[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).

Ismagulov, A.

Jauslin, H. R.

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

Kablukov, S.

Kibler, B.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

C. Michel, B. Kibler, J. Garnier, and A. Picozzi, Phys. Rev. A 86, 041801(R) (2012).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

Kudlinski, A.

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

Laegsgaard, J.

Lahini, Y.

Y. Silberberg, Y. Lahini, Y. Bromberg, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

Laurie, J.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Leonetti, M.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Lisak, M.

Marini, A.

Michel, C.

C. Michel, B. Kibler, J. Garnier, and A. Picozzi, Phys. Rev. A 86, 041801(R) (2012).
[CrossRef]

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

Millot, G.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).

Mitchell, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef]

Mitschke, F.

A. Schwache and F. Mitschke, Phys. Rev. E 55, 7720 (1997).
[CrossRef]

Montes, C.

C. Montes, Phys. Rev. A 20, 1081 (1979).
[CrossRef]

Morandotti, R.

Y. Silberberg, Y. Lahini, Y. Bromberg, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

Musher, S. L.

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
[CrossRef]

Nazarenko, S.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Österberg, U.

Picozzi, A.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, Phys. Rev. Lett. 111, 113902 (2013).
[CrossRef]

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

C. Michel, B. Kibler, J. Garnier, and A. Picozzi, Phys. Rev. A 86, 041801(R) (2012).
[CrossRef]

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

J. Garnier and A. Picozzi, Phys. Rev. A 81, 033831 (2010).
[CrossRef]

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).

Piskarskas, A.

A. Piskarskas, V. Pyragaite, and A. Stabinis, Phys. Rev. A 82, 053817 (2010).
[CrossRef]

Pitois, S.

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

Podivilov, E.

E. Turitsyna, S. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. Podivilov, D. Churkin, G. Falkovich, and S. Turitsyn, Nat. Photonics 7, 783 (2013).
[CrossRef]

S. Babin, D. Churkin, A. Ismagulov, S. Kablukov, and E. Podivilov, J. Opt. Soc. Am. B 24, 1729 (2007).
[CrossRef]

Pyragaite, V.

A. Piskarskas, V. Pyragaite, and A. Stabinis, Phys. Rev. A 82, 053817 (2010).
[CrossRef]

Randoux, S.

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.03.002 (to be published).

Residori, S.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Rotschild, C.

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, Nat. Photonics 2, 371 (2008).
[CrossRef]

Rubenchik, A. M.

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
[CrossRef]

Ruocco, G.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Schwache, A.

A. Schwache and F. Mitschke, Phys. Rev. E 55, 7720 (1997).
[CrossRef]

Schwartz, T.

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Figures (3)

Fig. 1.
Fig. 1.

Numerical simulations of the GNLSE [Eq. (1)] [left column (a) to (c)] and GKE [Eq. (2)] [right column (b) to (d)], for p=q=0 (Γ(ω)=γ0) [1st row, (a) to (b)], and for p=ω01, q=0.1ω01 [2nd row, (c) to (d)]. (e) to (f) Corresponding spectral profiles obtained by simulations of GNLSE [Eq. (1)] (gray line) and GKE [Eq. (2)] (red line) at z=200Lnl and z=600Lnl. The vertical dashed line denotes the physical zero frequency component, i.e., ω=ω0 [ω0/(2π)=282THz (λ0=1.06μm), η=2.6, τ0=β2Lnl/2, Lnl=1/(γ0P), where P is the average intensity of the incoherent wave].

Fig. 2.
Fig. 2.

Soliton trajectory Ωs versus z plotted from Eq. (8), in which V0 is given by Eq. (10): q=p=0, Ωs(z)=V0z (green); q=0, p=ω01 (red); q=0.2p, p=ω01 (black); q=0.2p, p=ω01 (blue). The corresponding crosses on the curves refer to the simulations of MGKE [Eq. (3)]; a quantitative agreement is obtained without adjustable parameters. The inset (a) compares the simulations of the MGKE [Eq. (3)] (green) and GNLSE [Eq. (1)] (gray) with the analytical SIS solution in Eqs. (9) and (10), in log10-scale. The superposition of five spectral profiles at z=200, 400, 600, 800, 1000 (in units of Lnl) has been plotted to stress the stationary character of the SIS solution obtained by simulation of MGKE [Eq. (3)]. The inset (b) shows the power decrease, N=|ψω|2dω versus z, in the GNLSE [Eq. (1)] (red), and the theoretical prediction in Eq. (7) (blue dashes) [ω0/(2π)=282THz, η=1].

Fig. 3.
Fig. 3.

Transition to a discrete behavior of generalized SIS in the presence of a small noise background, n0/nm0=107, nm0 being the initial spectral peak amplitude. Simulations of the (a) GNLSE [Eq. (1)] and (b) GKE [Eq. (2)] [ω0/(2π)=282THz, η=2.6, p=ω01, q=0.1ω01].

Equations (10)

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zψ˜ω(z)=ik(ω)ψ˜ωαψ˜ω(z)+iΓ(ω)F{ψR*|ψ|2},
znω=nωπG(ω,ω)nωdω,
zn˜ω=1πn˜ωΓ(ω)g(ωω)Γ(ω)n˜ωdω.
zn˜ΩzΩs(z)Ωn˜Ω=n˜Ωπg(ΩΩ)n˜Ω×Γ[Ω+Ωs(z)]Γ[Ω+Ωs(z)]dΩ,
zΩs(z)=V0Γ2(Ωs(z))/γ02,
V0Ωn˜Ωs=γ02πn˜Ωsg(ΩΩ)n˜ΩsdΩ.
N(z)=N˜Γ[Ωs(z)],
z(Ωs)=1V0(qp)3[2pqlog(1+qΩs1+pΩs)Qqp(Ωs)],
n˜Ωs=n0exp[log(nmn0)H(Ω)giωi],
V0=γ02π(n˜Ωsn0)dΩlog(n˜Ωs/n0)dΩH(Ω)dΩ.

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