Abstract

We study the influence of third-order dispersion effects on the propagation of an incoherent nonlinear wave in an optical fiber system. The wave spectrum is shown to exhibit a highly asymmetric deformation characterized by a lateral spectral shoulder and the subsequent formation of an unexpected constant spectral pedestal. A kinetic approach to the problem reveals the existence of an invariant that explains in detail the essential properties of such asymmetric spectral evolution of the wave.

© 2010 Optical Society of America

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  13. A. Picozzi, Opt. Express 15, 9063 (2007).
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2010

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

2009

2008

A. Picozzi, Opt. Express 16, 17171 (2008).
[CrossRef] [PubMed]

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, Opt. Lett. 33, 2833 (2008).
[CrossRef] [PubMed]

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

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

D. Dylov and J. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

2007

S. Lagrange, H. R. Jauslin, and A. Picozzi, Europhys. Lett. 79, 64001 (2007).
[CrossRef]

A. Picozzi, Opt. Express 15, 9063 (2007).
[CrossRef] [PubMed]

2006

2004

V. E. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).
[CrossRef]

Ania-Castañón, J.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Babin, S.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Barviau, B.

Bortolozzo, U.

Coen, S.

Conti, C.

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Dias, F.

V. E. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).
[CrossRef]

Douay, M.

Dylov, D.

D. Dylov and J. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

Fleischer, J.

D. Dylov and J. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

Fratalocchi, A.

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Harper, P.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Jauslin, H. R.

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

S. Lagrange, H. R. Jauslin, and A. Picozzi, Europhys. Lett. 79, 64001 (2007).
[CrossRef]

Karalekas, V.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Kibler, B.

Kolobov, M.

Kudlinski, A.

Lagrange, S.

S. Lagrange, H. R. Jauslin, and A. Picozzi, Europhys. Lett. 79, 64001 (2007).
[CrossRef]

Lahini, Y.

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

Laurie, J.

Louvergneaux, E.

Mezentsev, V.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Millot, G.

Morandotti, R.

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

Mussot, A.

Nazarenko, S.

Picozzi, A.

Pitois, S.

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

Podivilov, E.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Pushkarev, A.

V. E. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).
[CrossRef]

Randoux, S.

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

B. Barviau, S. Randoux, and P. Suret, Opt. Lett. 31, 1696 (2006).
[CrossRef] [PubMed]

Residori, S.

Ruocco, G.

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Silberberg, Y.

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

Small, E.

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

Suret, P.

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

B. Barviau, S. Randoux, and P. Suret, Opt. Lett. 31, 1696 (2006).
[CrossRef] [PubMed]

Taki, M.

Trillo, S.

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Turitsyn, S.

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).
[CrossRef]

Europhys. Lett.

S. Lagrange, H. R. Jauslin, and A. Picozzi, Europhys. Lett. 79, 64001 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rep.

V. E. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).
[CrossRef]

Phys. Rev. A

S. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper, J. Ania-Castañón, and S. Turitsyn, Phys. Rev. A 77, 033803 (2008).
[CrossRef]

D. Dylov and J. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

Phys. Rev. Lett.

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

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

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

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

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Figures (2)

Fig. 1
Fig. 1

First stage of the spectral evolution obtained by integrating numerically the NLSE (1) (dotted curve) and the kinetic Eq. (3) (solid curve) for α = 0.05 (left column) and α = 0.1 (right column): (a), (b) at z = 30 ; (c), (d) at z = 2500 ( σ = 1 ). The dashed curve shows the initial condition ( z = 0 ). (e), (f) Corresponding invariant J ( ω ) determined from the initial condition (dashed curve) and obtained by solving the NLSE (1) at z = 2500 (solid curve).

Fig. 2
Fig. 2

(a) Second stage of the spectral evolution obtained by integrating numerically the NLSE (1) (dotted curve) and the kinetic Eq. (3) (solid curve) at z = 20000 and (b) for different propagation lengths: a constant spectral pedestal emerges in the tails of the spectrum ( α = 0.05 , σ = 1 ). The spectrum slowly relaxes toward the equilibrium state n eq ( ω ) given by Eq. (4) (solid curve). (c), (d) Equilibrium spectrum n eq ( ω ) [Eq. (4)] (solid curve), initial condition (dashed curve), and corresponding invariant | J ω | (dashed–dotted curve) for (c) α = 0.05 and (d) α = 0.08 : the invariant J ω determines the essential properties of n eq ( ω ) .

Equations (4)

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i z u = σ t 2 u + i α t 3 u + | u | 2 u .
J ( ω ) = n ( ω , z ) n ( q ω , z ) .
z n ( ω , z ) = 1 3 π | α | F [ n , J ] | ω ω 1 | | ω + ω 1 q | d ω 1 ,
n eq ( ω ) = J ω / 2 + [ 1 + 1 + λ 2 J ω 2 / 4 ] / λ .

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