Abstract

We consider the incoherent nonlinear regime of the supercontinuum generation process in optical fibers. We show that, under certain conditions, the phenomenon of spectral broadening inherent to the supercontinuum generation may be described by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the supercontinuum generation process may be regarded as a thermalization process, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state, i.e., the state of maximum nonequilibrium entropy.

© 2008 Optical Society of America

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  1. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, Opt. Express 12, 299 (2004).
    [CrossRef] [PubMed]

2008 (4)

2007 (4)

2006 (2)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

2005 (1)

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

2004 (2)

2003 (1)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

1995 (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

1992 (1)

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D 57, 96 (1992).
[CrossRef]

Abrardi, L.

Akhmediev, N.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Beaugeois, M.

Biancalana, F.

Birks, T. A.

Bouazaoui, M.

Coen, S.

G. Genty, S. Coen, and J. M. Dudley, J. Opt. Soc. Am. B 24, 1771 (2007).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Connaughton, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

Corredera, P.

Cumberland, B.

Dias, F.

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

Dudley, J. M.

G. Genty, S. Coen, and J. M. Dudley, J. Opt. Soc. Am. B 24, 1771 (2007).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Dyachenko, S.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D 57, 96 (1992).
[CrossRef]

Genty, G.

G. Genty, S. Coen, and J. M. Dudley, J. Opt. Soc. Am. B 24, 1771 (2007).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gonzalez-Herraez, M.

Jauslin, H. R.

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

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Joly, N.

Josserand, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Knight, J. C.

Lagrange, S.

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

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Luan, F.

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Martin-Lopez, S.

Millot, G.

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

Mussot, A.

Newell, A. C.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D 57, 96 (1992).
[CrossRef]

Picozzi, A.

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

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

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

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

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

Pitois, S.

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

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Pomeau, Y.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

Popov, S. V.

Pushkarev, A.

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

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D 57, 96 (1992).
[CrossRef]

Rica, S.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

Russell, P. St. J.

Skryabin, D. V.

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

Sylvestre, T.

Taylor, J. R.

Travers, J. C.

Wadsworth, W. J.

Zakharov, V.

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

Zakharov, V. E.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D 57, 96 (1992).
[CrossRef]

Europhys. Lett. (1)

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

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

Opt. Express (6)

Phys. Rep. (1)

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

Phys. Rev. A (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

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

Physica D (1)

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D 57, 96 (1992).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science (1)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, Science 301, 1705 (2003).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Predictions of the kinetic wave theory for fibers with two (left) and one (right) ZDW(s). (a) and (b), fiber dispersion curves β 2 ( ν ) [ ps 2 km 1 ] , ω = 2 π ν ; (c) and (d), linear dispersion relation k ( ν ) (dashed curve) and effective kinetic potential F ( ν ) (solid curve) ( km 1 ) ; (e) and (f), equilibrium spectra n eq ( ν ) [Eq. (2)]; (g) and (h), evolutions of the nonequilibrium entropies S ( z ) corresponding to the simulations of Figs. 2b, 3a, respectively [a thermal equilibrium state is reached only in (g)].

Fig. 2
Fig. 2

NLSE simulations showing the evolution of the spectrum of the field for the dispersion curve of Fig. 1a (a) with and (b) without Raman and shocks terms. The pump frequency is ν 0 = 280.4 THz ( γ = 23 W 1 km 1 ) . The dashed lines show the fiber ZDWs. The top part in (b) shows the corresponding equilibrium spectrum 10 log [ n eq ( ν ) ] [i.e., Eq. (2), ω = 2 π ν ].

Fig. 3
Fig. 3

NLSE simulations without Raman and shock terms for the dispersion curve of Fig. 1b with pump frequencies (a) close to and (b) far from the (unique) ZDW, ν 0 = 280.4 and 380.4 THz , respectively, with, on top, the corresponding equilibrium spectra 10 log [ n eq ( ν ) ] [Eq. (2), ω = 2 π ν ].

Equations (3)

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z n ( z , ω ) = Coll [ n ] ,
W = γ 2 π δ ( ω 1 + ω 2 ω 3 ω 4 ) δ [ k ( ω 1 ) + k ( ω 2 ) k ( ω 3 ) k ( ω 4 ) ] ,
n eq ( ω ) = T k ( ω ) + λ ω μ ,

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