Abstract

We demonstrate that modulation instability gain of time-localized signals (i.e., pulsed signals) depends strongly on the third-order dispersion, contrary to the well-known case of time-extended signals (cw signals). This surprising contribution of an odd dispersion term on this four-photon-mixing process is established analytically and confirmed by numerical simulations.

© 2010 Optical Society of America

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2009

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

2008

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys.��78, 1135 (2008).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, th ed. (Academic, 2008).

2007

2003

1997

1996

1991

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveira-Neto, Phys. Rev. A��43, 6162 (1991).
[CrossRef] [PubMed]

1990

J. E. Rothenberg, Phys. Rev. A��42, 682 (1990).
[CrossRef] [PubMed]

1989

E. J. Greer, D. M. Patrick, P. G. Wigley, and J. R. Taylor, Electron. Lett.��25, 1246 (1989).
[CrossRef]

1986

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett.��135 (1986).
[CrossRef] [PubMed]

1982

R. H. Bjorkholm and J. E. Stolen, IEEE J. Quantum Electron.��18, 1062 (1982).
[CrossRef]

1967

T. B. Feir and J. E. Benjamin, J. Fluid Mech.��27, 417 (1967).
[CrossRef]

Agrawal, G.?P.

G. P. Agrawal, Nonlinear Fiber Optics, th ed. (Academic, 2008).

Akhmediev, N.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

Benjamin, J.?E.

T. B. Feir and J. E. Benjamin, J. Fluid Mech.��27, 417 (1967).
[CrossRef]

Bjorkholm, R.?H.

R. H. Bjorkholm and J. E. Stolen, IEEE J. Quantum Electron.��18, 1062 (1982).
[CrossRef]

Cavalcanti, S.?B.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveira-Neto, Phys. Rev. A��43, 6162 (1991).
[CrossRef] [PubMed]

Chiang, T.-K.

Coen, S.

Cressoni, J.?C.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveira-Neto, Phys. Rev. A��43, 6162 (1991).
[CrossRef] [PubMed]

da Cruz, H.?R.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveira-Neto, Phys. Rev. A��43, 6162 (1991).
[CrossRef] [PubMed]

Delage, L.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

Douay, M.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

Dudley, J.?M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys.��78, 1135 (2008).
[CrossRef]

Feir, T.?B.

T. B. Feir and J. E. Benjamin, J. Fluid Mech.��27, 417 (1967).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys.��78, 1135 (2008).
[CrossRef]

Gouveira-Neto, A.?S.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveira-Neto, Phys. Rev. A��43, 6162 (1991).
[CrossRef] [PubMed]

Greer, E.?J.

E. J. Greer, D. M. Patrick, P. G. Wigley, and J. R. Taylor, Electron. Lett.��25, 1246 (1989).
[CrossRef]

Haelterman, M.

Harvey, J.?D.

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett.��135 (1986).
[CrossRef] [PubMed]

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature��450, 1054 (2007).
[CrossRef] [PubMed]

Kagi, N.

Kazovsky, L.?G.

Knight, J.?C.

Kolobov, M.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature��450, 1054 (2007).
[CrossRef] [PubMed]

Kozyreff, G.

Kudlinski, A.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

Leonhardt, R.

Louvergneaux, E.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. Vladimirov, and M. Taki, Opt. Lett.��32, 662 (2007).
[CrossRef] [PubMed]

Marhic, M.?E.

Millot, G.

Millot, S.

S. Millot and G. Pitois, Opt. Commun.��226, 415 (2003).
[CrossRef]

Mussot, A.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. Vladimirov, and M. Taki, Opt. Lett.��32, 662 (2007).
[CrossRef] [PubMed]

Patrick, D.?M.

E. J. Greer, D. M. Patrick, P. G. Wigley, and J. R. Taylor, Electron. Lett.��25, 1246 (1989).
[CrossRef]

Pitois, G.

S. Millot and G. Pitois, Opt. Commun.��226, 415 (2003).
[CrossRef]

Pitois, S.

Reynaud, F.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature��450, 1054 (2007).
[CrossRef] [PubMed]

Rothenberg, J.?E.

J. E. Rothenberg, Phys. Rev. A��42, 682 (1990).
[CrossRef] [PubMed]

Russell, P.?St. J.

Solli, D.?R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature��450, 1054 (2007).
[CrossRef] [PubMed]

Stolen, J.?E.

R. H. Bjorkholm and J. E. Stolen, IEEE J. Quantum Electron.��18, 1062 (1982).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett.��135 (1986).
[CrossRef] [PubMed]

Taki, M.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. Vladimirov, and M. Taki, Opt. Lett.��32, 662 (2007).
[CrossRef] [PubMed]

Taylor, J.?R.

E. J. Greer, D. M. Patrick, P. G. Wigley, and J. R. Taylor, Electron. Lett.��25, 1246 (1989).
[CrossRef]

Tchofo Dinda, P.

Tlidi, M.

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett.��135 (1986).
[CrossRef] [PubMed]

Vladimirov, A.

Wadsworth, W.?J.

Wigley, P.?G.

E. J. Greer, D. M. Patrick, P. G. Wigley, and J. R. Taylor, Electron. Lett.��25, 1246 (1989).
[CrossRef]

Wong, G.?K. L.

Electron. Lett.

E. J. Greer, D. M. Patrick, P. G. Wigley, and J. R. Taylor, Electron. Lett.��25, 1246 (1989).
[CrossRef]

IEEE J. Quantum Electron.

R. H. Bjorkholm and J. E. Stolen, IEEE J. Quantum Electron.��18, 1062 (1982).
[CrossRef]

J. Fluid Mech.

T. B. Feir and J. E. Benjamin, J. Fluid Mech.��27, 417 (1967).
[CrossRef]

Nature

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature��450, 1054 (2007).
[CrossRef] [PubMed]

Opt. Commun.

S. Millot and G. Pitois, Opt. Commun.��226, 415 (2003).
[CrossRef]

Opt. Lett.

Phys. Lett. A

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, Phys. Lett. A��374, 691 (2009).
[CrossRef]

Phys. Rev. A

J. E. Rothenberg, Phys. Rev. A��42, 682 (1990).
[CrossRef] [PubMed]

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveira-Neto, Phys. Rev. A��43, 6162 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett.��135 (1986).
[CrossRef] [PubMed]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, Phys. Rev. Lett.��101, 113904 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys.��78, 1135 (2008).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, th ed. (Academic, 2008).

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Figures (3)

Fig. 1
Fig. 1

(a) MI gain (solid curve) for weak monochromatic signals launched inside an optical fiber with β 2 = 1.36 × 10 28 s 2 m , γ = 13 W km , L = 500 m with a continuous pump of 500 mW . The dashed curve corresponds to the input spectrum signal. (b) Comparison between analytical results and numerical simulations for an input Gaussian pulse of 0.95 ps of duration at FWHM and 2.1 nW of maximum power. The different pulses correspond to a logarithmic variation of the slope of the dispersion from 1 × 10 42 s 3 m to 1 × 10 39 s 3 m .

Fig. 2
Fig. 2

(a) Evolution of the gain of the maximum of the signal as a function of β 3 , solid curve for analytical results and circles for numerical simulations. The crosses represent the results of numerical simulations without pump plus 22 dB . (b) Solid curve, output pulses without pump with the same values of β 3 than in Fig. 1b and input one in dashed curves.

Fig. 3
Fig. 3

Evolution of the gain of the maximum of the pulse as a function of β 3 and of the pulse duration.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

E ( z , τ ) z = i β 2 2 2 E ( z , τ ) τ 2 + β 3 6 3 E ( z , τ ) τ 3 + i γ | E | 2 E ( z , τ ) ,
δ E 0 ( τ ) = δ E × exp [ ( τ 2 τ 0 ) 2 ] × exp ( i Ω c τ ) ,
E ( z , τ ) = 1 2 π 0 + E 0 ̃ ( Ω ) × exp { i [ Ω τ K ( Ω ) z ] } d Ω ,
K ( Ω ) = K C + | K ( Ω ) Ω | Ω = Ω C × ( Ω Ω C ) + 1 2 | 2 K ( Ω ) Ω 2 | Ω = Ω C × ( Ω Ω C ) 2 + O { ( Ω Ω C ) 3 } ,
E ( z , τ ) = 1 2 τ 0 τ 0 2 + i 1 2 K C z δ E × exp [ ( τ K C z ) 2 4 τ 0 2 + 2 i K C z ] × exp { i [ ( Ω τ K ( Ω ) z ) ] } .
G ( z ) = τ 0 2 4 ( τ 0 4 + 2 τ 0 2 | β 2 | z + z 2 β 2 2 + z 2 γ P 0 β 3 2 2 | β 2 | ) 1 2 × exp ( 2 γ P 0 z ) .

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