Abstract

We demonstrate that soliton perturbation theory, though widely used, predicts an incorrect phase distribution for solitons of stochastically driven nonlinear Schrödinger equations in physically relevant parameter regimes. We propose a simple variational model that accounts for the effect of radiation on phase evolution and correctly predicts its distribution.

© 2011 Optical Society of America

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  1. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  2. D. J. Kaup, Phys. Rev. A 44, 4582 (1991).
    [CrossRef] [PubMed]
  3. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).
  4. V. S. Grigoryan, C. R. Menyuk, and R.-M. Mu, J. Lightwave Technol. 17, 1347 (1999).
    [CrossRef]
  5. C. J. McKinstrie, C. Xie, and C. Xu, Opt. Lett. 28, 604 (2003).
    [CrossRef] [PubMed]
  6. X. Wei and X. Liu, Opt. Lett. 28, 2300 (2003).
    [CrossRef] [PubMed]
  7. J. Li, E. Spiller, and G. Biondini, Phys. Rev. A 75, 053805 (2007).
    [CrossRef]
  8. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  9. K.-P. Ho, IEEE J. Sel. Top. Quantum Electron. 10, 421 (2004).
    [CrossRef]
  10. R. O. Moore, G. Biondini, and W. L. Kath, SIAM Rev. 50, 523 (2008).
    [CrossRef]
  11. E. T. Spiller and G. Biondini, Phys. Rev. A 80, 011805 (2009).
    [CrossRef]
  12. I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
    [CrossRef]
  13. M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668(1998).
    [CrossRef]
  14. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  15. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 15, 1351 (1990).
    [CrossRef] [PubMed]
  16. T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, J. Comput. Phys. 114, 312 (1994).
    [CrossRef]
  17. M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
    [CrossRef]
  18. F. Ilday, F. Wise, and F. Kaertner, Opt. Express 12, 2731 (2004).
    [CrossRef] [PubMed]

2009 (1)

E. T. Spiller and G. Biondini, Phys. Rev. A 80, 011805 (2009).
[CrossRef]

2008 (2)

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

R. O. Moore, G. Biondini, and W. L. Kath, SIAM Rev. 50, 523 (2008).
[CrossRef]

2007 (1)

J. Li, E. Spiller, and G. Biondini, Phys. Rev. A 75, 053805 (2007).
[CrossRef]

2004 (2)

2003 (2)

1999 (1)

1998 (1)

1996 (1)

1994 (1)

T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, J. Comput. Phys. 114, 312 (1994).
[CrossRef]

1992 (1)

1991 (1)

D. J. Kaup, Phys. Rev. A 44, 4582 (1991).
[CrossRef] [PubMed]

1990 (1)

1986 (1)

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668(1998).
[CrossRef]

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Biondini, G.

E. T. Spiller and G. Biondini, Phys. Rev. A 80, 011805 (2009).
[CrossRef]

R. O. Moore, G. Biondini, and W. L. Kath, SIAM Rev. 50, 523 (2008).
[CrossRef]

J. Li, E. Spiller, and G. Biondini, Phys. Rev. A 75, 053805 (2007).
[CrossRef]

M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668(1998).
[CrossRef]

Gabitov, I. R.

Gordon, J. P.

Grigoryan, V. S.

Haus, H. A.

Ho, K.-P.

K.-P. Ho, IEEE J. Sel. Top. Quantum Electron. 10, 421 (2004).
[CrossRef]

Horikis, T. P.

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

Hou, T. Y.

T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, J. Comput. Phys. 114, 312 (1994).
[CrossRef]

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

Ilan, B.

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

Ilday, F.

Kaertner, F.

Kath, W. L.

R. O. Moore, G. Biondini, and W. L. Kath, SIAM Rev. 50, 523 (2008).
[CrossRef]

Kaup, D. J.

D. J. Kaup, Phys. Rev. A 44, 4582 (1991).
[CrossRef] [PubMed]

Li, J.

J. Li, E. Spiller, and G. Biondini, Phys. Rev. A 75, 053805 (2007).
[CrossRef]

Liu, X.

Lowengrub, J. S.

T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, J. Comput. Phys. 114, 312 (1994).
[CrossRef]

Matera, F.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

McKinstrie, C. J.

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

Menyuk, C. R.

Mollenauer, L. F.

Moore, R. O.

R. O. Moore, G. Biondini, and W. L. Kath, SIAM Rev. 50, 523 (2008).
[CrossRef]

Mu, R.-M.

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

Shelley, M. J.

T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, J. Comput. Phys. 114, 312 (1994).
[CrossRef]

Spiller, E.

J. Li, E. Spiller, and G. Biondini, Phys. Rev. A 75, 053805 (2007).
[CrossRef]

Spiller, E. T.

E. T. Spiller and G. Biondini, Phys. Rev. A 80, 011805 (2009).
[CrossRef]

Turitsyn, S. K.

Wei, X.

Wise, F.

Xie, C.

Xu, C.

IEEE J. Sel. Top. Quantum Electron. (1)

K.-P. Ho, IEEE J. Sel. Top. Quantum Electron. 10, 421 (2004).
[CrossRef]

J. Comput. Phys. (1)

T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, J. Comput. Phys. 114, 312 (1994).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (5)

J. Li, E. Spiller, and G. Biondini, Phys. Rev. A 75, 053805 (2007).
[CrossRef]

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

D. J. Kaup, Phys. Rev. A 44, 4582 (1991).
[CrossRef] [PubMed]

E. T. Spiller and G. Biondini, Phys. Rev. A 80, 011805 (2009).
[CrossRef]

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

SIAM Rev. (1)

R. O. Moore, G. Biondini, and W. L. Kath, SIAM Rev. 50, 523 (2008).
[CrossRef]

Other (1)

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

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Figures (1)

Fig. 1
Fig. 1

Top: Mean of phase versus number of simulation modes using the system Eq. (12) (solid lines) and Eq. (3) (markers) at z = 16 (squares), 28 (circles), and 40 (triangles) with d ^ = 5 . Bottom: Mean of phase versus transmission length using the system Eq. (12) (solid lines) and Eq. (3) (markers) for N = 256 (squares), 512 (circles), and 1024 (triangles) with d ^ = 5 . The dashed line is the first-order SPT approximation.

Equations (24)

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i u z + ( d 0 + 1 z p d 1 ( z ) ) u t t + | u | 2 u = R ^ ( z , t ) ,
d 1 ( z ) = [ d ^ 0 z < z p 4 d ^ z p 4 z < 3 z p 4 d ^ 3 z p 4 z < z p ] .
i u z + d 0 u t t + G ( t 1 , t 2 ) × u ( t + t 1 ) u ( t + t 2 ) u ¯ ( t + t 1 + t 2 ) d t 1 d t 2 R ( z , t ) ,
G ( t 1 , t 2 ) = e ( i ω 1 t 1 + i ω 2 t 2 ) ( 2 π ) 2 sinc ( d ^ ω 1 ω 2 2 ) d ω 1 d ω 2 .
L den = Im ( s s ¯ z ) + Im ( r r ¯ z ) d 0 ( | s t | 2 + | r t | 2 ) + 1 2 G ( t 1 , t 2 ) s ( t + t 1 ) s ( t + t 2 ) s ¯ ( t + t 1 + t 2 ) s ¯ ( t ) d t 1 d t 2 + 2 G ( t 1 , t 2 ) s ( t + t 1 ) s ¯ ( t ) r ( t + t 1 ) r ¯ ( t + t 1 + t 2 ) d t 1 d t 2 2 Re ( s ¯ R s ) 2 Re ( r ¯ R r ) ,
r = n = N / 2 + 1 N / 2 α n ( z ) exp ( i ω n t ) H ( w | t | ) ,
L avg ( α , α ˙ , p , p ˙ ) = L den ( s ( t , p ( z ) ) , r ( t , α ( z ) ) ) d t ,
s = A sech [ A ( t T ) ] exp ( i Ω t + i Φ )
A ˙ = σ f A ( z ) ,
Ω ˙ = σ f Ω ( z ) ,
T ˙ = Ω + σ f T ( z ) ,
Φ ˙ = 1 2 ( A 2 Ω 2 ) T Ω ˙ + 2 n | α n | 2 + σ f Φ ( z ) ,
α ˙ n = i ( 2 A 2 w 1 2 ω n 2 ) α n + σ f α n ( z ) .
Φ σ 0 z W A ( s ) d s + σ W Φ ( z ) + N σ 2 z 2 2 w ,
s = B W exp ( ( t T ) 2 2 W 2 + i C ( t T ) 2 2 W 2 + i Ω t + i Φ ) ,
B ˙ = σ f B ( z ) ,
Ω ˙ = σ f Ω ( z ) ,
T ˙ = 2 d 0 Ω + σ f T ( z ) ,
W ˙ = 2 d 0 C W B W 2 K C + σ f W ( z ) ,
C ˙ = 2 d 0 C 2 W 2 + 2 d 0 W 2 + B W 2 K W + σ f C ( z ) ,
Φ ˙ = d 0 Ω 2 d 0 W 2 + B 2 K B W 4 2 K W B C 2 2 K C + 2 n | α n | 2 + σ f Φ ( z ) ,
α ˙ n = 2 i ( π B w d 0 ω n 2 ) α n + σ f α n ( z ) ,
K ( W , C ) = 1 d ^ W 1 + C 2 ln ( κ 2 + 1 κ κ + 2 + 1 κ + )
κ ± = C ± 1 + C 2 2 W 2 d ^ .

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