Abstract

The evolution of the phase in a return-to-zero differential phase-shift keying system is studied by the generalized momentum method. The results show that phase fluctuation in the case of dispersion-managed solitons is much smaller than that in quasi-linear systems for a given launch power.

© 2005 Optical Society of America

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References

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  7. N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
    [CrossRef]

2004

K. P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
[CrossRef]

2003

2002

S. Kumar, J. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

1999

R. J. Essiambre, B. Mikkelson, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

1998

S. K. Turitsyn, T. Schaefer, and V. K. Mezentsev, Phys. Rev. E 58, R5264 (1998).
[CrossRef]

1997

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
[CrossRef]

1990

Chowdhury, D. Q.

S. Kumar, J. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Doran, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
[CrossRef]

Essiambre, R. J.

R. J. Essiambre, B. Mikkelson, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Forysiak, W.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
[CrossRef]

Gordon, J. P.

Ho, K. P.

K. P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
[CrossRef]

Knox, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
[CrossRef]

Kumar, S.

S. Kumar, J. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Liu, X.

Mauro, J.

S. Kumar, J. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Mezentsev, V. K.

S. K. Turitsyn, T. Schaefer, and V. K. Mezentsev, Phys. Rev. E 58, R5264 (1998).
[CrossRef]

Mikkelson, B.

R. J. Essiambre, B. Mikkelson, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Mollenauer, L. F.

Raghavan, S.

S. Kumar, J. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Raybon, G.

R. J. Essiambre, B. Mikkelson, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Schaefer, T.

S. K. Turitsyn, T. Schaefer, and V. K. Mezentsev, Phys. Rev. E 58, R5264 (1998).
[CrossRef]

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, T. Schaefer, and V. K. Mezentsev, Phys. Rev. E 58, R5264 (1998).
[CrossRef]

Wei, X.

Electron. Lett.

R. J. Essiambre, B. Mikkelson, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Kumar, J. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

K. P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
[CrossRef]

J. Lightwave Technol.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 151808 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. E

S. K. Turitsyn, T. Schaefer, and V. K. Mezentsev, Phys. Rev. E 58, R5264 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Phases of pulses in center bit slots as a function of trial number for a quasi-linear system. The length of the precompensating fiber is 5 km. (a) Phase of the pulse in bit slot 4, (b) phase of the pulse in bit slot 5.

Fig. 2
Fig. 2

Same as Fig. 1 but for the DM soliton regime.

Fig. 3
Fig. 3

Quasi-linear regime.

Fig. 4
Fig. 4

DM soliton regime.

Equations (22)

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q = n = 1 N q n ,
q n ( z , T ) = E n p n ( 2 π ) 1 4 exp [ ( p n 2 + i C n 2 ) s n 2 + i b n + i π r n ] ,
i q n z β 2 ( z ) 2 2 q n T 2 = γ a 2 ( z ) R ( q 1 , q 2 , q N ) ,
R ( q 1 , q 2 , q N ) = k + l m = n q k q l q m ,
a 2 ( z ) = exp [ 0 z α ( s ) d s ]
d E n d z = 2 γ a 2 ( z ) Im R q n d s n ,
d p n d z = p n C n β 2 + p n γ a 2 ( z ) E n Im [ 4 ( s n p n ) 2 1 ] R q n d s n ,
d C n d z = β 2 ( 4 p n 4 C n 2 ) + 8 p n 2 γ a 2 ( z ) K n E n ,
d b n d z = β 2 p n 2 + γ a 2 ( z ) E n ( K n + Re R q n d s n ) ,
K n = Re ( s n R q n s n + 1 2 R q n ) + C n s n 2 Im ( R q n ) d s n .
f n = f + γ f n ( 1 ) + γ 2 f n ( 2 ) + ,
d p d z = p C β 2 ,
d C d z = β 2 ( 4 p 4 C 2 ) + 2 γ a 2 ( z ) p 3 E π ,
d b d z = β 2 p 2 + 5 γ a 2 ( z ) p E 4 π ,
d p n ( 1 ) d z = β 2 [ p n ( 1 ) C + p C n ( 1 ) ] E ( a p ) 2 2 π k + l m = n ( 1 Δ 2 ) exp θ 1 sin θ 2 ,
d C n ( 1 ) d z = 2 β 2 [ 8 p 3 p n ( 1 ) C C n ( 1 ) ] + 2 E p 3 a 2 π k + l m = n ( 1 Δ 2 ) exp θ 1 cos θ 2 ,
d b n ( 1 ) d z = 2 p β 2 p n ( 1 ) + E p a 2 4 π k + l m = n ( 5 Δ 2 ) exp θ 1 cos θ 2 ,
θ 1 = ( p T b ) 2 [ ( k + l + m + n ) 2 4 ( k 2 + l 2 + m 2 + n 2 ) ] ,
θ 2 = Δ r π C T b 2 ( k 2 + l 2 m 2 n 2 ) 2 ,
Δ = p T b ( k + l + m 3 n ) 2 , Δ r = ( r k + r l r m r n ) .
s ( t ) = 4 A ( t ) A ( t T b ) cos ( Δ ϕ ) ,
q ( t ) = A ( t ) exp [ i ϕ ( t ) ] , Δ ϕ = ϕ ( t ) ϕ ( t T b ) .

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