Abstract

The variational method is used to derive correlation equations that model phase jitter in dispersion-managed soliton systems. The predictions of these correlation equations are consistent with numerical solutions of the nonlinear Schrödinger equation on which they are based.

© 2002 Optical Society of America

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References

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  1. L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 373–460.
    [CrossRef]
  2. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 23, 1351 (1990).
    [CrossRef]
  3. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communications Networks, (Wiley, New York, 1998), pp. 158 and 163.
  4. M. Hanna, H. Porte, J. P. Goedgebuer, and W. T. Rhodes, Opt. Lett. 24, 732 (1999).
    [CrossRef]
  5. C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
    [CrossRef]
  6. D. J. Kaup, Phys. Rev. A 27, 5689 (1990).
    [CrossRef]
  7. H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990).
    [CrossRef]
  8. W. J. Firth, Opt. Commun. 22, 226 (1977).
    [CrossRef]
  9. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]

2002 (1)

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

1999 (1)

1990 (3)

1983 (1)

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

1977 (1)

W. J. Firth, Opt. Commun. 22, 226 (1977).
[CrossRef]

Anderson, D.

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

Firth, W. J.

W. J. Firth, Opt. Commun. 22, 226 (1977).
[CrossRef]

Goedgebuer, J. P.

Gordon, J. P.

J. P. Gordon and L. F. Mollenauer, Opt. Lett. 23, 1351 (1990).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 373–460.
[CrossRef]

Hanna, M.

Haus, H. A.

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communications Networks, (Wiley, New York, 1998), pp. 158 and 163.

Kaup, D. J.

D. J. Kaup, Phys. Rev. A 27, 5689 (1990).
[CrossRef]

Lai, Y.

Mamyshev, P. V.

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 373–460.
[CrossRef]

Matera, F.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communications Networks, (Wiley, New York, 1998), pp. 158 and 163.

McKinstrie, C. J.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communications Networks, (Wiley, New York, 1998), pp. 158 and 163.

Mollenauer, L. F.

J. P. Gordon and L. F. Mollenauer, Opt. Lett. 23, 1351 (1990).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 373–460.
[CrossRef]

Porte, H.

Rhodes, W. T.

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communications Networks, (Wiley, New York, 1998), pp. 158 and 163.

Xie, C.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

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

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

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

Opt. Commun. (1)

W. J. Firth, Opt. Commun. 22, 226 (1977).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

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

D. J. Kaup, Phys. Rev. A 27, 5689 (1990).
[CrossRef]

Other (2)

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 373–460.
[CrossRef]

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communications Networks, (Wiley, New York, 1998), pp. 158 and 163.

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Figures (2)

Fig. 1
Fig. 1

Equilibrium chirp and width plotted as functions of distance. The dashed and solid curves represent solutions of the variational and the NS equations, respectively.

Fig. 2
Fig. 2

Equilibrium phase and phase deviation plotted as functions of distance. The dashed curves represent solutions of the variational a and correlation b equations, whereas the solid curves represent solution of the NS equation (a and b).

Tables (1)

Tables Icon

Table 1 Correlation Coefficients Based on Ansatz (2)

Equations (25)

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Az=g-αA-iβAtt/2+iγA2A+R,
Az,t=a expiϕ-1+ict2/2τ2,
Ez=δEz,
τz=δτz+βc/τ,
cz=δcz+β1+c2/τ2+γE/2π1/2τ,
ϕz=δϕz+β/2τ2+5γE/25/2π1/2τ,
β1z=βz/τ02z,
β2z=βz1+c02z/τ02z,
γz=γ0E0/2π1/2τ0z,
νz=βzc0z/τ02z,
Ez=δEz,
Tz=δTz-2νT+β1C,
Cz=δCz+γE-2β2+γT+2νC,
ϕz=δϕz+5γ/4E-β1+5γ/4T.
0z0zδpzzδqzzdzdz=σpqδz-z,
E2z=σee,
ETz=σet-2νET+β1EC,
ECz=σec+γE2-2β2+γET+2νEC,
Eϕz=σeϕ+5γ/4E2-β1+5γ/4ET,
T2z=σtt-4νT2+2β1TC,
TCz=σtc+γET-2β2+γT2+β1C2,
Tϕz=σtϕ+5γ/4ET-β1+5γ/4T2-2νTϕ+β1Cϕ,
C2z=σcc+2γEC-4β2+2γTC+4νC2,
Cϕz=σcϕ+5γ/4EC+γEϕ-β1+5γ/4×TC-2β2+γTϕ+2νCϕ,
ϕ2z=σϕϕ+5γ/2Eϕ-2β1+5γ/2Tϕ. 

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