Abstract

We perform a linear stability analysis of the Ablowitz–Biondini equations to explain the dynamic evolution of the noise squeezing, caused by the interplay among optical solitons and noise components, of initially uncorrelated statistics in fiber systems with dispersion management.

© 2003 Optical Society of America

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References

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  1. S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
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  9. P. M. Lushnikov, Opt. Lett. 26, 1535 (2001).
    [CrossRef]
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  11. C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
    [CrossRef]

2002

R. Holzlohner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

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

2001

2000

D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
[CrossRef]

T. I. Lakoba and D. E. Pelinovsky, Chaos 10, 539 (2000).
[CrossRef]

1998

1997

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

1996

1994

1987

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

1969

L. J. Lewis, D. K. Reynolds, F. R. Bergseth, and F. J. Alexandro, Jr., Linear System Analysis (McGraw-Hill, New York, 1969).

Ablowitz, M. J.

Aceves, A. B.

Alexandro, Jr., F. J.

L. J. Lewis, D. K. Reynolds, F. R. Bergseth, and F. J. Alexandro, Jr., Linear System Analysis (McGraw-Hill, New York, 1969).

Benedetto, S.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

Bergseth, F. R.

L. J. Lewis, D. K. Reynolds, F. R. Bergseth, and F. J. Alexandro, Jr., Linear System Analysis (McGraw-Hill, New York, 1969).

Biondini, G.

Borgo, G.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

Carena, A.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

Carter, S. J.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Curri, V.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

De Angelis, C.

Drummond, P. D.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Gabitov, I. R.

Gaudino, R.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

Grigoryan, V. S.

R. Holzlohner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Holzlohner, R.

R. Holzlohner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Kath, W. L.

R. Holzlohner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Lakoba, T. I.

T. I. Lakoba and D. E. Pelinovsky, Chaos 10, 539 (2000).
[CrossRef]

Lewis, L. J.

L. J. Lewis, D. K. Reynolds, F. R. Bergseth, and F. J. Alexandro, Jr., Linear System Analysis (McGraw-Hill, New York, 1969).

Lushnikov, P. M.

Luther, G.

McKinstrie, C. J.

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

Menyuk, C. R.

R. Holzlohner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
[CrossRef]

T. I. Lakoba and D. E. Pelinovsky, Chaos 10, 539 (2000).
[CrossRef]

Poggiolini, P.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

Reid, M. D.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Reynolds, D. K.

L. J. Lewis, D. K. Reynolds, F. R. Bergseth, and F. J. Alexandro, Jr., Linear System Analysis (McGraw-Hill, New York, 1969).

Rubenchik, A. M.

Shelby, R. M.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Turitsyn, S.

Xie, C.

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

Chaos

T. I. Lakoba and D. E. Pelinovsky, Chaos 10, 539 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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

IEEE Photon. Technol. Lett.

G. Borgo, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 9, 535 (1997).
[CrossRef]

R. Holzlohner, C. R. Menyuk, W. L. Kath, and V. S. Grigoryan, IEEE Photon. Technol. Lett. 14, 1079 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. E

D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
[CrossRef]

Phys. Rev. Lett.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Other

L. J. Lewis, D. K. Reynolds, F. R. Bergseth, and F. J. Alexandro, Jr., Linear System Analysis (McGraw-Hill, New York, 1969).

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Figures (4)

Fig. 1
Fig. 1

Discrete eigenvalues N>0 of matrix H at several DM-soliton energies. Solid curves (dashed curve) are for even-symmetry N=1,3 (odd-symmetry N=2) eigenfunctions.

Fig. 2
Fig. 2

Noise spectral density: in-phase even component ueω,z2. Inset, detailed profile of ueω,z2 in z=6 Mm (solid curve) averaging 80 realizations and normalizing to the background value σu2/2. Open circles, u1ω2 calculated from x1=u1,v1T.

Fig. 3
Fig. 3

Top, statistics of even-symmetry noise components in quadrature veω,z2 after 80 realizations. Bottom, the same for odd-symmetry quadrature statistics voω,z2.

Fig. 4
Fig. 4

Comparison of noise statistics veω,z2 (left) and voω,z2 (right) calculated over 200 realizations at z=16 Mm and normalized to the background value σv2/2. Dotted curves, the modes v0,eω2 and v0,oω2 calculated through the LSA.

Equations (6)

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idUdz-δω22U+-+-+rω1ω2Uω+ω1×Uω+ω2U*ω+ω1+ω2dω1dω2=0,rx=12π2-1/21/2expiCζxdζ,Cζ=-1/2ζDζ-δdζ.
Uω,z=Fω+uω,z+ivω,zexpiλ22z,
dudz=λ22v+δ2ω2v+-+Mω;ξ-2Nω;ξvω+ξdξ,dvdz=-λ22u-δ2ω2u+-+Mω;ξ+2Nω;ξuω+ξdξ.
Mω;ξ=-+rω1ξ-ω1Fω+ω1×Fω+ξ-ω1dω1,
Nω;ξ=-+rω1ξFω+ω1Fω+ξ+ω1dω1.
dxdz=H·x,

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