Abstract

Propagation of solitons in optical fibers is studied taking into account the polarization mode dispersion (PMD) effect. We show that the soliton interaction caused by the radiation emitted by solitons due to the PMD disorder leads to soliton jitter, and we find its statistical properties. The theoretical predictions are justified by direct numerical simulations.

© 2004 Optical Society of America

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    [CrossRef]
  2. P. K. A. Wai, C. R. Menyuk, and H. H. Chen, Opt. Lett. 16, 1231 (1991).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
    [CrossRef]
  20. C. D. Poole, Opt. Lett. 13, 687 (1988).
    [CrossRef]
  21. C. D. Poole, Opt. Lett. 14, 523 (1989).
    [CrossRef] [PubMed]
  22. C. D. Poole, J. H. Winters, and J. A. Nagel, Opt. Lett. 16, 372 (1991).
    [CrossRef] [PubMed]
  23. M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
    [CrossRef]
  24. T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  27. J. N. Elgin, Phys. Lett. A 110, 441 (1985).
    [CrossRef]
  28. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  29. D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
    [CrossRef] [PubMed]
  30. M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
    [CrossRef]
  31. M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
    [CrossRef]

2004 (1)

I. V. Kolokolov and K. S. Turitsyn, Zh. Eksp. Teor. Fiz. 125, 395 (2004).

2003 (1)

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

2001 (1)

M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
[CrossRef]

2000 (2)

1997 (3)

M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
[CrossRef]

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, J. Opt. Soc. Am. B 14, 2967 (1997).
[CrossRef]

1996 (2)

C. R. Menyuk and P. K. A. Wai, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

1995 (1)

1994 (2)

1991 (3)

1990 (1)

D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

1989 (2)

C. D. Poole, Opt. Lett. 14, 523 (1989).
[CrossRef] [PubMed]

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

1988 (2)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

C. D. Poole, Opt. Lett. 13, 687 (1988).
[CrossRef]

1987 (2)

N. S. Bergano, C. D. Poole, and R. E. Wagner, IEEE J. Lightwave Technol. 5, 1618 (1987).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, and B. Daino, Opt. Lett. 12, 844 (1987).
[CrossRef] [PubMed]

1986 (2)

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

1985 (1)

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

1981 (2)

I. P. Kaminow, IEEE J. Quantum Electron. 17, 15 (1981).
[CrossRef]

S. Machida, I. Sakai, and T. Kimura, Electron. Lett. 17, 494 (1981).
[CrossRef]

1979 (1)

1978 (1)

1973 (1)

S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Akagi, Y.

M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
[CrossRef]

Andresciani, D.

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

N. S. Bergano, C. D. Poole, and R. E. Wagner, IEEE J. Lightwave Technol. 5, 1618 (1987).
[CrossRef]

Chen, H. H.

Chen, Y.

Chertkov, M.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
[CrossRef]

Chung, Y.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Curti, F.

Daino, B.

Dyachenko, A.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Elgin, J. N.

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Gabitov, I.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
[CrossRef]

Gisin, B.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Gisin, N.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
[CrossRef]

Haus, H. A.

Jopson, R. M.

Kaminow, I. P.

I. P. Kaminow, IEEE J. Quantum Electron. 17, 15 (1981).
[CrossRef]

Kath, W. L.

Kaup, D. J.

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

Kimura, T.

S. Machida, I. Sakai, and T. Kimura, Electron. Lett. 17, 494 (1981).
[CrossRef]

Kogelnik, H.

Kolokolov, I.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
[CrossRef]

Kolokolov, I. V.

I. V. Kolokolov and K. S. Turitsyn, Zh. Eksp. Teor. Fiz. 125, 395 (2004).

Lakoba, T. I.

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

Lebedev, V.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
[CrossRef]

Machida, S.

S. Machida, I. Sakai, and T. Kimura, Electron. Lett. 17, 494 (1981).
[CrossRef]

Manakov, S. V.

S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Matera, F.

Matsumoto, M.

M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
[CrossRef]

Menyuk, C. R.

Nagel, J. A.

Nelson, L. E.

Passy, R.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Poole, C. D.

C. D. Poole, J. H. Winters, and J. A. Nagel, Opt. Lett. 16, 372 (1991).
[CrossRef] [PubMed]

C. D. Poole, Opt. Lett. 14, 523 (1989).
[CrossRef] [PubMed]

C. D. Poole, Opt. Lett. 13, 687 (1988).
[CrossRef]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

N. S. Bergano, C. D. Poole, and R. E. Wagner, IEEE J. Lightwave Technol. 5, 1618 (1987).
[CrossRef]

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Rashleigh, S. C.

Sakai, I.

S. Machida, I. Sakai, and T. Kimura, Electron. Lett. 17, 494 (1981).
[CrossRef]

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Simon, A.

Turitsyn, K. S.

I. V. Kolokolov and K. S. Turitsyn, Zh. Eksp. Teor. Fiz. 125, 395 (2004).

Ulrich, R.

Von der Weid, J. P.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

N. S. Bergano, C. D. Poole, and R. E. Wagner, IEEE J. Lightwave Technol. 5, 1618 (1987).
[CrossRef]

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Wai, P. K. A.

Winters, J. H.

Zhang, J. W.

Appl. Opt. (1)

Electron. Lett. (2)

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

S. Machida, I. Sakai, and T. Kimura, Electron. Lett. 17, 494 (1981).
[CrossRef]

IEEE J. Lightwave Technol. (2)

N. S. Bergano, C. D. Poole, and R. E. Wagner, IEEE J. Lightwave Technol. 5, 1618 (1987).
[CrossRef]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, IEEE J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

I. P. Kaminow, IEEE J. Quantum Electron. 17, 15 (1981).
[CrossRef]

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

J. Lightwave Technol. (2)

C. R. Menyuk and P. K. A. Wai, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
[CrossRef]

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, JETP Lett. 74, 535 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (11)

Phys. Lett. A (1)

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Phys. Rev. A (1)

D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (2)

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 67, 036615 (2003).
[CrossRef]

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

Zh. Eksp. Teor. Fiz. (2)

I. V. Kolokolov and K. S. Turitsyn, Zh. Eksp. Teor. Fiz. 125, 395 (2004).

S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

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Figures (2)

Fig. 1
Fig. 1

Parallel polarization state: mean-square intersoliton shift as a function of z for three phase mismatches. Dashed curve, theory; solid curve, numerics.

Fig. 2
Fig. 2

Orthogonal polarization state: mean-square intersoliton shift as a function of z. Dashed line, theory; solid curve, numerics.

Equations (9)

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

izΨ+imˆztΨ+t2Ψ+2Ψ2Ψ=0.
hj=0, hjz1hkz2=Dδjkδz1-z2,
Ψ=expiφηecoshηt-y+v.
zβ=Fvv+Fvh+Φvv,
zy=2β+h3+Π+P,
Fvv=2dx tanh x cosh-2 xv22, Fvh=-Imh1-ih2dxtanh xcosh xtv2, Π=-dxx cosh-1 x Reh1-ih2tv2, Φvv=dxtanh xcosh2 x4v12+v12+v1*2, P=idx cosh-2 xv12-v1*2,
δy1,22=43GD2z3+Dz,
δy1-δy22=831+cos2αGD2z3,
δy1,22=Dz, δy1-δy22=4Dz.

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