Abstract

Analytical expressions are presented for Manakov solitons perturbed by polarization mode dispersion (PMD). Comparison is made with computer simulations. Dispersion-managed solitons are also studied. It is concluded that at high bit rates solitons are superior to linear return-to-zero propagation with regard to PMD.

© 2000 Optical Society of America

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References

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  1. P. K. A. Wai, C. R. Menyuk, and H. H. Chen, Opt. Lett. 16, 1231 (1991); P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef] [PubMed]
  2. L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
    [CrossRef]
  3. M. Suzuki, N. Edagawa, I. Morita, S. Yamamoto, and S. Akiba, J. Opt. Soc. Am. B 14, 2953 (1997).
    [CrossRef]
  4. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [CrossRef]
  5. T. I. Kakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
    [CrossRef]
  6. M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997).
    [CrossRef]
  7. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  8. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  9. Y. Chen and H. A. Haus, J. Opt. Soc. Am. B 16, 24 (1999).
    [CrossRef]

1999 (1)

1997 (4)

M. Suzuki, N. Edagawa, I. Morita, S. Yamamoto, and S. Akiba, J. Opt. Soc. Am. B 14, 2953 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

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

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

1992 (1)

1991 (1)

1989 (1)

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
[CrossRef]

1986 (1)

Akagi, Y.

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

Akiba, S.

Chen, H. H.

Chen, Y.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Edagawa, N.

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Gordon, J. P.

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
[CrossRef]

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

Hasegawa, A.

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

Haus, H. A.

Kakoba, T. I.

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

Kaup, D. J.

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

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Matsumoto, M.

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

Menyuk, C. R.

P. K. A. Wai, C. R. Menyuk, and H. H. Chen, Opt. Lett. 16, 1231 (1991); P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef] [PubMed]

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
[CrossRef]

Morita, I.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Smith, K.

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
[CrossRef]

Suzuki, M.

Wai, P. K. A.

Yamamoto, S.

Electron. Lett. (1)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. B (3)

Opt. Lett. (3)

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

P. K. A. Wai, C. R. Menyuk, and H. H. Chen, Opt. Lett. 16, 1231 (1991); P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef] [PubMed]

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 21, 1219 (1989); L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, III A, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 12.
[CrossRef]

Phys. Rev. E (1)

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

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Figures (3)

Fig. 1
Fig. 1

Oscillation of relative position for initial position displacement. The solid curve and the filled circles represent initial polarizations of 45° and 75°, respectively, and zc=τ02/β. The dashed curve is the analytical prediction of Eq. (5).

Fig. 2
Fig. 2

Comparison of the analytical prediction (solid curves) with numerical simulations (filled circles) of the soliton pulse-width variation for D=18 ps/nm/km×β=23 ps2/km, τ0=28.4 ps FWHM =50 ps, zh=0.1 km, z0=55 km zc=τ02/β=35 km, and δ=dΔβ/dω21/2τ0/2β=2.5, 5. Each curve of numerical simulations is obtained by averaging of 20 sample solutions of the coupled nonlinear Schrödinger equations in a randomly varying birefringent fiber.

Fig. 3
Fig. 3

Comparison of the soliton pulse-width variation of a dispersion-managed soliton at net zero dispersion with the analytical prediction of the equivalent uniform system. The pulse width (FWHM) is 5 ps; the length and dispersion of the positive (negative) segment are L+L-=35 km and k+-k-=2 ps2/km, respectively; zh=0.1 km; and the effective dispersion9 Δβeff=-0.046 ps2/km. Each curve of numerical simulations is derived by averaging of 200 sample solutions of the coupled nonlinear Schrödinger equation for a dispersion-managed soliton in a randomly varying birefringent fiber.

Equations (8)

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

ΔtL2=Δβ2zhz,
ut,z=usolt,z+Δucontt,z.
Δtz=2E Re-dttusol*t,zΔucontt,z.
iUz+β22Ut2+89κU2+V2U=-iS1Δβ2Ut-iSc*Δβ2Vt,  iVz+β22Vt2+89κU2+V2V=iS1Δβ2Vt-iScΔβ2Ut.
Δtz=Δt00.54π23/2×cosβzτ02+tan-1βzτ0221+βz3.61τ0221/4,
Δts2=1.265π348τ02βΔβ2zh×lnβz3.61τ02+1+βz3.61τ0221/2.
ΔWz=iβ-αΔW+Sβ,
iaz+β+Δβeff22at2+A02δeff1-μt2τ02a=0.

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