Abstract

Using numerical simulation, we show that solitons of any pulse width can avoid splitting or excessive broadening in response to birefringence of randomly varying orientation as long as the fiber’s polarization-dispersion parameter (in psec/km1/2) is less than ~0.3D1/2, where D is the dispersion parameter (in psec nm−1 km−1). Nevertheless, we also find that polarization dispersion tends to produce a significant amount of dispersive wave radiation from the soliton.

© 1989 Optical Society of America

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References

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  1. C. D. Poole, Opt. Lett. 13, 687 (1988).
    [CrossRef] [PubMed]
  2. C. D. Poole, C. R. Giles, Opt. Lett. 13, 155 (1988).
    [CrossRef] [PubMed]
  3. C. R. Menyuk, Opt. Lett. 12, 614 (1987).
    [CrossRef] [PubMed]
  4. C. R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef]
  5. M. N. Islam, C. D. Poole, J. P. Gordon, Opt. Lett. 14, 1011 (1989).
    [CrossRef] [PubMed]
  6. L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
    [CrossRef]
  7. L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
    [CrossRef] [PubMed]
  8. L. F. Mollenauer, K. Smith, in Digest of Conference on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1989), paper WO1.
  9. C. D. Poole, Opt. Lett. 14, 523 (1989).
    [CrossRef] [PubMed]
  10. See, for example, W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (Wiley, New York, 1957), Chap. 3.
  11. We define D here in the usual way, i.e., as D = −(2πc/λ2)k″ (where k″ is the second frequency derivative of the propagation constant), whereas in Refs. 3 and 4D was taken as −(2πc2/λ)k″.
  12. See Eqs. (5)–(7) in J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]

1989 (2)

1988 (4)

1987 (1)

1986 (2)

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

See Eqs. (5)–(7) in J. P. Gordon, Opt. Lett. 11, 662 (1986).
[CrossRef] [PubMed]

Feller, W.

See, for example, W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (Wiley, New York, 1957), Chap. 3.

Giles, C. R.

Gordon, J. P.

Islam, M. N.

M. N. Islam, C. D. Poole, J. P. Gordon, Opt. Lett. 14, 1011 (1989).
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

Menyuk, C. R.

Mollenauer, L. F.

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

L. F. Mollenauer, K. Smith, in Digest of Conference on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1989), paper WO1.

Poole, C. D.

Smith, K.

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
[CrossRef] [PubMed]

L. F. Mollenauer, K. Smith, in Digest of Conference on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1989), paper WO1.

IEEE J. Quantum Electron. (1)

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

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

Opt. Lett. (7)

Other (3)

L. F. Mollenauer, K. Smith, in Digest of Conference on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1989), paper WO1.

See, for example, W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (Wiley, New York, 1957), Chap. 3.

We define D here in the usual way, i.e., as D = −(2πc/λ2)k″ (where k″ is the second frequency derivative of the propagation constant), whereas in Refs. 3 and 4D was taken as −(2πc2/λ)k″.

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Figures (4)

Fig. 1
Fig. 1

Sn as a function of total distance Z = 0. 1n km for two of the many random sequences used in the simulations.

Fig. 2
Fig. 2

Pulse-broadening factor τ/τ0 as a function of total distance traversed for solitons of initial width τ0 = 50 psec. Filled circles, δ = 1.25; crosses, δ = 2.5; open circles, δ = 4.0; squares, δ = 5.0. The slope of the arrow indicates the rate of component separation after fission of the pulse.

Fig. 3
Fig. 3

Energy of the best-fit sech2 pulse Ebf and the pulse area S, each normalized to the corresponding values at input, as functions of distance traversed; δ = 2.5.

Fig. 4
Fig. 4

Logarithm of the normalized pulse amplitude modulus and intensity as a function of time (in tc units) for δ = 2.5 and Z = 2000 km illustrating the radiation generated by polarization dispersion. The skirts of a perfect soliton would follow the dashed curve. The spread of the radiation is directly proportional to the distance traversed; its 1% amplitude point reached ±100 time units at approximately 1800 km. The high-frequency ripples near the extremes of the time span are the result of incompletely masked reflections at t = ±100.

Equations (2)

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Δ β / h 1 / 2 < ˜ 0 . 3 D 1 / 2 ,
Ω = ( 8 z 0 z p 1 ) 1 / 2 .

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