Abstract

In a soliton transmission system, spontaneous emission noise owing to optical amplifiers leads to timing jitter that is usually assumed to be Gaussian distributed. It is shown that the mutual interaction of solitons in neighboring time slots can lead to non-Gaussian tails on the distribution function and to a substantial increase in the bit-error rate. It is argued that the approach used here will also be of use in the study of non-return-to-zero systems.

© 1995 Optical Society of America

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References

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  1. L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Opt. Lett. 19, 704 (1994).
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1994 (1)

1991 (2)

1990 (1)

1986 (1)

1983 (1)

1965 (1)

R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965); L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).

Cohen, L. G.

Evangelides, S. G.

Feynman, R. P.

R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965); L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).

Gordon, J. P.

Haus, H. A.

Hibbs, A. R.

R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965); L. Arnold, Stochastic Differential Equations, Theory and Applications (Wiley, New York, 1974).

Lai, Y.

Mamyshev, P. V.

Mecozzi, A.

Mollenauer, L. F.

Moores, J. D.

Neubelt, M. J.

Simpson, J. R.

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Figures (4)

Fig. 1
Fig. 1

Solution for qM(z) determined from Eq. (3) at some special values of qfqGH(zf ).

Fig. 2
Fig. 2

Solution for qGH(zf ) as a function of qM(zf ). I calculated this function by first finding qM(qf ) at zf and then inverting, after recalling that qGH(zf ) = qf.

Fig. 3
Fig. 3

Comparison of the probability distribution functions fGH and fM. A significant increase in fM relative to fGH is visible beyond qM = 2.5.

Fig. 4
Fig. 4

Comparison of the escape distribution functions EGH and EM. These functions are directly related to the bit-error rate.

Equations (8)

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q ¨ 1 = - γ q ˙ 1 + α S 1 + 4 exp [ - ( q 2 - q 1 ) ] , q ¨ 2 = - γ q ˙ 2 + α S 2 - 4 exp [ - ( q 2 - q 1 ) ] ,
f M ( q M ) = d q GH d P f GH ( q GH ) × δ [ q M - q M ( q GH , P ) ] ,
q ¨ = - γ q ˙ + α S max + 4 exp [ - 2 ( q l - q ) ] ,
f M ( q M ) 1 2 f GH ( q M ) + 1 2 f GH 2 [ q GH ( q M ) ] - d q M { 1 2 f GH ( q M ) + 1 2 f GH 2 [ q GH ( q M ) ] } .
f GH ( q GH ) = γ α 2 π z exp ( - γ 2 q GH 2 / 2 α 2 z ) ,
f GH ( q , z ; q f , z f ) = γ 2 2 π α 2 z 1 / 2 ( z f - z ) 1 / 2 × exp { - γ 2 2 α 2 [ q 2 z + ( q f - q ) 2 z f - z ] } ,
f GH ( q , z ; q f , z f ) = γ 2 2 π α 2 z 1 / 2 ( z f - z ) 1 / 2 × exp [ - γ 2 2 α 2 z f z ( z f - z ) ( q - z z f q f ) 2 - γ 2 2 α 2 z f q f 2 ] .
E M ( q M ) = 2 q M f M ( q M ) d q M ,

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