Abstract

Probability density functions are given for nonlinear phase noise in a photonic communication system in which the information is encoded in the optical phase, both unconditioned and conditioned to the detection of a given amount of pulse energy. It is shown that the reach of a transmission system is increased by 41% by ideal postcompensation of the nonlinear phase noise.

© 2004 Optical Society of America

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References

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  1. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 15, 1351 (1990).
    [CrossRef] [PubMed]
  2. A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
    [CrossRef]
  3. H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
    [CrossRef]
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    [CrossRef]
  5. C. Xu and X. Liu, Opt. Lett. 27, 1619 (2002).
    [CrossRef]
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    [CrossRef]
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  8. K.-P. Ho, “Probability density function of Kerr effect phase noise,” http://arXiv.org/physics/0301018 .
  9. K.-P. Ho and J. M. Kahn, “Detection technique to mitigate Kerr effect phase noise,” http://arXiv.org/physics/0211097 .

2003 (1)

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

2002 (2)

1994 (1)

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

1993 (1)

1990 (1)

Gnauck, A. H.

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

Gordon, J. P.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 1058.

Kim, H.

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

Liu, X.

McKinstrie, C. J.

Mecozzi, A.

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

A. Mecozzi, J. Opt. Soc. Am. B 10, 2321 (1993).
[CrossRef]

Mollenauer, L. F.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 1058.

Slusher, R. E.

Wei, X.

Xu, C.

IEEE Photon. Technol. Lett. (1)

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

J. Lightwave Technol. (1)

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

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

Opt. Lett. (3)

Other (3)

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 1058.

K.-P. Ho, “Probability density function of Kerr effect phase noise,” http://arXiv.org/physics/0301018 .

K.-P. Ho and J. M. Kahn, “Detection technique to mitigate Kerr effect phase noise,” http://arXiv.org/physics/0211097 .

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Figures (2)

Fig. 1
Fig. 1

Probability density function of the optical phase for optical signal-to-noise ratios of 10 dB (solid curve), 15 dB (dashed curve), and 20 dB (dotted–dashed curve). The dotted curves are Gaussian distribution with the same variance. The nonlinear phase shift is set to the optimum value ϕNL=3/2.

Fig. 2
Fig. 2

Probability density function of the optical phase conditioned to the observation of the normalized amplitude a=0.9. The solid, dashed, and dotted–dashed lines correspond to 10, 15, and 20 dB of signal-to-noise ratio. The dotted curves are Gaussian distributions with the same variance. The nonlinear phase shift is set to the value that is optimum if an ideal compensator of the nonlinear phase noise is used, that is, ϕNL=3.

Equations (10)

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u=u0+WLexpiγ0Ldzu0+Wz2dz.
Cn=cosh-inϕNLPASE1/2,  n0,  C0=1,
Tn=tanh-inϕNLPASE1/2-inϕNLPASE1/2,  n0,  T0=1.
Pa,ϕ=n=-aπPASETnCnexp-Cn2a2+1PASETnCn2×In2aPASETnCn×exp-inϕ+ϕNL1-Tn,
Pϕ=n=-exp-inϕ+ϕNL1-Tn2π1/2Cn4PASETnCn2n/2Γn+1/2×exp-1PASETnCn2×Φn2+1,n+1,1PASETnCn2,
δϕa=ϕNLa-1+13a-12
σϕ2aPASE12a+ϕNL26a+1245a-12.
σϕ2aαLu0212a+γu02L26a+1245a-12.
σmax2=αLu0212+γu02L26.
σϕ2αLu0212+2γu02L23.

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