Abstract

Nonlinear penalties due to intrachannel four-wave mixing (IFWM) in highly dispersed return-to-zero differential-phase-shift-keyed transmission are studied for both symmetric and nonsymmetric dispersion maps. As the dispersion map changes from symmetric to nonsymmetric, the nonlinear amplitude fluctuation overtakes the effect of the nonlinear phase fluctuation and dominates the system’s nonlinear performance. The effect of IFWM on the bit error rate is assessed by using the semianalytical method.

© 2006 Optical Society of America

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References

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  1. R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
    [Crossref]
  2. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
    [Crossref]
  3. R.-J. Essiambre, G. Raybon, and B. Mikkelsen, in Optical Fiber Telecommunications IV B, I.P.Kaminow and T.Li, eds. (Academic, 2002).
  4. X. Wei and X. Liu, Opt. Lett. 28, 2300 (2003).
    [Crossref] [PubMed]
  5. J. X. Cai, D. G. Foursa, L. Liu, C. R. Davidson, Y. Cai, W. W. Patterson, A. J. Lucero, B. Bakhshi, G. Mohs, P. C. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, S. Jiang, M. Nissov, A. N. Pilipetskii, and N. S. Bergano, J. Lightwave Technol. 23, 95 (2005).
    [Crossref]
  6. D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.
  7. K.-P. Ho, IEEE Photon. Technol. Lett. 17, 789 (2005).
    [Crossref]
  8. A. Mecozzi, C. B. Clausen, and M. Shatif, IEEE Photon. Technol. Lett. 12, 392 (2000).
    [Crossref]

2005 (2)

2003 (1)

2001 (1)

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

2000 (2)

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
[Crossref]

A. Mecozzi, C. B. Clausen, and M. Shatif, IEEE Photon. Technol. Lett. 12, 392 (2000).
[Crossref]

Anderson, W.

Bakhshi, B.

Bayvel, P.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
[Crossref]

Bergano, N. S.

Cai, J. X.

Cai, Y.

Clausen, C. B.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

A. Mecozzi, C. B. Clausen, and M. Shatif, IEEE Photon. Technol. Lett. 12, 392 (2000).
[Crossref]

Corbett, P. C.

Davidson, C. R.

Domagala, G.

Essiambre, R.-J.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, in Optical Fiber Telecommunications IV B, I.P.Kaminow and T.Li, eds. (Academic, 2002).

Foursa, D. G.

Gnauck, A. H.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

Gupta, V.

Ho, K.-P.

K.-P. Ho, IEEE Photon. Technol. Lett. 17, 789 (2005).
[Crossref]

Jiang, S.

Killey, R. I.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
[Crossref]

Laperle, C.

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

Li, C.

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

Li, H.

Liu, L.

Liu, X.

Lucero, A. J.

Mak, G.

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

Mazurczyk, M.

McGhan, D.

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

Mecozzi, A.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

A. Mecozzi, C. B. Clausen, and M. Shatif, IEEE Photon. Technol. Lett. 12, 392 (2000).
[Crossref]

Mikhailov, V.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
[Crossref]

Mikkelsen, B.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, in Optical Fiber Telecommunications IV B, I.P.Kaminow and T.Li, eds. (Academic, 2002).

Mohs, G.

Nissov, M.

O'Sullivan, M.

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

Park, S.-G.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

Patterson, W. W.

Pilipetskii, A. N.

Raybon, G.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, in Optical Fiber Telecommunications IV B, I.P.Kaminow and T.Li, eds. (Academic, 2002).

Savchenko, A.

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

Shatif, M.

A. Mecozzi, C. B. Clausen, and M. Shatif, IEEE Photon. Technol. Lett. 12, 392 (2000).
[Crossref]

Shtaif, M.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

Thiele, H. J.

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
[Crossref]

Vaa, M.

Wei, X.

IEEE Photon. Technol. Lett. (4)

R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
[Crossref]

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, IEEE Photon. Technol. Lett. 13, 445 (2001).
[Crossref]

K.-P. Ho, IEEE Photon. Technol. Lett. 17, 789 (2005).
[Crossref]

A. Mecozzi, C. B. Clausen, and M. Shatif, IEEE Photon. Technol. Lett. 12, 392 (2000).
[Crossref]

J. Lightwave Technol. (1)

Opt. Lett. (1)

Other (2)

D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, in Optical Fiber Communication Conference (Optical Society of America, 2005), postdeadline paper PDP27.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, in Optical Fiber Telecommunications IV B, I.P.Kaminow and T.Li, eds. (Academic, 2002).

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Figures (3)

Fig. 1
Fig. 1

(a) Nonsymmetric and (b) symmetric dispersion maps used for the analysis. The dispersion of the transmission fiber is D = 17 ps nm km .

Fig. 2
Fig. 2

Calculated probability densities for (a) normalized amplitude a 11 + Δ a 11 and (b) differential phase cos 1 ( a 11 a 12 ) + Δ ϕ 11 , 12 . Note that (a) is for the nonsymmetric dispersion map only, whereas (b) is valid for both symmetric and nonsymmetric maps. Symbols are obtained from direct histogram counting, and the smooth curves are Gaussian fits. The mean nonlinear phase shift is Φ NL = 0.8 rad .

Fig. 3
Fig. 3

Calculated BER versus SNR for (a) nonsymmetric, and (b) symmetric maps. The different values of Φ NL indicate different power levels used for the calculation. The dashed curves in (a) are results obtained with the imaginary part of g k set to zero.

Equations (10)

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u k ( 0 , t ) = a k A 0 exp [ ( t k T ) 2 2 τ 2 ] ,
g k = i 2 Φ NL T τ 3 π β L l k , m k a l a m a l + m k E 1 [ i 2 ( l k ) ( m k ) T 2 β L ] ,
Δ a k = Re ( g k ) .
Δ ϕ k , k + 1 = Im ( g k a k ) Im ( g k + 1 a k + 1 ) .
h ( t ) = π 1 4 τ 1 2 exp ( t 2 2 τ 2 ) .
b k = E b ( a k + 3 2 g k ) + x k + i y k ,
p e = Q ( α , β ) 1 2 exp ( α 2 + β 2 2 ) I 0 ( α β ) ,
α = g 11 a 11 g 12 a 12 3 E b 4 N 0 ,
β = 2 + 3 2 ( g 11 a 11 + g 12 a 12 ) E b 2 N 0 .
p e = 1 2 exp ( E b N 0 ) .

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