Abstract

Intrachannel four-wave mixing (IFWM) in highly dispersed differential phase-shift keying (DPSK) transmission systems is studied with a simple analytical model and numerical simulation. It is found that the IFWM effect in DPSK systems is smaller and less dependent on the bit pattern than in on–off-keying systems with the same average power. The reduced pulse energy in DPSK and correlation between the nonlinear phase shifts of two adjacent pulses contribute to the robustness of DPSK versus IFWM.

© 2003 Optical Society of America

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[CrossRef]

2002

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[CrossRef]

2000

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R. I. Killey, H. J. Thiele, V. Mikhailov, and P. Bayvel, IEEE Photon. Technol. Lett. 12, 1624 (2000).
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A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

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A. Mecozzi, C. B. Clausen, and M. Shtaif, IEEE Photon. Technol. Lett. 12, 392 (2000).
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C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

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A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

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R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
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C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

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Gapontsev, D.

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[CrossRef]

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Gordon, J. P.

Grosz, D.

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Hunsche, S.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

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Kung, A.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

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A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Liu, F.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Liu, X.

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

X. Liu, X. Wei, A. H. Gnauck, C. Xu, and L. K. Wickham, Opt. Lett. 27, 1177 (2002).
[CrossRef]

X. Liu, C. Xu, and X. Wei, in Proceedings of the European Conference on Optical Communication (EEOC, Copenhagen, Denmark, 2002), paper 9.6.5.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Mamyshev, P.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Mamyshev, P. V.

Mamysheva, N. A.

Marhelyuk, A.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Marklund, M.

Mårtensson, J.

Maywar, D.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

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[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, 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, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Mollenauer, L. F.

Movassaghi, M.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

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]

Rasmussen, C.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Raybon, G.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Reeves-Hall, P.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Serbe, P.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Shtaif, M.

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. Shtaif, IEEE Photon. Technol. Lett. 12, 392 (2000).
[CrossRef]

Stulz, L.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Thiele, H. J.

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

van der Wagt, P.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

Wei, X.

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

X. Liu, X. Wei, A. H. Gnauck, C. Xu, and L. K. Wickham, Opt. Lett. 27, 1177 (2002).
[CrossRef]

X. Liu, C. Xu, and X. Wei, in Proceedings of the European Conference on Optical Communication (EEOC, Copenhagen, Denmark, 2002), paper 9.6.5.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Wickham, L. K.

Xu, C.

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

X. Liu, X. Wei, A. H. Gnauck, C. Xu, and L. K. Wickham, Opt. Lett. 27, 1177 (2002).
[CrossRef]

X. Liu, C. Xu, and X. Wei, in Proceedings of the European Conference on Optical Communication (EEOC, Copenhagen, Denmark, 2002), paper 9.6.5.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Electron. Lett.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

IEEE Photon. Technol. Lett.

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

IEEE Photon. Technol. Lett.

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

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

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

Opt. Lett.

OSA Trends in Optics and Photonics Series

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, in Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), postdeadline paper PD18.

OSA Trends in Optics and Photonics Series

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Other

X. Liu, C. Xu, and X. Wei, in Proceedings of the European Conference on Optical Communication (EEOC, Copenhagen, Denmark, 2002), paper 9.6.5.

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Figures (4)

Fig. 1
Fig. 1

ECF histograms for (a) DPSK and (b) OOK, each sampled over 8192 different bit patterns.

Fig. 2
Fig. 2

Distribution of the IFWM-induced Δϕ7 and Δϕ8 calculated for the 14-bit-long DPSK pulse train with 8192 different bit patterns.

Fig. 3
Fig. 3

Histograms of the nonlinear phase shift Δϕ7 and the differential phase error Δϕ7-Δϕ8. The fitting curves are simply guides to the eye.

Fig. 4
Fig. 4

Simulated differential phase eye diagram for RZ DPSK (left) and amplitude (square root of intensity) eye diagram for RZ OOK (right). The PRBS length is 29-1.

Equations (6)

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uk0,t=Ak exp-t-kT2/2τ2,
ΔukL,t=kT=l+m-n=k-L/2L/2dz×iγAlAmAn*1-2iβz/τ2+3βz/τ221/2×exp-3l-nm-nT2τ21+3iβz/τ2-l-m2T2τ21-2iβz/τ2+3βz/τ22,
Δuk-i2γτ23βl,mAlAmAl+m-k*×Ci2l-km-kT2βL,
Δϕk=Δuk/Ak.
ECFDPSK=2ΔϕN-ΔϕN+1π.
ECFOOK=ΔuN2A0.

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