Abstract

Strong dispersion management, in which an optical pulse is highly dispersed and the pulse width is extremely broadened, can suppress nonlinear interactions such as cross-phase modulation between neighboring pulses in optical time-division-multiplexed systems, but it causes intrachannel four-wave mixing, which is an obstacle to achieving high performance in the system. We study the physical mechanism of intrachannel four-wave mixing. The dependence of the effect on the initial pulse width, the initial phase difference, and the dispersion map is also discussed, and we conclude that a narrower initial pulse, a larger accumulated dispersion, or both are effective in suppressing the effect of four-wave mixing.

© 2002 Optical Society of America

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References

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  1. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
    [CrossRef]
  2. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
    [CrossRef]
  3. T. Yu, E. A. Golovchenko, A. N. Pillipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibres,” Opt. Lett. 22, 793–795 (1997).
    [CrossRef] [PubMed]
  4. M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibres,” IEEE Photon. Technol. Lett. 10, 373–375 (1998).
    [CrossRef]
  5. P. V. Mamyshev and N. A. Mamysheva, “Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing,” Opt. Lett. 24, 1454–1456 (1999).
    [CrossRef]
  6. I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
    [CrossRef]
  7. R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems,” Electron. Lett. 35, 1576–1578 (1999).
    [CrossRef]
  8. A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 392–394 (2000).
    [CrossRef]
  9. A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 1633–1635 (2000).
    [CrossRef]
  10. M. J. Ablowitz and T. Hirooka, “Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems,” Opt. Lett. 25, 1750–1752 (2000).
    [CrossRef]
  11. S. K. Turitsyn, E. G. Turitsyna, V. K. Mezentsev, and M. P. Fedoruk, “On the theory of intra-channel four-wave mixing,” in Conference on Lasers and Electro-Optics (CLEO/Europe), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper CThE42.
  12. F. Merlaud and S. K. Turitsyn, “Intra-channel four wave mixing and ghost pulses generation: time domain approach,” in Proceedings of the European Conference on Optical Communications (VDE Verlag, Berlin, 2000), Vol. 3, pp. 35–36.
  13. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
    [CrossRef]
  14. T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768–770 (1998).
    [CrossRef]
  15. H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547–1559 (1999).
    [CrossRef]
  16. T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
    [CrossRef]
  17. T. Inoue and A. Maruta, “Pre-spread RZ pulse transmission for reducing intra-channel nonlinear interactions,” in Proceedings of the IEEE LEOS 13th Annual Meeting (IEEE Lasers and Electro-Optics Society, Piscataway, N.J., 2000), Vol. 1, pp.92–93.
  18. P. K. Cheo, Fiber Optics & Optoelectronics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1990), Chap. 13.
  19. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), pp. 64–69.
  20. T. Inoue and A. Maruta, “Reduction of intra-channel four wave mixing in strongly dispersion-managed line for high speed OTDM system,” in Nonlinear Guided Waves and Their Applications, Vol. 55 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 211–213.
  21. S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
    [CrossRef]

2001 (1)

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

2000 (5)

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 392–394 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 1633–1635 (2000).
[CrossRef]

M. J. Ablowitz and T. Hirooka, “Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems,” Opt. Lett. 25, 1750–1752 (2000).
[CrossRef]

1999 (3)

1998 (3)

T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768–770 (1998).
[CrossRef]

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibres,” IEEE Photon. Technol. Lett. 10, 373–375 (1998).
[CrossRef]

1997 (1)

1996 (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

1995 (1)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Ablowitz, M. J.

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Clausen, C. B.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 392–394 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 1633–1635 (2000).
[CrossRef]

Doran, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Essiambre, R.-J.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems,” Electron. Lett. 35, 1576–1578 (1999).
[CrossRef]

Garrett, L. D.

S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
[CrossRef]

Gnauck, A. H.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
[CrossRef]

Golovchenko, E. A.

Hasegawa, A.

Hirooka, T.

Inoue, T.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Kato, H.

Kawanishi, S.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Kodama, Y.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Mamyshev, P. V.

Mamysheva, N. A.

Maruta, A.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Matsumoto, M.

M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibres,” IEEE Photon. Technol. Lett. 10, 373–375 (1998).
[CrossRef]

Mecozzi, A.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 392–394 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 1633–1635 (2000).
[CrossRef]

Menyuk, C. R.

Mikkelsen, B.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems,” Electron. Lett. 35, 1576–1578 (1999).
[CrossRef]

Mori, K.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Park, S.-G.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
[CrossRef]

Pillipetskii, A. N.

Raybon, G.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems,” Electron. Lett. 35, 1576–1578 (1999).
[CrossRef]

Shake, I.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

Shtaif, M.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 1633–1635 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 392–394 (2000).
[CrossRef]

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Sugahara, H.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Taga, H.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Takara, H.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

Wiesenfeld, J. M.

S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
[CrossRef]

Yamabayashi, Y.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

Yu, T.

Electron. Lett. (4)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems,” Electron. Lett. 35, 1576–1578 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (6)

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 392–394 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12, 1633–1635 (2000).
[CrossRef]

M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibres,” IEEE Photon. Technol. Lett. 10, 373–375 (1998).
[CrossRef]

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13, 445–447 (2001).
[CrossRef]

S.-G. Park, A. H. Gnauck, J. M. Wiesenfeld, and L. D. Garrett, “40-Gb/s transmission over multiple 120-km spans of conventional single-mode fiber using highly dispersed pulses,” IEEE Photon. Technol. Lett. 12, 1085–1087 (2000).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Lett. (4)

Other (6)

S. K. Turitsyn, E. G. Turitsyna, V. K. Mezentsev, and M. P. Fedoruk, “On the theory of intra-channel four-wave mixing,” in Conference on Lasers and Electro-Optics (CLEO/Europe), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper CThE42.

F. Merlaud and S. K. Turitsyn, “Intra-channel four wave mixing and ghost pulses generation: time domain approach,” in Proceedings of the European Conference on Optical Communications (VDE Verlag, Berlin, 2000), Vol. 3, pp. 35–36.

T. Inoue and A. Maruta, “Pre-spread RZ pulse transmission for reducing intra-channel nonlinear interactions,” in Proceedings of the IEEE LEOS 13th Annual Meeting (IEEE Lasers and Electro-Optics Society, Piscataway, N.J., 2000), Vol. 1, pp.92–93.

P. K. Cheo, Fiber Optics & Optoelectronics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1990), Chap. 13.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), pp. 64–69.

T. Inoue and A. Maruta, “Reduction of intra-channel four wave mixing in strongly dispersion-managed line for high speed OTDM system,” in Nonlinear Guided Waves and Their Applications, Vol. 55 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 211–213.

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Figures (9)

Fig. 1
Fig. 1

Overlap of adjacent pulses and magnitude of XPM.

Fig. 2
Fig. 2

Pulse degradation caused by intrachannel FWM.

Fig. 3
Fig. 3

Highly dispersed pulses (ui) and their instantaneous frequencies.

Fig. 4
Fig. 4

Energy growth of ghost pulse u0.

Fig. 5
Fig. 5

Transmissible distance and spectral efficiency versus various initial pulse widths for 80-Gbit/s PRBS inputs in model (a). Solid curve, transmissible distance; dotted curve, spectral efficiency.

Fig. 6
Fig. 6

Transmissible distance with a pulse energy of 0.05 pJ for 40-, 80-, and 160-Gbit/s systems.

Fig. 7
Fig. 7

(i) Schematic profiles of dispersion maps and (ii) accumulated dispersion versus propagation distance for models (a)–(d).

Fig. 8
Fig. 8

Eye diagrams of waveforms after 1000-km propagation for models (a)–(d).

Fig. 9
Fig. 9

Waveforms after 1000-km transmission for model (d) with the effects of amplifier noise and guiding filters. Calculated Q factor, 14.7.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

iuZ+d(Z)22uT2+S(Z)|u|2u=0,
uj(T, Z)=2Eτπexp-2(1-iC)T-Tjτ2-iκj(T-Tj)+iθj.
dκdZ=2π8ES(Z)Ts2F(x),
Δωj(T, Z)=-T-jTsD(Z)+τ04/16D(Z)+ω0,
Δωj(T, Z)-T-jTsD(Z).
Ωj=(m+n-l-j-α)Ts/D(Z).
dτdZ=4d(Z)Cτ,
dCdZ=4d(Z)(1+C2)τ2-2πS(Z)Eτ,
dθjdZ=-2d(Z)τ2+5S(Z)E22πτ.
iu0Z+d(Z)22u0T2=R(T, Z)=-S(Z)m,n umunum+n*.
u0˜(ω, Z)=-i 0Z R˜(ω, ζ)expiω22[D(ζ)-D(Z)]dζ
R˜(ω, Z)=-S(Z)2E3ππ(3-iC)τ1/2 m,n exp(Θm,n),
Θm,n=I(θm+θn-θm+n)-4Tsτ2(m2+mn+n2+imnC)+23-iC(m+n)2Tsτ+iω4τ2.
θm(Z)=θj(Z)+(m-j)Δθ0,
θm+θn-θm+n-j=[θj+(m-j)Δθ0]+[θj+(n-j)Δθ0]-[θj+(m+n-2j)Δθ0]=θj.
R˜(0, Z)=-S(Z) 2E3ππτ03/2D(Z)exp[i(θ0+π/4)]×m,n exp[-α(m, n)+iβ(m, n)],

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