Abstract

We compare nonlinear channel interactions in classical soliton, periodically-stationary dispersion-managed soliton (DMS), and chirped-return-to-zero (CRZ) systems. We studied multichannel systems with a single pulse in each channel and a more general case with multiple bit streams in each channel. First, we find that in classical soliton systems, the distortions are reversible, while in the DMS and CRZ systems they are not. Second, we find that the classical soliton system shows no increase in the degradation as the number of channels increases, while both the DMS and CRZ systems do show an increase in the degradation.

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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-Hauss 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. F. Le Guen, S. Del Burgo, M. L. Moulinard, D. Grot, M. Henry, F. Favre, and T. Georges, "Narrow band 1.02 Tbit/s (51x20 Gbit/s) soliton DWDM transmission over 1000 km of standard fiber with 100 km amplifier spans," in Optical Fiber Communication Conference}, OSA Technical Digest (Optical Society of America, Washington DC, 1999), PD4.
  4. A. Hasegawa, S. Kumar, and Y. Kodama, "Reduction of collision-induces timing jitters in dispersion-managed soliton transmission systems," Opt. Lett. 21, 39-41 (1996).
    [CrossRef] [PubMed]
  5. N. S. Bergano, C. R. Davidson, M. A. Mills, P. Corbett, S. G. Evangelides, B. Pedersen, R. Menges, J. L. Zyskind, J. W. Sulhoff, A. K. Srivastava, C. Wolf, and J. Judkins, "Long-haul WDM transmission using optimal channel modulation" in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 1997), PD16.
  6. R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, "Convergence of the CRZ and DMS formats in WDM systems using dispersion management" in Optical Fiber Communication Conference, OSA Technical digest (Optical Society of America, Washington DC, 2000), FC1, 32-34.
  7. C. R. Menyuk, "Application of multiple-length scale methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).
    [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, CA 1995).
  9. V. S. Grigoryan, C. R. Menyuk, and R.-M. Mu, "Calculation of timing and amplitude jitter in dispersion-managed optical fiber communications using linearization," J. Lightwave Technol. 17, 1347-1356 (1999).
    [CrossRef]
  10. M. J. Ablowitz, G. Biondini, S. Chakravarty, R. B. Jenkins, and J. R. Sauer, "Four-wave mixing in wavelength-division-multiplexed soliton systems: ideal fibers," J. Opt. Soc. Am. B 14, 1788-1794 (1997).
    [CrossRef]
  11. M. J. Ablowitz, G. Biondini, S. Chakravarty, R. B. Jenkins, and J. R. Sauer, "Four-wave mixing in wavelength-division-multiplexed soliton systems: damping and amplification," Opt. Lett. 21, 1646-1648 (1996).
    [CrossRef] [PubMed]
  12. A. Hasegawa, Solitons in Optical Communications (Clarendon Press, Oxford, NY 1995).
  13. F. Foghieri, R. W. Tkach, A. R. Chraplyvy, "Fiber nonlinearities and their impact on transmission systems" in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, CA 1997).

Other (13)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, "Reduction of Gordon-Hauss 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]

F. Le Guen, S. Del Burgo, M. L. Moulinard, D. Grot, M. Henry, F. Favre, and T. Georges, "Narrow band 1.02 Tbit/s (51x20 Gbit/s) soliton DWDM transmission over 1000 km of standard fiber with 100 km amplifier spans," in Optical Fiber Communication Conference}, OSA Technical Digest (Optical Society of America, Washington DC, 1999), PD4.

A. Hasegawa, S. Kumar, and Y. Kodama, "Reduction of collision-induces timing jitters in dispersion-managed soliton transmission systems," Opt. Lett. 21, 39-41 (1996).
[CrossRef] [PubMed]

N. S. Bergano, C. R. Davidson, M. A. Mills, P. Corbett, S. G. Evangelides, B. Pedersen, R. Menges, J. L. Zyskind, J. W. Sulhoff, A. K. Srivastava, C. Wolf, and J. Judkins, "Long-haul WDM transmission using optimal channel modulation" in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 1997), PD16.

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, "Convergence of the CRZ and DMS formats in WDM systems using dispersion management" in Optical Fiber Communication Conference, OSA Technical digest (Optical Society of America, Washington DC, 2000), FC1, 32-34.

C. R. Menyuk, "Application of multiple-length scale methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, CA 1995).

V. S. Grigoryan, C. R. Menyuk, and R.-M. Mu, "Calculation of timing and amplitude jitter in dispersion-managed optical fiber communications using linearization," J. Lightwave Technol. 17, 1347-1356 (1999).
[CrossRef]

M. J. Ablowitz, G. Biondini, S. Chakravarty, R. B. Jenkins, and J. R. Sauer, "Four-wave mixing in wavelength-division-multiplexed soliton systems: ideal fibers," J. Opt. Soc. Am. B 14, 1788-1794 (1997).
[CrossRef]

M. J. Ablowitz, G. Biondini, S. Chakravarty, R. B. Jenkins, and J. R. Sauer, "Four-wave mixing in wavelength-division-multiplexed soliton systems: damping and amplification," Opt. Lett. 21, 1646-1648 (1996).
[CrossRef] [PubMed]

A. Hasegawa, Solitons in Optical Communications (Clarendon Press, Oxford, NY 1995).

F. Foghieri, R. W. Tkach, A. R. Chraplyvy, "Fiber nonlinearities and their impact on transmission systems" in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, CA 1997).

Supplementary Material (9)

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Figures (14)

Figure 1.
Figure 1.

(240 kB) Animation of a two-soliton collision. The normalized frequency spacing is 15, corresponding to 210 GHz.

Figure 2.
Figure 2.

Evolution of the pulse distortion δ(z) and sideband energy ε(z) with distance in two-soliton collisions. The blue, green and red curves correspond to frequency separations of 70, 140 and 210 GHz respectively.

Figure 3.
Figure 3.

(256 kB) Animation of a two-pulse collision in the DMS system. The normalized frequency spacing is 10, corresponding to 140 GHz.

Figure 4.
Figure 4.

Evolution of the pulse distortion δ(z) and sideband energy ε(z) with distance in the DMS system. The blue, green and red curves correspond to the frequency separations of 70, 140 and 210 GHz respectively.

Figure 5.
Figure 5.

(180 kB) Animation of a two-pulse collision in the CRZ system. The normalized frequency spacing is 15, corresponding to 210 GHz.

Figure 6.
Figure 6.

Evolution of the pulse distortion δ(z) and sideband energy ε(z) with distance in the CRZ system. The blue, green and red curves correspond to frequency separations of 70, 140 and 210 GHz respectively.

Figure 7.
Figure 7.

(396 kB) Animation of a three-soliton collision. The normalized frequency spacing is 10, corresponding to 140 GHz.

Figure 8.
Figure 8.

(228 kB) Animation of a three-pulse collision in the DMS system. The normalized frequency spacing is 10, corresponding to 140 GHz.

Figure 9.
Figure 9.

(204 kB) Animation of a three-pulse collision in the CRZ system. The normalized frequency spacing is 15, corresponding to 210 GHz.

Figure 10.
Figure 10.

Dependence of the pulse distortion and sideband energy on the channel spacing in the DMS system. The green and blue curves correspond to the mean plus standard deviation and the mean minus standard deviation for the three-pulse interactions. The red curve corresponds to the two-pulse collision.

Figure 11.
Figure 11.

Dependence of the pulse distortion and sideband energy on the channel spacing in the CRZ system. The green and blue curves correspond to the mean plus standard deviation and the mean minus standard deviation for the three-pulse interactions. The red curve corresponds to the two-pulse collision.

Figure 12.
Figure 12.

(332 kB animation) Evolution of the electrical eye diagram in the DMS system.

Figure 13.
Figure 13.

(220 kB animation) Evolution of the electrical eye diagram in the CRZ system.

Figure 14.
Figure 14.

(324 kB animation) Evolution of the electrical eye diagram in the classical soliton system.

Equations (4)

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i q z 1 2 β ( z ) 2 q t 2 + i 6 β ( z ) 3 q t 3 + γ q 2 q = i Γ ( z ) q ,
q ( z = 0 , t ) = u ( t t 1 ) exp ( i ω 1 t ) + u ( t t 2 ) exp ( i ω 2 t ) ,
ε sb ( z ) = Ω sb q ˜ ( z , ω ) 2 d ω Ω 1 q ˜ ( z , ω ) 2 d ω ,
δ ( z ) = Ω 1 q ˜ ( z , ω ) q ˜ 1 ( z , ω ) d ω Ω 1 q ˜ 1 ( z , ω ) d ω ,

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