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## Soliton interaction in dispersion-managed links

Thierry Georges »View Author Affiliations

*France Télécom-CNET, 22307 Lannion, France*

JOSA B, Vol. 15, Issue 5, pp. 1553-1560 (1998)

http://dx.doi.org/10.1364/JOSAB.15.001553

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### Abstract

Terrestrial systems based on dispersion-managed solitons are limited by the signal-to-noise-ratio degradation that is due to amplifier noise and soliton interaction. The propagation of dispersion-managed solitons is modeled with two parameters. Rules for determining easily the steady propagation conditions are given. For the study of the soliton interaction, two more parameters per soliton are required (time and frequency). An accurate modeling of the time and frequency shifts induced by the interaction is derived with a Lagrangian formalism. Both single and alternate polarizations are considered. The interaction is shown to be increased with dispersion-managed solitons as compared to path-averaged solitons; however, system performance is shown to be better with dispersion-managed solitons thanks to increased soliton energy.

© 1998 Optical Society of America

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

(190.0190) Nonlinear optics : Nonlinear optics

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(260.2030) Physical optics : Dispersion

**Citation**

Thierry Georges, "Soliton interaction in dispersion-managed links," J. Opt. Soc. Am. B **15**, 1553-1560 (1998)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-15-5-1553

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### References

- F. M. Knox, P. Harper, P. N. Kean, I. Bennion, and N. J. Doran, “Soliton transmission at 10 Gbit/s over 2022 km of standard fibre with dispersion compensation,” in 22nd European Conference on Optical Communication (IEEE, New York, 1996), paper WeC.3.2, pp. 101–104.
- D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, “200Gbit/s 100km-span soliton WDM transmission over 1000km of standard fibre with dispersion compensation and pre-chirping,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper PD17.
- D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, F. Devaux, B. Charbonnier, and T. Georges, “320 Gbit/s soliton WDM transmission over 1100 km with 100 km dispersion-compensated spans of standard,” in 23rd European Conference on Optical Communication (IEEE, New York, 1997), postdeadline paper, p. 25–28.
- N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, “20 Gbit/s, 8100 km straight-line single-channel soliton-based RZ transmission experiment using periodic dispersion compensation,” in 21st European Conference on Optical Communication (IEEE, New York, 1995), postdeadline paper ThA3.5, pp. 983–986.
- J. Jacob, E. A. Golovchenko, A. N. Philipetski, G. M. Carter, and C. R. Menyuk, “Long-haul, 10 Gbit/s error-free transmission of NRZ data and dispersion-managed solitons using the same transmission system,” in 23rd European Conference on Optical Communication (IEEE, New York, 1997), pp. 1.11–1.14.
- H. Kubota and M. Nakazawa, “Partial soliton communication system,” Opt. Commun. 87, 15–18 (1992).
- F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fiber at 1.55 μm and the use of dispersion compensation,” IEEE J. of Lightwave Technol. 13, 1955–1963 (1995).
- M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Tage, and S. Akiba, “Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1195).
- I. Gabitov and S. K. Turitsyn, “Average pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1997).
- A. B. Grudinin and I. A. Goncharenko, “Increased amplifier spacing in soliton system with partial dispersion compensation,” Electron. Lett. 33, 1602–1603 (1997).
- T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).
- I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
- B. A. Malomed, “Pulse propagation in a nonlinear optical fi-ber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).
- 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).
- N. J. Smith, W. Forysiak, N. J. Doran, “Gordon-Haus jitter reduction in enhanced power soliton systems,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper ThN5.
- T. Georges and B. Charbonnier, “Pre-chirping and dispersion compensation for long-haul 20-Gbit/s soliton transmission at 1.55 μm on non dispersion shifted fibers,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper WH2.
- P. K. A. Wai, C. R. Menyuk, H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1735–1737 (1991).
- A. B. Grudinin, I. A. Goncharenko, S. Gray, and D. N. Payne, in 21st European Conference on Optical Communication (IEEE, New York, 1995), paper TuL1.3, pp. 295–298.
- F. Favre, D. Le Guen, M. L. Moulinard, M. Henry, G. Michaud, F. Devaux, E. Legros, B. Charbonnier, and T. Georges, “Demonstration of soliton transmission at 20 Gbit/s over 2200 km of standard fibre with dispersion compensation and pre-chirping,” Electron. Lett. 33, 511–512 (1997).
- F. Favre, D. Le Guen, and F. Devaux, “4×20 Gbit/s soliton WDM transmission over 2000 km with 100 km dispersion-compensated spans of standard fibre,” Electron. Lett. 33, 1234–1235 (1997).
- E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “Numerical and experimental comparison between the dispersion-allocated soliton, RZ and NRZ pulses at zero group velocity dispersion,” in 23rd European Conference on Optical Communication (IEEE, New York, 1997), pp. 3.327–3.330.
- A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).
- N. Kikuchi, S. Sasaki, and K. Sekine, “10 Gbit/s dispersion-compensated transmission over 2245 km conventional fibers in a recirculating loop,” Electron. Lett. 31, 375–377 (1995).
- R. W. Tkach, R. M. Derosier, F. Forghieri, A. H. Gnauk, A. M. Vengsarkar, D. W. Peckham, J. L. Zyskind, J. W. Sulhoff, and A. R. Chraplyvy, “Transmission of 8 20-Gbit/s channels over 232 km of conventional fiber,” IEEE Photonics Technol. Lett. 7, 1359–1371 (1995).
- P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Effects of randomly varying birefringence on soliton interactions in optical fibers,” Opt. Lett. 16, 1735–1737 (1991).
- D. Anderson, Phys. Rev. A 6, 3135–3137 (1983); T. Ueda and W. L. Kath, Phys. Rev. A 42, 563–570 (1990).
- B. Charbonnier and T. Georges, “Numerical investigation of the path-averaged soliton validity domain without soliton control,” Electron. Lett. 32, 126–128 (1996); B. Charbonnier and T. Georges, “Influence of power variations along a transmission line on soliton interaction,” Opt. Commun. 132, 232–235 (1996).

**Akiba, S.**

- M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Tage, and S. Akiba, “Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1195).

**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).

**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).

**Charbonnier, B.**

- F. Favre, D. Le Guen, M. L. Moulinard, M. Henry, G. Michaud, F. Devaux, E. Legros, B. Charbonnier, and T. Georges, “Demonstration of soliton transmission at 20 Gbit/s over 2200 km of standard fibre with dispersion compensation and pre-chirping,” Electron. Lett. 33, 511–512 (1997).

**Chen, H. H.**

- P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Effects of randomly varying birefringence on soliton interactions in optical fibers,” Opt. Lett. 16, 1735–1737 (1991).
- P. K. A. Wai, C. R. Menyuk, H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1735–1737 (1991).

**Chraplyvy, A. R.**

- R. W. Tkach, R. M. Derosier, F. Forghieri, A. H. Gnauk, A. M. Vengsarkar, D. W. Peckham, J. L. Zyskind, J. W. Sulhoff, and A. R. Chraplyvy, “Transmission of 8 20-Gbit/s channels over 232 km of conventional fiber,” IEEE Photonics Technol. Lett. 7, 1359–1371 (1995).

**Derosier, R. M.**

- R. W. Tkach, R. M. Derosier, F. Forghieri, A. H. Gnauk, A. M. Vengsarkar, D. W. Peckham, J. L. Zyskind, J. W. Sulhoff, and A. R. Chraplyvy, “Transmission of 8 20-Gbit/s channels over 232 km of conventional fiber,” IEEE Photonics Technol. Lett. 7, 1359–1371 (1995).

**Devaux, F.**

- F. Favre, D. Le Guen, and F. Devaux, “4×20 Gbit/s soliton WDM transmission over 2000 km with 100 km dispersion-compensated spans of standard fibre,” Electron. Lett. 33, 1234–1235 (1997).
- F. Favre, D. Le Guen, M. L. Moulinard, M. Henry, G. Michaud, F. Devaux, E. Legros, B. Charbonnier, and T. Georges, “Demonstration of soliton transmission at 20 Gbit/s over 2200 km of standard fibre with dispersion compensation and pre-chirping,” Electron. Lett. 33, 511–512 (1997).

**Doran, N. J.**

- F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fiber at 1.55 μm and the use of dispersion compensation,” IEEE J. of Lightwave Technol. 13, 1955–1963 (1995).

**Durkin, M.**

- A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).

**Edagawa, N.**

- M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Tage, and S. Akiba, “Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1195).

**Favre, F.**

- F. Favre, D. Le Guen, and F. Devaux, “4×20 Gbit/s soliton WDM transmission over 2000 km with 100 km dispersion-compensated spans of standard fibre,” Electron. Lett. 33, 1234–1235 (1997).

**Forghieri, F.**

**Forysiak, W.**

- F. M. Knox, W. Forysiak, and N. J. Doran, “10 Gbit/s soliton communication systems over standard fiber at 1.55 μm and the use of dispersion compensation,” IEEE J. of Lightwave Technol. 13, 1955–1963 (1995).

**Franco, P.**

- A. B. Grudinin, M. Durkin, M. Ibsen, R. I. Laming, A. Schiffini, P. Franco, E. Grandi, and M. Romagnoli, “Straight-line 10 Gbit/s soliton transmission over 100 km of standard fibre with in-line chirped fibre grating for partial dispersion compensation,” Electron. Lett. 33, 1572–1573 (1997).

**Gabitov, I.**

- I. Gabitov and S. K. Turitsyn, “Average pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1997).
- I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).

**Georges, T.**

- T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).

**Gnauk, A. H.**

**Goncharenko, I. A.**

- A. B. Grudinin and I. A. Goncharenko, “Increased amplifier spacing in soliton system with partial dispersion compensation,” Electron. Lett. 33, 1602–1603 (1997).

**Grandi, E.**

**Grudinin, A. B.**

- A. B. Grudinin and I. A. Goncharenko, “Increased amplifier spacing in soliton system with partial dispersion compensation,” Electron. Lett. 33, 1602–1603 (1997).

**Henry, M.**

**Ibsen, M.**

**Kikuchi, N.**

- N. Kikuchi, S. Sasaki, and K. Sekine, “10 Gbit/s dispersion-compensated transmission over 2245 km conventional fibers in a recirculating loop,” Electron. Lett. 31, 375–377 (1995).

**Knox, F. M.**

**Kubota, H.**

- H. Kubota and M. Nakazawa, “Partial soliton communication system,” Opt. Commun. 87, 15–18 (1992).

**Laming, R. I.**

**Le Guen, D.**

**Legros, E.**

**Malomed, B. A.**

- B. A. Malomed, “Pulse propagation in a nonlinear optical fi-ber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).

**Menyuk, C. R.**

- P. K. A. Wai, C. R. Menyuk, H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1735–1737 (1991).
- P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Effects of randomly varying birefringence on soliton interactions in optical fibers,” Opt. Lett. 16, 1735–1737 (1991).

**Michaud, G.**

**Morita, I.**

**Moulinard, M. L.**

**Nakazawa, M.**

- H. Kubota and M. Nakazawa, “Partial soliton communication system,” Opt. Commun. 87, 15–18 (1992).

**Peckham, D. W.**

**Romagnoli, M.**

**Sasaki, S.**

- N. Kikuchi, S. Sasaki, and K. Sekine, “10 Gbit/s dispersion-compensated transmission over 2245 km conventional fibers in a recirculating loop,” Electron. Lett. 31, 375–377 (1995).

**Schiffini, A.**

**Sekine, K.**

**Shapiro, E. G.**

- I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).

**Smith, N. J.**

**Sulhoff, J. W.**

**Suzuki, M.**

**Tage, H.**

**Tkach, R. W.**

**Turitsyn, S. K.**

- I. Gabitov and S. K. Turitsyn, “Average pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1997).

**Vengsarkar, A. M.**

**Wai, P. K. A.**

**Yamamoto, S.**

**Zyskind, J. L.**

### Electron. Lett.

### IEEE J. of Lightwave Technol.

### IEEE Photonics Technol. Lett.

### Opt. Commun.

- B. A. Malomed, “Pulse propagation in a nonlinear optical fi-ber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).
- H. Kubota and M. Nakazawa, “Partial soliton communication system,” Opt. Commun. 87, 15–18 (1992).

### Opt. Lett.

- T. Georges, “Extended path-averaged soliton regime in highly dispersive fibers,” Opt. Lett. 22, 679–681 (1997).

### Other

- D. Anderson, Phys. Rev. A 6, 3135–3137 (1983); T. Ueda and W. L. Kath, Phys. Rev. A 42, 563–570 (1990).
- B. Charbonnier and T. Georges, “Numerical investigation of the path-averaged soliton validity domain without soliton control,” Electron. Lett. 32, 126–128 (1996); B. Charbonnier and T. Georges, “Influence of power variations along a transmission line on soliton interaction,” Opt. Commun. 132, 232–235 (1996).
- A. B. Grudinin, I. A. Goncharenko, S. Gray, and D. N. Payne, in 21st European Conference on Optical Communication (IEEE, New York, 1995), paper TuL1.3, pp. 295–298.
- F. M. Knox, P. Harper, P. N. Kean, I. Bennion, and N. J. Doran, “Soliton transmission at 10 Gbit/s over 2022 km of standard fibre with dispersion compensation,” in 22nd European Conference on Optical Communication (IEEE, New York, 1996), paper WeC.3.2, pp. 101–104.
- D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, “200Gbit/s 100km-span soliton WDM transmission over 1000km of standard fibre with dispersion compensation and pre-chirping,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper PD17.
- D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, F. Devaux, B. Charbonnier, and T. Georges, “320 Gbit/s soliton WDM transmission over 1100 km with 100 km dispersion-compensated spans of standard,” in 23rd European Conference on Optical Communication (IEEE, New York, 1997), postdeadline paper, p. 25–28.
- N. Edagawa, I. Morita, M. Suzuki, S. Yamamoto, H. Taga, and S. Akiba, “20 Gbit/s, 8100 km straight-line single-channel soliton-based RZ transmission experiment using periodic dispersion compensation,” in 21st European Conference on Optical Communication (IEEE, New York, 1995), postdeadline paper ThA3.5, pp. 983–986.
- J. Jacob, E. A. Golovchenko, A. N. Philipetski, G. M. Carter, and C. R. Menyuk, “Long-haul, 10 Gbit/s error-free transmission of NRZ data and dispersion-managed solitons using the same transmission system,” in 23rd European Conference on Optical Communication (IEEE, New York, 1997), pp. 1.11–1.14.
- N. J. Smith, W. Forysiak, N. J. Doran, “Gordon-Haus jitter reduction in enhanced power soliton systems,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper ThN5.
- T. Georges and B. Charbonnier, “Pre-chirping and dispersion compensation for long-haul 20-Gbit/s soliton transmission at 1.55 μm on non dispersion shifted fibers,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper WH2.
- E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “Numerical and experimental comparison between the dispersion-allocated soliton, RZ and NRZ pulses at zero group velocity dispersion,” in 23rd European Conference on Optical Communication (IEEE, New York, 1997), pp. 3.327–3.330.

**1997, Gabitov, Opt. Commun.**

**1997, Malomed, Opt. Commun.**

**1997, Favre, Electron. Lett.**

**1997, Favre, Electron. Lett.**

**1997, Grudinin, Electron. Lett.**

**1997, Grudinin, Electron. Lett.**

**1997, Georges, Opt. Lett.**

**1997, Gabitov, Opt. Lett.**

**1996, Smith, Electron. Lett.**

**1995, Knox, IEEE J. of Lightwave Technol.**

**1995, Kikuchi, Electron. Lett.**

**1995, Tkach, IEEE Photonics Technol. Lett.**

**1992, Kubota, Opt. Commun.**

- H. Kubota and M. Nakazawa, “Partial soliton communication system,” Opt. Commun. 87, 15–18 (1992).

**1991, Wai, Opt. Lett.**

**1991, Wai, Opt. Lett.**

**1195, Suzuki, Electron. Lett.**

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