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

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1997 (8)

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

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

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef] [PubMed]

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

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 (3)

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

1992 (1)

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

1991 (2)

1195 (1)

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).
[CrossRef]

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).
[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]

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).
[CrossRef]

Chen, H. H.

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[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]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Forghieri, F.

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Georges, T.

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

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).
[CrossRef]

Gnauk, A. H.

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).
[CrossRef]

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.

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).
[CrossRef]

Grudinin, A. B.

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).
[CrossRef]

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.

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).
[CrossRef]

Ibsen, 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).
[CrossRef]

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).
[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]

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).
[CrossRef]

Kubota, H.

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

Laming, R. I.

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).
[CrossRef]

Le Guen, D.

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).
[CrossRef]

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).
[CrossRef]

Legros, E.

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).
[CrossRef]

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).
[CrossRef]

Menyuk, C. R.

Michaud, G.

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).
[CrossRef]

Morita, I.

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).
[CrossRef]

Moulinard, M. L.

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).
[CrossRef]

Nakazawa, M.

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

Peckham, D. W.

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).
[CrossRef]

Romagnoli, 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).
[CrossRef]

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).
[CrossRef]

Schiffini, A.

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).
[CrossRef]

Sekine, K.

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).
[CrossRef]

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).
[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]

Sulhoff, J. W.

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).
[CrossRef]

Suzuki, M.

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).
[CrossRef]

Tage, H.

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).
[CrossRef]

Tkach, R. W.

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).
[CrossRef]

Turitsyn, S. K.

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

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.

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Figures (8)

Fig. 1
Fig. 1

Setup of transmission line.

Fig. 2
Fig. 2

Phase diagram of the propagation of dispersion-managed solitons for D=100, zA=0.2, c=-19.8 (99% dispersion compensation), E=75, and G=100.

Fig. 3
Fig. 3

Interaction of two orthogonally polarized solitons: evolution of α1, analytic (point B, thick solid curve; points A and C, lower and upper thin solid curves) and numeric (circles) results. D=100, zA=0.2, c=-19.8, G=100, E=75, C(0)=-1.72, and γ(0)=0.675.

Fig. 4
Fig. 4

Interaction force f/E versus C (solid curve) for α=4, γ=0.675, E=75, and κ=1.

Fig. 5
Fig. 5

Soliton-interaction-induced-frequency shift as a function of the input parameters γ and C for α=4, γ=0.675, E=75, and κ=1.

Fig. 6
Fig. 6

Same as Fig. 3 with D=-98, zA=0.2, c=19.8, G=100, E=75, C(0)=2.14, and γ(0)=0.604.

Fig. 7
Fig. 7

Analytical (point B, thick solid curve; points A and C, lower and upper thin solid curves) and numerical (in-phase, circles; opposition phase, crosses) values of α and of the frequency shift (dashed curve).

Fig. 8
Fig. 8

Experimental log10 (bit error rate) of a 20-Gbit/s soliton transmission over 1100 km (thin solid curves) and theoretical limits (thick solid curves).

Equations (19)

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iqz+12D(z)qtt+a(z)|q|2q=0.
WWz=-bD,
W2bz=-(1+b2)D+aE2π W,
ϕz=5aE4W2π,
Cz=D+C2-1γ2 aEW32π,
γz=-2γC aEW32π.
iq1z+12D(z)q1tt+a(z)[|q1|2+κ|q2|2]q1=0,
iq2z+12D(z)q2tt+a(z)[|q2|2+κ|q1|2]q2=0,
2Lj=i(qjzqj*-qjqjz*)-D|qjt|2+a|qj|4forj=1, 2,
L12=aκ|q1|2|q2|2,
qj(z, t)=Bj exp-(1+ibj) (t-αj)22Wj2-iωjt+iϕj
forj=1, 2.
z LXz=LX,
αjz=-Dωj,
E1ω1z=-E2ω2z=2aκE1E22π αW3 exp-2 α2W2=af,
γjz=-2γjCjFj,
Cjz=D+(Cj2-γj-2)Fj,
EjFj=a2π Ej2Wj3+κ E1E2W3 1-4 α2W2exp-2 α2W2.
fmax/E=334 exp(3/2)2π κEα2,

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