Timing-jitter reduction for a dispersion-managed soliton system: experimental evidence

We have measured the timing jitter for dispersion-managed solitons in a recirculating loop for distances up to 20,000 km. The data were obtained with modulated data, 2(7) - 1 and 2(23) - 1 pseudorandom binary sequence patterns, at 10-Gbit/s rates and with an unmodulated pulse train at 10 GHz. We have obtained good agreement with our data, using a filtered Gordon-Haus model for the timing jitter reduced by the energy enhancement of our solitons relative to solitons in a fiber with a constant dispersion equal to our map's path-average dispersion. We have also measured a bit-error rate of <10(-9) at a distance of 15,000 km.     

Analysis of soliton collisions in a wavelength-division- multiplexed dispersion-managed soliton transmission system

Timing jitter induced by soliton collisions is the leading nonlinear penalty in wavelength-division-multiplexed (WDM) dispersion-managed soliton transmission. Through analysis and numerical simulations we show that consecutive complete collisions together with partial collisions at the system output cause approximately the same amount of timing shift as partial collisions at the system input. We further show that the worst-case timing shift diverges logarithmically with the total number of WDM channels and linearly with the total transmission distance. However, the probability for such worst cases to occur decreases exponentially with channel spacing, total number of WDM channels, and transmission distance. We conclude that only the effects caused by adjacent channels need to be considered in a high channel count WDM system.     

Stochastic perturbation in quasi—ideal dispersion—managed soliton system

The model of stochastic perturbation is built up systematically in quasi-ideal dispersion-managed soliton system,its influence on soliton propagation is investigated by both the variational approach and the numerical simulation,and it is found that the stochastic perturbation leads to disintegration of soliton and enhances the interaction between solitons.The nonlinear gain and filter are introduced to suppress effectively the influence on both soliton propagation and interaction.     

Collisions in dispersion-managed soliton propagation

We study collisions in dispersion-managed soliton propagation for wavelength-division multiplexing application at zero net dispersion when the Gordon-Haus timing jitter is removed. We show that the collisions can lead to group-velocity changes and spectral collapse. Large channel separation ameliorates the effects. Filters prevent spectral collapse but do not affect the velocity changes.     

Collision-induced timing jitter in dispersion-managed WDM soliton system with filtering

Taking into account the randomicity of collision positions and the arbitrary encoding of data in channel,the influences of different dispersion management on collision-induced timing jitter in a filtered wavelength division multiplexing (WDM) soliton system are obtained statistically and numerically by applying a set of coupled ordinary differential equations which are derived through variational procedure. The optimal dispersion managements which can greatly reduce the collision-induced timing jitter are found. The multi-channel collision-induced timing jitters in a filtered WDM soliton system are given with an optimal dispersion management and constant dispersion.     

Long-range soliton interactions in dispersion-managed links

A numerical analysis of soliton propagation in a dispersion-compensated transmission system reveals the presence of a small dispersive-wave contribution to the propagating soliton that increases dramatically whenever the input soliton energy is detuned from its optimal value. A straightforward consequence of the dispersive-wave emission is an unexpectedly strong contribution to the long-range soliton-soliton interaction. We show that the combination of long- and short-range interactions induces soliton timing jitter that grows larger than that which arises from the Gordon-Haus effect.     

Optimal allocation of amplifiers in a dispersion-managed line for a wavelength-division-multiplexed soliton transmission system

Optimal allocation of amplifiers in a dispersion-managed line is theoretically derived by means of minimizing the collision-induced frequency shift in a two-channel wavelength-division-multiplexed soliton transmission system. Almost complete cancellation of the frequency shift can be obtained for such a system with any strength of dispersion management.     

10-Gbit/s dispersion-managed soliton transmission over 16,500 km in standard fiber by reduction of soliton interactions

We show experimentally and numerically that in high-speed strongly dispersion-managed standard fiber soliton systems nonlinear interactions limit the propagation distance. We present results that show that the effect of these interactions can be significantly reduced by appropriate location of the amplifier within the dispersion map. Using this technique, we have been able to extend the propagation distance of 10-Gbit/s 2(31)-1pseudorandom binary sequence soliton data to 16, 500km over standard fiber by use of dispersion compensation. To our knowledge this distance is the farthest transmission over standard fiber without active control ever reported, and it was achieved with the amplifier placed after the dispersion-compensating fiber in a recirculating loop.     

Correlation between randomly varying birefringence and random dispersion map in a dispersion-managed soliton system

The correlation between perturbations caused by randomly varying birefringence and a random dispersion map is considered in a dispersion-managed soliton system, and their effects on soliton propagation and interaction are investigated numerically. These perturbations lead to the disintegration of a soliton, and enhance the interaction between solitons. The correlation plays an important role, and reinforces these effects. Furthermore, there is a stochastic resonance between two perturbations in the system; here the effect is the largest, and the corresponding distance until disintegration is the shortest. Finally, nonlinear gain and a filter are introduced to effectively suppress these effects.     

Collision-induced timing shifts in dispersion-managed soliton systems

The frequency and timing shifts associated with dispersion-managed solitons in a wavelength-division multiplexed system are computed by the numerically efficient Poisson sum technique. Analytical formulas are attainable by use of this approach with a Gaussian approximation for the soliton. The results are favorably compared with known results for the frequency shift. The method also applies to quasi-linear return-to-zero transmission formats.     

Gordon Haus effect in dispersion-managed soliton systems

We derive an expression for the timing jitter of a soliton owing to amplifier noise in dispersion-managed fiber systems. We show that the timing jitter is a function of the pulse width as well as of the chirp at the amplifier location and that it can be minimized by a proper choice of the amplifier position relative to the dispersion map.     

Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems

We theoretically analyze nonlinear interactions between chirped solitons in dispersion-managed wavelength-division-multiplexing (WDM) systems. We employ the perturbation method to evaluate frequency and chirp shifts caused by collisions among different WDM channels. It is shown that a chirped soliton suffers less frequency shift and time displacement than an ideal soliton, indicating its potential applicability for WDM systems.     

Propagation properties of strongly dispersion-managed soliton trains

We analyze the intra-channel interactions of strongly dispersion-managed soliton trains. We systematically study the transmission system in terms of a coalescence distance. The impact of third-order dispersion and the positions of the amplifiers are evaluated. We also study the effect produced on the interaction patterns by the modifications in the pulse timings and relative amplitudes. Based on the results obtained, we propose a channel encoding scheme which gives a noiseless capacity very close to that of the conventional binary soliton signaling and, yet, provides a significant improvement in the interaction limitations.     

Stability and optimization of dispersion-managed soliton control

Dispersion-managed solitons with in-line all-optical regeneration are shown to be subject to amplitude and timing-jitter instabilities. We identify and discuss the different natures of these instabilities by means of a linear stability analysis, which is in good agreement with the full numerical solutions of the governing equations. Stable pulse propagation can be achieved through appropriate choices of dispersion map and pulse energy.     

Efficient modeling of phase jitter in dispersion-managed soliton systems

The variational method is used to derive correlation equations that model phase jitter in dispersion-managed soliton systems. The predictions of these correlation equations are consistent with numerical solutions of the nonlinear Schr?dinger equation on which they are based.     

Noise-induced amplitude and chirp jitter in dispersion-managed soliton communications

An analytic theory is presented that demonstrates that noise-induced amplitude and quadratic chirp jitter in a dispersion-managed soliton system can impose a fundamental transmission limit. Using a variational method, we show that the nonlinear amplitude and chirp dynamics are well approximated by a two-dimensional random-walk process.     

Disintegration of a soliton in a dispersion-managed optical communication line with random parameters

The propagation of dispersion-managed solitons in optical fiber links with a random dispersion map has been studied. Two types of randomness are considered:random dispersion magnitudes and random lengths of the spans. By numerical simulations, disintegration of a soliton propagating in such an optical communication line is shown to occur. It is observed that the stability of the soliton propagation is affected more by modulations of the dispersion magnitudes of the spans than by modulations of the span lengths. Results of numerical simulations of the soliton breakup distance confirm theoretical predictions in the averaged dynamics limit.     

On the boundary of the dispersion-managed soliton existence

A breathing soliton-like structure in a dispersion-managed optical fiber system is studied. It is proved that, for negative average dispersion, the breathing soliton is forbidden, provided that the modulus of average dispersion exceeds a threshold which depends on the soliton amplitude.     

Nonlinearity management in a dispersion-managed system

We propose using a nonlinear phase-shift interferometric converter (NPSIC), a new device, for lumped compensation for nonlinearity in optical fibers. The NPSIC is a nonlinear analog of the Mach-Zehnder interferometer and provides a way to control the sign of the nonlinear phase shift. We investigate a potential use of the NPSIC for compensation for nonlinearity to develop a dispersion-managed system that is closer to an ideal linear system. More importantly, the NPSIC can be used to essentially improve single-channel capacity in the nonlinear regime.     

Noise evolution and soliton internal modes in dispersion-managed fiber systems

We perform a linear stability analysis of the Ablowitz-Biondini equations to explain the dynamic evolution of the noise squeezing, caused by the interplay among optical solitons and noise components, of initially uncorrelated statistics in fiber systems with dispersion management.