Optimal dispersion maps for wavelength-division-multiplexed soliton transmission

We propose an advantageous dispersion-management scheme for wavelength-division-multiplexed soliton transmission in which optimal launch points are obtained whose locations are independent of the fibers' dispersion parameters. Inasmuch as using such optimal launch points minimizes dispersively shed radiation, it is possible to optimize the transmission simultaneously in several different channels. For the particular case of a two-step dispersion map we demonstrate that this result can be achieved by proper choice of the fiber lengths.     

Collision-induced time shift of a dispersion-managed soliton and its minimization in wavelength-division-multiplexed transmission

The formula for the time shift of a dispersion-managed soliton that results from its collision with other solitons in different channels consists of two terms, one related to the frequency shift during collision, and the other related to the residual frequency shift after collision. It is found that an optimal relative delay exists between pulses in adjacent channels after each dispersion-managed span that balances the contributions from the two terms and minimizes the overall time shift, leading to a substantial improvement in transmission performance.     

Optimal design of dispersion management for a soliton wavelength-division-multiplexed system

We obtain analytical formulas for minimizing chirp and timing jitter that lead to optimal designs for a soliton-wavelength-division-multiplexed system with dispersion management and lumped amplifiers. The method used here is the guiding-center theory, from which we obtain a stationary pulse shape (guiding-center soliton) that has enhanced power and an increased time-bandwidth product compared with those of a soliton alone.     

Dispersion management for wavelength-division-multiplexed soliton transmission

Residual frequency shifts that are due to two-soliton collisions in stepwise exponentially dispersion-tapered fiber are calculated. Two-step dispersion profiles to minimize the frequency shifts and associated timing jitter are specifically identified. These profiles will improve the performance of wavelength-division-multiplexed soliton systems and permit operation with longer amplifier spans over an increased bandwidth.     

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.     

Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines

We investigate interactions between pulses in dispersion-managed multichannel wavelength-division-multiplexed soliton systems, using an improved variational approximation. The frequency shifts are found to be smallest for moderate, i.e., relatively short-scale, dispersion management. The position shifts increase monotonically with map strength.     

Timing-jitter reduction in a dispersion-managed soliton system

We found by using Monte Carlo simulations that the timing jitter in a dispersion-managed soliton system decreases as the strength of the dispersion management and hence the ratio of the pulse energy to the pulse bandwidth increases. The results are in qualitative but not quantitative agreement with earlier predictions that the decrease is inversely proportional to the square root of the pulse energy. Using an improved semi-analytical theory, we obtained quantitative agreement with the simulations.     

Soliton collisions in dispersion-managed wavelength-division-multiplexed systems

We show that collision-induced frequency shifts in wavelength-division-multiplexed (WDM) soliton transmission systems are strongly suppressed with increasing dispersion management. We predict new oscillations in the residual frequency shift response, owing to the relative motion induced by the dispersion map, and demonstrate a direct correlation between these oscillations and the modified soliton-collision dynamics. Simple analytical expressions for the oscillation minima are obtained, and implications for WDM soliton system design are discussed.     

Soliton collisions in wavelength-division-multiplexed dispersion-managed systems

In dense wavelength-division-multiplexed transmission with strong dispersion management, most pulses inevitably have many partial collisions with pulses of an interacting channel. These partial collisions, in conjunction with the effects of complete collisions, tend to produce unacceptably large timing jitter in high-bit-rate, long-distance transmission. With the use of frequency-guiding filters, however, the timing jitter is dramatically reduced and tends to remain indefinitely clamped to acceptably small levels.     

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.     

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.     

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.     

Fully parallel algorithm for simulating dispersion-managed wavelength-division-multiplexed optical fiber systems

An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent parallel calculations of fast Fourier transforms on multiple central processor units (CPUs). The algorithm allows one to implement numerical simulations M/2 times faster than a direct numerical simulation by a split-step method, where M is a number of CPUs in a parallel network.     

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.     

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.     

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.     

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.     

Analysis of a DPSK soliton transmission system

We present a closed form expression to analyse the error performance of a differential phase-shift keying (DPSK) digital modulation format in an optical soliton communication system. In the analysis we include the effect of Gordon-Haus jitter, which is mainly due to the amplified spontaneous emission noise of the amplifiers. Gordon-Haus jitter is found to be less significant when the bit period is 15 times greater than the jitter variance and becomes more significant when the signal-to-noise ratio is greater than 20 dB. Due to a good bit error rate (BER) performance (BER ≈ 10⁻²⁰at SNR= 21 dB), the DPSK modulation format has a potential application for a high-bit-rate and low-noise soliton communication system.     

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.     

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.