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

Phase fluctuations of linearly chirped solitons in a noisy optical fiber channel with varying dispersion, nonlinearity, and gain

The phase fluctuations of arbitrarily nonlinearity- and dispersion-managed solitons propagating in a noisy fiber channel are studied both analytically and numerically. We begin by discussing the stability problem of such linearly chirped solitons with a full linear stability analysis. It is shown that these sophisticated solitons possess an enhanced stability against perturbations and therefore hold promise for applications in optical telecommunications. We then make an approach to the phase statistics of these solitons, which stems from an inevitable random walk in phase evolutions due to amplified spontaneous emission noise. By using the variational approach together with impulse-response (Green) functions, an elegant closed-form expression for the phase variance is derived based on an unconstrained self-similar soliton ansatz in which the effect of chirp fluctuations has been critically taken into account as well as the dispersive and nonlinear effects. An inspection of the intriguing subtleties of the interplay among these effects reveals that the chirp fluctuations effect does play an important role in the control of nonlinear phase noise via fiber dispersion, independently of whether the input solitons are initially chirped or not. Our analytical result also offers many possibilities of optimally manipulating nonlinear phase noise with engineered fiber parameters that may lead to the steady pulse propagation, broadening, or compression under favorable parametric conditions. Last, we demonstrate our result by several convincible examples and show an excellent agreement between analytical predictions and numerical simulations.

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.

Collective variable theory for optical solitons in fibers

We present a projection-operator method to express the generalized nonlinear Schrödinger equation for pulse propagation in optical fibers, in terms of the pulse parameters, called collective variables, such as the pulse width, amplitude, chirp, and frequency. The collective variable (CV) equations of motion are derived by imposing a set of constraints on the CVs to minimize the soliton dressing during its propagation. The lowest-order approximation of this CV approach is shown to be equivalent to the variational Lagrangian method. Finally, we demonstrate the application of this CV theory for pulse propagation in dispersion-managed optical fiber links.

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.

Coupled-field description of zero-average dispersion management

Using a coupled-field formalism and a standard perturbation analysis, we analyze a dispersion-managed system under zero-average dispersion conditions. A nonlinear integral equation in the spectral domain allows the determination of the critical strength parameter of a two-step dispersion map. Higher-order correction terms confirm the difference observed in the pulse shapes in each fiber and comparisons with fully numerical results reveal a good agreement. The existence of an antisymmetric dispersion-managed soliton is also confirmed.

Influence of the Raman effect on dispersion-managed solitons and their interchannel collisions

We calculate the self-frequency shift experienced by a soliton in a dispersion-managed fiber that is due to the Raman effect, as well as the energy and frequency shifts that result from a collision of such solitons with different wavelengths. We find that dispersion management suppresses both types of frequency shift but does not significantly affect the energy shift that is accumulated over a large propagation distance. The latter shift may represent a potential problem for wavelength-division-multiplexed systems with several gigabits per second in a single channel.

Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management

We develop a perturbation theory to analytically calculate the effects of complete and incomplete interchannel collisions of Gaussian pulses in a wavelength-division-multiplexed system with strong dispersion management. We show that, for complete collisions, the collision-induced frequency shift of a Gaussian pulse is negligible, whereas its position shift is significant and can be found in a simple analytical form. For strong dispersion management we find that incomplete collisions can be neglected, whereas for dispersion management of moderate strength the contribution of the incomplete collisions can be significant. The analytical predictions are in satisfactory agreement with numerical results. We also give an estimate of the limit imposed on the transmission distance by such collisions.