Solitons and polarization mode dispersion

Interaction of solitons through radiation in optical fibers with randomly varying birefringence

Propagation of solitons in optical fibers is studied taking into account the polarization mode dispersion (PMD) effect. We show that the soliton interaction caused by the radiation emitted by solitons due to the PMD disorder leads to soliton jitter, and we find its statistical properties. The theoretical predictions are justified by direct numerical simulations.

Nonlinear optics in a birefringent optical fiber

We extend the perturbation theory of the nonlinear Schrödinger equation for the study of perturbed (nonintegrable) forms of the vector equation. We derive a set of linear equations that describe the radiation field shed by the soliton as it propagates down a birefringent optical fiber. The formalism is applied to the case when strong birefringence and higher-order dispersion are present in the fiber and to the study of polarization mode dispersion. Finally we discuss an analytical treatment of the mechanism that generates the soliton shadow.

Nonlinear theory of polarization-mode dispersion for fiber solitons

We consider the evolution of optical solitons inside a nonlinear dispersive fiber with random birefringence, causing polarization-mode dispersion. We convert the pair of coupled nonlinear Schrödinger equations satisfied by the orthogonally polarized components into a Fokker-Planck equation using the collective-variable approach. We solve this equation and derive expressions for the probability density functions associated with the differential group delay and the pulse width in the limit of large propagation distances.

Solitons in fibers with polarization mode dispersion

Evaluating the relative time displacement of the two orthogonally polarized components of a pulse propagating down a birefringent optical fiber is considered. A method that provides analytical expressions for this time displacement is described and generalizes analytical results already published.

Role of polarization mode dispersion on modulational instability in optical fibers

We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we give the explicit form of the effective matrix and numerically compute the maximal eigenvalue. In the anomalous dispersion regime, polarization dispersion widens the unstable bandwidth. Depending on the type of variations of the birefringence parameters, polarization dispersion reduces or enhances the MI gain peak. In the normal dispersion regime, random effects may extend the instability domain to the whole spectrum of modulations. The linear stability analysis is confirmed by numerical simulation of the full stochastic coupled nonlinear Schrödinger equations.

Enhanced robustness of dispersion-managed solitons with respect to polarization mode dispersion

Polarization mode dispersion causes solitons to emit background radiation, which degrades transmission quality. It is shown theoretically and confirmed by numerical simulations that dispersion-managed solitons can trap part of that radiation into localized eigenmodes, thus yielding improvement in transmission quality compared with that of conventional solitons.