Dispersion-managed Nonlinear Schrodinger Equation Research Articles

Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation

The dispersion-managed nonlinear Schrodinger equation contains a small parameter $$\varepsilon $$ , a rapidly changing piecewise constant coefficient function, and a cubic nonlinearity. Typical solutions are highly oscillatory and have a discontinuous time-derivative, and hence solving this equation numerically is a challenging task. We present and analyze a tailor-made time integrator which attains the desired accuracy with a significantly larger step-size than traditional methods. The construction of this method is based on a favorable transformation to an equivalent problem and the explicit computation of certain integrals over highly oscillatory phases. The error analysis requires the thorough investigation of various cancellation effects which result in improved accuracy for special step-sizes.

Phase noise of dispersion-managed solitons

We quantify noise-induced phase deviations of dispersion-managed solitons (DMS) in optical fiber communications and femtosecond lasers. We first develop a perturbation theory for the dispersion-managed nonlinear Schr\odinger equation (DMNLSE) in order to compute the noise-induced mean and variance of the soliton parameters. We then use the analytical results to guide importance-sampled Monte Carlo simulations of the noise-driven DMNLSE. Comparison of these results with those from the original unaveraged governing equations confirms the validity of the DMNLSE as a model for many dispersion-managed systems and quantify the increased robustness of DMS with respect to noise-induced phase jitter.

A Unified Design Framework for Single-Channel Dispersion-Managed Terrestrial Systems

This paper provides a unified framework to the design, performance optimization, and accurate numerical simulation of periodic, dispersion-managed (DM) single-channel long-haul optical transmission systems for nonsoliton on-off keying (OOK) modulation. The focus is on DM terrestrial systems, with identical spans composed of a long transmission fiber compensated at the span end by a linear dispersion compensating module, with pre- and postcompensation fibers at the beginning and end of the link. The framework is based on the dispersion-managed nonlinear Schrodinger equation (DM-NLSE). First, expressions of the DM-NLSE kernel are provided both in the frequency and the time domain, and a novel map strength parameter, appropriate for terrestrial systems, is introduced. It is then shown that the DM-NLSE contains all the basic information needed for system design, as summarized by three parameters: i) nonlinear phase, ii) in-line dispersion, and iii) map strength. Through a large-signal perturbative analysis of the DM-NLSE, the well-known linear relationship between the in-line dispersion and the optimal precompensation is derived, along with the large-signal step response of the DM link, from which the ghost pulses energy growth and a first estimation of the link memory are derived. The DM-NLSE is then linearized around the average signal field to get the amplitude/phase small-signal system matrix of the overall DM link, including pre- and postcompensation. By a singular-value decomposition of the small-signal DM link matrix, a novel expression of the memory of the optimized DM link is finally provided. Knowledge of such a memory is mandatory to run accurate numerical simulations and laboratory measurements with a sufficiently long pseudorandom bit sequence to avoid patterning effects.

Dispersion-Managed Solitons in Multiple-Core Nonlinear Fiber Arrays

The variational principle is employed to obtain the evolution of the parameters of Gaussian and super-Gaussian chirped solitons that propagates through multiple-core nonlinear optical fiber arrays. This is governed by the dispersion-managed nonlinear Schrodinger's equation with strong dispersion management in the presence of linear coupling between the adjacent cores. The results are valid for any configuration of the cores.