Coupled-field description of zero-average dispersion management

Dispersion management and the direct scattering transform

It is shown that the direct scattering transform may be used to derive a perturbative theory of quasiperiodic field propagation in nonlinear fiber lines managed through zero-average, piecewise-constant dispersion maps. In this scheme, the field is propagated exactly and it is the quasiperiodicity property which is approximated. The resulting quasiperiodicity conditions are shown to agree with the dispersion managed nonlinear Schrödinger equation up to order 4.

Instabilities of dispersion-managed solitons in the normal dispersion regime

Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of different pulse duration and energy at a fixed propagation constant. We show that the short soliton with a larger energy is linearly (exponentially) unstable. The other (long) soliton with a smaller energy is linearly stable but hits a resonance with excitations of the dispersion map. The results are compared with the results from recent publications [Bernston et al., Opt. Lett. 23, 900 (1998); Nijhof et al., ibid. 23, 1674 (1998); Grigoryan and Menyuk, ibid. 23, 609 (1998)].

Spectral domain analysis of dispersion management without averaging

It is shown how a straightforward regular perturbative analysis can be used to derive an integral equation for the spectral shape of a dispersion-managed soliton that takes fiber loss and amplification into account without resorting to averaging. Using functional analysis, one can then find an accurate approximate Gaussian solution that should prove useful for the design of a dispersion-managed transmission link.