Gap solitons in asymmetric dual-core nonlinear optical fibers

Abstract

We demonstrate that an asymmetric dual-core fiber, with opposite signs of the dispersion in its two cores, supports bright gap solitons. Such a fiber is a new nonlinear optical medium, the fabrication of which is technologically feasible. There are three nontrivial features of these new gap solitons: (i) Their exponential tails may oscillate as they decay; (ii) the energy in the normal-core component may be equal to or larger than the energy in the anomalous-core one, despite the obvious fact that the normal-dispersion core, in isolation, cannot support any bright solitons; and (iii) a part of the finite gap available for soliton solutions remains empty, having no solitons inside it. In addition, we show that such fibers can also support weakly delocalized solitons, which sit on a small-amplitude, nonvanishing, continuous-wave background. We also investigate the case in which the dispersion in both cores is anomalous but in which the cores are asymmetric and have different magnitudes of dispersion. In this case the general picture of the soliton solutions, including their bifurcations and stability, is qualitatively the same as when one has equal dispersions in the two cores, but with an asymmetry produced by a phase-velocity mismatch. These studies have been carried out by a combination of an analysis of the dispersion relation for the linearized system, the variational approximation for the full nonlinear one, and direct numerical methods.