Abstract
We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. Using coupled-mode equations for this system, we identify MI conditions from the linearization with respect to small perturbations. First, we compare the MI spectra of the asymmetric system and its symmetric counterpart in the case of the anomalous group-velocity dispersion (GVD). In particular, it is demonstrated that the increase of the inter-core linear-coupling coefficient leads to a reduction of the MI gain spectrum in the asymmetric coupler. The analysis is extended for the asymmetric system in the normal-GVD regime, where the coupling induces and controls the MI, as well as for the system with opposite GVD signs in the two cores. Following the analytical consideration of the MI, numerical simulations are carried out to explore nonlinear development of the MI, revealing the generation of periodic chains of localized peaks with growing amplitudes, which may transform into arrays of solitons.
Highlights
The modulational instability (MI) is a ubiquitous phenomenon originating from the interplay of linear dispersion or diffraction and the nonlinear self-interaction of wave fields
The analysis demonstrates that the variation of ρ produces almost no effect on the MI gain in the case when the asymmetry is determined by the difference in the nonlinearity coefficients (Γ 6= 1), while the group-velocity dispersion (GVD)
We have investigated the MI in the model of asymmetric dual-core nonlinear directional couplers (NLDC), based on the system of nonlinear Schrödinger equations, which include differences in the GVD and nonlinearity coefficient in the two cores, as well as the group- and phase-velocity mismatch between them
Summary
The modulational instability (MI) is a ubiquitous phenomenon originating from the interplay of linear dispersion or diffraction and the nonlinear self-interaction of wave fields. The linear-coupling coefficient determines the critical value of the power, which gives rise to the spontaneous breaking of the symmetry between the two cores [34] Based on such power-dependent transmission characteristics, many applications of the NLDC have been proposed, such as all-optical switching and power splitting [25], logic operations [35,36], pulse compression [37] and bistability [38]. The asymmetry can be imposed by deforming transverse shapes of the cores, while maintaining their areas equal In such birefringent couplers, one can induce a phase-velocity mismatch without a change in the nonlinearity coefficients. Switching of bright solitons has been studied [49] in the model taking into regard the group- and phase-velocity mismatch and differences in the GVD coefficients and effective mode areas of the two cores.
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