Spatial, temporal, and spatio-temporal modulational instabilities in a planar dual-core waveguide

We investigate modulational instability (MI) in a planar dual-core waveguide (DWG), with a Kerr and non-Kerr polarizations based on coupled nonlinear Schrödinger equations in the presence of linear coupling term, coupling coefficient dispersion (CCD) and other higher order effects such as third order dispersion (TOD), fourth order dispersion (FOD), and self-steepening (ss). By employing a standard linear stability analysis, we obtain analytically, an explicit expression for the MI growth rate as a function of spatial and temporal frequencies of the perturbation and the material response time. Pertinently, we explicate three different types of MI-spatial, temporal, and spatio-temporal MI for symmetric/antisymmetric continuous wave (cw), and spatial MI for asymmetric cw, and emphasize that the earlier studies on MI in DWG do not account for this physics. Essentially, we discuss two cases: (i) the case for which the two waveguides are linearly coupled and the CCD term plays no role and (ii) the case for which the linear coupling term is zero and the CCD term is nonzero. In the former case, we find that the MI growth rate in the three different types of MI, seriously depends on the coupling term, quintic nonlinearity, FOD, and ss. In the later case, the presence of quintic nonlinearity, CCD, FOD, and ss seriously enhances the formation of MI sidebands, both in normal as well as anomalous dispersion regimes. For asymmetric cw, spatial MI is dependent on linear coupling term and quintic nonlinearity.