  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.
