Modulational instabilities in the dual-core nonlinear optical fiber

We describe modulational instability (MI) of the continuous-wave (cw) state s in the dual-core nonlinear optical fiber with normal dispersion. We show that the asymmetric cw states (existing above the bifurcation point), as we ll as the symmetric ones (below the bifurcation point) exhibit MI at all va lues of the intensity (the instability of the symmetric cw states was known previously). Below the bifurcation, the MI's peak gain (with respect to th e perturbation frequency, holding the intensity of the symmetric cw state c onstant) increases with intensity. Above the bifurcation - considering the asymmetric cw solution - the peak gain of this branch of the perturbation d ecreases with intensity; however, at the bifurcation point another branch g oes unstable, its peak gain growing with intensity, and saturating at large intensities. The symmetric state's instability is non-oscillatory, while t hat of the asymmetric state is oscillatory. Direct simulations show that, i n either case, MI eventually leads to full "optical turbulence," both the i nitial symmetric and initial asymmetric cw states giving rise to statistica lly symmetric turbulent states, which have equal average intensities in eac h core. Thus, the transition to turbulence restores the spontaneously broke n symmetry.