Modulational instabilities in the dual-core nonlinear optical fiber

We describe modulational instability (MI) of the continuous-wave (cw) states in the dual-core nonlinear optical fiber with normal dispersion. We show that the asymmetric cw states (existing above the bifurcation point), as well as the symmetric ones (below the bifurcation point) exhibit MI at all values of the intensity (the instability of the symmetric cw states was known previously). Below the bifurcation, the MI's peak gain (with respect to the perturbation frequency, holding the intensity of the symmetric cw state constant) increases with intensity. Above the bifurcation - considering the asymmetric cw solution - the peak gain of this branch of the perturbation decreases with intensity; however, at the bifurcation point another branch goes unstable, its peak gain growing with intensity, and saturating at large intensities. The symmetric state's instability is non-oscillatory, while that of the asymmetric state is oscillatory. Direct simulations show that, in either case, MI eventually leads to full "optical turbulence," both the initial symmetric and initial asymmetric cw states giving rise to statistically symmetric turbulent states, which have equal average intensities in each core. Thus, the transition to turbulence restores the spontaneously broken symmetry.