Modulational instability due to cross-phase modulation versus multiple four-wave mixing: the normal dispersion regime

We investigate the propagation of two parallel polarized pump beams in the framework of a single nonlinear Schrödinger equation in order to thoroughly understand the modulation instability process in the regime of normal group-velocity dispersion. A linear stability analysis based on Floquet theory allows us to account for four-wave mixing and to contrast the results with those arising from incoherent nonlinear coupling due to cross-phase modulation only. Based on the nature of the unstable eigenvectors, we explain why, in the normal dispersion regime, modulation instability is not observed in the scalar configuration. Numerical simulations validate the analysis.