Modulation instability induced by high-order dispersion to a coupled nonlinear Schrodinger equation in a single-mode optical fiber with Kerr nonlinearity

We investigate the modulation instability of two incoherently copropagating optical waves in a nonlinear fiber taking into account the relaxing Kerr nonlinearity, walk-off effects, delay response time and cross-phase modulation. We intend to provide a detailed analysis of the interplay between the instantaneous and noninstantaneous Kerr response for the beams experiencing a normal group velocity dispersion (GVD) regime and for the other beams undergoing an anomalous GVD regime. We unveil the influence of the parameters on the generation of the modulational instability gain with particular attention to the delay response time as well as the high-order dispersion. We show that the high-order dispersion particularly influences the magnitude as well as the sidebands of the gain spectrum.