Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity

We analyze the modulational instability (MI) of light waves in glass fibers with a local saturable nonlinear refractive index. We identify and discuss the salient features of the effect of the fourth order of the fiber dispersion, in the MI spectra. Particularly, we find that in fibers with negative sign of the second-order dispersion and positive sign of the fourth-order dispersion (FOD), the two existing types of MI processes, called processes of type I, which generate a single pair of sidebands, and processes of type II, which lead to two pairs of sidebands, become highly sensitive to the magnitude of the FOD, both quantitatively and qualitatively. We demonstrate the existence of a critical FOD and two branches of critical pump powers, from which we construct the global map of the MI behaviors in the system, including clear delimitations of the respective domains of the existence of MI processes of types I and II.