Modulation instability in an optical fiber with high-order dispersion and a new kind of saturable nonlinearity

Based on the extended coupled nonlinear Schrödinger equations including high-order dispersion and a new kind of saturable nonlinearity (NSN) in the optical fiber, the linearized nonlinear Schrödinger equation is derived. Subsequently, the corresponding condition and gain spectra of modulation instability (MI) are deduced and calculated. And the variations of the critical perturbation frequencies (or spectral widths) and the peak s with the input powers are calculated and compared with those of conventional saturable nonlinearity (CSN) and exponential saturable nonlinearity (ESN) in different dispersion regions. The results show that, being similar to the cases of CSN and ESN, the spectral width and the peak gain here increase with the input power, reach a maximum value, and then decrease. These features lead to a unique value of peak gain and critical frequency for two different input powers. In comparison, however, when the other parameters are the same, the varying rates will be faster than those of CSN but slower than those of ESN. This work may be beneficial to further study of new types of bistable or multistable optical solitons.