In this paper, based on the extended coupled nonlinear Schrödinger equations including exponential saturable
nonlinearity (ESN) in optical fibers, the linearized coupled nonlinear Schrödinger equations are derived. Subsequently,
the corresponding condition and gain spectra of cross-phase modulation induced modulation instability (MI) are deduced
and calculated. And the variations of the critical perturbation frequency and the peak gain with the input powers are
calculated and compared with the case of conventional saturable nonlinearity (CSN) in both the normal and anomalous
dispersion regions. The results show that, the critical perturbation frequency and the peak gain increase with the input
power, reach a maximum value, and then decrease. Moreover, in comparison, when the other parameters are the same,
the varying rates will be faster than those of CSN. These features lead to a unique value of peak gain and critical
frequency for two different input powers. This work may be beneficial to further study of new types of bistable or
multistable optical solitons.
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