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The influence of a saturable nonlinearity on the modulation instability inoppositely directed coupler in the presence of high-order effects isinvestigated. By using the standard linear stability analysis, we obtain theinstability gain that exhibits a significant change in the bands of instabilitydue to the effects of a saturable nonlinearity. We also show that even in thepresence of saturation there is no change in instability gain when we comparethe results obtained for both channels not influenced by self-steepening effector for both channels influenced by self-steepening effect but opposite in sign.Regarding the Raman effect, there is reflection symmetry (asymmetry) to thegain at zero perturbation frequency when the values of the Raman coefficientsin each directional coupler are equal and with same (opposite) sign. For theanomalous group velocity dispersion regime we observe that the growth of thesaturation parameter is followed by an increase in the null gain region near{\Omega} = 0, enlarging the separation of the instability bands close to thispoint. Finally, we show that an efficient control of the modulation instabilitycan be realized by adjusting self-steepening effect and intrapulse Ramanscattering, even in the presence of a saturable nonlinearity.

Modulation instability in high-order coupled nonlinear Schr\"odinger equations with saturable nonlinearities