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We report a novel optical multistability in two core oppositely directedsaturable coupler (ODSC) with negative index material (NIM) channel. Thedynamics are studied using the Langrangian variational method and Jacobielliptic functions are used to construct the analytical solutions. The ODSCexhibits a bandgap as a consequence of the effective feedback mechanism due tothe opposite directionality of the phase velocity and Poynting vector in theNIM channel. We observe that the system admits multiple stable states for somecontrol parameter, which is a result of the combination of nonlinear saturationand the unique backward-coupling mechanism in the NIM channel. The number ofmultiple stable states increase with the strength of the nonlinear saturation.Taking the advantage of multiple stable states, one can construct ultrafastswitching devices with a flexible switching operation. The studies on thetransmission characteristics of the ODSC implies the existence of multipletransmission resonance windows, which could help in the realization of gapsoliton in homogeneous systems like coupler. With more degrees of designfreedom and controllability, the ODSC could be the choice for a futuregeneration of all-optical switching.

Multistability and Switching in Oppositely Directed Saturable Coupler