  We report a novel optical multistability in two core oppositely directed
saturable coupler (ODSC) with negative index material (NIM) channel. The
dynamics are studied using the Langrangian variational method and Jacobi
elliptic functions are used to construct the analytical solutions. The ODSC
exhibits a bandgap as a consequence of the effective feedback mechanism due to
the opposite directionality of the phase velocity and Poynting vector in the
NIM channel. We observe that the system admits multiple stable states for some
control parameter, which is a result of the combination of nonlinear saturation
and the unique backward-coupling mechanism in the NIM channel. The number of
multiple stable states increase with the strength of the nonlinear saturation.
Taking the advantage of multiple stable states, one can construct ultrafast
switching devices with a flexible switching operation. The studies on the
transmission characteristics of the ODSC implies the existence of multiple
transmission resonance windows, which could help in the realization of gap
soliton in homogeneous systems like coupler. With more degrees of design
freedom and controllability, the ODSC could be the choice for a future
generation of all-optical switching.
