# Multistability and Switching in Oppositely Directed Saturable Coupler

## TL;DR

This paper introduces a novel optical multistability phenomenon in an oppositely directed saturable coupler with negative index material, revealing multiple stable states and potential for ultrafast all-optical switching devices.

## Contribution

The study presents the first analytical demonstration of multistability in an ODSC with NIM, highlighting the role of nonlinear saturation and backward coupling in creating multiple stable states.

## Key findings

- Multiple stable states increase with nonlinear saturation strength.
- Existence of multiple transmission resonance windows.
- Potential for ultrafast, flexible all-optical switching devices.

## Abstract

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.