  Following the concept of $\mathcal{PT}$-symmetric couplers, we propose a
linearly coupled system of nonlinear waveguides, made of positive- and
negative-index materials, which carry, respectively, gain and loss. We report
novel bi- and multi-stability states pertaining to transmitted and reflective
intensities, which are controlled by the ratio of the gain and loss
coefficients, and phase mismatch between the waveguides. These states offer
transmission regimes with extremely low threshold intensities for transitions
between coexisting states, and very large amplification ratio between the input
and output intensities leading to an efficient way of controlling light with
light.
