  We propose a possibility to simulate the exciton-polariton (EP) system in the
lossless limit, which is not currently available in semiconductor
microcavities, by means of a simple optical dual-core waveguide, with one core
carrying the nonlinearity and operating close to the
zero-group-velocity-dispersion (GVD) point, and the other core being linear and
dispersive. Both 2D and 1D EP systems may be emulated by means of this optical
setting. In the framework of this system, we find that, while the uniform state
corresponding to the lower branch of the nonlinear dispersion relation is
stable against small perturbations, the upper branch is always subject to the
modulational instability (MI). The stability and instability are verified by
direct simulations too. We analyze collective excitations on top of the stable
lower-branch state, which include a Bogoliubov-like gapless mode and a gapped
one. Analytical results are obtained for the corresponding sound velocity and
energy gap. The effect of a uniform phase gradient (superflow) on the stability
is considered too, with a conclusion that the lower-branch state becomes
unstable above a critical wavenumber of the flux. Finally, we demonstrate that
the stable 1D state may carry robust dark solitons.
