  We study an initial-boundary-value problem (IBVP) for a system of coupled
Maxwell-Bloch equations (CMBE) that model two colors or polarizations of light
resonantly interacting with a degenerate, two-level, active optical medium with
an excited state and a pair of degenerate ground states. We assume that the
electromagnetic field approaches non-vanishing plane waves in the far past and
future. This type of interaction has been found to underlie nonlinear optical
phenomena including electromagnetically induced transparency, slow light,
stopped light, and quantum memory. Under the assumptions of unidirectional,
lossless propagation of slowly-modulated plane waves, the resulting CMBE become
completely integrable in the sense of possessing a Lax Pair. In this paper, we
formulate an inverse scattering transform (IST) corresponding to these CMBE and
their Lax pair, allowing for the spectral line of the atomic transitions in the
active medium to have a finite width. The scattering problem for this Lax pair
is the same as for the Manakov system. The main advancement in this IST for
CMBE is calculating the nontrivial spatial propagation of the spectral data and
determining the state of the optical medium in the distant future from that in
the distant past, which is needed for the complete formulation of the IBVP. The
Riemann-Hilbert problem is used to extract the spatio-temporal dependence of
the solution from the evolving spectral data. We further derive and analyze
several types of solitons and determine their velocity and stability, as well
as find dark states of the medium which fail to interact with a given pulse.
