  We study the (characteristic) Cauchy problem for the Maxwell-Bloch equations
of light-matter interaction via asymptotics, under assumptions that prevent the
generation of solitons. Our analysis clarifies some features of the sense in
which physically-motivated initial/boundary conditions are satisfied. In
particular, we present a proper Riemann-Hilbert problem that generates the
unique causal solution to the Cauchy problem, that is, the solution vanishes
outside of the light cone. Inside the light cone, we relate the leading-order
asymptotics to self-similar solutions that satisfy a system of ordinary
differential equations related to the Painlev\'e-III (PIII) equation. We
identify these solutions and show that they are related to a family of PIII
solutions recently discovered in connection with several limiting processes
involving the focusing nonlinear Schr\"odinger equation. We fully explain a
resulting boundary layer phenomenon in which, even for smooth initial data (an
incident pulse), the solution makes a sudden transition over an infinitesimally
small propagation distance. At a formal level, this phenomenon has been
described by other authors in terms of the PIII self-similar solutions. We make
this observation precise and for the first time we relate the PIII self-similar
solutions to the Cauchy problem. Our analysis of the asymptotic behavior
satisfied by the optical field and medium density matrix reveals slow decay of
the optical field in one direction that is actually inconsistent with the
simplest version of scattering theory. Our results identify a precise generic
condition on an optical pulse incident on an initially-unstable medium
sufficient for the pulse to stimulate the decay of the medium to its stable
state.
