  We study the Maxwell-Bloch model, which describes the propagation of a laser
through a material and the associated interaction between laser and matter
(polarization of the atoms through light propagation, photon emission and
absorption, etc.). The laser field is described through Maxwell's equations, a
classical equation, while matter is represented at a quantum level and
satisfies a quantum Liouville equation known as the Bloch model. Coupling
between laser and matter is described through a quadratic source term in both
equations. The model also takes into account partial relaxation effects, namely
the trend of matter to return to its natural thermodynamic equilibrium. The
whole system involves $6$+$N \, (N+1)/2$ unknowns, the six-dimensional
electromagnetic field plus the $N \, (N+1)/2$ unknowns describing the state of
matter, where $N$ is the number of atomic energy levels of the considered
material. We consider at once a high-frequency and weak coupling situation, in
the general case of anisotropic electromagnetic fields that are subject to
diffraction. Degenerate energy levels are allowed. The whole system is stiff
and involves strong nonlinearities. We show the convergence to a nonstiff,
nonlinear, coupled Schr\"o\-din\-ger-Boltzmann model, involving $3$+$N$
unknowns. The electromagnetic field is eventually described through its
envelope, one unknown vector in $\C^3$. It satisfies a Schr\"o\-din\-ger
equation that takes into account propagation and diffraction of light inside
the material. Matter on the other hand is described through a $N$-dimensional
vector describing the occupation numbers of each atomic level. It satisfies a
Boltzmann equation that describes the jumps of the electrons between the
various atomic energy levels, as induced by the interaction with light. The
rate of exchange between the atomic levels is proportional to the intensity of
the laser field. The whole system is the physically natural nonlinear model. In
order to provide an important and explicit example, we completely analyze the
specific (two dimensional) Transverse Magnetic case, for which formulae turn
out to be simpler. Technically speaking, our analysis does not enter the usual
mathematical framework of geometric optics: it is more singular, and requires
an \emph{ad hoc} Ansatz.
