  We consider the Maxwell-Bloch system which is a finite-dimensional
approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The
approximation consists of one-mode Maxwell field coupled to two-level molecule.
We construct time-periodic solutions to the factordynamics which is due to the
symmetry gauge group. For the corresponding solutions to the Maxwell--Bloch
system, the Maxwell field, current and the population inversion are
time-periodic, while the wave function acquires a unit factor in the period.
The proofs rely on high-amplitude asymptotics of the Maxwell field and a
development of suitable methods of differential topology: the transversality
and orientation arguments. We also prove the existence of the global compact
attractor.
