  We consider an integrable system of reduced Maxwell-Bloch equations that
describes the evolution of an electromagnetic field in a two-level medium that
is inhomogeneously broadened. We prove that the relevant Backlund
transformation preserves the reality of the n-soliton potentials and establish
their pole structure with respect to the broadening parameter. The natural
phase space of the model is embedded in an infinite dimensional loop algebra.
The dynamical equations of the model are associated to an infinite family of
higher order Hamiltonian systems that are in involution. We present the
Hamiltonian functions and the Poisson brackets between the extended potentials.
