PROJECTING THE UNSTABLE SOLUTIONS OF THE INTEGRODIFFERENTIAL MAXWELL-BLOCH EQUATIONS ON TO FINITE-DIMENSIONAL SUBSPACES - METHODS AND PERFORMANCES

This paper aims at discussing the extent of validity of two procedures that project the infinite-dimensional Maxwell-Bloch equations onto fi nite-dimensional subspaces. A first model, which consists of four diff erential equations, shows a clear match in the rate-equations approxim ation but is revealed to be completely inadequate for the description of the unstable regime of operation. A second model, constructed with a limited number of spectral components, judiciously chosen under the gain profile, is shown to yield a much better fit to the unstable phas e-space trajectories of the infinite-dimensional equations.