  We investigate the reduced Maxwell-Bloch (RMB) equations which describe the
propagation of short optical pulses in dielectric materials with resonant
non-degenerate transitions. The general Nth-order periodic solutions are
provided by means of the Darboux transformation, and from two different
limiting cases of the obtained general periodic solutions, the Nth-order
degenerate periodic and Nth-order rational solutions containing several free
parameters with compact determinant representations are derived, respectively.
Explicit expressions of these solutions from first to second order are
presented. Typical nonlinear wave patterns for the four components of the RMB
equations such as single-peak, double-peak-double-dip, double-peak and
single-dip structures in the second-order rational solutions are shown. This
kind of the rational solutions correspond to rogue waves in the reduced
Maxwell-Bloch equations.
