Unidirectional Propagation of an Ultra-Short Electromagnetic Pulse in a Resonant Medium with High Frequency Stark Shift

We consider in the unidirectional approximation the propagation of an ultra short electromagnetic pulse in a resonant medium consisting of molecules characterized by a transition operator with both diagonal and non-diagonal matrix elements. We find the zero-curvature representation of the reduced Maxwell-Bloch equations in the sharp line limit. This can be used to develop the inverse scattering transform method to solve these equations. Finally we obtain two types of exact traveling pulse solutions, one with the usual exponential decay and another with an algebraic decay.