Theory of self-induced transparency without the approximation of slowly varying amplitudes and phases

An analysis is made of the propagation of an ultrashort optical radiation pulse under conditions of inhomogeneous broadening of a resonance line. By dispensing with the approximation of a slowly varying complex pulse envelope, constraints on the duration are removed and any phase modulation is automatically taken into account. It is shown that if the boundary conditions determining the attenuation of the pulse at its leading edges are defined, the appropriate reduced Maxwell–Bloch equations can be integrated using the method of the inverse problem of scattering theory. Higher conservation laws, whose existence has been doubted, are found.