Inverse scattering transform for 3-level coupled Maxwell–Bloch equations with inhomogeneous broadening

In this paper we study the propagation of optical pulses in an optical medium with coherent three-level atomic transitions. The interaction between the pulses and the medium is described by the coupled Maxwell–Bloch equations, which we investigate by applying the method of inverse scattering transform. The details of the inverse scattering method and the non-trivial evolution of the associated scattering data are discussed. The one- and two-soliton solutions, polarization shifts due to two-soliton interactions, and the explicit form of the transmission matrix associated with pure soliton solutions are also derived.