Maxwell-Bloch Equations for Two-Level System

The Maxwell-Bloch equations for a two-level system are solved in a particular case. The example follows that of P. Siddons, "Light propagation through atomic vapours," Journal of Physics B: Atomic, Molecular, and Optical Physics 47, 093001 (2014). In the reference, the optical intensity, population of the upper state and coherence are given for light with a carrier frequency which is on resonance. Here, the same example is worked, but the result is given at intermediate times as well as at the entrance and exit faces as in the example. The solution is found using Mathematica's NDSolve for the time dimension and the Method of Lines for propagation in space.