Numerical demonstration of high sensitivity to initial conditions in solutions of the complete Maxwell–Bloch equations for certain parameters

• Model: Complete Maxwell–Bloch Equations including the longitudinal and transverse relaxation terms.
• No single mode approximation. No Rotating Wave Approximation. No Slowly Varying Envelope Approximation.
• Method: Expansion in the eigenfunctions of the 1-D Lienard–Wiechert kernel.
• Flip from forward to backward emission for small changes in initial conditions in slabs approximately nλ02 wide.

The solutions of Maxwell–Bloch equations in a slab of homogeneously broadened two-level atoms almost all initially inverted and prepared in a coherent state exhibit high sensitivity to initial conditions for slabs having width in narrow windows around nλ0/2nλ0/2 (n   is an integer and λ0λ0 is the wavelength of the atomic transition). Sectors with two dominant modes define these windows. I compute the changes in the ratio of the forward over backward fluxes, in these sectors, as a function of the slab width and the difference in initial atomic population.