Solutions of the Maxwell–Bloch equations in (1,1)-d in the presence of a pulsed pump

Abstract Using the basis formed by the eigenfunctions of the Lienard–Wiechert Green function, we develop and test an algorithm for solving exactly the Maxwell–Bloch equations in (1-space, 1-time). We use this algorithm to search for patterns in the solutions of a pulse pumped slab of two-level systems when the slab’s thickness L = p + 1 / 4 λ , λ being the wavelength of the resonant radiation and p being an integer. Both non-linearity and saturation effects are manifest as the strength of the pump is increased. For thicknesses on this lattice, the behavior of the slab is dominated by a single mode in the spectrum of the Green’s function. The resulting patterns do not appear at other thicknesses, because of the interference between competing modes