Studies of group-velocity reduction and pulse regeneration with and without the adiabatic approximation

We present a detailed semiclassical study of the propagation of a pair of optical fields in resonant media with and without the adiabatic approximation. In the case of near- and on-resonance excitation, we show detailed calculations, both analytical and numerical, of the extremely slowly propagating probe pulse and the subsequent regeneration of a pulse via a coupling laser. Further discussions of the adiabatic approximation provide much subtle understanding of the process, including the effect on the bandwidth of the regenerated optical field. We show that the adiabatic condition does not generally predict that the regenerated field will have the same bandwidth as that of the original probe pulse. Indeed, we show analytically that for a set of coupling pulses well satisfying the adiabatic conditions, the regenerated field usually has a different bandwidth from the original probe pulse. For very-far-off resonance excitations, we show that the analytical solution is nearly detuning independent, providing a simple condition is satisfied. This surprising result is vigorously tested and compared to numerical calculations with very good agreement.