Superluminal pulse reflection and transmission in a slab system doped with dispersive materials

The reflection and transmission of a pulse through a slab which is doped with two-level or three-level atoms are investigated theoretically. The doped atoms can be passive (absorptive) or active (gain). We find that both the reflected and transmitted pulses can be superluminal simultaneously for the slab doped with absorptive two-level atoms at the slab thickness equal to [Formula presented] (where [Formula presented] is the center wavelength of the incident pulse, and [Formula presented] is the background dielectric constant of the slab) or with active three-level atoms at any thickness. By adjusting the thickness or background dielectric constant of the slab, the reflected pulse can be controlled from superluminal to subluminal or vice versa for the slab doped with absorptive two-level or absorptive three-level atoms. The energy percentage in the reflected pulse can also be controlled by changing the thickness of the slab, and the doped atoms.