Negative Group Velocity

In more detail, consider a classical model of matter in which spectral lines are associated with oscillators. In particular, consider a gas of atoms with two closely spaced spectral lines of angular frequencies ω1,2 = ω0 ± Δ/2, where Δ ω0. Each line has the same damping constant (and spectral width) γ. Ordinarily, the gas would exhibit strong absorption of light in the vicinity of the spectral lines. But suppose that lasers of frequencies ω1 and ω2 pump the both oscillators into inverted populations. This can be described classically by assigning negative oscillator strengths to these oscillators. Deduce an expression for the group velocity vg(ω0) of a pulse of light centered on frequency ω0 in terms of the (univalent) plasma frequency ωp of the medium, given by