Electromagnetically Induced Transparency: Answering a Question of Romain

At the request of Romain, I derive analytical results describing the response of a three-level medium subjected to a strong pump beam and two weak probe beams. All three beams have a constant intensity. The results are the real and imaginary parts of the medium coherence, which is related to the nonlinear susceptibility. The main feature is that the three beams mix absorption and dispersion. There is a finite window of gain bounded by a point of electromagnetically induced transparency. This revised version was published online in July 2006 with corrections to the Cover Date.