Impact of amplifying media on the Casimir force

On the basis of macroscopic quantum electrodynamics, a theory of Casimir forces in the presence of on linearly amplifying bodies is presented which provides a consistent framework for studying the effect of, e.g., amplifying left-handed metamaterials on dispersion forces. A general formula for the Casimir force acting on an amplifying body is derived. It is shown that the force can be given in terms of the classical Green tensor and that it can be decomposed into a resonant component associated with emission processes and an off-resonant Lifshitz-type component looking formally the same as for a purely absorbing body. It is explicitly demonstrated that the result generalizes microscopic approaches beyond the perturbative domain: In the dilute-gas limit, the force acting on an amplifying body reduces to a sum over the Casimir--Polder forces acting on the excited body atoms.