Derivative expansion of the electromagnetic Casimir energy for two thin   mirrors
  We extend our previous work on a derivative expansion for the Casimir energy, to the case of the electromagnetic field coupled to two thin, imperfect mirrors. The latter are described by means of vacuum polarization tensors localized on the mirrors. We apply the results so obtained to compute the first correction to the proximity force approximation to the static Casimir effect. 
Cesar D. Fosco, Fernando C. Lombardo, and Francisco D. Mazzitelli
hep-th quant-ph