Screened Casimir forces

We demonstrate that a very recently obtained formula for the force on a slab in a material planar cavity based on the calculation of the vacuum Lorentz force [C. Raabe and D.-G. Welsch, Phys. Rev. A 71, 013814 (2005)] describes a (medium) modified Casimir force and, in addition to it, a medium-assisted force. The latter force also describes the force on the cavity medium. For dilute media, it implies the atom-mirror interaction of the Casimir-Polder type at large and of the Coulomb type at small atom-mirror distances of which the sign is insensitive to the polarizability type (electric or magnetic) of the atom.

Figure 1

A slab in a planar cavity shown schematically. The (complex) refraction index of the slab is $n_s\left(\omega \right)=\sqrt{{\epsilon }_s\left(\omega \right){\mu }_s\left(\omega \right)}$ and that of the cavity $n\left(\omega \right)=\sqrt{\epsilon \left(\omega \right)\mu \left(\omega \right)}$. The cavity walls are described by their reflection coefficients $R_1^q(\omega ,k)$ and $R_2^q(\omega ,k)$, with $k$ being the in-plane wave vector of a wave. The arrow indicates the direction of the force on the slab.