Casimir force between two dielectric slabs

Abstract

We examine the Casimir effect between two dispersive dissipative slabs in three dimensions. The dielectric function of the slabs is assumed to be an arbitrary complex function of frequency satisfying Kramers-Kronig relations. The Maxwell stress tensor is used to evaluate the vacuum radiation pressure of the electromagnetic field on each slab in terms of the field correlation functions. These correlations are simply related to the imaginary part of the vector potential Green function by using the fluctuation dissipation theorem and Kubo's formula. The response function is obtained by employing the standard method for the present configuration. The formalism enables us to calculate the attractive Casimir force between a pair of dielectric slabs without resorting to the electromagnetic field quantization. Special attention is paid to the various limits of the general expression and the results are compared with previous work whenever possible. The Lorentz model of the dielectric function is also used to show the typical behavior of this force in terms of the slab thickness. We also consider the effect of finite temperature on the Casimir force between two dielectric slabs.