ELECTROMAGNETIC EIGENMODES IN MATTER. VAN DER WAALS-LONDON AND CASIMIR FORCES

Abstract

We derive van der Waals-London and Casimir forces by calculating the eigenmodes of the electromagnetic fleld interacting with two semi-inflnite bodies (two halves of space) with parallel separated by distance d. We adopt simple models for metals and dielectrics, well-known in the elementary theory of dispersion. In the non-retarded (Coulomb) limit we get a d i3 -force (van der Waals-London force), arising from the zero-point energy (vacuum ∞uctuations) of the surface plasmon modes. When retardation is included we obtain a d i4 -(Casimir) force, arising from the zero- point energy of the surface plasmon-polariton modes (evanescent modes) for metals, and from propagating (polaritonic) modes for identical dielectrics. The same Casimir force is also obtained for \flxed surfaces boundary conditions, irrespective of the pair of bodies. The approach is based on the equation of motion of the polarization and the electromagnetic potentials, which lead to coupled integral equations. These equations are solved, and their relevant eigenfrequencies branches are identifled.