Field theoretic description of electromagnetic boundaries: The Casimir effect between dissimilar mirrors from external potentials

TL;DR

This paper develops a field theoretic model for electromagnetic boundaries, calculating the Casimir effect between dissimilar dielectric mirrors using an exact photon propagator correction, revealing unique interaction behaviors.

Contribution

It introduces an exact calculation of the photon propagator correction for dissimilar dielectric mirrors, extending previous models to more realistic boundary conditions.

Findings

The corrected Green function is continuous across space.

In certain limits, the propagator matches that of perfect conductors.

Numerical analysis shows unique interaction behaviors between dissimilar mirrors.

Abstract

In a previous work we formulated a model of semitransparent dielectric surfaces, coupled to the electromagnetic field by means of an effective potential. Here we consider a setup with two dissimilar mirrors, and compute exactly the correction undergone by the photon propagator due to the presence of both plates. It turns out that this new propagator is continuous all over the space and, in the appropriate limit, coincides with the one used to describe the Casimir effect between perfect conductors. The amended Green function is then used to calculate the Casimir energy between the uniaxial dielectric surfaces described by the model, and a numerical analysis is carried out to highlight the peculiar behavior of the interaction between the mirrors.