Eur. Phys. J. C (2014) 74: 3113
https://doi.org/10.1140/epjc/s10052-014-3113-y

Regular Article - Theoretical Physics

Field theoretic description of electromagnetic boundaries

The Casimir effect between dissimilar mirrors from external potentials

¹ IFQ-Universidade Federal de Itajubá, Av. BPS 1303, Pinheirinho, Caixa Postal 50, Itajubá, MG, 37500-903, Brazil
² Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil

^* e-mail: febarone@cbpf.br

Received: 3 July 2014
Accepted: 30 September 2014
Published online: 18 October 2014

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 we 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.