2012/06/30 by Prachi Parashar, Kimball A. Milton, K. V. Shajesh +2 · 1 citation
Mathematics · Physics and Astronomy · #Casimir effect #Classical mechanics #Cosmology and Gravitation Theories #Energy (signal processing) #Function (biology) #Infinitesimal #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1103/physrevd.86.085021
21 pages, 7 figures, references added
arxiv created 2012/09/12 · openalex publication_date 2012/10/09 · arxiv updated 2015/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We derive boundary conditions for electromagnetic fields on a \ensuremathδ-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting \ensuremathδ-function plate in the limit of infinite dielectric response. We show that a material does not ``optically vanish'' in the thin-plate limit. The thin-plate limit of a plasma slab of thickness d with plasma frequency \ensuremathωp2=\ensuremathζp/d reduces to a \ensuremathδ-function plate for frequencies (\ensuremathω=i\ensuremathζ) satisfying \ensuremathζd\ensuremath≪√\ensuremathζpd\ensuremath≪1. We show that the Casimir interaction energy between two parallel perfectly conducting \ensuremathδ-function plates is the same as that for parallel perfectly conducting slabs. Similarly, we show that the interaction energy between an atom and a perfect electrically conducting \ensuremathδ-function plate is the usual Casimir-Polder energy, which is verified by considering the thin-plate limit of dielectric slabs. The ``thick'' and ``thin'' boundary conditions considered by Bordag are found to be identical in the sense that they lead to the same electromagnetic fields.