Electromagnetic normal modes and Casimir effects in layered structures

TL;DR

This paper develops a general method to find electromagnetic normal modes in layered structures, enabling calculations of Casimir effects, including for novel 2D materials like graphene, with explicit formulas for various geometries.

Contribution

It introduces a unified procedure for determining electromagnetic modes in layered geometries, applicable to 2D materials, and derives explicit conditions for Casimir energies in these systems.

Findings

Explicit mode conditions for layered structures.

Formulation applicable to graphene and 2D electron gases.

Derived Casimir and van der Waals interactions for atoms.

Abstract

We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces on atoms in layered structures are obtained. One side-result is the van der Waals and Casimir-Polder interaction between two atoms.