Electromagnetic Casimir Energies of Semi-Infinite Planes

TL;DR

This paper calculates electromagnetic Casimir energies for semi-infinite planes using scattering theory, providing approximate and exact results that highlight edge and orientation effects relevant for microelectromechanical device design.

Contribution

It introduces a novel application of scattering theory to semi-infinite plane geometries, offering simple approximation methods and exact calculations for Casimir energies.

Findings

Approximate analytic formulas for Casimir energy

Exact results with modest numerical effort

Edges and orientation significantly influence Casimir forces

Abstract

Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices. We obtain both approximate analytic formulae and exact results requiring only modest numerical computation. Using these results, we analyze the effects of edges and orientation on the Casimir energy. We also demonstrate the accuracy, simplicity, and utility of our approximation scheme, which is based on a multiple reflection expansion.