Electromagnetic Casimir Forces in Elliptic Cylinder Geometries

TL;DR

This paper calculates the electromagnetic Casimir forces for elliptic cylinder geometries using scattering theory, extending exact methods to a new class of shapes and analyzing special cases like the strip.

Contribution

It implements the scattering theory approach for electromagnetic Casimir energies in elliptic cylinders, completing the set of geometries with separable scattering problems.

Findings

Exact Casimir energy calculations for elliptic cylinders.

Analysis of the zero-radius limit, reducing to a strip.

Extension of scattering theory methods to new geometries.

Abstract

The scattering theory approach makes it possible to carry out exact calculations of Casimir energies in any geometry for which the scattering T-matrix and a partial wave expansion of the free Green's function are available. We implement this program for the case of a perfectly conducting elliptic cylinder, thereby completing the set of geometries where electromagnetic scattering is separable. Particular emphasis is placed on the case of zero radius, where the elliptic cylinder reduces to a strip.